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Q: How can I observe attributes in custom elements using CoffeeScript? I'm trying to observe changes in a custom element's attributes. Unfortunately all of the documentation I can find for custom elements (which is next to nothing) is written in JS, and I don't know how to convert some of this code into CoffeeScript.
The JS:
class HelloElement extends HTMLElement {
// Monitor the 'name' attribute for changes.
static get observedAttributes() {return ['name']; }
// Respond to attribute changes.
attributeChangedCallback(attr, oldValue, newValue) {
if (attr == 'name') {
this.textContent = `Hello, ${newValue}`;
}
}
}
So far I have written this:
class HelloElement extends HTMLElement
#STUCK HERE!
#I can't figure out how to convert the get observedAttributes() method....
attributeChangedCallback(attr, oldValue, newValue): ->
if attr == 'name'
@textContent = 'Hello, ' + newValue
But I have no idea how to write the "get observedAttributes" method in CoffeeScript. Could someone help me please? :)
Thanks
A: class HelloElement extends HTMLElement
@observedAttributes: ['name']
attributeChangedCallback: (attr, oldValue, newValue) ->
console.log("attr #{ attr } changed from #{ oldValue } to #{ newValue }")
Thanks to Reddit user _redka (https://www.reddit.com/user/_redka/) for this solution!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,021 |
{"url":"https:\/\/artofproblemsolving.com\/wiki\/index.php?title=2005_AMC_8_Problems\/Problem_17&diff=prev&oldid=80384","text":"# Difference between revisions of \"2005 AMC 8 Problems\/Problem 17\"\n\n## Problem\n\nThe results of a cross-country team's training run are graphed below. Which student has the greatest average speed? $[asy] for ( int i = 1; i <= 7; ++i ) { draw((i,0)--(i,6)); } for ( int i = 1; i <= 5; ++i ) { draw((0,i)--(8,i)); } draw((-0.5,0)--(8,0), linewidth(1)); draw((0,-0.5)--(0,6), linewidth(1)); label(\"O\", (0,0), SW); label(scale(.85)*rotate(90)*\"distance\", (0, 3), W); label(scale(.85)*\"time\", (4, 0), S); dot((1.25, 4.5)); label(scale(.85)*\"Evelyn\", (1.25, 4.8), N); dot((2.5, 2.2)); label(scale(.85)*\"Briana\", (2.5, 2.2), S); dot((4.25,5.2)); label(scale(.85)*\"Carla\", (4.25, 5.2), SE); dot((5.6, 2.8)); label(scale(.85)*\"Debra\", (5.6, 2.8), N); dot((6.8, 1.4)); label(scale(.85)*\"Angela\", (6.8, 1.4), E); [\/asy]$\n\n$\\textbf{(A)}\\ \\text{Angela}\\qquad\\textbf{(B)}\\ \\text{Briana}\\qquad\\textbf{(C)}\\ \\text{Carla}\\qquad\\textbf{(D)}\\ \\text{Debra}\\qquad\\textbf{(E)}\\ \\text{Evelyn}$\n\n## Solution\n\nAverage speed is distance over time, or the slope of the line through the point and the origin. $\\boxed{\\textbf{(E)}\\ \\text{Evelyn}}$ has the steepest line, and runs the greatest distance for the shortest amount of time.\n\n 2005 AMC 8 (Problems \u2022 Answer Key \u2022 Resources) Preceded\u00a0byProblem 16 Followed\u00a0byProblem 18 1 \u2022 2 \u2022 3 \u2022 4 \u2022 5 \u2022 6 \u2022 7 \u2022 8 \u2022 9 \u2022 10 \u2022 11 \u2022 12 \u2022 13 \u2022 14 \u2022 15 \u2022 16 \u2022 17 \u2022 18 \u2022 19 \u2022 20 \u2022 21 \u2022 22 \u2022 23 \u2022 24 \u2022 25 All AJHSME\/AMC 8 Problems and Solutions","date":"2019-11-21 09:31:18","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\": 3, \"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\": 0.43446993827819824, \"perplexity\": 4935.557319603941}, \"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-2019-47\/segments\/1573496670743.44\/warc\/CC-MAIN-20191121074016-20191121102016-00067.warc.gz\"}"} | null | null |
\section{INTRODUCTION}\label{sec.1}
The discrepancy between the results of the exact calculations for the binding
energy of the triton using a number of realistic nucleon-nucleon potentials
and the experimental value of 8.48~MeV, has been an outstanding problem in
nuclear physics for a number of years~\cite{G93}. A commonly accepted
solution has been the introduction of a three-nucleon force that will bridge
the gap between the calculated binding energy \cite{SI86,IS86,FG88,FPSd93},
based on a two-body interaction, and the experimental binding energy.
The origin of such a three-body force is partly the result of the fact that
the nucleons are treated as point particles interacting via a two-body meson
exchange potential that is often assumed to be local. The fact that the formal
division of the interaction into a two- and three-body part is not unique,
given the on-shell two-body data \cite{PG90}, suggests that the contribution
of the three-body force is partly determined by the definition of the
two-nucleon interaction. Thus under ideal conditions the division of the
interaction, in the three-nucleon system, between a two- and three-body force
will require a consistent formulation of these two potentials within a
meson-nucleon theory.
In the absence of such a formulation one may assume that a meson-nucleon
theory should give the correct binding energy for the three-nucleon system, in
which case the three-body force is by definition that force which when added
to the chosen two-nucleon force will give the three-nucleon binding
energy~\cite{CP83,SC86,Pa86}. A second approach is to assume that the
three-nucleon force is the result of meson exchanges that are possible only
when the number of nucleons is greater than two. In this second approach one
expects the dominant mechanism to be one in which one nucleon emits a meson
that scatters off a second nucleon and then gets absorbed on the third
nucleon, see Fig.~\ref{Fig.1}. In this case the three-nucleon force is
determined by the off-shell meson-nucleon amplitude that goes into the
calculation of the diagram in Fig.~\ref{Fig.1}. In the present investigation
we will consider the second approach involving a $\pi$ meson exchange. In
particular, we will examine the role of the energy dependence of this $\pi N$
amplitude on the contribution of this three-body force to the binding energy
of the triton. We will also examine the relative contribution of the different
$\pi N$ partial waves to this three-body force.
Over the past ten years three approaches have been developed to
determine a three-nucleon interaction from $\pi N$ dynamics.
(i)~The Tucson-Melbourne (TM) \cite{Co79,CG81} three-nucleon potential is
based on the idea that the off-mass shell $\pi N$ amplitude should satisfy
current algebra constraints and the soft pion theorems~\cite{BG68}. These
constraints allow a covariant parameterization of the off-mass shell amplitude.
To be consistent with the meson exchange $NN$ interaction, the $\pi N$
amplitude is
expanded in powers of $\frac{q}{m_N}$, where $q$ is the pion momentum and $m_N$
the
nucleon mass. This gives a $\pi N$ amplitude that includes both $S$- and
$P$-wave
scattering, but where the energy dependence is reduced to $\nu=(s-u)/4m_N =
(q'+q)\cdot (p'+p)/4m_N=0$, as a result of the expansion in $q \over m_N$.
Here,
$s$
and $u$ are the usual Mandelstam variables while $q$ $(q')$ and $p$ $(p')$ are
the
initial (final) four momentum of the pion and nucleon respectively, The
$\pi NN$ form factor is constructed to satisfy the Goldberger-Treiman
relation\cite{GT58,CS90}. Although the original TM potential included only the
$\pi-\pi$ three-body force, $\pi-\rho$ and $\rho-\rho$ contributions have
recently been
included~\cite{CP93}. (ii)~A similar approach is to assume that the $\pi N$
dynamics
is determined by an effective chiral Lagrangian~\cite{CD83,RI84,RC86,CF86,We90}
which when used to calculate the $\pi N$ amplitude at the tree level, will
give an effective three-nucleon force given by the diagram in
Fig.~\ref{Fig.1}. The evaluation of the $\pi N$ amplitude at the tree level
gives rise to an energy independent $\pi N$ amplitude, and therefore a
three-body force. Both approaches (i) and (ii) give similar results, and
emphasize the chiral symmetry of the $\pi N$ amplitude. (iii)~The $N-\Delta$
coupled channel approach~\cite{HSS83,HSY83,S86,PHS90,PRB91} takes as its
starting point the fact that the $\pi N$ amplitude is dominated at medium
energies by the $\Delta(1230)$ or the $P_{33}$ partial wave. This dominance of
the $\Delta$ suggests that we could extend our Hilbert space to include not
only the nucleon, but also the $\Delta$ as an excited state of the nucleon.
The approach of treating the $N$ and $\Delta$ on equal footing effectively
includes, in a consistent manner, that part of the original three-body force
corresponding to $\pi N$ scattering in the $P_{33}$ channel, or at least the
resonance part of it~\cite{SS92}. The advantage of this approach is that now
we can construct the two-body and the three-body forces with some
consistency, to the extent that the $NN-N\Delta$ transition potential used in
the two-body interaction can also be used to generate the three-body
potential. The inclusion of coupling between the $NN$, $N\Delta$ and
$\Delta\Delta$ channels allows a consistent treatment of the $BB$ and $BBB$
system, where $B=N,\Delta$\cite{PRB91}. In this approach, since the $\pi N$
amplitude is basically approximated by $\pi N\rightarrow\Delta\rightarrow\pi
N$, the energy dependence of the total $\pi N$ amplitude is completely
determined by the energy dependence of the $P_{33}$ channel which has the
$\Delta$ resonance. Although the $NN$ and transition potentials can be local
and energy independent, the effective three-body force in this model is
energy dependent and this energy dependence is determined by the $\Delta$
resonance, i.e. the $P_{33}$ amplitude. More recently there have been
extensions of the $N-\Delta$ coupled channel approach that have included the
$S$-wave component of the TM potential~\cite{SS92}. Also Pe\~na {\it et
al.}~\cite{PSSK93} have examined the importance of the coupling of the $\Delta$
to
the $\pi N$ channel. This latter calculation gives a $\pi N$ amplitude in
the $P_{33}$ channel that fits the phase shifts and has an
energy dependent mass and width for the $\Delta$. The inclusion of this
energy dependence in the $\Delta$ mass and width does not effect the final
result appreciably.
The questions which arise from the above approaches to the $\pi N$ dynamics
that go into the derivation of the three-nucleon force and its contribution
to the binding energy of the three-nucleon system are:
(i)~What are the contributions of the different $\pi N$ partial waves to
the three-body force?
(ii)~If there is any cancellation between the contribution of the
different partial waves,
should the $P_{33}$ partial wave be treated via the $N-\Delta$
coupled channel while the rest of the $\pi N$ amplitude gives rise to a
three-body force as depicted in Fig.~\ref{Fig.1}?
(iii)~Would a cancellation between the different $\pi N$ channels be
sensitive to the energy dependence of the amplitudes?
The main aim of this investigation
is to examine these questions.
To motivate our interest in the importance of the energy dependence of
the $\pi N$ amplitude, let us examine the role of the $NN$ amplitude in
calculating the binding energy of the three-nucleon system within the
framework of the Faddeev equations. Here we observe that we require the fully
off-energy-shell $NN$ amplitude in a given partial wave $\alpha$,
$t_\alpha^{NN}(k,k';E_{NN})$, for all energies in the range
$-\infty<E_{NN}<-E_T$, where $E_T$ is the three-nucleon binding energy, see
Fig.~\ref{Fig.2}. The fact that we need this amplitude over the full
specified energy domain is a result of the fact that in the three-nucleon
system, the total energy is fixed at $E=-E_T$, and the spectator particle can
have any energy from zero to $\infty$. To consider the contribution of
Fig.~\ref{Fig.1} and in particular the energy dependence of the $\pi N$
amplitude, we consider the $NNN-\pi NNN$ equations\cite{AM83,CCS93}
which are an extension of the $NN-\pi NN$ equations to the $A=3$ sector.
Within the framework of the above $\pi NN$ dynamics, to calculate the
contribution of
the three-body force as defined in Fig.~1 to the three-nucleon binding, we must
determine to know the fully off-energy-shell $\pi N$ amplitudes \cite{Foot1},
$t_\alpha^{\pi N}(k,k';E_{\pi N})$, for all energies in the range
$-\infty<E_{\pi N}<(m_N-E_T)$, where in this case we have included the rest
mass of the nucleon and pion in the $\pi N$ energy $E_{\pi N}$. In other
words we have to calculate the fully off-energy-shell $\pi N$ amplitude for all
energies from $-\infty$ to $E_T$ below the nucleon pole ( see
Fig.~\ref{Fig.3}). Thus to calculate a three-body force which is defined in
terms of the $\pi N$ amplitude, we need to know this amplitude off-shell for
energies far below ($(m_\pi + E_T)\approx 145$~MeV), the $\pi N$ threshold.
Here the need for the $\pi N$ amplitude over this energy domain is a result
of the fact that the total energy is still $-E_T$, but now we have two
spectator nucleons with kinetic energy between zero and $\infty$. At these
energies it is not clear that the $\Delta(1230)$ is dominant or that the
$P$-wave amplitudes are more important than the $S$-wave amplitudes.
Clearly, the threshold behavior of the amplitude is essential, but we need to
know the
$\pi N$ partial wave amplitudes over a wide range of energies above
threshold, if we are to extrapolate these amplitudes to the energies required
in calculating the three-body force. This suggests that we have to fit the
energy dependence of the experimental $\pi N$ phase shifts in order to improve
the
accuracy of the extrapolation in the energy.
In Sec.~\ref{sec.a} we will derive the three-body force using
the coupled channel method and we will discuss approximation which we
take to avoid the dressing problem\cite{SS85}.
In Sec.~\ref{sec.2} we will discuss a parameterization for the $\pi N$
amplitude, and
in particular will discuss the division of this amplitude into a pole and
non-pole component. It is only the non-pole part of the
$\pi N$ amplitude that goes into the $\pi N$ scattering that generates the
three-body force. This division is essential if we are to avoid double
counting. We will choose the $\pi NN$ form factor as the residue of the pole
term
in the $\pi N$ amplitude to keep the consistency with the $\pi N$ formulation.
We will then proceed in Sec.~\ref{sec.3} to a discussion of the $\pi-\pi$
three-body
force given in Fig.~\ref{Fig.1} in terms of our parameterization of the $\pi N$
amplitude. As a result of using a separable representation for the $\pi N$
amplitude,
we find that the three-body force is reduced to the product of the amplitude
for
$NN\rightarrow NN^*_\alpha$, followed by the propagation of the $NNN^*_\alpha$
system, and the final transition amplitude for
$NN^*_\alpha\rightarrow NN$, where $\alpha$ runs over all $\pi N$ partial
waves.
This $\pi-\pi$ three-body force is employed in Sec.~\ref{sec.4} to calculate,
in the
Born approximation, the contribution of this force to the binding energy of
the three-nucleon system. The three-nucleon wave function will be calculated by
using
Paris (PEST) potential\cite{HP84}. Since the Paris potential does not have any
energy dependence, our approach for the three-nucleon interaction is
inconsistent
with the two-nucleon interaction. To that extent, the overall magnitude of
the resultant three-body force contribution may not have great significance.
However, we would like to examine the relative contribution of the
different $\pi N$ partial waves, and see how this contribution is sensitive to
the
energy dependence of the $\pi N$ amplitude in the subthreshold region.
In particular, we would like to demonstrate how the energy dependence of both
the
non-pole amplitude and the $\pi NN$ form factor play a role in the importance
of
this
three-nucleon force. Here we will find that the energy dependence of the
non-pole
amplitude has a significant effect on the contribution of the three-body force.
Furthermore, we will demonstrate that there is a cancellation between the
contribution of the different $\pi N$ partial waves. This cancellation turns
out
to
be very sensitive to the approximations used. Finally, in Sec.~\ref{sec.5} we
will
conclude our discussion by considering some open questions that can influence
our
final results.
\section{COUPLED CHANNEL FORMULATION OF THREE-BODY FORCE}\label{sec.a}
In this section, we will establish the approximation involved
in writing Fig.~\ref{Fig.1} as the lowest order contribution
to the binding energy of the three-nucleon system from a
$\pi$-$\pi$ three-body force. Our starting point is the Hamiltonian
of Mizutani and Koltun\cite{MK77}
\begin{equation}
{\cal H} = {\cal K} + {\cal V}_{NN} + {\cal V}_{\pi N}
+ {\cal A} + {\cal A}^\dagger\ , \label{eq:1.1}
\end{equation}
where ${\cal K}$ is the kinetic energy of the nucleons and pions, while ${\cal
V}_{NN}$ and ${\cal V}_{\pi N}$ are the $NN$ interaction in the absence of one
pion
exchange, and the $\pi N$ interaction in the absence of the s-channel nucleon
pole,
respectively. In Eq.~(\ref{eq:1.1}), ${\cal A}$ is the pion absorption vertex
while
${\cal A}^\dagger$ is the corresponding production vertex. The Schr\"odinger
equation for this Hamiltonian is
\begin{equation}
{\cal H} |\Psi \rangle = E \, |\Psi \rangle\ . \label{eq:1.2}
\end{equation}
Clearly, the operators ${\cal A}$ and ${\cal A}^\dagger$ change
the number of pions. To that extent, the present Hamiltonian has some
of the features of a field theory in that the number of pions is not fixed
while
the
number of nucleons is fixed. As a first approximation, we restrict the Hilbert
space
to $(nN)$ and $\pi (nN)$ systems only, where $n$ is the number of nucleons,
which is
conserved. We define the Feshbach~\cite{Fe62} projection operators onto $(nN)$
and
$\pi (nN)$ spaces as $P$ and $Q$, respectively. By using these projection
operators
and by assuming that this truncated space is complete, {\it i.e.} $P + Q = 1$,
the wave
functions of the $(nN)$ and $\pi (nN)$ components (~$P\Psi$ and $Q\Psi$,
respectively)
are solutions of the equations
\begin{equation}
\Bigl(E - H_{PP} - H_{PQ} {1\over E-H_{QQ}}
H_{QP} \Bigr) | P \Psi \rangle = 0\ , \label{eq:1.3}
\\
\end{equation}
and
\begin{equation}
\Bigl(E - H_{QQ} - H_{QP} {1\over E-H_{PP}}
H_{PQ} \Bigr) | Q \Psi \rangle = 0\ . \label{eq:1.4}
\end{equation}
In writing Eqs.~(\ref{eq:1.3}) and (\ref{eq:1.4}) we have made use of
the definitions,
\begin{eqnarray}
H_{PP} \equiv P{\cal H}P\ ,\quad &\quad&\quad H_{PQ} \equiv P{\cal H}Q\ ,
\nonumber \\
H_{QP} \equiv Q{\cal H}P\ ,\quad &\mbox{and}&\quad H_{QQ} \equiv Q{\cal H}Q
\ . \label{eq:1.5}
\end{eqnarray}
The Green's function for the $\pi(nN)$ system, $(E - H_{QQ})^{-1}$, which
including
the $\pi N$ and $NN$ interactions, can be written as
\begin{equation}
{1\over E - H_{QQ}} = G^{(0)}_{\pi (nN)}(E) +
G^{(0)}_{\pi (nN)}(E) \,T(E) \, G^{(0)}_{\pi (nN)}(E)\ , \label{eq:1.6}
\end{equation}
where $G^{(0)}_{\pi (nN)}(E)$ is the free $\pi (nN)$ propagator. The
corresponding
T-matrix, $T(E)$, can be written as
\begin{equation}
T(E) = \sum_a \, t_a(E) + \sum_{ab} \,
t_a(E) \, G^{(0)}_{\pi (nN)}(E) \, U_{ab}(E) \, G^{(0)}_{\pi (nN)}(E)
\, t_b(E)\ , \label{eq:1.7}
\end{equation}
where $U_{ab}(E)$ is the AGS amplitude\cite{AGS67} for the $(n+1)$
particle system and satisfies a set of coupled equations. Here, $t_a(E)$
is the $\pi N$ or $NN$ amplitudes resulting from the potential ${\cal V}_{NN}$
or
${\cal V}_{\pi N}$, respectively.
We will first consider the simplest case of $n=1$ \cite{EA89}. Here, on the one
hand,
Eq.(\ref{eq:1.3}) can be regarded as the equation for the dressed nucleon with
the
self-energy, $\Sigma(E)$, defined to be
\begin{equation}
\Sigma(E) = H_{PQ} \, {1\over E - H_{QQ}} \, H_{QP}\ .
\label{eq:1.8}
\end{equation}
Therefore the dressed nucleon propagator, $G_N(E)$, can be written as
\begin{equation}
G_N(E) = \left(E - H_{PP} - H_{PQ} \, {1 \over E - H_{QQ} } \,
H_{QP} \right) ^{-1}\ ,
\label{eq:1.9}
\end{equation}
with $H_{PP}$, the bare mass of the nucleon. On the other hand,
Eq.~(\ref{eq:1.4})
describes $\pi N$ scattering. Now since $H_{QQ}= K_{QQ} + {\cal V}_{\pi N}$,
with
$K_{QQ}$ the kinetic energy of the $\pi N$ system, the $\pi N$ interaction in
Eq.~(\ref{eq:1.4}) is the sum of two contributions. The first is the $\pi N$
interaction in the original Hamiltonian, ${\cal V}_{\pi N}$, while the second
term,
$H_{QP}\left(E-H_{PP}\right)^{-1}H_{PQ}$, results from the coupling of the
$\pi N$ channel to the $N$ channel. The $\pi N$ T-matrix, $T_{\pi N}(E)$, in
this
case is the sum of two terms, and is given by
\begin{equation}
T_{\pi N}(E) = F_{QP}(E) \, G_N(E) \, F_{PQ}(E) + t_B(E)\ , \label{eq:1.10}
\end{equation}
where
\begin{equation}
F_{PQ}(E)=H_{PQ}\left[1+\frac{1}{E - K_{QQ}}\,t_B(E)\right]\ , \label{eq:1.11}
\end{equation}
and $t_B(E)$ is the solution to the two-body equation
\begin{equation}
t_B(E) = V_{QQ} + V_{QQ} \, \frac{1}{ E - K_{QQ}} \, t_B(E)\ , \label{eq:1.12}
\end{equation}
with $V_{QQ}={\cal V}_{\pi N}$. Here we note that the first term on the right
hand
side of Eq.~(\ref{eq:1.10}) corresponds to the process $\pi N\rightarrow
N\rightarrow
\pi N$, and as a result the pion absorption (emission) vertex is given by
$F_{PQ}(E)$ ($F_{QP}(E)$). To establish that this term has the nucleon pole
contribution to the $\pi N$ amplitude, we note that the Green's function,
$G_N(E)$,
given in Eq.~(\ref{eq:1.9}), has a pole at the nucleon mass, and therefore can
be
written as
\begin{equation}
G_N(E)=\frac{1}{E-H_{PP}-\Sigma(E)}=\frac{Z_2(E)}{E-m_N}\ , \label{eq:1.13}
\end{equation}
where $Z_2(E)$ is the wave function renormalization. Making use of this result
in
Eq.~(\ref{eq:1.10}) allows us to write the $\pi N$ T-matrix as
\begin{equation}
T_{\pi N}(E) = f^{R\dag}_{\pi NN}(E)\,\frac{1}{E-m_N}\,f^{R}_{\pi NN}(E)
+ t_B(E)\ , \label{eq:1.14}
\end{equation}
where the renormalized $\pi NN$ form factor, which is energy dependent, is
given
by
\begin{equation}
f^R_{\pi NN}(E) = Z^{1\over2}_2(E) \, F_{PQ}(E)\ .
\label{eq:1.15}
\end{equation}
In this formulation the normalized physical nucleon wave function, which is a
solution to Eq.~(\ref{eq:1.3}) is given by
\begin{equation}
\Psi_N = Z^{\frac{1}{2}}_2(m_N)\,P\Psi\ .
\label{eq:1.16}
\end{equation}
We consider next the case of $n>1$. Since we have restricted the Hilbert space
to
include $n$ nucleons, and up to one pion only, this truncation effects the
dressing of
the nucleons for the case $n>1$. From Fig.~\ref{Fig.4}, we observe that the
nucleons
can only be dressed separately after absorbing an initial pion and before
emitting the
final pion, because of the limitation imposed on the Hilbert space. We can
neither
include the nucleon dressing before the pion absorption nor after the final
pion
emission. This incomplete dressing makes the renormalized $\pi NN$ form
factor,
$f^R_{\pi NN}(E)$, smaller\cite{SS85}. To overcome this problem we need to
guarantee
that all the nucleons are fully dressed at the same time, and this dressing is
on both
sides of the $\pi NN$-vertex\cite{KB94}, see Fig.~\ref{Fig.5}. We will avoid
this
problem in the present investigation in the following manner. In the $NN-\pi
NN$
equations the nucleon dressing was introduced to satisfy the unitarity of the
$NN$
amplitude above the pion production threshold. In the present investigation
however,
we are considering a bound state problem which is below the threshold for
pion
production. We therefore expect that the nucleon dressing will not be
essential,
and
does not have to be included explicitly to satisfy unitarity. We therefore
assume that
each nucleon line has been renormalized to give the physical nucleon mass and
correct
$\pi NN$ coupling constant, {\it i.e.}; (i)~The nucleon propagator is given by
$(E-m_N)^{-1}$. (ii)~The $\pi NN$ vertex is given by the renormalized vertex
function,
$f^R_{\pi NN}(E)$.
Using the above assumptions, the interaction term resulting from the coupling
of
the
$NNN$ and $\pi NNN$ Hilbert space in Eq.~(\ref{eq:1.3}) can be rewritten as
\begin{equation}
H_{PQ} \, {1\over E - H_{QQ}} \, H_{QP} = {\cal V}_{OPE}
+ {\cal V}_{disp} + {\cal V}_{3B} + \cdots\ ,
\label{eq:1.17}
\end{equation}
where the series is generated by iterating the equation for $U_{ab}$ in
Eq.~(\ref{eq:1.7}), and making use of the resultant $\pi NNN$ T-matrix in
Eq.~(\ref{eq:1.6}). In particular, if we go to third order in the
$\pi N$ amplitude $t_a$, the $\pi NN$ form factors in ${\cal V}_{3B}$ get
dressed
as detailed in Eqs.~(\ref{eq:1.14}) and (\ref{eq:1.15}). Each of the terms in
Eq.~(\ref{eq:1.17}) is shown schematically in Fig.~\ref{Fig.6}. We note that
${\cal
V}_{OPE}$ and ${\cal V}_{disp}$ are two-body operators. Since we will be
calculating
perturbatively the contribution of the three-body force to the binding energy
of
$^3$H, the three nucleon wave function used results from the solution of the
Faddeev
equations for a given nucleon-nucleon interaction. Assuming that the
nucleon-nucleon
interaction includes ${\cal V}_{OPE}$ and ${\cal V}_{disp}$, we omit these
terms
from
Eq.~(\ref{eq:1.17}). This leaves us with the three-nucleon force ${\cal
V}_{3B}$,
illustrated in Figs.~\ref{Fig.6}(c) and \ref{Fig.1}, which gives the lowest
order
correction to the binding energy of the three-nucleon system. The detail of
the
numerical framework of the $\pi N$ scattering will be presented in next
section.
\section{THE $\pi N$ AMPLITUDE}\label{sec.2}
To include the full energy dependence of the $\pi N$ amplitude into the
determination of the $\pi-\pi$ three-nucleon interaction and its contribution
to the binding energy of the triton, we have to:
(i)~Remove the nucleon pole contribution from the $\pi N$ amplitude to avoid
double counting in the three nucleon force calculation.
(ii)~Define a $\pi NN$ form factor for the emission and absorption vertices in
Fig.~\ref{Fig.1} that is consistent with the $\pi N$ amplitude used and
the scattering data.
(iii)~Treat the nucleon in the $\pi N$ system using non-relativistic
kinematics to maintain consistency between the $NNN$ and $\pi N$ systems since
the nucleons in the three-nucleon system are treated non-relativistically.
{}From the previous section we observe
the first two conditions can be satisfied if we choose a formulation of the
$\pi N$ scattering problem that is motivated by a Hamiltonian that includes a
$\pi NN$ vertex and a $\pi N$ interaction, e.g. the Cloudy Bag
Model~\cite{Th84}. Thus a choice for the $\pi N$ potential, motivated by the
lowest order contribution to the amplitude and based on a Lagrangian of the
form suggested by the Cloudy Bag Model with volume coupling~\cite{Th81},
consists of an
$s$-channel nucleon pole diagram, Fig.~\ref{Fig.7}, and the cross diagram
and contact term, Fig.~\ref{Fig.8}.
For the present investigation, to simplify the parameterization of the $\pi
N$ amplitude, we replace the cross diagram and contact term in
Fig.~\ref{Fig.8} by a one term separable potential in each partial wave. This
allows us to write the $\pi N$ potential in a given partial wave $\alpha$ as
\begin{equation}
v_\alpha(k,k';E) = f_0(k)\,\frac{1}{E-m_0}\,f_0(k') +
g_\alpha(k)\,\lambda_\alpha\,g_\alpha(k')\ , \label{eq:2.1}
\end{equation}
where the first term corresponds to the nucleon pole diagram with a bare
nucleon mass of $m_0$, and a bare form factor $f_0(k)$. Since we
are using non-relativistic kinematics for the nucleon, this $s$-channel pole
diagram contributes to the $P_{11}$ partial wave only. As a result, the
potential in all partial waves other than the $P_{11}$ channel is given by
the second term on the right hand side of Eq.~(\ref{eq:2.1}). This separable
$\pi N$ potential gives an amplitude of the form
\begin{equation}
t_\alpha(k,k';E) = g_\alpha(k)\,\tau_\alpha(E)\,g_\alpha(k')
\quad\mbox{for}\quad \alpha\neq P_{11} \label{eq:2.2}
\end{equation}
where
\begin{equation}
\tau_\alpha(E) = \left[\lambda_\alpha^{-1} -
\langle g_\alpha|G_{\pi N}(E)|g_\alpha\rangle\right]^{-1}\ , \label{eq:2.3}
\end{equation}
with
\begin{equation}
\langle g_\alpha|G_{\pi N}(E)|g_\alpha\rangle = \int\limits^\infty_0 \,dk\,k^2
\frac{[g_\alpha(k)]^2} {E- \omega_k - \frac{\textstyle{k^2}}
{\textstyle{2m_N}} - m_N}\ . \label{eq:2.4}
\end{equation}
This amplitude is a solution of the Lippmann-Schwinger equation with the pion
energy treated relativistic since $\omega_k = \sqrt{k^2 + m_\pi^2}$. The
strength of the potential $\lambda_\alpha$, and the form factor $g_\alpha(k)$
are
adjusted to fit the experimental $\pi N$ phase shifts in all $S$- and
$P$-waves other than the $P_{11}$ channel. For the present investigation we
will use the parameterization used by Thomas~\cite{Th76} for $\pi d$
scattering.
The form factor used for $S_{11}$ and $S_{31}$ $\pi N$ partial waves is:
\begin{equation}
g_\alpha(k) = {S_1 \over k^2 + \alpha_1^2} + {S_2 \over k^2 + \alpha_2^2},
\label{eq:2.a1}
\end{equation}
and
\begin{equation}
g_\alpha(k) = k \Biggl[{S_1\over k^2 + \alpha_1^2} +
{S_2 \, k^2 \over (k^2 + \alpha_2^2)^2 } \Biggr]
\label{eq:2.a2}
\end{equation}
for $P_{13}$, $P_{31}$ and $P_{33}$.
This parameterization has also been used extensively in the
$NN-\pi NN$ calculation for $\pi d$ scattering and $\pi d\rightarrow pp$
reactions~\cite{BA81,AM85}.
The $P_{11}$ channel plays the important role in this analysis of the
three-nucleon interaction as it has the nucleon pole contribution that needs
to be removed to avoid double counting. It also has the information about the
$\pi NN$ form factor which is defined as the residue of the off-shell $\pi N$
amplitude at the nucleon pole. In this way we can subtract the nucleon pole
contribution to the $\pi N$ amplitude, and extract a $\pi NN$ form factor
while maintaining a fit to the $\pi N$ scattering data in this channel. Since
the potential in this channel is the sum of two contributions, see
Eq.~(\ref{eq:2.1}), we can write the corresponding amplitude as a solution of
the Lippmann-Schwinger equation using a two-potential theory to be~\cite{AS81}
\begin{equation}
t_\alpha(k,k';E) = f(k;E)\,\frac{1}{E-m_0-\Sigma(E)}\,f(k';E) +
g_\alpha(k)\,\tau_\alpha(E)\,g_\alpha(k')\ , \label{eq:2.5}
\end{equation}
where the dressed $\pi NN$ form factor, $f(k;E)$, is given by
\begin{equation}
f(k;E) = f_0(k) + g_\alpha(k)\,\tau_\alpha(E)\,
\langle g_\alpha|G_{\pi N}(E)|f_0\rangle\ , \label{eq:2.6}
\end{equation}
and $\alpha$ in Eq.~(\ref{eq:2.5}) and (\ref{eq:2.6}) refers to the
$P_{11}$ channel. In Eq.~(\ref{eq:2.5}), the mass renormalization factor
$\Sigma(E)$ is given by
\begin{eqnarray}
\Sigma(E) &=& \langle f_0|G_{\pi N}(E)|f(E)\rangle\nonumber \\
&=& \langle f_0|G_{\pi N}(E)|f_0\rangle +
\langle f_0|G_{\pi N}(E)|g\rangle\,\tau(E)\,
\langle g|G_{\pi N}(E)|f_0\rangle \ , \label{eq:2.7}
\end{eqnarray}
where we have dropped the channel label $\alpha$ with the understanding that
we are considering the $P_{11}$ partial wave only.
In writing the amplitude in the $P_{11}$ channel ( Eq.~(\ref{eq:2.5}) ) as
the sum of a pole and a background term, we are able to define that part of
the $\pi N$ amplitude which will be included in the evaluation of the
three-body force. At the same time, we can determine the $\pi NN$ form factor
that is required for the pion emission and absorption vertices in
Fig.~\ref{Fig.1}. To establish that this $\pi NN$ form factor gives the correct
$\pi NN$ coupling constant as the residue of the $\pi N$ amplitude at the
nucleon pole, we expand $\Sigma(E)$ about the physical nucleon mass
as~\cite{MA85}
\begin{equation}
\Sigma(E) = \Sigma(m_N) + (E-m_N)\,\Sigma_1(m_N) +
(E-m_N)^2\,\Sigma_2(E)\ . \label{eq:2.8}
\end{equation}
If we now fix the bare mass $m_0$ such that
\begin{equation}
m_0 + \Sigma(m_N) = m_N \ , \label{eq:2.9}
\end{equation}
we can write the pole amplitude as
\begin{equation}
f(k;E)\,\frac{1}{E-m_0 -\Sigma(E)}\,f(k';E) =
f^R(k;E)\,\frac{1}{E - m_N}\,f^R(k';E) \label{eq:2.10}
\end{equation}
where the renormalized $\pi NN$ form factor $f^R(k;E)$ is defined as
\begin{equation}
f^R(k;E) = \frac{Z_2^{1/2}}
{[1 - (E-m_N)\Sigma^R_2(E)]^{1/2}}\,f(k;E)\ , \label{eq:2.11}
\end{equation}
and the wave function renormalization constant $Z_2$ is given by
\begin{equation}
Z_2 = \left[1 - \Sigma_1(m_N)\right]^{-1}
\equiv 1 + \Sigma^R_1(m_N)\ , \label{eq:2.12}
\end{equation}
with
\begin{equation}
\Sigma_i^R(E) \equiv Z_2\, \Sigma_i(E)\quad\mbox{for}\quad i=1,2\ .
\label{eq:2.13}
\end{equation}
In this way we have defined the renormalized $\pi NN$ form factor, $f^R(k;E)$,
which will be used for the emission and absorption vertices in
Fig.~\ref{Fig.1}. More important is the fact that this form factor is
constrained by the $\pi N$ phase shifts in the $P_{11}$ channel and the
requirement that we have the correct $\pi NN$ coupling constant. We note at
this point that the renormalized $\pi NN$ form factor $f^R(k;E)$ is energy
dependent and that this energy dependence is determined by unitarity through
$\tau_\alpha(E)$, and has to be included if we are to fit the phase shifts in
this channel.
To determine the $\pi NN$ coupling constant resulting from the above
formulation of $\pi N$ scattering, we need to compare our results for the pole
amplitude with the corresponding Feynman diagram for the Lagrangian with the
pseudoscalar coupling, i.e.
\begin{equation}
-ig_0(k)\bar{u}\,(\bbox{\tau}\cdot\bbox{\phi})\,(i\gamma_5)\,u\ .
\label{eq:2.14}
\end{equation}
where the coupling constant $g_0$ is made a function of the momentum. In
Eq.~(\ref{eq:2.14}), $\bbox{\tau}$ is the Pauli isospin matrix, $\bbox{\phi}$
is the pion field, and $u$ is the usual Dirac spinor. This interaction
Lagrangian allows us to determine the invariant amplitude corresponding to the
$s$-channel nucleon pole diagram~\cite{BD64}, and the corresponding
$S$-matrix. Making use of the relation between the $S$-matrix and the
$T$-matrix~\cite{AT76}, which is a solution of the Lippmann-Schwinger
equation, we can calculate the $\pi NN$ coupling constant as a result of the
relation between the $T$-matrix, $t(k,k';E)$, and the invariant amplitude
${\cal T}(k,k';E)$ as
\begin{equation}
t(k,k';E) = C(k;E)\,{\cal T}(k,k';E)\,C(k';E) \label{eq:2.15}
\end{equation}
where
\begin{equation}
C(k;E) = \sqrt{\frac{m_N(\omega_k +
\varepsilon_k)}{(2\pi)^3\,\omega_k\varepsilon_k(E + \omega_k + \varepsilon_k)}}
\ , \label{eq:2.16}
\end{equation}
with $\varepsilon_k = \sqrt{k^2 + m_N^2}$. The coupling constant is now
defined as the residue of the invariant $\pi N$ amplitude at the nucleon pole
with all the legs of the $\pi NN$ vertex on-mass-shell. This corresponds to
taking $E=m_N$ and $k=k_0$, where
\begin{equation}
k_0^2 = - m_\pi^2\left(1 - \frac{m_\pi^2}{4m_N^2}\right)\ . \label{eq:2.17}
\end{equation}
This definition allows us to write the $\pi NN$ coupling constant $f_{\pi
NN}$ in terms of the renormalized $\pi NN$ form factor $f^R(k;E)$ as
\begin{eqnarray}
f^2_{\pi NN}(k) &=& \frac{m_\pi^2}{4m_N^2}\ g_0^2(k)
\nonumber \\
&=& \frac{m_\pi^2}{4 m_N^2}\,\frac{m_N(\varepsilon_k+ m_N)}
{6\pi [C(k,m_N)]^2}
\ \left[\frac{f^R(k;m_N)}{k}\right]^2 \ , \label{eq:2.18}
\end{eqnarray}
where
\begin{equation}
\frac{1}{4\pi}\,f_{\pi NN}^2(k_0) = 0.079\ . \label{eq:2.19}
\end{equation}
For the present investigation we make use of the $P_{11}$ $\pi N$
parameterization of McLeod and Afnan~\cite{MA85}, where the bare $\pi NN$ form
factor $f_0(k)$ is taken to be
\begin{equation}
f_0(k) = \frac{c_0}{\sqrt{\omega_k}}\
\frac{k}{(k^2 + \alpha^2)^{n_0}} \ , \label{eq:2.20}
\end{equation}
while for the background separable potential form factor, we take
\begin{equation}
g(k) = \frac{k}{\sqrt{\omega_k}}\ \left[\frac{c_1}{k^2 + \beta_1^2} +
\frac{c_2 (k^2)^{n_1}}{(k^2 + \beta_2^2)^3}\right]\ . \label{eq:2.21}
\end{equation}
This choice of form factor is basically the same as that used by Thomas
( Eqs.(\ref{eq:2.a1}) and (\ref{eq:2.a2}) ). The factor of $\sqrt{\omega_k}$
was introduced to get the covariant phase space to determine the
coupling constant at the nucleon pole with all legs on-mass-shell.
In Table~\ref{Table.1} we present two parameterizations of the $P_{11}$
amplitude~\cite{MA85} corresponding to a monopole ( $n_0=1$ ) or a dipole (
$n_0=2$ ) bare $\pi NN$ form factor. The parameters were adjusted to give the
phase shifts below the pion production threshold, the position of the nucleon
pole, and the $\pi NN$ coupling constant of 0.079. In Table~\ref{Table.2} we
present the scattering volume $a_{11}$ in this channel, the wave function
renormalization $Z_2$ and the value of the coupling constant at $k=0$. We note
that the values in Tables~\ref{Table.1} and \ref{Table.2} are the corrected
values for the parameters of these potentials and their predictions.
We note that the
renormalized form factor $f^R(k;E)$ is substantially different from the bare
form factor $f_0(k)$ due to the wave function renormalization $Z_2$
and the contribution of the non-pole amplitude to the form factor dressing
(see Eq.(\ref{eq:2.6}) and (\ref{eq:2.11})). Finally, the value of
the coupling constant at $k=0$, when compared with the value at $k=k_0$, can
be used as a measure of the deviation from the Goldberger-Treiman relation.
The present definition of the $\pi NN$ form factor is different from that
commonly used in $NN$ potentials, and three-nucleon force calculations.
However it is consistent with the formulation of $\pi N$ scattering where
the $\pi N$ amplitude is a solution to a two-body equation\cite{PJ91}.
Traditionally the $\pi NN$ form factor, introduced as a cutoff in the
$NN$ amplitude, is a function of the pion momentum only. This is a result of
taking both nucleons in the vertex on-mass-shell. However in a
non-relativistic or time ordered theory, intermediate particles are off the
energy shell. As a result, the $\pi NN$ form factor becomes
a function of the energy and the relative momentum. The energy dependence of
the
$\pi NN$ form factor is the result of the dressing. This dressing is
necessitated by
the requirement that the full $\pi N$ amplitude, even in the $P_{11}$ channel,
should
be a solution of the Lippmann-Schwinger equation. In this way we can maintain
consistency with both of the treatments for the $\pi N$ and $NN$ amplitudes as
solutions of two-body equations when used in the three-nucleon system.
\section{THE THREE-BODY FORCE}\label{sec.3}
Having defined our $\pi N$ amplitude, and in particular how the nucleon pole
is subtracted from the $\pi N$ amplitude to give us a $\pi NN$ form factor
that is both momentum and energy dependent, we turn our attention to our
definition of the three-body force as given in Fig.~\ref{Fig.1}. At this stage
it is important to note that this definition of the three-body force does not
include
all possible pion exchange diagrams that are not included in the
nucleon-nucleon
interaction. However, we expect the diagram in Fig.~\ref{Fig.1} to give the
dominant
contribution to the three-body force.
To evaluate the diagram in Fig.~\ref{Fig.1} we introduce Jacobi variables in
the $\pi NNN$ center of mass. These are defined in Fig.~\ref{Fig.9}. This
choice for the momenta will allow us to take matrix elements of the three-body
force between three-nucleon wave functions resulting from the solution of the
Faddeev equation in momentum space for a given two-nucleon interaction. At the
same time we will be able to include the $\pi N$ amplitudes defined in
Sec.~\ref{sec.2} with their full energy dependence with no approximations. The
momenta in the initial state in Fig.~\ref{Fig.9} are
\begin{eqnarray}
{\bf q}_3 &=& - {\bf k}_3 \label{eq:3.1} \\
{\bf p}_3 &=& \frac{m_N ({\bf k}_\pi + {\bf k}'_1) -
(m_N+m_\pi){\bf k}_2 }{(2m_N + m_\pi)} \label{eq:3.2} \\
{\bf Q}_3 &=& \frac{m_N {\bf k}_\pi - m_\pi {\bf k}'_1 }
{ (m_N + m_\pi)}\ , \label{eq:3.3}
\end{eqnarray}
where ${\bf k}'_1$, ${\bf k}_2$, ${\bf k}_3$ and ${\bf k}_\pi$ are the
momenta of the three nucleon and pion after the pion emission vertex. Here,
${\bf Q}_3$ is the $\pi N$ relative momentum for the pion production vertex,
while ${\bf Q}'_3$ is the relative $\pi N$ momentum in the $\pi N$ amplitude.
In a similar manner we can define all the Jacobi momenta before and after the
$\pi N$ scattering and before the pion absorption. In this way all momenta
are defined in terms of the initial and final momenta of the three
nucleons. At this stage we should point out that in a non-relativistic theory,
the $\pi NN$ vertex is not Galilean invariant since mass is not conserved. As
a result, the relative momenta ${\bf p}_3$ and ${\bf q}_3$ are not the same
before and after the pion emission. For practical calculations we will assume
that not to be the case. In other words the relative momenta ${\bf p}_3$ and
${\bf q}_3$ are those used in the three-nucleon wave function resulting from
the solution of the Faddeev equations.
The pion absorption and emission vertices in Fig.~\ref{Fig.9} have the form
factor $f^R(Q_i;E_i), i=1,3$ respectively, where the energy $E_i$ is the
energy available to the $\pi N$ system, and is given by
\begin{equation}
E_i = E + m_N - \frac{q_i^2}{2\mu_2} - \frac{p_i^2}{2\mu_1}\ , \label{eq:3.4}
\end{equation}
where $E = - E_T$ is the total energy of the system not including rest
masses, and the reduced masses $\mu_1$ and $\mu_2$ are defined by the relations
\begin{equation}
\frac{1}{\mu_1} = \frac{1}{m_N} + \frac{1}{m_N + m_\pi}\ , \quad\mbox{and}\quad
\frac{1}{\mu_2} = \frac{1}{m_N} + \frac{1}{2m_N + m_\pi}\ . \label{eq:3.5}
\end{equation}
In a similar manner, the $\pi N$ scattering in channel $\alpha$ in
Fig.~\ref{Fig.9}, is represented by the amplitude $t_\alpha(Q_1^\prime,
Q_3^\prime;E_2)$ which is given by
\begin{equation}
t_\alpha(Q_1^\prime,Q_3^\prime;E_2) =
g_\alpha(Q_1^\prime) \tau_\alpha(E_2) g_\alpha(Q_3^\prime)\ , \label{eq:3.6}
\end{equation}
where the energy available to the $\pi N$ system, $E_2$, is given by
\begin{equation}
E_2 = E + m_N - \frac{q_3^2}{2\mu_2} - \frac{{p'_3}^2}{2\mu_1}
= E + m_N - \frac{q_1^2}{2\mu_2} - \frac{{p'_1}^2}{2\mu_1}\ .
\label{eq:3.7}
\end{equation}
In this way we have made use of the general
structure of the $\pi N$ amplitude in terms of a one-particle reducible (the
$s$-channel pole amplitude) and the one-particle irreducible (the non-pole
amplitude) to determine the three-body force contribution from
Fig.~\ref{Fig.1}. Although we have used a separable potential for the non-pole
amplitude, there is no reason why we could not have made use of the non-pole
contribution from a chiral Lagrangian~\cite{PJ91}, or a separable
approximation to such a chiral $\pi N$ amplitude~\cite{PA89}, other than the
fact that this would have imposed an additional complexity to the evaluation of
such an amplitude.
Having defined the basic ingredients required to calculate the contribution
from the diagram in Fig.~\ref{Fig.1}, we turn our attention to the practical
problem of calculating the overall contribution of the diagram in
Fig.~\ref{Fig.1}. The contribution from the process whereby nucleon 1 emits a
pion that scatters off nucleon 2 in the $\pi N$ channel $\alpha$, and then
gets absorbed on nucleon 3 is given by the expression
\begin{eqnarray}
W^\alpha_{\beta_1 \beta_3} (p_1,q_1,p_3,q_3;E) &=&
\langle f^R(E_1) | Q_1 \rangle
\langle p_1 q_1 | G_{\pi NNN}(E) | p_1' q_1 \rangle
\langle Q_1' | g_\alpha \rangle
\tau_\alpha(E_2) \, \Gamma_{\beta_1\beta_3} \nonumber \\
&&\quad\times\ \langle g_\alpha | Q_3' \rangle
\langle p_3'q_3 | G_{\pi NNN}(E) | p_3 q_3 \rangle
\langle Q_3 | f^R(E_3) \rangle\ , \label{eq:3.8}
\end{eqnarray}
where $\beta_1$ and $\beta_3$ represent the set of quantum numbers that label
the three-body channels in the final and initial states, respectively. The
coefficient $\Gamma_{\beta_1 \beta_3}$ is a factor determined by the
transformation between the different Jacobi momenta in the three-nucleon
system. The four-body Green's function $G_{\pi NNN}(E)$ can be written in
terms of the $\pi NN$ Green's function, $G_{\pi NN}$, as
\begin{eqnarray}
G_{\pi NNN}(E) &=& G_{\pi NN}\left(E- \frac{q_i^2}{2\mu_2}\right) \nonumber \\
&=& \left(E_i - m_N - \frac{Q_i^2}{2m_N} -
\sqrt{Q_i^2 + m_\pi^2}\right)^{-1},\quad(i=1,3) \ . \label{eq:3.9}
\end{eqnarray}
This allows us to employ the methods developed for pion exchange in the
$NN-\pi NN$ problem and to write the partial wave projection of the process
whereby nucleon 1 emits a pion that will scatter off nucleon 2 in channel
$\alpha$ as
\begin{eqnarray}
Z_{\alpha'_3,\beta'_3}^{j^\prime_3,t^\prime_3}
\left(p_3^\prime,p_3;E - \frac{q_3^2}{2\mu_2}\right) &=&
\langle g_\alpha|Q_3'\rangle\langle p_3'\,q_3 | G_{\pi NNN}(E) |p_3
\,q_3 \rangle \langle Q_3 | f^R(E_3) \rangle \nonumber \\
&=&\sum_{L,a,b}\,A^{L,a,b}_{\alpha'_3,\beta'_3}
\ p_3^{\ell_\pi-a+b}\ {p_3'}^{1+a-b} \ \rho_2^{a+b} \nonumber \\
&&\quad\times
\frac{1}{2}\int\limits_{-1}^1 dy \, {{Q_3^\prime}^{-\ell_\pi}
\,g_\alpha(Q_3')\, f^R (Q_3;E_3)\,Q_3^{-1}
\over E_3 - m_N - {1\over 2m_N}Q_3^2 -\sqrt{Q_3^2+m_\pi^2} }
\, P_L(y)\ , \label{eq:3.10}
\end{eqnarray}
where $\ell_\pi$ is the relative $\pi N$ orbital angular momentum in the $\pi
N$ amplitude. Here $\beta'_3$ gives the set of quantum numbers for the
coupling scheme $[(\pi N_1)_N,N_2]$ resulting in a total angular momentum
$j^\prime_3$ and total isospin $t^\prime_3$. In a similar manner
$\alpha'_3=(\alpha,\gamma_3)$ gives the set of quantum numbers for the
coupling scheme $[(\pi N_2)_\alpha, N_1]$ giving rise to the same total
angular momentum $j^\prime_3$ and total isospin $t^\prime_3$. The quantum
numbers of $N_1$ are given by $\gamma_3 = (\ell^\prime_3,S^\prime_3)$, where
$\ell^\prime_3$ is the orbital angular momentum of $N_1$ relative to the
center of mass of $(\pi N_2)$, and $S^\prime_3$ ( the corresponding channel
spin) is the sum of the total angular momentum ($j_\pi$) of $(\pi N_2)$, and
the spin ($s_1$) of nucleon $N_1$, i.e., ${\bf S}^\prime_3 = {\bf j}_\pi + {\bf
s}_1$. In writing the above expression for the one pion exchange amplitude, we
have made use of the fact that both ${\bf Q}_3$ and ${\bf Q}_3'$ can be written
in terms of the momenta ${\bf p}_3$ and ${\bf p}_3'$ as
\begin{equation}
{\bf Q}_3 = {\bf p}_3' + \rho_2\,{\bf p}_3 \ , \qquad
{\bf Q}_3' = {\bf p}_3 + \rho_2 \,{\bf p}_3' \ , \label{eq:3.11}
\end{equation}
where
\begin{equation}
\rho_2 = {m_N \over m_N + m_\pi}\ , \label{eq:3.12}
\end{equation}
and $y=\hat{\bf p}_3\cdot\hat{\bf p}_3'$. The coefficients
$A^{L,a,b}_{\alpha'_3,\beta'_3}$ are those used in the partial wave expansion
of the Faddeev equation for a separable potential~\cite{AG90}. For the case
when the $\pi N$ channel $\alpha$ corresponds to the $P_{33}$ partial wave,
Eq.~(\ref{eq:3.10}) gives the $(j'_3,t'_3)$ partial wave projection of the
$NN-N\Delta$ transition potential. In general, since we have restricted our
analysis to the case of separable non-pole $\pi N$ amplitudes, we can
interpret the $\pi N$ amplitude in each partial wave to be dominated by an
$N^*$ in which case $Z_{\alpha'_3,\beta'_3}^{j'_3,t'_3}$ can be considered as
the transition potential for $NN\rightarrow NN^*$. The difference
between the traditional $NN-N\Delta$ transition potential and the above result
in Eq.~(\ref{eq:3.10}) is the fact that the present transition potential is
energy dependent and the parameters of the potential are determined by the
$\pi N$ data rather than by the $NN$ data.
This interpretation of $Z_{\alpha'_3,\beta_3'}^{j'_3,t'_3}$ as a partial wave
projected
transition potential will allow us to regards the diagram in Fig.~\ref{Fig.1}
to
correspond to an initial state of three nucleons with nucleons 1 and 2 in the
channel
$\beta_3'$ going to two nucleons plus an $N^*$, followed by the $N^*$ coupling
to nucleon 3 to form a final state of nucleon 2 and 3 in channel $\beta_1'$
with nucleon 1 as spectator. This corresponds to the exchange of an $N^*$ and
will allow us to partial wave expand the three-body force in a similar manner
to the expansion of the one pion exchange diagram treated above. The resultant
partial wave expansion of the diagram in Fig.~\ref{Fig.1} is given as
\begin{eqnarray}
W_{\beta_1, \beta_3}^\alpha(p_1,q_1,p_3,q_3;E) &=&
{1\over2}\sum_{\gamma_1,\gamma_3}\sum_{L,a,b}\ \int\limits_{-1}^1 dx\,
(-)^R\ {q_1^{\ell_3'-a+b}\,q_3^{\ell_1'+a-b}
\over {p_1'}^{\ell_1'} {p_3'}^{\ell_3'}}\ \rho_1^{a+b}\
A^{L,a,b}_{\beta_1,\beta_3}\,P_L(x) \nonumber \\
& & \nonumber \\
&&\times\, Z_{\beta_1',\alpha'_1}^{j'_1,t'_1}
\left(p_1,p_1';E-\frac{q_1^2}{2\mu_2}\right)\,\tau_\alpha(E_2)\,
Z_{\alpha'_3,\beta_3'}^{j'_3,t'_3}
\left(p_3',p_3;E-\frac{q_3^2}{2\mu_2}\right)\ ,\label{eq:3.13}
\end{eqnarray}
where the phase, $R=j_\pi+t_\pi + \ell_3' +S_3' +t_3'$, results from changing
the coupling scheme to maintain consistency with the definition of the Jacobi
coordinates. Here, $(j_\pi,t_\pi)$ are the total angular momentum and isospin
of the pion with nucleon 2, i.e., they define the $\pi N$ channel $\alpha$,
while $\ell_i'$ $(i=1,3)$ are the orbital angular momenta corresponding to the
momenta $p'_i$, e.g. $\ell'_3$ is the orbital angular momentum of $N_1$
relative to the center of mass of $(\pi N_2)$. In this case, we have written
the momenta ${\bf p}'_3$ and ${\bf p}'_1$ in terms of the momenta ${\bf q}_3$
and
${\bf q}_1$ as
\begin{equation}
{\bf p}'_3 = {\bf q}_1 + \rho_1\,{\bf q}_3 \ ,\qquad
{\bf p}'_1 = {\bf q}_3 + \rho_1\,{\bf q}_1 \ , \label{eq:3.14}
\end{equation}
where
\begin{equation}
\rho_1 = {m_N \over 2m_N + m_\pi } \ , \label{eq:3.15}
\end{equation}
and $x=\hat{\bf q}_1\cdot\hat{\bf q}_3$. Here again the coefficient
$A^{L,a,b}_{\beta_1,\beta_3}$ is the coefficient resulting from the angular
momentum recoupling, i.e., $[(N_1N_2)_{\beta'_3},N_3] \rightarrow N_1
+ N^*_2 + N_3 \rightarrow [(N_2 N_3)_{\beta'_1},N_1]$.
To compare the three-body force given in Eq.~(\ref{eq:3.13}) with that
resulting from the $NN-N\Delta$ coupled channel approach\cite{PRB91}, we note
that the expression in Eq.~(\ref{eq:3.13}) basically consists of a transition
potential $NN\rightarrow NN^*$ followed by the propagation of the $N^*$
quasiparticle and finally the transition potential $NN^*\rightarrow NN$.
Making use of the definition of $\tau_\alpha(E_2)$, ( Eqs.~(\ref{eq:2.3}) and
(\ref{eq:2.4}) ), we can write this quasi-particle propagator for the case when
$\alpha$ refers to the $P_{33}$ channel as
\begin{eqnarray}
\tau_\alpha(E_2) &=& \left[(E_2-E_\Delta)\langle g_\alpha|G_{\pi N}(E_2)G_{\pi
N}(E_\Delta)|g_\alpha\rangle\right]^{-1}\nonumber \\
&& \nonumber \\
&=& {\left[\langle g_\alpha|G_{\pi N}(E_2)G_{\pi N}(E_\Delta)
|g_\alpha\rangle\right]^{-1}}\over
{\left[E + m_N -E_\Delta - \frac{q_3^2}{2\mu_2} - \frac{{p'}^2_3}{2\mu_1}
\right]}
\ . \label{eq:3.16}
\end{eqnarray}
In writing this equation we have made use of the fact that
$\tau^{-1}_\alpha(E_\Delta) = 0$, where $E_\Delta= m_\Delta -
\frac{i}{2}\Gamma = 1230 - 50 i$~MeV is the position of the $\Delta(1230)$
resonance, and $\alpha$ refers to the $P_{33}$ partial wave. This illustrates
the fact that our quasi-particle propagator is the free $NN\Delta$ propagator
for which the $\Delta$ has a width, and this width has the correct energy
dependence as dictated by unitarity and the experimental phase shifts in this
channel. Thus if we include the contribution to the three-body force from the
$P_{33}$ $\pi N$ channel only, we have effectively included, to lowest order,
the contribution from the three-body force resulting from the $NN-N\Delta$
coupling. However, our result differs from the standard definition of this
contribution to the three-body force\cite{PRB91} in that we have employed the
$\pi N$ data rather than the $NN$ data to fix the parameters of this force,
and our $\Delta$ is a proper resonance in the $\pi N$ system and not a real
particle as it is often considered. The other difference between this
approach and that used in the $NN-N\Delta$ coupled channel approach is in the
choice of the pion propagator in the ``transition potential''. In the
$N\Delta$ coupled channel approach, the pion propagator is taken to be
$(k_\pi^2 + m_\pi^2)^{-1}$, which corresponds to the Feynman propagator with
the nucleons on-mass-shell. This propagator has no energy dependence. On the
other hand we have chosen the standard non-relativistic four particle Green's
function with a relativistic expression for the pion kinetic energy. This is
consistent with four-particle unitarity and is equivalent to a time ordered
propagator, and to that extent we have only one time order for our pion
exchange. Finally, we should note that the $NN-N\Delta$ coupled channel
approach treats the contribution of the $\Delta$ to all orders and as a
result includes the dispersive contribution which to a large extent cancels
the contribution of the three-body force.
The recent three-nucleon force results, reported by Pe\~na~{\it et
al.}\cite{PSSK93}, treat the $\Delta$ as a $\pi N$ resonance. To that
extent, the $\pi N$ amplitude in the $P_{33}$ channel is similar to that
presented here, in that the mass and width of the $\Delta$ have energy
dependence as dictated by $\pi N$ scattering data. Pe\~na~{\it et al.} have the
additional advantage that they not only have included the $\Delta$
contribution to the three-body force to all orders, but have also included the
dispersive contribution. However, by restricting their Hilbert space to $N$
and $\Delta$ and turning off all interaction in the pionic part of the
Hilbert space, they have not included the contribution of the $\pi N$
amplitude in other than the $P_{33}$ partial wave.
They find that the contribution of the non-resonant $\pi N$ amplitude is
very small as a result of the fact that the pionic component of the
three-nucleon wave function is small.
We now try to relate our three-body force with that used in the TM approach.
In the TM approach, the final $\pi N$ amplitude is written in terms of the pion
momenta, where as we use the $\pi N$ relative momenta ${\bf Q}'_1$ and ${\bf
Q}'_3$~\cite{Foot4}. To achieve their result, we recall that the partial wave
expansion of the $\pi N$ amplitude is given by
\begin{equation}
\langle{\bf Q}|t(E)|{\bf Q}'\rangle =
\sum_{\alpha} P_\alpha(\hat{\bf Q},\hat{\bf Q}')
\ t_\alpha(Q,Q';E) \ , \label{eq:3.17}
\end{equation}
where $\alpha = (\ell,j,T)$ are the quantum numbers corresponding to the
orbital and total angular momentum and isospin of the $\pi N$ system, i.e.
$\alpha$ labels the different partial waves. The partial wave projection
operator
$P_\alpha(\hat{\bf Q},\hat{\bf Q}')$ is defined as
\begin{equation}
P_\alpha(\hat{\bf Q},\hat{\bf Q}') = P_T \sum_m \,
\langle\hat{\bf Q}|{\cal Y}_{\ell jm}\rangle\,
\langle{\cal Y}_{\ell jm}|\hat{\bf Q}'\rangle\ , \label{eq:3.18}
\end{equation}
with $P_T$ the projection operator for a given isospin channel, and
$\langle\hat{\bf Q}|{\cal Y}_{\ell jm}\rangle$ the eigenstates of the
orbital and total angular momentum of the $\pi N$ system. If we now write the
angular momentum projection operator in terms of ${\bf Q}\cdot{\bf Q}'$ and
${\bf Q}\times{\bf Q}'\cdot {\bbox{\sigma}}$ and the isospin projection
operator in terms of the Pauli isospin operator, we can write our
$\pi N$ amplitude, assuming the pion scatters of nucleon 1, in the form
presented by the
Tucson-Melbourne formulation as
\begin{equation}
t^{TM}({\bf Q},{\bf Q}') = ({\bbox{\tau}}_2\cdot{\bbox{\tau}}_3)\,
\left[ a + b {\bf Q}\cdot{\bf Q}' + c(Q^2 + {Q'}^2)\right]
+ d({\bbox{\tau}}_1\cdot({\bbox{\tau}}_3\times{\bbox{\tau}}_2))
({\bbox{\sigma}}_1\cdot({\bf Q}\times{\bf Q}') ) \ . \label{eq:3.19}
\end{equation}
For the factors $a$, $b$, $c$ and $d$ to be constant, as required by the
Tucson-Melbourne definition of the three-body force, we have to make the
following approximations:
(i)~Since the TM potential is derived from the off-mass-shell $\pi N$ amplitude
$T(\nu,t,q,q')$, where $t$ is the Mandelstam variable and $q$ $(q')$ is the
four momentum of the initial (final) pion, by expanding the amplitude about
$\nu=0$,
we need to determine the corresponding approximation for our off-energy-shell
$\pi
N$ amplitude. For the off-mass-shell amplitude the nucleon pole ($s=m_N^2$)
traces a
curve in the $\nu-t$ plane that crosses the $\nu$-axes close to
$\nu=0$\cite{C86}.
Since we find it difficult to directly relate the variables that in the
off-mass-shell
amplitude with the corresponding variables in off-energy-shell amplitude, we
have
chosen the position of the nucleon pole, i.e. $E=m_N$ or $s=m_N^2$, to be the
closest
approximation to $\nu=0$. In this way we approximate the energy in our
amplitude
to
be the nucleon mass, {\it i.e.}, $\tau(E_2)\rightarrow\tau(m_N)$.
(ii)~The separable potential form factors
$g_\alpha(Q)$ have to be expanded in a power series in the momentum $Q$,
keeping those terms such that the final amplitude does not have any powers of
the momentum higher than the momentum squared. With these approximations, the
Thomas separable potential, in conjunction with the potential $PJ$ in the
$P_{11}$ channel, can be written in the above form with the constants $a$,
$b$, $c$ and $d$ given in Table~\ref{Table.3}. Included in the table are also
the corresponding parameters from the Tucson-Melbourne potential\cite{CP93}.
In next section, we will present our numerical result and show:
(i) How the contribution to the three-body force from each $\pi N$ partial
wave
depends on the energy in the $\pi N$ amplitude.
(ii) How the three-nucleon force is sensitive to the choice of the $\pi NN$
form
factor which is determined as the residue of the $P_{11}$ pole term.
Though we have not included all the diagrams that would
contribute to the three-body force, we have included the most important
contribution, which will allow us to examine these effects.
\section{Numerical Results}\label{sec.4}
Having defined our three-nucleon force in terms of the $\pi N$ potential
whose parameters have been adjusted to fit the $\pi N$ data, and in
particular, the phase shifts up to the threshold for pion production, we turn
our attention in this section to the calculation of the contribution of this
force to the binding energy of the three-nucleon system. As a first
calculation with a three-body potential that includes the energy dependence of
the $\pi N$ amplitude, we have chosen to use the first order perturbation
theory
to calculate this three-body force contribution. Therefore, we can write our
three-body force as
\begin{eqnarray}
W &=& \sum_{{i,j=1}\atop{i\neq j}}^3\ W(j,i) \nonumber \\
&=& \sum_{{i,j=1}\atop{i\neq j}}^3 \sum_\alpha \
W_{j,i}^\alpha({\bf p}_j,{\bf q}_j;{\bf p}^\prime_i,{\bf q}^\prime_i)
\ , \label{eq:4.1}
\end{eqnarray}
where $j$ in the sum refers to the nucleon that emits the pion, and $i$
refers to the nucleon that absorbs the pion. Here, $\alpha$ refers to the $\pi
N$ partial wave used to calculate the three-body force. Since the
three-nucleon wave function used is a solution of the Faddeev equations, we
can write this wave function as the sum of three components, i.e.
\begin{eqnarray}
|\Psi\rangle &=& |\psi_1\rangle + |\psi_2\rangle + |\psi_3\rangle \nonumber \\
&=& \left[ 1 + (123) + (132)\right]\,|\psi_1\rangle\ ,
\label{eq:4.2}
\end{eqnarray}
where we have written the total wave function in terms of the elements of the
permutation operators. Making use of the properties of the permutation group,
we can write the total contribution to the binding energy from this three-body
force as
\begin{equation}
\Delta E^{(3)} =6\,\langle\Psi|\,W(1,3)\,|\Psi\rangle \ . \label{eq:4.3}
\end{equation}
The three-body potential $W(1,3)$ can now be partial wave expanded in terms
of the partial wave potential given in Eq.~(\ref{eq:3.13}) as
\begin{equation}
\langle{\bf p}_1{\bf q}_1|\,W(1,3)\,|{\bf p}_3{\bf q}_3\rangle =
\sum_{\alpha}\,\sum_{\beta_1\beta_2}\ \langle{\bf \hat{p}}_1{\bf \hat q}_1|
\beta_1\rangle\,W^\alpha_{\beta_1\beta_3}(p_1,q_1,p_3,q_3;E)\,
\langle\beta_3|{\bf \hat p}_3{\bf \hat q}_3\rangle\ , \label{eq:4.4}
\end{equation}
where $\beta_i$ defines the three-body partial wave quantum number in which
nucleon $i$ is the spectator. In Eq.~(\ref{eq:4.4}), $\alpha$ refers to the
$\pi N$ partial wave that contributes to the three-body potential. In a
similar manner we have to expand the three-nucleon wave function in terms of
the angular momentum and isospin bases
$\langle{\bf \hat{p}}_1{\bf \hat q}_1| \beta_1\rangle$. This is given by
\begin{eqnarray}
\langle{\bf p}_1{\bf q}_1|\Psi\rangle &=&
\sum_{\beta_1}\ \langle{\bf \hat p}_1{\bf \hat q}_1|\beta_1\rangle\,
\langle\beta_1;p_1 q_1|\Psi\rangle \nonumber \\
&=&\sum_{\beta_1=1}^{N_2}\ \langle{\bf \hat p}_1{\bf \hat q}_1|\beta_1\rangle\,
\left[\langle p_1 q_1|\psi_{\beta_1}\rangle +
\sum_{j=2,3}\ \sum_{\beta_j=1}^{N_1}\ \langle\beta_1|\beta_j\rangle\,
\langle p_j q_j|\psi_{\beta_j}\rangle\right]\ . \label{eq:4.5}
\end{eqnarray}
In Eq.~(\ref{eq:4.5}) the sum over $N_1$ extends to the number of three-body
channels included in the solution of the Faddeev equations which in turn is
determined by the number of two-body $NN$ channels included. On the other
hand, the sum over $N_2$ is an infinity sum which we have truncated for
practical calculations. For $N_2>N_1$ the first term $\langle
p_1q_1|\psi_{\beta_1}\rangle$ contributed only to the first $N_1$ terms in the
$N_2$ sum. This restriction is the result of truncating the number of $NN$
partial waves included in the solution of the Faddeev equations. We will test
the convergence of our final results to both the sum over $N_1$ and $N_2$.
Making use of the partial wave expansion for the three-body potential and the
three-nucleon wave function, we can write the total contribution of the
three-body force to the binding energy of the triton as
\begin{eqnarray}
\Delta E^{(3)} &=& 6\ \sum_\alpha\ \sum_{\beta_1\beta_3}\
\int\limits_0^\infty\,dp_1\,p_1^2\,\int\limits_0^\infty\,dp_3\,p_3^2\,
\int\limits_0^\infty\,dq_1\,q_1^2\,\int\limits_0^\infty\,dq_3\,q_3^2\nonumber\\
& & \qquad\times \langle\Psi|p_1 q_1;\beta_1\rangle\,
W^\alpha_{\beta_1\beta_3}(p_1,q_1,p_3,q_3;E)\,
\langle\beta_3;q_3 p_3|\Psi\rangle\ , \label{eq:4.6}
\end{eqnarray}
where $E$ is the energy of the three-nucleon system as determined by the
solution of the Faddeev equations for a given two-nucleon interaction, and the
partial wave three-body potential, $W^\alpha_{\beta_1\beta_3}$, as given in
Eq.~(\ref{eq:3.13}).
In the present investigation we have chosen to use the Paris nucleon-nucleon
potential~\cite{LL80}.
The Paris potential is energy independent while our three-nucleon
force has been derived to be energy-dependent.
To that extent, our two- and three-body potentials are not consistent in
that they are not derived from the same Lagrangian.
However, since we are
examining the energy dependence of the three-body force for each
$\pi N$ partial wave, we hope that the present perturbative calculation may
allow us
to gain some insight into this problem.
To simplify the construction of the
three-nucleon wave function needed to evaluate the integrals in
Eq.~(\ref{eq:4.6}), we have chosen the separable representation of the Paris
potential~\cite{HP84}. This representation has been tested for the
three-nucleon observables with considerable success~\cite{PK91}. In
Table~\ref{Table.4}, we give the rank of the separable expansion we have
chosen. This choice was dictated by the requirement that we should reproduce
the binding energy of the triton and the different percentages of $S-$, $S'-$,
and $D-$state probability for the triton. However, before we compare our
results with the coordinate space calculation for the Paris potential, we
present in Table~\ref{Table.5} the convergence of these quantities as we
increase the number of three-body channels, $N_1$, in the solution of the
Faddeev equations. From this table we can see that as far as the three-nucleon
wave function is concerned, the 18 channel Faddeev equations give good
convergence for all quantities. These 18 channels in the Faddeev equations
correspond to the truncation of the $NN$ interaction to include all two-body
partial
waves with total angular momentum less than or equal to two, including the
coupled
$^3P_2-^3F_2$ $NN$ channels. To justify the use of the separable expansion to
the Paris
potential, PEST~\cite{HP84}, we compare, in Table~\ref{Table.6}, our results
for
the 18
channel calculation with the corresponding results based on the coordinate
space solution of the Faddeev equations for the Paris potential. Taking the
difference between the two coordinate space calculations as a measure of the
numerical uncertainty in the solution of the Faddeev equations, we have good
agreement with previous results for the Paris potential. This suggests that
the three-nucleon wave function resulting from the PEST approximation is
comparable to that resulting from a solution of the Faddeev equations in
coordinate space for the exact Paris potential.
Having established the fact that the three-nucleon wave function generated by
the separable expansion to the Paris potential is of comparable quality to
that resulting from the solution of the Faddeev equations in coordinate space,
we turn our attention to the convergence of the contribution of the three-body
force to the number of three-body channels in the solution of the Faddeev
equations, $N_1$, and the number of three-body channels included in the
partial wave expansion of the wave function, $N_2$.
For this study we make use of the $P_{11}$ potential $PJ$ of McLeod and Afnan
\cite{MA85}. In Table~\ref{Table.7} we present
the contribution to the binding energy from the more important $\pi N$ partial
waves
for 5, 10, and 18 channel Faddeev calculations. In all cases we have taken 18
partial waves for the expansion of the wave function. All energies in
Table~\ref{Table.7} are in keV. We note at this stage that although the
contribution
to the binding energy is small, the 18 channel Faddeev calculation has
converged,
while the 5 channel calculation gives an incorrect result. With the 18
channel Faddeev calculation, we tested the convergence of our result to the
number of terms in the partial wave expansion of the three-body wave
function, $N_2$. From the results in Table~\ref{Table.8} we may conclude that
$N_2=18$ is sufficient to give us a 1~keV accuracy for the contribution from a
given
$\pi N$ partial wave. If the need arises we might have to resort to more terms
in
the partial wave expansion of the wave function.
In Table~\ref{Table.9} we present the contribution of the three-body force to
the binding energy of the triton from the different $\pi N$ partial waves for
two different $P_{11}$ potentials. Here we have taken $N_1=N_2=18$, with all
energies given in keV. The most surprising result of our calculations is the
overall small contribution of the three-body force. From the results in
Tables~\ref{Table.7} and \ref{Table.8}, it is clear that the inclusion of more
three-body partial waves in the wave function expansion and the solution of
the Faddeev equation will not change the results substantially. Before we
address the origin of this small contribution from our three-nucleon force it
is interesting to note: (i)~The comparable contribution from the $S-$ and
$P-$waves $\pi N$ partial wave, and in particular the large contribution of
the $S_{31}$ compared to the $S_{11}$. This suggests that we need to include
both $S-$ and $P-$wave $\pi N$ amplitudes into the calculation. Furthermore,
models based on the dominance of the $\Delta(1230)$ resonance might not be
valid since they neglect the contribution from the $S_{31}$ and $P_{11}$
partial waves. In fact, in the present formulation, the contribution of the
$P_{33}$ partial wave amplitude is for $\pi N$ energies below the nucleon
pole, some 300~MeV below the $\Delta$ resonance. (ii)~There is a cancellation
between the $S-$ and $P-$wave $\pi N$ contributions requiring a consistent
treatment of both sets of partial wave amplitudes. (iii)~The $P-$ wave
contribution comes equally from the non-pole part of the $P_{11}$, and the
$P_{33}$ partial wave amplitudes. This is despite the fact that the overall
$P_{11}$ phase shifts are small when compared with the $P_{33}$ phase shifts.
However, if we recall that it is the non-pole part of the amplitude that
contributes to the three-body force, and this non-pole part, on its own, has
phase shifts that are comparable to those in the $P_{33}$
channel~\cite{MF81,MA82}, then the results reported in Table~\ref{Table.9}
are not surprising. Finally, if we compare the results for the two potentials,
we find that the potential $M1$ gives a larger contribution to the binding
energy than the potential $PJ$. To understand this difference, we compare the
dressed form factors for these two potentials in Fig.~\ref{Fig.10}. Here we
observe that the potential $M1$ has a harder form factor than the potential
$PJ$, i.e., the dressed form factor for potential $M1$ is greater than the
corresponding form factor for the potential $PJ$ for large $k$. This is
consistent with results of the fact that the three-body force contribution to
the binding energy increases as the form factor gets harder. We will come back
to this point later in our discussion when we consider the role of the $\pi
NN$ form factor in the contribution of the three-nucleon force to the binding
energy of the triton.
We now turn to the question of why the contribution of this three-body force
is small. From Table~\ref{Table.3}, we may expect the maximum difference
between
our prediction and the TM result for the three-body force contribution
to be at most an order of magnitude, but not three orders of magnitude.
Since the unique feature of the present calculation is the inclusion
of the energy dependence in both the $\pi NN$ form factor and the $\pi N$
amplitude, we will commence by turning this energy dependence off. We will
also concentrate on those $\pi N$ partial waves that give a substantial
contribution to the three-body force. We will restrict our results to
$N_1=N_2=18$. As a first approximation, denoted (i) in Table~\ref{Table.10},
we fix the energy in the $\pi NN$ form factor to be
the position of the nucleon pole, i.e.
\begin{equation}
f^R(k;E) \rightarrow f^R(k;m_N) \ . \label{eq:4.7}
\end{equation}
Although this approximation changes our final result by increasing the
contribution of the three-body force to the binding energy, the magnitude of
the increase is not substantial because the cancellation between the
repulsive $S_{31}$ and the attractive $P_{11}$ and $P_{33}$ contributions is
still present. In particular, we note that both the attractive and repulsive
contributions have increased in magnitude. We next take the energy dependence
in the $\pi N$ amplitude to be the position of the nucleon pole
(approximation (ii)), i.e.
\begin{equation}
\tau_\alpha(E) \rightarrow \tau_\alpha(m_N)\ . \label{eq:4.8}
\end{equation}
In this case, we have increased the total contribution of the three-body
force to the binding energy by an order of magnitude as compared to the exact
result. This substantial increase in binding is mainly due to the fact that
the $S_{31}$ contribution is reduced in magnitude while the $P_{11}$ and
$P_{33}$ contributions have increased, thus reducing the cancellation between
the attraction and repulsion when compared with the exact calculation. To
understand why the contribution of the $S_{31}$ partial wave is suppressed as
the energy in $\tau_\alpha$ is increased (i.e. brought closer to the $\pi N$
threshold, see Fig.~\ref{Fig.3}), we recall from Eqs.~(\ref{eq:2.3}) and
(\ref{eq:2.4}) that $\lambda = +1$ for repulsive potentials such as the
$S_{31}$, while $\lambda= -1$ for attractive potentials such as the $P_{33}$.
On the other hand, $\langle g_\alpha|G_{\pi N}(E)|g_\alpha\rangle$ is negative
for $E<(m_\pi+m_N)$ and increases in value as we approach the $\pi N$
threshold from below. Thus for attractive potentials there is a cancellation
in the denominator of $\tau_\alpha(E)$ giving rise to an increase in the value
of $\tau_\alpha(E)$ as $E$ approaches the threshold. On the other hand, for
repulsive potentials, e.g. the $S_{31}$ channel, the value of $\tau_\alpha(E)$
decreases as we approach the elastic threshold from below, resulting in a
suppression of the repulsive contribution. To demonstrate the validity of
this argument, we have proceeded to change the energy in the $\pi N$
amplitude, to be the threshold for $\pi N$ scattering, i.e.,
\begin{equation}
\tau_\alpha(E) \rightarrow \tau_\alpha(m_N+m_\pi) \ . \label{eq:4.9}
\end{equation}
The result of this approximation is labeled (iii) in Table~\ref{Table.10}.
Here, we observe that the contribution of the $S_{31}$ is further reduced,
while the $P_{11}$ and $P_{33}$ contributions are increased in magnitude,
giving even more attraction. We now fix the energy of both the $\pi NN$ form
factor and the $\pi N$ scattering amplitude to the nucleon pole, i.e. $E=m_N$,
(i) \& (ii) in Table~\ref{Table.10}. This gives even more binding than fixing
the energy in either the $\pi N$ scattering amplitude or the $\pi NN$ form
factor. Finally, we can increase binding further by fixing the energy of the
$\pi NN$ form factor at the nucleon pole, while the energy in the $\pi N$
amplitude is taken to be the threshold energy, (i) \& (iii) in
Table~\ref{Table.10}. From the above analysis we may conclude that it is the
energy dependence in both the $\pi NN$ form factor and the $\pi N$ amplitude
that has substantially reduced the contribution of the three-nucleon force to
the binding energy of the triton, and this reduction is a result of the
cancellation between the repulsive $S_{31}$ contribution and attractive
$P_{11}$ and $P_{33}$ contributions.
However, the approximation of fixing the energy in the $\pi N$ amplitude
and $\pi NN$ form factor does not give us a sufficiently large contribution
which is comparable with the result for the TM potential.
Finally, to fully understand the origin of this small contribution to the
binding energy from the three-nucleon force, we turn our attention to the form
factors used in the separable potential and the form factor in the $\pi NN$
vertex. It is common practice to take the $\pi NN$ form factor in $NN$
scattering to be either of a dipole or monopole form. Therefore, as a first
step in examining the sensitivity of our final three-body force contribution
to the binding energy, we replace the $\pi NN$ form factor $f^R(k;E)$ by a
monopole, i.e.
\begin{equation}
f^R(k;E) \rightarrow \frac{f^R(k;m_N)}{k}\Bigg|_{k=0}\,k\,
F_0(k)\ , \label{eq:4.10}
\end{equation}
where the monopole form factor $F_0(k)$ is given by
\begin{equation}
F_0(k) = \frac{\Lambda^2}{\Lambda^2 + k^2} \label{eq:4.11}
\end{equation}
with the cutoff mass $\Lambda$, varied. In Table~\ref{Table.11} we compare
exact results for the $P_{11}$ potential $PJ$~\cite{MA85} with the result for
the approximations in Eqs.~(\ref{eq:4.7}) and (\ref{eq:4.8}), referred to as
(i)~\&~(ii), and the approximations in Eqs.~(\ref{eq:4.8}) and (\ref{eq:4.10})
with $\Lambda = 400$ and $800$~MeV. The results in lines 2, 3 and 4 of
Table~\ref{Table.11} have the energy in the $\pi N$ amplitude fixed to be the
energy at the nucleon pole, i.e. $E_{\pi N} = m_N$. Here we observe that the
final total contribution of the three-body force increases by an order of
magnitude when the energy in both the $\pi NN$ form factor and $\pi N$
amplitude is fixed at the nucleon pole. There is a further order of magnitude
increase when the $\pi NN$ form factor is replaced by a monopole form factor
with a cutoff mass of 400 and then 800~MeV. In fact, half of this increase is
achieved when the cutoff mass is increased from 400 to 800~MeV. This
establishes the sensitivity of our result to the choice of $\pi NN$ form
factor. In this case it is interesting to observe that the $S_{31}$ and
$P_{11}$ contributions to the three-nucleon force almost completely cancel,
leaving the $P_{33}$ contribution to be approximately the total contribution.
Thus in this approximation, the contribution to the three-nucleon force is
predominantly due to the channel in which the $\Delta(1230)$ dominates the
scattering amplitude. This result should be compared with the exact results,
line 1 of Table~\ref{Table.11}, where the $S_{31}$ contribution cancels the
sum of the $P_{11}$ and $P_{33}$ contributions.
In the spirit of the TM approach, the $\pi N$ amplitude is expanded to
lowest order in $q\over m_N$ and a monopole $\pi NN$ form factor is
introduced. This approximation may be implemented by the following
replacement:
\begin{eqnarray}
f^R(k;E) &\rightarrow& \frac{f^R(k;m_N)}{k}\Bigg|_{k=0}\,k\, F_0(k)
\nonumber \\
\tau_\alpha(E) &\rightarrow& \tau_\alpha(m_N) \label{eq:4.12}
\\ g_\alpha(k)&\rightarrow& \frac{g_\alpha(k)}{k^\ell}\Bigg|_{k=0}
\ k^\ell\, F_0(k) \
,\nonumber
\end{eqnarray}
where $\ell$ is the angular momentum in channel $\alpha$ and the monopole
form factor $F_0(k)$ is defined in Eq.~(\ref{eq:4.11}).
However in our formulation, this replacement will destroy the fit to the
experimental $\pi N$ phase shifts. In
Table~\ref{Table.13}, we compare our exact result for the $P_{11}$ potential
$PJ$~\cite{MA85}, with the results of the approximation in Eq.~(\ref{eq:4.12})
with $\Lambda = 400$ and $800$~MeV. The approximation in Eq.~(\ref{eq:4.12})
gives rise to an increase in the contribution of the $P$-waves substantially,
while the $S$-wave contribution remains relatively unchanged, and therefore
negligible. In fact we can now adjust the cutoff mass $\Lambda$ to get the
difference between the experimental binding energy and the calculated
three-nucleon result for any of the two-nucleon interactions.
To understand this large change in the magnitude of the total contribution of
the three-body force when we introduce the form factor $F_0(k)$, we compare in
Fig.~\ref{Fig.10} the monopole form factor with $\Lambda =400$ and $800$~MeV
and
the
dressed $\pi NN$ form factor for the potentials $PJ$ and $M1$. Here we
observe that the form factor $F_0(k)$ with $\Lambda = 800$~MeV is almost a
factor of 3 larger than the dressed $\pi NN$ form factor at $k\approx
3$~fm$^{-1}$. Furthermore, this form factor comes raised to the power of two
in the case when only the $\pi NN$ form factor is replaced by a monopole form
factor, or a power of four when the approximations in Eq.~(\ref{eq:4.12}) are
implemented, i.e. we have a power of two from the $\pi NN$ vertices and another
power of two from the form factor of separable $\pi N$ amplitudes. Thus the
difference between the result of including $f^R(k,m_N)$ and
$F_0(k)$ should be roughly one order of magnitude in Tables~\ref{Table.11},
and two
orders of magnitude in Table~\ref{Table.13}. In the latter case we assume the
separable potential form factors have similar ranges to the dressed $\pi NN$
form
factor. This explains the drastic change in the contribution of the three-body
force
to the binding energy when we introduced the monopole form factor $F_0(k)$ into
our
calculation.
Finally, to get the closest approximation to the TM three-nucleon force, we
have modified the propagator for the exchanged pion by replacing our
propagator by the corresponding Feynman propagator, i.e.,
\begin{equation}
\frac{1}{Q_0 - \omega_Q}\rightarrow
\sqrt{2\omega_Q}\,\frac{1}{Q^2-m_\pi^2}\,\sqrt{2\omega_Q} \ ,\label{eq:4.13}
\end{equation}
where $\omega_Q = \sqrt{Q^2+m_\pi^2}$. To understand the difference between
these two propagators, we recall that the Feynman propagator has both a
positive energy and negative energy component, since
\begin{equation}
\frac{1}{Q^2 - m^2_\pi} = \frac{1}{2\omega_Q}\left[\frac{1}{Q_0 - \omega_Q} -
\frac{1}{Q_0 + \omega_Q}\right]\ . \label{eq:4.14}
\end{equation}
and our choice of propagator, i.e. $(Q_0-\omega_Q)^{-1}$, corresponds to
taking the positive energy component of the Feynman propagator. However in any
energy independent approximation, the Feynman propagator reduces to $-
1/\omega^2_Q$. The substitution in Eq.~(\ref{eq:4.13}) gives us the last line
of Table~\ref{Table.13}, and results in the reduction of the contribution of
the three-body force so that a monopole form factor with a cutoff mass of
800~MeV will give a three-body force contribution of about 0.6~MeV, which is
consistent with the results reported in the literature for the TM
three-nucleon force.
Thus, to get a substantial contribution from the three-body force we have had
to make two approximations. (i) We have dropped the energy dependence of the
$\pi N$ amplitude and the $\pi NN$ form factor. (ii) We have modified the
off-shell behavior of the $\pi N$ amplitude by introducing the same monopole
form
factor in all partial waves, at the sacrifice of the fit to the experimental
data, in
order to get a substantial increase to the three-body force contribution.
Although
the first approximation is not justified, the second could be accepted on the
ground
that we have chosen the wrong off-shell behavior. In particular, we should
consider changes the cutoff mass in the bare $\pi NN$ form factor $f_0(k)$,
and make use of the Goldberger-Treiman~\cite{GT58} relation to constrain the
dressed $\pi NN$ form factor $f^R(k;E)$. This point is presently under further
investigation.
\section{Conclusion}\label{sec.5}
The main motivation for this investigation was to establish the relative
contribution of the different partial waves of the $\pi N$ amplitude in
determining the $\pi-\pi$ three-nucleon force and its contribution to the
binding energy of the triton. To achieve this, we made use of a separable
potential formulation of the $\pi N$ scattering, taking into consideration
that such a parameterization of the off-shell $\pi N$ amplitude has been
used in $\pi d$ scattering and in the derivation of the pion-nucleus optical
potential with considerable success. In particular, we maintained the
energy dependence of the $\pi N$ amplitude since that could effect the overall
contribution to the three-body force. More importantly, the cancellation
between the contribution of the different partial waves could be sensitive to
the inclusion of this energy dependence. Since the energy domain, important
to the determination of the three-nucleon force, is in the unphysical region
and below the position of the nucleon pole in the energy plane, we chose to
fit the scattering data closest to this region. In particular we chose to fit
the scattering lengths, the phase shifts up to the pion production threshold,
and the position and the residue of the $\pi N$ amplitude at the nucleon
pole. This parameterization allowed us to determine the $\pi NN$ form factor
and that part of the $\pi N$ amplitude that gives rise to the three-body
force.
{}From the numerical results of our calculation we can conclude that: (i)~The
energy dependence of both the $\pi NN$ form factor and $\pi N$ amplitude gives
a suppression of the contribution of Fig.~\ref{Fig.1} to the three-nucleon
force. Given the fact that this diagram has always been considered to give the
main contribution to this force, we can conclude that the three-nucleon force
for this $\pi N$ parameterization is small, and will not change substantially
if we include this three-body force in an exact calculation rather than in the
perturbative approach used in the present investigation. (ii)~The inclusion
of the energy dependence gives rise to a substantial cancellation between the
contribution from the repulsive $S_{31}$ partial wave and the attractive
$P_{11}$ and $P_{33}$ partial waves. (iii)~The contribution from the $P_{33}$
partial wave is not as dominant as we would expect. In fact the attraction
comes equally from the $P_{11}$ and $P_{33}$, while the repulsion comes from
the $S_{31}$. This raises a question about the validity of including the
three-body force in terms of the $NN-N\Delta$ coupled channel approach while
neglecting the $S-$wave and the $P_{11}$ $\pi N$ contributions. (iv)~The
choice of the $\pi NN$ form factor, to be determined by the residue of the $\pi
N$ amplitude at the nucleon pole, is the other main reason for the reduction in
the overall magnitude of the three-nucleon force contribution to the binding
energy. The question of the possibility of choosing the cutoff mass in the
bare form factor $f_0(k)$ to be consistent with the $\pi N$ data, while
maintaining a substantial three-body force, will need further investigation.
Furthermore, the Goldberger-Treiman relation~\cite{GT58,CS90} should be used
to constrain the momentum dependence of the dressed $\pi NN$ form factor
$f^R(k;E)$.
To further substantiate the above conclusions, we may need to examine a number
of questions: (i)~How sensitive are our results to the choice of the $\pi N$
interaction? In particular, would we get a small contribution from the
three-nucleon force, and specifically the diagram in Fig.~\ref{Fig.1}, if we
commenced with a chiral Lagrangian such as that used by Pearce and
Jennings~\cite{PJ91}? (ii)~Would our final results be substantially different
if this three-body force were to be included to all orders? Examination of the
perturbation series for the Paris potential with the TM three-body
force\cite{Bo86} suggests that higher order contributions are not negligible,
but the magnitude of the overall contribution does not change by more than a
factor of two. This further suggests that an exact calculation will not effect
our
final conclusion. (iii)~How important are the dispersive effects? The latest
results based on the $NN-N\Delta$ coupled channel\cite{PRB91} approach suggests
that there is a substantial cancellation between the three-body force
contribution and the dispersive effects in the $P_{33}$ channel. What happens
to this cancellation when other $\pi N$ partial waves are included? If this
cancellation is present for all $\pi N$ partial waves then it would lead to
further reduction in the three-body force.
\newpage
\section{ACKNOWLEDGMENT}
The authors would like to thank the Australian Research Council and Flinders
University Board of Research for their financial support during the course of
this work. The authors would also like to thank J. Haidenbauer for supplying
them
with the parameters of the PEST potential, and D.R.~Lehman for the comparison
of
triton results for the PEST potential. Finally we would like to thank
B.F.~Gibson for supplying us with the results of the coordinate space
calculation for the triton with the Paris potential.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,140 |
{"url":"https:\/\/www.physicsforums.com\/threads\/a-property-of-meromorphic-functions.772958\/","text":"# A property of meromorphic functions (?)\n\n1. Sep 25, 2014\n\n### evilcman\n\nIs this statement true: \"If two meromorphic functions have the same poles(all simple) and the same\nzeros(all simple), than they are proportional.\"? If it is true, than why? Thanks for the help...\n\n2. Sep 26, 2014\n\n### Wizlem\n\nI believe all meromorphic functions can be written as the ratio of two holomorphic functions. A holomorphic function can be written as a (possibly infinite) product of monomials which are of the form (x-a) where a is a zero of the function. So if f(x) is meromorphic we can write it as g(x)\/h(x) where the zeros of g(x) are the zeros of f(x) and the zeros of h(x) are the poles of f(x). If two functions have the same zeros and poles their g(x) and h(x) can only differ by a multiplicative constant.\n\n3. Sep 26, 2014\n\n### evilcman\n\nAll meromorphic functions can be written as the ratio of two holomorphic functions, that is true.\n\nThe second statement is not true. In general a holomorphic function can't be written as a product of monomials.\nYou will in general also have an exponential in it. And the exponential in it can have a holomorphic function in the\nargument: http:\/\/en.wikipedia.org\/wiki\/Weierstrass_factorization_theorem\n\nSo is you have the meromorphic functions f1(x)\/g1(x) and f2(x)\/g2(x), where the fs and gs are holomorphic,\nthan for example you could have for example f1(x) = exp(h(x)) f2(x) with h(x) some holomorphic function.\n\n4. Sep 27, 2014\n\n### FactChecker\n\nWhat about ez and e2*z? Is that a counterexample?","date":"2017-09-20 11:39:36","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8294664621353149, \"perplexity\": 594.2403639249635}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-39\/segments\/1505818687255.13\/warc\/CC-MAIN-20170920104615-20170920124615-00040.warc.gz\"}"} | null | null |
{"url":"http:\/\/www.territorioscuola.com\/wikipedia\/en.wikipedia.php?title=Direct_shear_test","text":"# Direct shear test\n\nA direct shear test is a laboratory or field test used by geotechnical engineers to measure the shear strength properties of soil12 or rock2 material, or of discontinuities in soil or rock masses.32. A detailed description of the testing equipment and procedure can be also found on geotechdata.info direct shear test page.\n\nThe U.S. and U.K. standards defining how the test should be performed are ASTM D 3080 and BS 1377-7:1990, respectively. For rock the test is generally restricted to rock with (very) low shear strength. The test is, however, standard practice to establish the shear strength properties of discontinuities in rock.\n\nThe test is performed on three or four specimens from a relatively undisturbed soil sample.14 A specimen is placed in a shear box which has two stacked rings to hold the sample; the contact between the two rings is at approximately the mid-height of the sample. A confining stress is applied vertically to the specimen, and the upper ring is pulled laterally until the sample fails, or through a specified strain. The load applied and the strain induced is recorded at frequent intervals to determine a stress-strain curve for each confining stress. Several specimens are tested at varying confining stresses to determine the shear strength parameters, the soil cohesion (c) and the angle of internal friction (commonly friction angle) ($\\phi$). The results of the tests on each specimen are plotted on a graph with the peak (or residual) stress on the x-axis and the confining stress on the y-axis. The y-intercept of the curve which fits the test results is the cohesion, and the slope of the line or curve is the friction angle.\n\nDirect shear tests can be performed under several conditions. The sample is normally saturated before the test is run, but can be run at the in-situ moisture content. The rate of strain can be varied to create a test of undrained or drained conditions, depending whether the strain is applied slowly enough for water in the sample to prevent pore-water pressure buildup.\n\nThe advantages of the direct shear test over other shear tests are the simplicity of setup and equipment used, and the ability to test under differing saturation, drainage, and consolidation conditions. These advantages have to be weighed against the difficulty of measuring pore-water pressure when testing in undrained conditions, and possible spuriously high results from forcing the failure plane to occur in a specific location.\n\nThe test equipment and procedures are slightly different for test on discontinuities.5\n\n## References\n\n1. ^ a b Bardet, J.-P. (1997). Experimental Soil Mechanics. Prentice Hall. ISBN\u00a0978-0-13-374935-9.\n2. ^ a b c Price, D.G. (2009). In De Freitas, M.H. Engineering Geology: Principles and Practice. Springer. p.\u00a0450. ISBN\u00a03-540-29249-7.\n3. ^ ISRM (2007). In Ulusay, R.; Hudson, J.A. The Blue Book - The Complete ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 1974-2006. Ankara: ISRM & ISRM Turkish National Group. p.\u00a0628. ISBN\u00a0978-975-93675-4-1.\n4. ^ Direct shear test from geotechnical lab notes. University of Texas Arlington.\n5. ^ Hencher, S. R.; Richards, L. R. (1989). \"Laboratory direct shear testing of rock discontinuities\". Ground Engineering 22 (2): 24\u201331.\n\n HPTS - Area Progetti - Edu-Soft - JavaEdu - N.Saperi - Ass.Scuola.. - TS BCTV - TSODP - TRTWE TSE-Wiki - Blog Lavoro - InterAzioni- NormaScuola - Editoriali - Job Search - DownFree !\n TerritorioScuola. Some rights reserved. Informazioni d'uso \u261e","date":"2013-05-25 08:53:50","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\": 0.49375906586647034, \"perplexity\": 4204.357137398655}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368705790741\/warc\/CC-MAIN-20130516120310-00022-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
Lidiya Hrebets (born 11 April 1943) is a Ukrainian former freestyle swimmer. She competed in three events at the 1968 Summer Olympics for the Soviet Union.
References
External links
1943 births
Living people
Ukrainian female freestyle swimmers
Olympic swimmers of the Soviet Union
Swimmers at the 1968 Summer Olympics
Sportspeople from Poltava
Soviet female freestyle swimmers | {
"redpajama_set_name": "RedPajamaWikipedia"
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Q: Custom TF2 v_ and w_models not showing up in-game Short version: I made a custom TF2 stock Scattergun model, and I'm trying to get it to work in-game. I'm modifying the v_model for the Scattergun (models/weapons/v_models/v_scattergun.mdl), and it works when I use HLMV, but it doesn't work in TF2.
More info:
I placed it under my tf/custom folder, as tf/custom/newmodels/models/weapons/v_models/v_scattergun.mdl. However, when I load it in TF2, the model is the same as the default Scattergun.
I thought maybe it was the Scattergun that had a problem, so I chose the Bat (another v_model), but that didn't work either. I also thought maybe the models were unused (since most of the weapons are c_models), so I made a w_model version of the Scattergun, but it still didn't work, and the world model was still the same. I even tested it on my own server with sv_pure set to 0, but all I saw was my default Bat and Scattergun.
I went back and checked my files to make sure the model was compiling properly, and it was. I even tried deleting any extra unused files I had in the model's folder, but nothing changed.
What's going on? I know I'm placing the models in the correct location, since I made a flamethrower and it works fine in-game. HLMV also shows the model properly, it's just TF2 that doesn't show the model.
Is there something I'm doing wrong, or do the v_ and w_ models no longer work?
A: Apparently the Scattergun was changed to use a c_model in the Love and War update.
Source
A: You're using an incorrect folder structure.
In order to replace a model, the folder path must match the path listed in the applicable .gcf file following your mod folder name. The correct directory you want to use is:
tf/custom/my_mod_name/models/weapons/v_models/v_scattergun.mdl
| {
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This is the home page of the UT Austin Villa robot soccer team. We are a RoboCup soccer team from the Department of Computer Science at the University of Texas at Austin. We compete in both the legged and simulation leagues of RoboCup soccer. Our team name is a play on the name of a prominent English football club, Aston Villa.
UT Austin Villa won the 3D Simulation League competition at RoboCup 2019 in Sydney, Australia!
UT Austin Villa won the 3D Simulation League competition at RoboCup 2018 in Montreal, Canada!
UT Austin Villa won the 3D Simulation League competition at RoboCup IranOpen 2018 in Tehran, Iran!
UT Austin Villa won the 3D Simulation League, took third place in the @Home Domestic Standard Platform League, and took fourth place in the Standard Platform League at RoboCup 2017 in Nagoya, Japan!
UT Austin Villa won the 3D Simulation League and took second place in the Standard Platform League at RoboCup 2016 in Leipzig, Germany!
UT Austin Villa won the 3D Simulation League competition at RoboCup 2015 in Hefei, China!
UT Austin Villa won the 3D Simulation League competition at RoboCup 2014 in Joao Pessoa, Brazil!
UT Austin Villa took second place in the 3D Simulation League and third place in the Standard Platform League at RoboCup 2013 in Eindhoven, Netherlands!
UT Austin Villa took first place in the Standard Platform League and the 3D Simulation League at RoboCup 2012 in Mexico City!
UT Austin Villa won the 2012 RoboCup US Open championship in the Standard Platform League!
UT Austin Villa won the 3D Simulation League competition at RoboCup 2011 in Istanbul, Turkey!
TT-UT Austin Villa finished in the top 8 in the Standard Platform League at RoboCup 2011 in Istanbul, Turkey!
TT-UT Austin Villa took 3rd place in the Standard Platform League competition at RoboCup 2010 in Singapore.
TT-UT Austin Villa won the 2010 RoboCup US Open championship in the Standard Platform League!
TT-UT Austin Villa finished 4th in the Standard Platform League at RoboCup 2009, losing to only two teams.
UT Austin Villa finished in second place at the RoboCup US Open 2008!
UT Austin Villa finished in second place in the @Home competition and made it to the quarterfinals in the Legged League at RoboCup 2007!
In the award ceremony, team leader Peter Stone played in a human vs. robots match against the middle size league champions, the Tribots from The University of Osnabruck. (Google videos version).
UT Austin Villa won the simulation coach competition and made it to the quarterfinals in the legged league at RoboCup 2005!
The team is just getting back from the 2005 US Open where we placed third. While we lost our semifinal match 1-0 to Penn, we played an exhibition match against the eventual first place team, CMU, and won 2-1. In official play, we outscored our opponents 24-1. With a little bit of luck we could have wound up in 2nd or even 1st. We're coming home with a lot of ideas for improvement though, so we're looking forward to Robocup 2005 in Osaka!
UT Austin Villa made it to the quarterfinals in the legged league at RoboCup 2004! We only lost one game, and we lost that game by one goal, in a game that was arguably the best of the competition. We are now attending the RoboCup Symposium where we are presenting a poster and two papers.
Our new website is up! (replacing the old one)
UT Austin Villa won third place in the legged league at the US Open 2004! We competed against 7 other teams from the United States, Mexico, and Germany. UT Austin Villa also won second in the simulated coach competition.
Supporters of UT Austin Villa
Teams can contact emerchantbroker.com �for advice on business funding. Surgeons at LASIK San Antonio use robots for surgery.
Nao League
3D Sim. League
Sim. Leagues
4 Legged League | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 252 |
HomeLatest NewsGulfBahrain latest news27th Arab League Summit launched, Syria & Yemen top agenda
27th Arab League Summit launched, Syria & Yemen top agenda
July 25, 2016 Ahmed Rashed Bahrain latest news, Egypt Latest News, Iraq Latest News, Jordan Latest News, Kuwait Latest News, Lebanon, Palestine Latest News, Qatar Latest News, Saudi Arabia News, Syria Latest News, Uae Latest News, Yemen Latest News
The works of the 27th normal session of the Arab League Summit was launched Monday morning in the Mauritanian capital, Nouakchott.
Chaired by Mauritanian President Mohamed Ould Abdel Aziz, the two-day conference opened on Monday inside a large tent in Nouakchott, with the crises in Syria, Iraq, Yemen and Libya the main focus of talks.
The countries participating in the Summit were Jordan, UAE, Qatar, Algeria, Tunisia, Yemen and fifteen other Arab countries, while the Syrian seat was suspended "because of the ongoing war in the country."
Representative of the head of the African Union, the Secretary General of the Arab League, Ahmad Abu el-Gheit, the secretary general of the Organization of Islamic Cooperation, the secretary general of the Gulf Cooperation Council, the representative of the UN's secretary general, in addition to a number of other representatives, were present at the Summit.
Arab leaders, speaking at the opening of the Arab League summit in the Mauritanian capital, have pledged to "defeat terrorism" , with the ongoing threat of violence in the region dominating the agenda
Mauritania is now presiding the 27th Arab League Summit following Egypt which presided the 26th version.
Egypt's statement
Sherif Ismail, Egypt's prime minister, was one of the first of the 21 leaders to speak and blamed foreign intervention in the region for the rise of groups such as the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) and for the radicalisation of young people.
"Foreign intervention in Arab affairs is one of the major reasons for the current crisis, therefore we should work together to cement our domestic fronts in order to be able to stand up to these foreign interventions," Ismail said.
For his part, Adel al-Jubeir, the Saudi foreign minister, addressed the conflict in Syria, saying there could be no solution while President Bashar al-Assad was still in power.
"Thousands have been killed and millions displaced in addition to the destruction of the infrastructure of the country, as a result it is impossible for Bashar al-Assad to have any place in the future of Syria, especially since his hands are tainted with the blood of his own people," he said.
More than 450.000 Syrians were killed during the past 5 years, and 12 millions were driven out of their homes. 7 million Syrians are now refugees around the globe.
Yemen's president called on his country's Houthi fighters to surrender their weapons and withdraw from territories they control as Arab coalition air raids continue to strike the armed group's positions.
Abd-Rabbu Mansour Hadi, who has fled the Arabian Peninsula country, called the continuation of air strikes "a spark of hope".
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"redpajama_set_name": "RedPajamaCommonCrawl"
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{"url":"https:\/\/plus.tuni.fi\/data.ml.310\/spring-2022\/m05\/nim\/","text":"# Programming task: Nim\u00b6\n\nDownload Nim.zip file. The file contains a pdf file that has more detailed description of the task, as well as some useful code templates.\n\nAttention\n\nDue to the nature of this week\u2019s problem. This exercise is peer-reviewed by a fellow student and there is no automated grading.\n\nBe sure to test your program well before submitting! Also notice that only the last submitted version of your code is seen and reviewed by the other student!\n\nPeer-review of this exercise opens only after this module has closed and you will then have 5 days to complete the review of your fellow student\u2019s program.\n\nNOTE: Even though programming exercises are not mandatory you must submit a program to this exercise to be eligible to review another student\u2019s program. You will not be able to peer-review another student\u2019s program if you decide not to submit this week\u2019s program.\n\nNote\n\nPoints from this exercise will be reviewed and possibly adjusted by the course staff. The staff will consider the peer-reviews each program receives and how well the program actually performs compared to the peer-reviews.\n\nThe final points from this exercise will be available during the week starting on the 28th of February.\n\nTo receive points from your submission, you have to complete the grading of your peers\u2019 submissions assigned to you.\n\nNim.zip\n\nA+ presents the exercise submission form here.\n\nPosting submission...","date":"2022-08-09 17:37:38","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.17439167201519012, \"perplexity\": 1145.9472446042398}, \"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-2022-33\/segments\/1659882571056.58\/warc\/CC-MAIN-20220809155137-20220809185137-00753.warc.gz\"}"} | null | null |
\section{Introduction}
In this paper,
we consider the minimizing problem:
$$
S_{p,1,\alpha,\mu}:=
\inf_{u\in W^{1,p}(\mathbb{R}^{N})\setminus\{0\}}
\frac{
\int_{\mathbb{R}^{N}}|\nabla u|^{p}\mathrm{d}x
-
\mu
\int_{\mathbb{R}^{N}}
\frac{|u|^{p}}{|x|^{p}}
\mathrm{d}x}
{\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{p^{*}_{\alpha}}|u(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)^{\frac{p}{2\cdot p^{*}_{\alpha}}}},
\eqno(\mathcal{P})
$$
where
$N\geqslant3$,
$p\in(1,N)$,
$\mu\in
\left[
0,
\left(
\frac{N-p}{p}
\right)^{p}
\right)$,
$\alpha\in(0,N)$
and
$p^{*}_{\alpha}=
\frac{p}{2}\left(\frac{2N-\alpha}{N-p}\right)$
is the Hardy--Littlewood--Sobolev upper critical exponent.
The paper was motivated by some works appeared in recent years.
For
$p=2$,
problem
$(\mathcal{P})$
is closely related to the nonlinear Choquard equation as follows:
\begin{equation}\label{1}
-\Delta u
+
V(x)u
=
\left(
|x|^{\alpha}*|u|^{q}
\right)
|u|^{q-2}u,
\mathrm{~in~}
\mathbb{R}^{N},
\end{equation}
where
$\alpha\in(0,N)$
and
$\frac{2N-\alpha}{N}\leqslant q\leqslant\frac{2N-\alpha}{N-2}$.
For
$q=2$
and
$\alpha=1$,
the equation
(\ref{1})
goes back to the description of the quantum theory of a polaron at rest by Pekar in 1954
\cite{Pekar1954}
and the modeling of an electron trapped in its own hole in
1976
in the work of
Choquard,
as a certain approximation to Hartree--Fock theory of one--component plasma
\cite{Penrose1996}.
For
$q=\frac{2N-1}{N-2}$
and
$\alpha=1$,
by using the Green function,
it is obvious that
equation
$(\ref{1})$
can be regarded as a generalized version of
Schr\"{o}dinger--Newton system:
\begin{equation*}
\begin{aligned}
\begin{cases}
-\Delta u
+
V(x)u
=
|u|^{\frac{N+1}{N-2}}
\phi,
&
\mathrm{~in~}
\mathbb{R}^{N},\\
-\Delta \phi
=
|u|^{\frac{N+1}{N-2}},&
\mathrm{~in~}
\mathbb{R}^{N}.
\end{cases}
\end{aligned}
\end{equation*}
The existence and qualitative properties of solutions of Choquard type equations
(\ref{1})
have been widely studied in the last decades
(see \cite{Moroz2016}).
Moroz and Van Schaftingen
\cite{Moroz2015}
considered equation (\ref{1}) with lower critical exponent
$\frac{2N-\alpha}{N}$
if the potential
$1-V(x)$
should not decay to zero at infinity faster than the inverse of
$|x|^{2}$.
In
\cite{O.Alves2016},
the authors studied the equation (\ref{1}) with critical growth in the sense of Trudinger--Moser inequality and studied the existence and concentration of the ground states.
In 2016,
Gao and Yang \cite{Gao2016} firstly investigated the following critical Choquard equation:
\begin{equation}\label{2}
\begin{aligned}
-\Delta u
=
\left(
\int_{\mathbb{R}^{N}}
\frac{|u|^{2^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}y
\right)
|u|^{2^{*}_{\alpha}-2}u
+\lambda u,
\mathrm{~in~}
\Omega,
\end{aligned}
\end{equation}
where
$\Omega$
is a bounded domain of
$\mathbb{R}^{N}$,
with lipschitz boundary,
$N\geqslant3$,
$\alpha\in(0,N)$
and
$\lambda>0$.
By using variational methods,
they established the existence, multiplicity and nonexistence of nontrivial solutions to equation (\ref{2}).
In 2017,
Mukherjee and Sreenadh \cite{Gao2016} considered the following fractional Choquard equation:
\begin{equation}\label{3}
\begin{aligned}
(-\Delta)^{s} u
=
\left(
\int_{\mathbb{R}^{N}}
\frac{|u|^{2^{*}_{\alpha,s}}}{|x-y|^{\alpha}}
\mathrm{d}y
\right)
|u|^{2^{*}_{\alpha,s}-2}u
+\lambda u,
\mathrm{~in~}
\Omega,
\end{aligned}
\end{equation}
where
$\Omega$
is a bounded domain of
$\mathbb{R}^{N}$
with $C^{1,1}$ boundary,
$s\in(0,1)$,
$N\geqslant2s$,
$\alpha\in(0,N)$
and
$\lambda>0$,
$2^{*}_{\alpha,s}=\frac{2N-\alpha}{N-2s}$
is the critical exponent in the sense of Hardy--Littlewood--Sobolev inequality.
By using variational methods,
they established the existence, multiplicity and nonexistence of nontrivial solutions to problem (\ref{3}).
For
$p\not=2$,
in 2017,
Pucci,
Xiang
and
Zhang
\cite{Pucci2017}
studied
the
Schr\"{o}dinger--Choquard--Kirchhoff equations involving the fractional p--Laplacian as follows:
\begin{equation}\label{4}
\begin{aligned}
(a+b\|u\|_{s}^{p(\theta-1)})
[(-\Delta)^{s}_{p} u+V(x)|u|^{p-2}u]
=
\lambda
f(x,u)
+
\left(
\int_{\mathbb{R}^{N}}
\frac{|u|^{p^{*}_{\alpha,s}}}{|x-y|^{\alpha}}
\mathrm{d}y
\right)
|u|^{p^{*}_{\alpha,s}-2}u
\mathrm{~in~}
\mathbb{R}^{N},
\end{aligned}
\end{equation}
where
$\|u\|_{s}=\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+ps}}
\mathrm{d}x
\mathrm{d}y
+
\int_{\mathbb{R}^{N}}
V(x)|u|^{p}
\mathrm{d}x
\right)$,
$a,b\in \mathbb{R}^{+}_{0}$
with
$a+b>0$,
$\lambda>0$
is a parameter,
$s\in (0,1)$,
$N>ps$,
$\theta\in [1,\frac{N}{N-ps})$,
$\alpha\in(0,N)$,
$p^{*}_{\alpha,s}=\frac{p(2N-\alpha)}{2(N-sp)}$
is the critical exponent in the sense of Hardy--Littlewood--Sobolev inequality,
and
$f:\mathbb{R}^{N}\rightarrow\mathbb{R}$
is a Caratheodory function,
$V:\mathbb{R}^{N}\rightarrow\mathbb{R}^{+}$
is a potential function.
By using variational methods,
they established the existence of nontrivial nonnegative solution to problem (\ref{4}).
There is an open problem in
\cite{Pucci2017}.
We define the best constant:
\begin{equation}\label{5}
\begin{aligned}
S_{p,s,\alpha,\mu}:=&
\inf_{u\in W^{s,p}(\mathbb{R}^{N})\setminus\{0\}}
\frac{\int_{\mathbb{R}^{N}}
\int_{
\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+ps}}
\mathrm{d}x
\mathrm{d}y
-
\mu
\int_{\mathbb{R}^{N}}
\frac{|u|^{p}}{|x|^{ps}}
\mathrm{d}x}
{\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{p^{*}_{\alpha,s}}|u(y)|^{p^{*}_{\alpha,s}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)^{\frac{p}{2\cdot p^{*}_{\alpha,s}}}},
\end{aligned}
\end{equation}
where
$N\geqslant3$,
$p\in(1,N)$,
$s\in(0,1]$,
$\alpha\in(0,N)$
and
$\mu\in[0,\mathcal{C}_{N,s,p})$,
$\mathcal{C}_{N,s,p}$
is defined in
\cite[Theorem 1.1]{Frank2008}.
And
$p^{*}_{\alpha,s}=\frac{p(2N-\alpha)}{2(N-sp)}$
is the critical exponent in the sense of Hardy--Littlewood--Sobolev inequality.
\noindent
{\bf Open problem:}
Is the best constant
$S_{p,s,\alpha,\mu}$
achieved?
\noindent
{\bf (Result 1)}
For
$p=2$,
$s=1$,
$\mu=0$
and
$\alpha\in(0,N)$,
Gao and Yang \cite{Gao2016}
showed that
$S_{2,1,\alpha,0}$
is achieved in
$\mathbb{R}^{N}$
by the extremal function:
\begin{equation*}
\begin{aligned}
w_{\sigma}(x)
=
\mathfrak{C}_{1}\sigma^{-\frac{N-2}{2}}
w(x),
~~
w(x)
=
\frac{b_{1}}{(b_{1}^{2}
+
|x-a_{1}|^{2})^{\frac{N-2}{2}}},
\end{aligned}
\end{equation*}
where
$\mathfrak{C}_{1}>0$
is a fixed constant,
$a_{1}\in \mathbb{R}^{N}$
and
$b_{1}\in (0,\infty)$.
\noindent
{\bf (Result 2)}
For
$p=2$,
$s\in(0,1)$,
$\mu=0$
and
$\alpha\in(0,N)$,
Mukherjee and Sreenadh \cite{Gao2016}
proved that
$S_{2,s,\alpha,0}$
is achieved in
$\mathbb{R}^{N}$
by the extremal function:
\begin{equation*}
\begin{aligned}
w_{\sigma}(x)
=
\mathfrak{C}_{2}\sigma^{-\frac{N-2s}{2}}
w(x),
~~
w(x)
=
\frac{b_{2}}{(b_{2}^{2}
+
|x-a_{2}|^{2})^{\frac{N-2s}{2}}},
\end{aligned}
\end{equation*}
where
$\mathfrak{C}_{2}>0$
is a fixed constant,
$a_{2}\in \mathbb{R}^{N}$
and
$b_{2}\in (0,\infty)$.
\noindent
{\bf (Result 3)}
For
$p=2$,
$s\in(0,1)$,
$\mu\in
\left[
0,
4^{s}\frac{\Gamma^{2}(\frac{N+2s}{4})}{\Gamma^{2}(\frac{N-2s}{4})}
\right)$
and
$\alpha\in(0,N)$,
Yang and Wu \cite{Yang2017}
showed that
$S_{2,s,\alpha,\mu}$
is achieved in
$\mathbb{R}^{N}$.
For Open problem,
we study the case of
$p\in(1,N)$,
$s=1$,
$\mu\in
\left[
0,\left(\frac{N-p}{p}\right)^{p}
\right)$
and
$\alpha\in(0,N)$.
By using
the refinement of Sobolev inequality in
\cite[Theorem 2]{Palatucci2014},
we show that
$S_{p,1,\alpha,\mu}$
is achieved in
$\mathbb{R}^{N}$
(see Theorem \ref{theorem1}).
For the case
$p\not=2$,
one expects that the minimizers of
$S_{p,s,\alpha,\mu}$
have a form similar to the function
$\omega_{\sigma}$.
However,
it is not known the explicit formula of the extremal function.
We give the estimation of
extremal function
(see Theorem \ref{theorem2} and Theorem \ref{theorem3}).
The first main result of this paper reads as follows.
\begin{theorem}\label{theorem1}
Let
$N\geqslant3$,
$p\in(1,N)$,
$\alpha\in(0,N)$
and
$\mu\in
\left[
0,\left(\frac{N-p}{p}\right)^{p}
\right)$.
Then
$S_{p,1,\alpha,\mu}$
is achieved in
$\mathbb{R}^{N}$
by a radially symmetric, nonincreasing and nonnegative function.
\end{theorem}
The second main
result of this paper reads as follows.
For
$p=2$
and
$s\in(0,1)$,
by using
Coulomb--Sobolev space
and
endpoint refined Sobolev inequality
in
\cite{Bellazzini2016},
we give
a estimation of
extremal function.
\begin{theorem}\label{theorem2}
Let
$N\geqslant3$,
$p=2$,
$\alpha\in(0,N)$,
$s\in(0,1)$
and
$\mu\in
\left[
0,
\bar{\mu}
\right)$.
Any nonnegative minimizer
$u$
of
$S_{2,s,\alpha,\mu}$
is radially symmetric and nonincreasing,
and it satisfies for
$x\not=0$
that
\begin{align*}
C_{4}
\left(
\left(
\frac{\bar{\mu}}{\bar{\mu}-\mu}
\right)
S_{2,s,\alpha,\mu}
\right)
^{\frac{(N-\alpha)(N-2s)}{2N(N+2s-\alpha)}}
\left(
\frac{N}{\omega_{N-1}}
\right)
^{\frac{N-2s}{2N}}
\frac{1}{
|x|^{\frac{N-2s}{2}}}
\geqslant
u(x),
\end{align*}
where
$\omega_{N-1}$
is the area of the unit sphere in
$\mathbb{R}^{N}$.
\end{theorem}
The third main
result of this paper reads as follows.
For
$p\not=2$
and
$s=1$,
we give
a estimation of
extremal function.
\begin{theorem}\label{theorem3}
Let
$N\geqslant3$,
$p\in(1,N)$,
$\alpha\in(0,N)$
and
$\mu\in
\left[
0,
\tilde{\mu}
\right)$.
Any nonnegative minimizer
$u$
of
$S_{p,1,\alpha,\mu}$
is radially symmetric and nonincreasing,
and it satisfies for
$x\not=0$
that
\begin{align*}
\left(
\frac{2^{\alpha}N^{2}}{\omega^{2}_{N-1}}
\right)^{\frac{1}{2\cdot p^{*}_{\alpha}}}
\frac{1}{|x|^{\frac{N-p}{p}}}
\geqslant
u(x),
\end{align*}
where
$\omega_{N-1}$
is the area of the unit sphere in
$\mathbb{R}^{N}$.
\end{theorem}
\section{Preliminaries}
The Sobolev space
$W^{1,p}(\mathbb{R}^{N})$
is the completion of
$C^{\infty}_{0}(\mathbb{R}^{N})$
with respect to the norm
$$
\|u\|_{W}^{p}=\int_{\mathbb{R}^{N}}|\nabla u|^{p}\mathrm{d}x.
$$
For
$s\in(0,1)$
and
$p\in(1,N)$,
the fractional Sobolev space
$W^{s,p}(\mathbb{R}^{N})$
is defined by
$$
W^{s,p}(\mathbb{R}^{N}):=
\left\{
u\in L^{\frac{Np}{N-sp}}(\mathbb{R}^{N})|
\int_{\mathbb{R}^{N}}
\int_{
\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+ps}}
\mathrm{d}x
\mathrm{d}y
<
\infty
\right\}.
$$
For
$s\in(0,1)$
and
$p\in(1,N)$,
we introduce the Hardy inequalities:
$$
\bar{\mu}
\int_{\mathbb{R}^{N}}
\frac{|u|^{2}}{|x|^{2s}}
\mathrm{d}x
\leqslant
\int_{\mathbb{R}^{N}}
\int_{
\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{2}}{|x-y|^{N+2s}}
\mathrm{d}x
\mathrm{d}y,
~\mathrm{for~any}~u\in W^{s,2}(\mathbb{R}^{N})
~\mathrm{and}~
\bar{\mu}=4^{s}\frac{\Gamma^{2}(\frac{N+2s}{4})}{\Gamma^{2}(\frac{N-2s}{4})},
$$
and
$$
\tilde{\mu}
\int_{\mathbb{R}^{N}}
\frac{|u|^{p}}{|x|^{p}}
\mathrm{d}x
\leqslant
\int_{
\mathbb{R}^{N}}
|\nabla u|^{p}
\mathrm{d}x,
~\mathrm{for~any}~u\in W^{1,p}(\mathbb{R}^{N})
~\mathrm{and}~\tilde{\mu}=\left(\frac{N-p}{p}\right)^{p}.$$
The Coulomb--Sobolev space \cite{Bellazzini2016} is defined by
\begin{align}\label{8}
\mathcal{E}^{s,\alpha,2^{*}_{\alpha,s}}(\mathbb{R}^{N})
\!
=
\!
\left\{
\!
\int_{\mathbb{R}^{N}}
\!\!
\int_{\mathbb{R}^{N}}
\!\!\!
\frac{|u(x)-u(y)|^{2}}
{|x-y|^{N+2s}}
\mathrm{d}x
\mathrm{d}y
\!<
\!
\infty
~\mathrm{and}
\int_{\mathbb{R}^{N}}
\!\!
\int_{\mathbb{R}^{N}}
\!\!\!
\frac{|u(x)|^{2^{*}_{\alpha,s}}|u(y)|^{2^{*}_{\alpha,s}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y<\infty
\!
\right\}.
\end{align}
We endow the space
$\mathcal{E}^{s,\alpha,2^{*}_{\alpha,s}}(\mathbb{R}^{N})$
with the norm
\begin{align}\label{9}
\|u\|_{\mathcal{E},\alpha}^{2}
=
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{2}}
{|x-y|^{N+2s}}
\mathrm{d}x
\mathrm{d}y
+
\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{2^{*}_{\alpha,s}}|u(y)|^{2^{*}_{\alpha,s}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)^{\frac{1}{2^{*}_{\alpha,s}}}.
\end{align}
We could define the best constant:
\begin{equation}\label{10}
\begin{aligned}
S_{p,1,0,\mu}:=&
\inf_{u\in W^{1,p}(\mathbb{R}^{N})\setminus\{0\}}
\frac{
\|u\|^{p}_{W}
-
\mu
\int_{\mathbb{R}^{N}}
\frac{|u|^{p}}{|x|^{p}}
\mathrm{d}x
}
{(\int_{\mathbb{R}^{N}}
|u|^{p^{*}}
\mathrm{d}x)^{\frac{p}{p^{*}}}},
\end{aligned}
\end{equation}
where
$S_{p,1,0,\mu}$
is attained in
$\mathbb{R}^{N}$.
\begin{lemma}\label{lemma1}
$(Hardy-Littlewood-Sobolev~inequality,~\cite{Lieb2001})$
Let
$t,r>1$
and
$0<\mu<N$
with
$\frac{1}{t}+\frac{1}{r}+\frac{\mu}{N}=2$,
$f\in L^{t}(\mathbb{R}^{N})$
and
$h\in L^{r}(\mathbb{R}^{N})$.
There exists a sharp constant
$C_{2}>0$,
independent of
$f,g$
such that
$$\int_{\mathbb{R}^{N}}\int_{\mathbb{R}^{N}}
\frac{|f(x)||h(y)|}
{|x-y|^{\mu}}
\mathrm{d}x\mathrm{d}y
\leqslant
C_{2}
\|f\|_{t}
\|h\|_{r}.$$
\end{lemma}
A measurable function
$u:\mathbb{R}^{N}\rightarrow \mathbb{R}$
belongs to the Morrey space
$\|u\|_{\mathcal{L}^{r,\varpi}(\mathbb{R}^{N})}$
with
$r\in[1,\infty)$
and
$\varpi\in(0,N]$
if and only if
$$
\|u\|
_{\mathcal{L}^{r,\varpi}(\mathbb{R}^{N})}^{r}
=
\sup_{R>0,x\in\mathbb{R}^{N}}
R^{\varpi-N}
\int_{B(x,R)}
|u(y)|^{r}
\mathrm{d}y
<\infty.
$$
\begin{lemma}\label{lemma2}
~\cite{Palatucci2014}
For any
$1< p<N$,
let
$p^{*}=\frac{Np}{N-p}$.
There exists
$C_{3}>0$
such that
for
$\theta$
and
$\vartheta$
satisfying
$\frac{p}{p^{*}}\leqslant\theta<1$,
$1\leqslant \vartheta<p^{*}=\frac{Np}{N-p}$,
we have
\begin{align*}
\left(
\int_{\mathbb{R}^{N}}
|u|^{p^{*}}
\mathrm{d}x
\right)^{\frac{1}{p^{*}}}
\leqslant
C_{3}
\|u\|_{W}^{\theta}
\|u\|_{\mathcal{L}^{\vartheta,\frac{\vartheta(N-p)}{p}}(\mathbb{R}^{N})}^{1-\theta},
\end{align*}
for any
$u\in W^{1,p}(\mathbb{R}^{N})$.
\end{lemma}
\begin{lemma}\label{lemma3}
$(Endpoint~refined~Sobolev~inequality,~
\cite[Theorem 1.2]{Bellazzini2016})$
Let
$\alpha\in(0,N)$
and
$s\in(0,1)$.
Then there exists a constant
$C_{4}>0$
such that the inequality
\begin{align*}
\|u\|_{L^{\frac{2N}{N-2s}}(\mathbb{R}^{N})}
\leqslant&
C_{4}
\left(
\int_{R^{N}}
\int_{R^{N}}
\frac{|u(x)-u(y)|^{2}}
{|x-y|^{N+2s}}
\mathrm{d}x
\mathrm{d}y
\right)
^{\frac{(N-\alpha)(N-2s)}{2N(N+2s-\alpha)}}\\
&~~~~~~~~~\cdot
\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{\frac{2N-\alpha}{N-2s}}|u(y)|^{\frac{2N-\alpha}{N-2s}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)
^{\frac{s(N-2s)}{N(N+2s-\alpha)}}
\end{align*}
holds for all
$u\in \mathcal{E}^{s,\alpha,2^{*}_{\alpha,s}}(\mathbb{R}^{N})$.
\end{lemma}
\section{The proof of Theorem \ref{theorem1}}
We show the refinement of Hardy-Littlewood-Sobolev inequality.
This inequality plays a key role in the proof of Theorem \ref{theorem1}.
\begin{lemma}\label{lemma4}
For any
$1< p<N$
and
$\alpha\in(0,N)$,
there exists
$C_{5}>0$
such that
for
$\theta$
and
$\vartheta$
satisfying
$\frac{p}{p^{*}}\leqslant\theta<1$,
$1\leqslant \vartheta<p^{*}=\frac{Np}{N-p}$,
we have
\begin{align*}
\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{p^{*}_{\alpha}}|u(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)^{\frac{1}{p^{*}_{\alpha}}}
\leqslant
C_{5}
\|u\|_{W}^{2\theta}
\|u\|_{\mathcal{L}^{\vartheta,\frac{\vartheta(N-p)}{p}}(\mathbb{R}^{N})}^{2(1-\theta)},
\end{align*}
for any
$u\in W^{1,p}(\mathbb{R}^{N})$.
\end{lemma}
\noindent
{\bf Proof.}
By using
Lemma \ref{lemma2},
we have
\begin{align}\label{11}
\left(
\int_{\mathbb{R}^{N}}
|u|^{p^{*}}
\mathrm{d}x
\right)^{\frac{1}{p^{*}}}
\leqslant
C_{3}
\|u\|_{W}^{\theta}
\|u\|_{\mathcal{L}^{\vartheta,\frac{\vartheta(N-p)}{p}}(\mathbb{R}^{N})}^{1-\theta}.
\end{align}
By Hardy-Littlewood-Sobolev inequality
and
(\ref{11}),
we obtain
\begin{equation*}
\begin{aligned}
\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{p^{*}_{\alpha}}|u(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)^{\frac{1}{p^{*}_{\alpha}}}
\leqslant&
C_{2}^{\frac{1}{p^{*}_{\alpha}}}
\|u\|_{L^{p^{*}}(\mathbb{R}^{N})}^{2}
\leqslant
C_{2}^{\frac{1}{p^{*}_{\alpha}}}
C_{3}^{2}
\|u\|_{W}^{2\theta}
\|u\|_{\mathcal{L}^{\vartheta,\frac{\vartheta(N-p)}{p}}(\mathbb{R}^{N})}^{2(1-\theta)}.
\end{aligned}
\end{equation*}
\qed
In \cite{Palatucci2014},
there is a misprint,
the authors point out it by themselves.
The right one is
\begin{align}\label{12}
L^{p^{*}}(\mathbb{R}^{N})
\hookrightarrow
\mathcal{L}^{r,r\frac{N-p}{p}}(\mathbb{R}^{N}),
\end{align}
for any
$p\in(1,N)$
and
$r\in[1,p^{*})$.
This embedding plays a key role in the proof of Theorem \ref{theorem1}.
\noindent
{\bf Proof of Theorem \ref{theorem1}:}
\noindent
{\bf Step 1.}
Suppose now
$0\leqslant\mu<\tilde{\mu}=\left(\frac{N-p}{p}\right)^{p}$.
Applying
Lemma
\ref{lemma4}
with
$\vartheta=p$,
we have
\begin{align}\label{13}
\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{p^{*}_{\alpha}}|u(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)^{\frac{1}{p^{*}_{\alpha}}}
\leqslant
C
\left(\|u\|_{W}^{p}-
\mu
\int_{\mathbb{R}^{N}}
\frac{|u|^{p}}{|x|^{p}}
\mathrm{d}x\right)^{\frac{2\theta}{p}}
\|u\|_{\mathcal{L}^{p,N-p}(\mathbb{R}^{N})}^{2(1-\theta)},
\end{align}
for
$u\in W^{1,p}(\mathbb{R}^{N})$.
Let
$\{u_{n}\}$
be a minimizing sequence of
$S_{p,1,\alpha,\mu}$,
that is
\begin{align*}
\|u_{n}\|_{W}^{p}-
\mu
\int_{\mathbb{R}^{N}}
\frac{|u_{n}|^{p}}{|x|^{p}}
\mathrm{d}x
\rightarrow
S_{p,1,\alpha,\mu},
~\mathrm{as}~
n\rightarrow\infty,
\end{align*}
and
\begin{align*}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u_{n}(x)|^{p^{*}_{\alpha}}|u_{n}(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
=1.
\end{align*}
Inequality
(\ref{13})
enables us to find
$C>0$
independent of $n$
such that
\begin{align}\label{14}
\|u_{n}\|_{\mathcal{L}^{p,N-p}(\mathbb{R}^{N})}
\geqslant
C>0.
\end{align}
We have the chain of inclusions
\begin{align}\label{15}
W^{1,p}(\mathbb{R}^{N})
\hookrightarrow
L^{p^{*}}(\mathbb{R}^{N})
\hookrightarrow
\mathcal{L}^{p,N-p}
(\mathbb{R}^{N}),
\end{align}
which implies that
\begin{align}\label{16}
\|u_{n}\|_{\mathcal{L}^{p,N-p}(\mathbb{R}^{N})}
\leqslant
C.
\end{align}
Applying
(\ref{14})
and
(\ref{16}),
there exists
$C>0$
such that
\begin{align*}
0<C
\leqslant
\|u_{n}\|_{\mathcal{L}^{p,N-p}(\mathbb{R}^{N})}
\leqslant
C^{-1}.
\end{align*}
Combining the definition of Morrey space and above inequalities,
for all $n\in \mathbb{N}$,
we get the existence of
$\lambda_{n}>0$
and
$x_{n}\in \mathbb{R}^{N}$
such that
\begin{align*}
\frac{1}{\lambda_{n}^{p}}
\int_{B(x_{n},\lambda_{n})}
|u_{n}(y)|^{p}
\mathrm{d}y
\geqslant
\|u_{n}\|_{\mathcal{L}^{p,N-p}(\mathbb{R}^{N})}^{p}
-
\frac{C}{2n}
\geqslant
\tilde{C}
>0
\end{align*}
for some new positive constant $\tilde{C}$ that does not depend on $n$.
Let
$v_{n}(x)=\lambda_{n}^{\frac{N-p}{p}}u_{n}(\lambda_{n}x)$.
Notice that,
by using the scaling invariance,
we have
\begin{align*}
\|v_{n}\|_{W}^{p}-
\mu
\int_{\mathbb{R}^{N}}
\frac{|v_{n}|^{p}}{|x|^{p}}
\mathrm{d}x
\rightarrow
S_{p,1,\alpha,\mu},
~\mathrm{as}~
n\rightarrow\infty,
\end{align*}
and
\begin{align*}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|v_{n}(x)|^{p^{*}_{\alpha}}|v_{n}(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
=1.
\end{align*}
Then
\begin{align*}
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
|v_{n}(y)|^{p}
\mathrm{d}y
\geqslant
\tilde{C}
>0.
\end{align*}
We can
also show that
$v_{n}$
is bounded in
$W^{1,p}(\mathbb{R}^{N})$.
Hence, we may assume
$$
v_{n}\rightharpoonup v~
\mathrm{in}
~
W^{1,p}(\mathbb{R}^{N}),
v_{n}\rightarrow v
~
\mathrm{a.e. ~in}
~
\mathbb{R}^{N},
v_{n}\rightarrow v
~\mathrm{in}~
L^{q}_{loc}(\mathbb{R}^{N})~~\mathrm{for~all~}q\in[p,p^{*} ).
$$
We claim that
$\{\frac{x_{n}}{\lambda_{n}}\}$
is uniformly bounded in
$n$.
Indeed, for any $0<\beta<p$,
by H\"{o}lder's inequality,
we observe that
\begin{align*}
0<
\tilde{C}
\leqslant&
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
|v_{n}|^{p}
\mathrm{d}y
=
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
|y|^{\frac{p\beta}{\frac{p(N-\beta)}{N-p}}}
\frac{|v_{n}|^{p}}
{|y|^{\frac{p\beta}{\frac{p(N-\beta)}{N-p}}}}
\mathrm{d}y\\
\leqslant&
\left(
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
|y|^{{\frac{\beta(N-p)}{p-\beta}}}
\mathrm{d}y
\right)
^{1-\frac{N-p}{N-\beta}}
\left(
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
\frac{|v_{n}|^{\frac{p(N-\beta)}{N-p}}}
{|y|^{\beta}}
\mathrm{d}y
\right)^{\frac{N-p}{N-\beta}}\textcolor{red}{.}
\end{align*}
By the rearrangement inequality,
see
\cite[Theorem 3.4]{Lieb2001},
we have
\begin{align*}
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
|y|^{{\frac{\beta(N-p)}{p-\beta}}}
\mathrm{d}y
\leqslant
\int_{B(0,1)}
|y|^{{\frac{\beta(N-p)}{p-\beta}}}
\mathrm{d}y
\leqslant
C.
\end{align*}
Therefore,
\begin{align}\label{17}
0<
C
\leqslant
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
\frac{|v_{n}|^{\frac{p(N-\beta)}{N-p}}}
{|y|^{\beta}}
\mathrm{d}y.
\end{align}
Now, suppose on the contrary, that
$\frac{x_{n}}{\lambda_{n}}\rightarrow\infty$
as
$n\rightarrow\infty$.
Then, for any
$y\in B(\frac{x_{n}}{\lambda_{n}},1)$,
we have
$|y|\geqslant |\frac{x_{n}}{\lambda_{n}}|-1$
for
$n$
large.
Thus,
\begin{align*}
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
\frac{|v_{n}|^{\frac{p(N-\beta)}{N-p}}}
{|y|^{\beta}}
\mathrm{d}y
\leqslant&
\frac{1}
{(|\frac{x_{n}}{\lambda_{n}}|-1)^{\beta}}
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
|v_{n}|^{\frac{p(N-\beta)}{N-p}}
\mathrm{d}y\\
\leqslant&
\frac{
\left|
B(\frac{x_{n}}{\lambda_{n}},1)
\right|
^{\frac{\beta}{N}}
}
{(|\frac{x_{n}}{\lambda_{n}}|-1)^{\beta}}
\left(
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
|v_{n}|^{\frac{Np}{N-p}}
\mathrm{d}y
\right)
^{\frac{N-\beta}{N}}\\
\leqslant&
\frac{
\left|
B(\frac{x_{n}}{\lambda_{n}},1)
\right|
^{\frac{\beta}{N}}
}
{(|\frac{x_{n}}{\lambda_{n}}|-1)^{\beta}}
\cdot
\frac{\|v_{n}\|^{\frac{N-\beta}{N}}_{W}}{S_{p,1,0,0}^{\frac{N-\beta}{N-p}}}
\leqslant
\frac{C}
{(|\frac{x_{n}}{\lambda_{n}}|-1)^{\beta}}
\rightarrow0
~\mathrm{as}~
n\rightarrow\infty,
\end{align*}
which contradicts
(\ref{17}).
Hence,
$\{\frac{x_{n}}{\lambda_{n}}\}$
is bounded,
and there exists
$R>0$
such that
\begin{align*}
\int_{B(0,R)}
|v_{n}(y)|^{p}
\mathrm{d}y
\geqslant
\int_{B(\frac{x_{n}}{\lambda_{n}},1)}
|v_{n}(y)|^{p}
\mathrm{d}y
\geqslant
\tilde{C}
>0.
\end{align*}
Since the embedding
$W^{1,p}(\mathbb{R}^{N})\hookrightarrow L_{loc}^{q}(\mathbb{R}^{N})$
$q\in[p,p^{*})$
is compact,
we deduce that
\begin{align*}
\int_{B(0,R)}
|v(y)|^{p}
\mathrm{d}y
\geqslant
\tilde{C}
>0,
\end{align*}
which means
$v\not\equiv0$.
\noindent
{\bf Step 2.}
Set
$$h(t)=t^{\frac{2\cdot p^{*}_{\alpha}}{p}},~t\geqslant0~(1<p<N).$$
Since
$p\in(1,N)$
and
$\alpha\in(0,N)$,
we get
$$\frac{2\cdot p^{*}_{\alpha}}{p}=\frac{2N-\alpha}{N-p}>1~\mathrm{and}~N+p-\alpha>0.$$
We know that
$$h^{''}(t)=\frac{(2N-\alpha)(N+p-\alpha)}{(N-p)^{2}} t^{\frac{2p-\alpha}{N-p}}\geqslant0,$$
which implies that
$h(t)$
is a convex function.
By using
$h(0)=0$
and
$l\in[0,1]$,
we know
\begin{align}\label{110}
h(lt)=h(lt+(1-t)\cdot0)\leqslant lh(t)+(1-l)h(0)=lh(t).
\end{align}
For any
$t_{1},t_{2}\in[0,\infty)$,
applying last inequality with
$l=\frac{t_{1}}{t_{1}+t_{2}}$
and
$l=\frac{t_{2}}{t_{1}+t_{2}}$,
we get
\begin{equation}\label{111}
\begin{aligned}
h(t_{1})+h(t_{2})
=&
h
\left(
(t_{1}+t_{2})\frac{t_{1}}{t_{1}+t_{2}}
\right)
+
h
\left(
(t_{1}+t_{2})\frac{t_{2}}{t_{1}+t_{2}}
\right)\\
\leqslant&
\frac{t_{1}}{t_{1}+t_{2}}
h
\left(
t_{1}+t_{2}
\right)
+
\frac{t_{2}}{t_{1}+t_{2}}
h
\left(
t_{1}+t_{2}
\right)
~(\mathrm{by}~(\ref{110}))\\
=&h
\left(
t_{1}+t_{2}
\right).
\end{aligned}
\end{equation}
Now,
we claim that
$v_{n}\rightarrow v~\mathrm{strongly~in}~W^{1,p}(\mathbb{R}^{N}).$
Set
$$K(u,v)=
\int_{\mathbb{R}^{N}}
|\nabla u|^{p-2}
\nabla u \nabla v
\mathrm{d}x
-
\mu
\int_{\mathbb{R}^{N}}
\frac{|u|^{p-2}uv}{|x|^{p}}
\mathrm{d}x.$$
Since
$\{v_{n}\}$
is a minimizing sequence,
$$\lim\limits_{n\rightarrow\infty}K(v_{n},v_{n})=S_{p,1,\alpha,\mu}.$$
By using Br\'{e}zis--Lieb type lemma
\cite{Brezis1983}
and
\cite[Theorem 2.3]{Pucci2017},
we know
\begin{align}\label{113}
K(v,v)+\lim\limits_{n\rightarrow\infty}K(v_{n}-v,v_{n}-v)=
\lim\limits_{n\rightarrow\infty}K(v_{n},v_{n})+o(1)=
S_{p,1,\alpha,\mu}+o(1),
\end{align}
and
\begin{equation}\label{114}
\begin{aligned}
&\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|v_{n}(x)|^{p^{*}_{\alpha}}|v_{n}(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
-
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|v_{n}(x)-v(x)|^{p^{*}_{\alpha}}|v_{n}(y)-v(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y\\
=&
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|v(x)|^{p^{*}_{\alpha}}|v(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
+
o(1).
\end{aligned}
\end{equation}
where
$o(1)$
denotes a quantity that tends to zero as
$n\rightarrow\infty$.
Therefore,
\begin{align*}
1
=&
\lim\limits_{n\rightarrow\infty}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|v_{n}(x)|^{p^{*}_{\alpha}}|v_{n}(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y\\
=&
\lim\limits_{n\rightarrow\infty}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|v_{n}(x)-v(x)|^{p^{*}_{\alpha}}|v_{n}(y)-v(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y\\
&+
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|v(x)|^{p^{*}_{\alpha}}|v(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y\\
\leqslant&
S_{p,1,\alpha,\mu}^{-\frac{2\cdot p^{*}_{\alpha}}{p}}
\left(
\lim\limits_{n\rightarrow\infty} K(v_{n}-v,v_{n}-v)
\right)^{\frac{2\cdot p^{*}_{\alpha}}{p}}
+
S_{p,1,\alpha,\mu}^{-\frac{2\cdot p^{*}_{\alpha}}{p}}
\left(
K(v,v)
\right)^{\frac{2\cdot p^{*}_{\alpha}}{p}}\\
\leqslant&
S_{p,1,\alpha,\mu}^{-\frac{2\cdot p^{*}_{\alpha}}{p}}
\left(
\lim\limits_{n\rightarrow\infty} K(v_{n}-v,v_{n}-v)
+
K(v,v)
\right)^{\frac{2\cdot p^{*}_{\alpha}}{p}}
~(\mathrm{by}~(\ref{111}))\\
\leqslant&1~(\mathrm{by}~(\ref{113})).
\end{align*}
Therefore, all the inequalities above have to be equalities.
We know that
\begin{equation}\label{115}
\begin{aligned}
&
\left(
\lim\limits_{n\rightarrow\infty} K(v_{n}-v,v_{n}-v)
\right)^{\frac{2\cdot p^{*}_{\alpha}}{p}}
+
\left(
K(v,v)
\right)^{\frac{2\cdot p^{*}_{\alpha}}{p}}\\
=&
\left(
\lim\limits_{n\rightarrow\infty} K(v_{n}-v,v_{n}-v)
+
K(v,v)
\right)^{\frac{2\cdot p^{*}_{\alpha}}{p}}.
\end{aligned}
\end{equation}
We show that
$\lim\limits_{n\rightarrow\infty} K(v_{n}-v,v_{n}-v)=0$.
Combining
\eqref{111}
and
\eqref{115},
we know that
$$\mathrm{eithor}~\lim\limits_{n\rightarrow\infty} K(v_{n}-v,v_{n}-v)=0~\mathrm{or}~K(v,v)=0.$$
Since
$v\not\equiv0$,
so $K(v,v)\not=0$.
Therefore,
\begin{align}\label{116}
\lim\limits_{n\rightarrow\infty} K(v_{n}-v,v_{n}-v)=0.
\end{align}
This implies that
$v_{n}\rightarrow v~\mathrm{strongly~in}~W^{1,p}(\mathbb{R}^{N}).$
Moreover,
we get
\begin{align}\label{117}
\lim\limits_{n\rightarrow\infty}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|v_{n}(x)-v(x)|^{p^{*}_{\alpha}}|v_{n}(y)-v(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y=0.
\end{align}
\noindent
{\bf Step 3.}
Since
$v\not\equiv0$,
putting
(\ref{116})
into
(\ref{113}),
and
inserting
(\ref{117})
into
(\ref{114}),
we know
\begin{align*}
\lim\limits_{n\rightarrow\infty}
\left(
\|v_{n}\|_{W}^{p}-
\mu
\int_{\mathbb{R}^{N}}
\frac{|v_{n}|^{p}}{|x|^{p}}
\mathrm{d}x
\right)
\rightarrow
S_{p,1,\alpha,\mu}
=
\|v\|_{W}^{p}-
\mu
\int_{\mathbb{R}^{N}}
\frac{|v|^{p}}{|x|^{p}}
\mathrm{d}x,
\end{align*}
and
\begin{align*}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|v(x)|^{p^{*}_{\alpha}}|v(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
=1.
\end{align*}
Then
$v$
is an extremal.
In addition,
$|v|\in W^{1,p}(\mathbb{R}^{N})$
and
$|\nabla |v||=|\nabla v|$
a.e. in
$\mathbb{R}^{N}$,
therefore,
$|v|$
is also an extremal,
and then there exist non--negative extremals.
Let
$\bar{v}\geqslant0$
be an extremal.
Denote by $\bar{v}_{*}$ the symmetric--decreasing rearrangement
of
$\bar{v}$
(See \cite[Section 3]{Lieb2001}).
From
\cite{Polya1951}
it follows that
\begin{align}\label{19}
\int_{\mathbb{R}^{N}}
|\nabla \bar{v}_{*}|^{p}
\mathrm{d}x
\leqslant
\int_{\mathbb{R}^{N}}
|\nabla \bar{v}|^{p}
\mathrm{d}x.
\end{align}
According to the simplest rearrangement inequality in \cite[Theorem 3.4]{Lieb2001},
we get
\begin{align}\label{20}
\int_{\mathbb{R}^{N}}
\frac{|\bar{v}|^{p}}{|x|^{p}}
\mathrm{d}x
\leqslant
\int_{\mathbb{R}^{N}}
\frac{|\bar{v}_{*}|^{p}}{|x|^{p}}
\mathrm{d}x.
\end{align}
By using Riesz's rearrangement inequality in \cite[Theorem 3.7]{Lieb2001},
we have
\begin{align}\label{21}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|\bar{v}(x)|^{p^{*}_{\alpha}}|\bar{v}(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\leqslant
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|\bar{v}_{*}(x)|^{p^{*}_{\alpha}}|\bar{v}_{*}(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y.
\end{align}
Combining
(\ref{19}),
(\ref{20})
and
(\ref{21}),
and the fact that
$\mu\geqslant0$,
we get that
$\bar{v}_{*}$
is also an extremal,
and then there exist radially symmetric and nonincreasing extremal.
\qed
\section{Proof of Theorem \ref{theorem2}}
For
$p=2$
and
$s\in(0,1)$,
we give
a estimation of extremal function
$u(x)$.
The proof of Theorem \ref{theorem2}
is based on the Coulomb--Sobolev space
$\mathcal{E}^{s,\alpha,2^{*}_{\alpha,s}}(\mathbb{R}^{N})$
and
the endpoint refined Sobolev inequality in Lemma \ref{lemma3}.
\noindent
{\bf Proof of Theorem \ref{theorem2}:}
In this step,
we show some properties of
radially symmetric, nonincreasing and nonnegative function
$u(x)$.
Let
$\bar{\mu}=4^{s}\frac{\Gamma^{2}(\frac{N+2s}{4})}{\Gamma^{2}(\frac{N-2s}{4})}$.
By the definition of extremal
$u$
(see the proof of Theorem \ref{theorem1}),
we know
\begin{align}\label{22}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{2}}
{|x-y|^{N+2s}}
\mathrm{d}x
\mathrm{d}y
-
\mu
\int_{\mathbb{R}^{N}}
\frac{|u|^{2}}{|x|^{2}}
\mathrm{d}x
=
S_{2,s,\alpha,\mu},
\end{align}
and
\begin{align}\label{23}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{2^{*}_{\alpha,s}}|u(y)|^{2^{*}_{\alpha,s}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
=1.
\end{align}
Applying
(\ref{22}),
(\ref{23})
and
the definition of
Coulomb--Sobolev space
$\mathcal{E}^{s,\alpha,2^{*}_{\alpha,s}}(\mathbb{R}^{N})$,
we get
$u\in\mathcal{E}^{s,\alpha,2^{*}_{\alpha,s}}(\mathbb{R}^{N})$.
By using
(\ref{22}),
(\ref{23}),
$u\in\mathcal{E}^{s,\alpha,2^{*}_{\alpha,s}}(\mathbb{R}^{N})$
and
Lemma \ref{lemma3},
we have
\begin{equation}\label{24}
\begin{aligned}
\|u\|_{L^{\frac{2N}{N-2s}}(\mathbb{R}^{N})}
\leqslant&
C_{4}
\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{2}}
{|x-y|^{N+2s}}
\mathrm{d}x
\mathrm{d}y
\right)
^{\frac{(N-\alpha)(N-2s)}{2N(N+2s-\alpha)}}\\
&~~~~~~~~~\cdot
\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{\frac{2N-\alpha}{N-2s}}|u(y)|^{\frac{2N-\alpha}{N-2s}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)
^{\frac{s(N-2s)}{N(N+2s-\alpha)}}\\
=&
C_{4}
\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{2}}
{|x-y|^{N+2s}}
\mathrm{d}x
\mathrm{d}y
\right)
^{\frac{(N-\alpha)(N-2s)}{2N(N+2s-\alpha)}}\\
\leqslant&
C_{4}
\left(
\left(
\frac{\bar{\mu}}{\bar{\mu}-\mu}
\right)
S_{2,s,\alpha,\mu}
\right)
^{\frac{(N-\alpha)(N-2s)}{2N(N+2s-\alpha)}}.
\end{aligned}
\end{equation}
For any
$0<R<\infty$
and
$B(R)=B(0,R)\subset\mathbb{R}^{N}$,
we obtain
\begin{align*}
C_{4}
\left(
\left(
\frac{\bar{\mu}}{\bar{\mu}-\mu}
\right)
S_{2,s,\alpha,\mu}
\right)
^{\frac{(N-\alpha)(N-2s)}{2N(N+2s-\alpha)}}
\geqslant&
\left(
\int_{\mathbb{R}^{N}}
|u(x)|^{\frac{2N}{N-2s}}
\mathrm{d}x
\right)^{\frac{N-2s}{2N}}\\
\geqslant&
\left(
\int_{B(R)}
|u(x)|^{\frac{2N}{N-2s}}
\mathrm{d}x
\right)^{\frac{N-2s}{2N}}\\
\geqslant&
|u(R)|
\omega_{N-1}^{\frac{N-2s}{2N}}
\left(
\int_{0}^{R}
\rho^{N-1}
\mathrm{d}\rho
\right)
^{\frac{N-2s}{2N}}\\
=&
|u(R)|
\left(
\frac{\omega_{N-1}}{N}
\right)
^{\frac{N-2s}{2N}}
R
^{\frac{N-2s}{2}},
\end{align*}
which implies
\begin{align*}
C_{4}
\left(
\left(
\frac{\bar{\mu}}{\bar{\mu}-\mu}
\right)
S_{2,s,\alpha,\mu}
\right)
^{\frac{(N-\alpha)(N-2s)}{2N(N+2s-\alpha)}}
\left(
\frac{N}{\omega_{N-1}}
\right)
^{\frac{N-2s}{2N}}
\frac{1}{
|x|^{\frac{N-2s}{2}}}
\geqslant&
|u(x)|.
\end{align*}
\qed
\section{Proof of Theorem \ref{theorem3}}
For
$p\not=2$
and
$s\in(0,1)$,
we give
a estimation of extremal function
$u(x)$.
From Theorem \ref{theorem1},
we know that
$u(x)$
is a radially symmetric, nonincreasing and nonnegative function.
The proof of Theorem \ref{theorem3}
is different from
Theorem \ref{theorem2}.
The endpoint refined Sobolev inequality in Lemma \ref{lemma3}
is true for
$p=2$.
However,
we don't know that
the endpoint refined Sobolev inequality
is true or not for
$p\not=2$.
\noindent
{\bf Proof of Theorem \ref{theorem3}:}
Let
$\tilde{\mu}=\left(\frac{N-p}{p}\right)^{p}$.
By the definition of extremal
$u$,
we know
\begin{align}\label{25}
\|u\|_{W}^{p}
-
\mu
\int_{\mathbb{R}^{N}}
\frac{|u|^{p}}{|x|^{p}}
\mathrm{d}x
=
S_{p,1,\alpha,\mu},
\end{align}
and
\begin{align}\label{26}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{p^{*}_{\alpha}}|u(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
=1.
\end{align}
For any
$R\in(0,\infty)$
and
$B(R)=B(0,R)\subset\mathbb{R}^{N}$,
by
H\"{o}lder's inequality,
we obtain
\begin{align*}
\left(
\int_{B(R)}
|u|^{p^{*}_{\alpha}}
\mathrm{d}x
\right)^{\frac{1}{p^{*}_{\alpha}}}
\leqslant&
\left[
\left(
\int_{B(R)}
\mathrm{d}x
\right)^{1-\frac{p^{*}_{\alpha}}{p^{*}}}
\left(
\int_{B(R)}
|u|^{p^{*}_{\alpha}\cdot\frac{p^{*}}{p^{*}_{\alpha}}}
\mathrm{d}x
\right)^{\frac{p^{*}_{\alpha}}{p^{*}}}
\right]
^{\frac{1}{p^{*}_{\alpha}}}\\
=&
|B(R)|
^{\frac{1}{p^{*}_{\alpha}}-\frac{1}{p^{*}}}
\left(
\int_{B(R)}
|u|^{p^{*}}
\mathrm{d}x
\right)^{\frac{1}{p^{*}}}\\
\leqslant&
|B(R)|
^{\frac{1}{p^{*}_{\alpha}}-\frac{1}{p^{*}}}
S_{p,1,0,\mu}^{-\frac{1}{p}}\|u\|_{W}\\
\leqslant&
|B(R)|^{\frac{1}{p^{*}_{\alpha}}-\frac{1}{p^{*}}}
S_{p,1,0,\mu}^{-\frac{1}{p}}
\left(
\left(
\frac{\tilde{\mu}}{\tilde{\mu}-\mu}
\right)
S_{p,1,\alpha,\mu}
\right)
^{\frac{1}{p}}
<\infty.
\end{align*}
By Fubini's theorem,
we get
\begin{align*}
(2R)^{-\alpha}
\left(
\int_{B(R)}
|u(x)|^{p^{*}_{\alpha}}
\mathrm{d}x
\right)^{2}
=&
(2R)^{-\alpha}
\int_{B(R)}
|u(x)|^{p^{*}_{\alpha}}
\mathrm{d}x
\int_{B(R)}
|u(y)|^{p^{*}_{\alpha}}
\mathrm{d}y\\
=&
(2R)^{-\alpha}
\int_{B(R)}
\int_{B(R)}
|u(x)|^{p^{*}_{\alpha}}
|u(y)|^{p^{*}_{\alpha}}
\mathrm{d}x
\mathrm{d}y\\
\leqslant&
\int_{B(R)}
\int_{B(R)}
\frac{|u(y)|^{p^{*}_{\alpha}}|u(x)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y,
\end{align*}
which implies
\begin{align}\label{27}
\left(
\int_{B(R)}
|u(x)|^{p^{*}_{\alpha}}
\mathrm{d}x
\right)^{2}
\leqslant&
(2R)^{\alpha}
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(y)|^{p^{*}_{\alpha}}|u(x)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y.
\end{align}
According to
(\ref{25}),
(\ref{26})
and
(\ref{27}),
we have
\begin{equation*}
\begin{aligned}
1=&
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{p^{*}_{\alpha}}|u(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y\\
\geqslant&
(2R)^{-\alpha}
\left(
\int_{B(R)}
|u|^{p^{*}_{\alpha}}
\mathrm{d}x
\right)^{2}\\
\geqslant&
(2R)^{-\alpha}
|u(R)|^{2\cdot p^{*}_{\alpha}}
\left(
\omega_{N-1}
\int_{0}^{R}
\rho^{N-1}
\mathrm{d}\rho
\right)^{2}\\
\geqslant&
\frac{\omega^{2}_{N-1}}{2^{\alpha}N^{2}}
|u(R)|^{2\cdot p^{*}_{\alpha}}
R^{2N-\alpha}.
\end{aligned}
\end{equation*}
Then we know
\begin{equation*}
\begin{aligned}
\left(
\frac{2^{\alpha}N^{2}}{\omega^{2}_{N-1}}
\right)^{\frac{1}{2\cdot p^{*}_{\alpha}}}
\frac{1}{R^{\frac{N-p}{p}}}
\geqslant
|u(R)|.
\end{aligned}
\end{equation*}
Hence,
for any
$0<|x|<\infty$,
we obtain
\begin{equation*}
\begin{aligned}
\left(
\frac{2^{\alpha}N^{2}}{\omega^{2}_{N-1}}
\right)^{\frac{1}{2\cdot p^{*}_{\alpha}}}
\frac{1}{|x|^{\frac{N-p}{p}}}
\geqslant
u(x).
\end{aligned}
\end{equation*}
\qed
\section{Conclusions and future works}
The results in this paper set the foundation for the study of a number of questions
related to minimizing problem
$$
S_{p,1,\alpha,\mu}:=
\inf_{u\in W^{1,p}(\mathbb{R}^{N})\setminus\{0\}}
\frac{
\int_{\mathbb{R}^{N}}|\nabla u|^{p}\mathrm{d}x
-
\mu
\int_{\mathbb{R}^{N}}
\frac{|u|^{p}}{|x|^{p}}
\mathrm{d}x}
{\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{p^{*}_{\alpha}}|u(y)|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)^{\frac{p}{2\cdot p^{*}_{\alpha}}}},
$$
where
$N\geqslant3$,
$p\in(1,N)$,
$\alpha\in(0,N)$
and
$\mu\in
\left(
0,
\left(
\frac{N-p}{p}
\right)^{p}
\right)$.
During the preparation of the manuscript we faced several problems which are worth to be tackled in forthcoming investigations.
In the sequel,
we shall formulate some of them:
{\bf (a)}
The challenging problems are to prove the rest of Open problem:
the case of
$N\geqslant3$,
$p\in(1,N)$,
$s\in(0,1)$,
$\alpha\in(0,N)$
and
$\mu\in[0,\mathcal{C}_{N,s,p})$,
and
$\mathcal{C}_{N,s,p}$
is defined in
\cite[Theorem 1.1]{Frank2008}.
{\bf (b)}
In \cite{ZhangBL2017},
the authors studied the following minimizing problem:
$$
I_{2,s,\alpha,\mu}(u,v):=
\inf_{
u,v\in W^{s,2}(\mathbb{R}^{N})\setminus\{0\}}
\frac{
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{2}+|v(x)-v(y)|^{2}}{|x-y|^{N+2s}}
\mathrm{d}x
\mathrm{d}y
-
\mu
\int_{\mathbb{R}^{N}}
\left(
\frac{|u|^{2}}{|x|^{2s}}
+
\frac{|v|^{2}}{|x|^{2s}}
\right)
\mathrm{d}x
}
{\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)|^{2^{*}_{\alpha,s}}|u(y)|^{2^{*}_{\alpha,s}}+|v(x)|^{2^{*}_{\alpha,s}}|v(y)|^{2^{*}_{\alpha,s}}}
{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)^{\frac{1}{ 2^{*}_{\alpha}}}},
$$
where
$N\geqslant3$,
$p=2$,
$s\in(0,1)$,
$\mu\in
\left[
0,4^{s}\frac{\Gamma^{2}(\frac{N+2s}{4})}{\Gamma^{2}(\frac{N-2s}{4})}
\right)$
and
$\alpha\in(0,N)$.
It is worth to extend the study of
$I_{2,\textcolor{red}{s},\alpha,\mu}(u,v)$
to the following minimizing problem:
$$
I_{p,s,\alpha,\mu}(u,v):=
\inf_{
u\in W^{s,p}(\mathbb{R}^{N})\setminus\{0\}}
\frac{
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{|u(x)-u(y)|^{p}+|v(x)-v(y)|^{p}}{|x-y|^{N+ps}}
\mathrm{d}x
\mathrm{d}y
-
\mu
\int_{\mathbb{R}^{N}}
\left(
\frac{|u|^{p}}{|x|^{ps}}
+
\frac{|v|^{p}}{|x|^{ps}}
\right)
\mathrm{d}x
}
{\left(
\int_{\mathbb{R}^{N}}
\int_{\mathbb{R}^{N}}
\frac{
|u(x)|^{p^{*}_{\alpha,s}}
|u(y)|^{p^{*}_{\alpha,s}}
+
|v(x)|^{p^{*}_{\alpha,s}}
|v(y)|^{p^{*}_{\alpha,s}}
}
{|x-y|^{\alpha}}
\mathrm{d}x
\mathrm{d}y
\right)^{\frac{p}{2\cdot p^{*}_{\alpha,s}}}},
$$
where
$N\geqslant3$,
$p\in(1,N)$,
$s\in(0,1)$,
$\mu\in[0,\mathcal{C}_{N,s,p}$)
and
$\alpha\in(0,N)$.
{\bf (c)}
By using Theorem \ref{theorem1}
and
Lemma
\ref{lemma4},
we could
study
the
Choquard--equation involving two critical nonlinearities:
\begin{equation*}
\begin{aligned}
-\Delta_{p} u
-\mu
\frac{|u|^{p-2}u}{|x|^{p}}
=
\left(
\int_{\mathbb{R}^{N}}
\frac{|u|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}y
\right)
|u|^{p^{*}_{\alpha}-2}u
+
|u|^{p^{*}-2}u,
\mathrm{~in~}
\mathbb{R}^{N},
\end{aligned}
\end{equation*}
where
$N\geqslant3$,
$p\in(1,N)$,
$\mu\in[0,\left(
\frac{N-p}{p}
\right)^{p}$)
and
$\alpha\in(0,N)$.
{\bf (d)}
Ambrosetti,
Brezis
and
Cerami
\cite{Ambroseiti1994}
proved the existence of infinity many solutions to the following problem
\begin{equation*}
\begin{aligned}
\begin{cases}
-\Delta u
=
|u|^{2^{*}-2}u
+
\lambda|u|^{q-2}u
&
\mathrm{~in~}
\Omega,\\
u=0&
\mathrm{~in~}
\partial \Omega,
\end{cases}
\end{aligned}
\end{equation*}
where
$\Omega\subset \mathbb{R}^{N}$
is a smooth bounded domain,
$N\geqslant3$,
$\lambda>0$
and
$q\in(1,2)$.
Garcia
and
Peral
\cite{Garcia1991}
proved the existence of infinity many solutions to following problem
\begin{equation*}
\begin{aligned}
\begin{cases}
-\Delta_{p} u
=
|u|^{p^{*}-2}u
+
\lambda|u|^{q-2}u
&
\mathrm{~in~}
\Omega,\\
u=0&
\mathrm{~in~}
\partial \Omega,
\end{cases}
\end{aligned}
\end{equation*}
where
$-\Delta_{p}$
is the $p$--Laplacian operator,
$\Omega\subset \mathbb{R}^{N}$
is a smooth bounded domain,
$N\geqslant3$,
$\lambda>0$,
$q\in(1,p)$
and
$p^{*}=\frac{NP}{N-p}$.
Gao and Yang
\cite{Gao2017JMAA}
proved the existence of infinity many solutions to following problem
$$
\begin{cases}
-\Delta u
=
\left(
\int_{\Omega}
\frac{|u|^{2^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}y
\right)
|u|^{2^{*}_{\alpha}-2}u
+
\lambda|u|^{q-2}u
&
\mathrm{~in~}
\Omega,\\
u=0&
\mathrm{~in~}
\mathbb{R}^{N}\setminus \Omega,
\end{cases}
$$
where
$\Omega\subset \mathbb{R}^{N}$
is a bounded domain
with $C^{0,1}$ bounded boundary,
$N\geqslant3$,
$\lambda>0$,
$q\in(1,2)$,
$0<\alpha<N$
and
$2^{*}_{\alpha}=\frac{2N-\alpha}{N-2}$
is the critical Hardy--Littlewood--Sobolev upper exponent.
It is natural to ask:
Does there exist a solution to following problem?
$$
\begin{cases}
-
\Delta_{p} u
=
\left(
\int_{\Omega}
\frac{|u|^{p^{*}_{\alpha}}}{|x-y|^{\alpha}}
\mathrm{d}y
\right)
|u|^{p^{*}_{\alpha}-2}u
+
\lambda|u|^{q-2}u
&
\mathrm{~in~}
\Omega,\\
u=0&
\mathrm{~in~}
\mathbb{R}^{N}\setminus \Omega,
\end{cases}
$$
where
$\Omega\subset \mathbb{R}^{N}$
is a bounded domain
with $C^{0,1}$ bounded boundary,
$N\geqslant3$,
$\lambda>0$,
$p\in(1,N)$,
$q\in(1,p)$
and
$0<\alpha<N$.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,686 |
12. ročník předávání cen asociace St. Louis Film Critics Association se konal dne 20. prosince 2015. Nominace byly oznámeny dne 13. prosince 2015.
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Výroční ceny za rok 2015 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,472 |
\section{Introduction}
We consider the following fractional $L^2$-critical nonlinear Schr\"{o}dinger equation(NLS)
\begin{equation}\label{F}
(-\Delta)^{s} u(x)+V(x)u(x)-a|x|^{-b}|u|^{2\beta^2}u(x)=\mu u(x)\ \ \mbox{in}\ \ \R^{N},
\end{equation}
where $s\in(\frac{1}{2},1)$, $N>2s$, $a>0$, $0<b<\min\{2s,\frac{N}{2}\}$, $\beta=\sqrt{\frac{2s-b}{N}}$ is the $L^2$-critical exponent and the fractional Laplacian operator is defined by
\begin{equation}\label{01}
\begin{split}
(-\Delta)^su(x)&=C(N,s)P.V.\int_{\R^N}\frac{u(x)-u(y)}{|x-y|^{N+2s}}dy\\
&=C(N,s)\lim\limits_{r\rightarrow0}\int_{\R^N\backslash B_r(x)}\frac{u(x)-u(y)}{|x-y|^{N+2s}}dy.
\end{split}
\end{equation}
The P.V. in \eqref{01} stands for the Cauchy principal value and $C(N,s)$ is a positive dimensional constant that depends on $N$ and $s$, precisely given by
\begin{equation}\label{02}
C(N,s)=\Big(\int_{\R^N}\frac{1-cos \xi_1}{|\xi|^{N+2s}}d\xi\Big)^{-1}.
\end{equation}
Equation \eqref{F} arises in various physical contexts like nonlinear optics, plasma physics and Bose-Einstein condensates (BECs) (cf.\cite{AG, BGC,Liu,Za}), where $V(x)$ and $\mu\in\R$ describe the trapping potential and the chemical potential respectively. The function $a|u|^{2\beta^2}|x|^{-b}$ in \eqref{F} stands for corrections to the nonlinear power-law response or some inhomogeneities in the medium. The nonlocal operator $(-\Delta)^s$ can be seen as the infinitesimal generators of L$\acute{e}$vy stable diffusion processes \cite{A}, which appears in many physical models such as water models, quantum mechanics and the fractional Brownian motion \cite{D, RS} and so on. From the physical point of view, we assume that the trapping potential $V(x)$ satisfie
\begin{itemize}
\item[\rm($V_{1})$.] $0\leq V(x)\in {L^{\infty}_{loc}} (\R^{N})$ and $ \lim_{|x|\rightarrow\infty}V(x)=\infty$.
\end{itemize}
It is well known that normalized $L^{2}$-norm solutions of equation \eqref{F} can be described by minimizers of the following $L^2$-critical constraint variational problem
\begin{equation}\label{e(a)}
e(a)=\inf _{\{u\in\mathcal{H}, \|u\|^{2}_{2}=1\}}E_{a}(u),\,\ a>0,
\end{equation}
where $E_{a}(u)$ is defined by
\begin{equation}\label{Eau}
E_{a}(u):=\int_{\R^{N}}(|(-\Delta)^{\frac{s}{2}} u|^{2}+V(x)|u|^{2})dx-\frac{a}{1+\beta^2}\int_{\R^{N}}\frac{|u(x)|^{2+2\beta^2}}{|x|^{b}}dx
\end{equation}
with
\begin{equation}\label{04}
\beta=\sqrt{\frac{2s-b}{N}}\,\, \hbox{and}\,\,\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} u|^{2}dx=\frac{C(N,s)} {2}\iint_{\R^{2N}}\frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dxdy.
\end{equation}
The space $\mathcal{H}$ in \eqref{e(a)} is defined as
\begin{equation}
\mathcal{H}:=\Big\{u\in H^{s}(\R^{N}):\int_{\R^{N}}V(x)|u(x)|^{2}dx<\infty\Big\}
\end{equation}
with the associated norm $\|u\|_{\mathcal{H}}=\Big\{\displaystyle\int_{\R^N}\Big(|(-\Delta)^{\frac{s}{2}} u(x)|^{2}+[1+V(x)]|u(x)|^{2}\Big)dx\Big\}^{\frac{1}{2}}$.
When $s=1$, \eqref{e(a)} is the so-called $L^2$-constraint variational problem of Schr\"{o}dinger equations. In the last two decades, the existence and nonexistence of constrained minimizers and various quantitative properties of these equations have been investigated extensively, see \cite{AD,FG,SC,GR,GW,GZ}. More specifically, when $s=1$ and $b=0$, (\ref{e(a)}) is a homogeneous problem.
Guo, Zhang and their collaborators in \cite{GR,ZJ} proved that there is a critical constant $a_0>0$ such that minimizers of $e(a)$ exist if and only if $0<a<a_0.$ For different kinds of trapping potentials, the authors in \cite{GR,GW,GZ} also analyzed the detailed limit behavior of minimizers as $a\nearrow a_0$. By constructing Pohozaev identities, Guo, Lin, and Wei in \cite{GLW} obtained the uniqueness of minimizers for $e(a)$ as $a\nearrow a_0$. While $b\neq0$, (\ref{e(a)}) is an inhomogeneous problem which contains the nonlinear term $K(x)|u(x)|^{2+2\beta^2}$ with $K(x)=|x|^{-b}$. Deng, Guo and Lu in \cite{DGL1,DGL2} analyzed the existence, nonexistence and limit behavior of minimizers for the inhomogeneous problems with $K(x)\in L^\infty(\R^N)$. Furthermore, Genoud in \cite{FG} also studied the existence of minimizers for \eqref{e(a)} in the special case $V(x)\equiv 1$. More recently, for $K(x)=|x|^{-b}$ and $V(x)$ satisfies the assumption $(V_1)$ in \cite{LZ}, on the one hand we obtained the classification results of the existence and nonexistence of minimizers for $e(a)$. On the other hand, limit behavior and uniqueness of minimizers for $e(a)$ were also analyzed as $a\nearrow a_1$.
In recent years, the investigation of $L^2$-constraint variational problems involving a fractional Laplacian has attracted much attention of many mathematicians, see \cite{D1,DT,HL} and the references therein. When $0<s<1$, $b=0$ and $\beta^2=\frac{4s}{N}$, He and Long in \cite{HL} proved the existence and nonexistence of minimizers for $e(a)$ with both trapping potentials satisfying $(V_1)$ and bounded potentials satisfying $(V_2)$
\begin{itemize}
\item[\rm($V_{2})$.] $V(x)\in C(\R^N),\ \ \ 0=\inf_{x\in\R^N }V(x)<\sup_{x\in\R^N }V(x)=\lim_{|x|\rightarrow\infty}V(x)<\infty$.
\end{itemize}
Subsequently, when $0<s<1$, $b=0$ and $0<\beta^2\leq\frac{4s}{N}$, the authors in \cite{D1} and \cite{DT} gave a complete classification of the existence and nonexistence of minimizers for $e(a)$ with periodic potentials and trapping potentials respectively. Furthermore, for the case of mass critical and under a suitable assumption of potentials, they also analyzed the blow-up behavior of minimizers when the mass tends to a critical value.
Motivated by the aforementioned papers, in the present paper we mainly aim to study the existence and nonexistence of minimizers for e(a), and then analyze the limit behavior and local uniqueness of minimizers. In order to achieve our goals, we firstly need to establish the following theorem concerning a fractional Gagliardo-Nirenberg sobolev inequality.
\begin{thm}\label{pro1}
Let $s\in(\frac{1}{2},1)$, $N>2s$, $0<b<\min\{2s,\frac{N}{2}\}$ and $\beta^2=\frac{2s-b}{N}$, then the following fractional Gagliardo-Nirenberg sobolev inequality holds
\begin{equation}\label{GN}
\frac{a^*}{1+\beta^2}\int_{\R^{N}}|x|^{-b}|u(x)|^{2+2\beta^2}dx\leq \|(-\Delta)^{\frac{s}{2}} u(x)\|^{2}_{2}\|u(x)\|^{2\beta^2}_{2} \ \mbox{in}\ \ H^{s}(\R^{N}),
\end{equation}
where the optimal constant $a^*>0$ is given by
\begin{equation}\label{a8}
a^*:=\|Q\|^{2\beta^2}_{2}.
\end{equation}
The above $Q>0$ solves the following equation
\begin{equation}\label{Eq}
(-\Delta)^{s} u+u-|x|^{-b}|u|^{2\beta^2}u=0\ \ \mbox{in}\ \ \R^{N}
\end{equation}
and satisfies the following equality
\begin{equation}\label{DS}
\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} Q|^{2}dx=\frac{1}{\beta^2}\int_{\R^{N}}|Q|^{2}dx=\frac{1}{1+\beta^2}\int_{\R^{N}}|x|^{-b}|Q|^{2+2\beta^2}dx.
\end{equation}
Further, $Q\in \mathrm{C}^1(\R^N\backslash\{0\})$ admits the following polynomially decay
\begin{equation}\label{ds}
|Q(x)|\leq C|x|^{-N-2s}\quad \mbox{and} \quad|\nabla Q(x)|\leq C|x|^{-N-1}\ \ \mbox{for all}\ \ |x|\geq 1.
\end{equation}
\end{thm}
By making full use of the Gagliardo-Nirenberg inequality (\ref{GN}), the existence and nonexistence of minimizers for (\ref{e(a)}) can be stated as follows.
\begin{thm}\label{th1}
Let $s\in(\frac{1}{2},1)$, $N>2s$, $0<b<\min\{2s,\frac{N}{2}\}$, $\beta^2=\frac{2s-b}{N}$, $a^*=\|Q\|^{2\beta^2}_{2}$, and $V(x)$ satisfies $(V_{1})$, then
\begin{enumerate}
\item If $0<a< a^{\ast}$, there exists at least one minimizer for (\ref{e(a)}).
\item If $a>a^{\ast}$, there is no minimizer for (\ref{e(a)}).
\end{enumerate}
Moreover, we also have $e(a)>0$ for $a<a^{\ast}$ and $e(a)=-\infty$ for $a>a^{\ast}$.
\end{thm}
In Theorem \ref{th1}, we firstly note that $(-\Delta)^s$ with $\frac{1}{2} < s < 1$ is a nonlocal operator which then causes some difficulties. In particular, we need to estimate the Gagliardo semi-norm of some trial function, see \eqref{Gj} in Section 3. Inspired by \cite[Proposition 21]{SV}, we have established Lemma \ref{lem2.2} to circumvent this obstacle. Moreover, the function $Q(x)$ given in Theorem \ref {pro1} is polynomially decay at infinity which is quite different from the case of $Q(x)$ exponentially decays at infinity for $s = 1$ in \eqref{e(a)}, we need to give more detailed analyses to establish the desired estimates of the trial function. Finally, due to the singular nonlinearity $\int_{\R^{N}}|u(x)|^{2+2\beta^2}|x|^{-b}dx$ in \eqref{Eau}, we need also verify the convergence in \eqref{2.1}.
In view of Theorem \ref{th1}, a natural question is whether there exist minimizers for $e(a)$ when $a=a^*$.
In contrast to the homogeneous $b=0$,
our following results show that $e(a)$ may admit minimizers at the threshold $a^*$ for some trapping potentials $V(x)$ satisfying $(V_1)$.
Indeed, applying the Gagliardo-Nirenberg inequality, we deduce from the nonnegativity of $V(x)$ that $e(a^*)\geq 0$. Taking the same test function as in \eqref{st} and letting $\tau\to\infty$, one can obtain that $e(a^*)\leq E_a(u_\tau)\leq V(0)$. Therefore, one can conclude from above that
$$0\leq e(a^*)\leq V(0)$$
and the result for the case of $a=a^*$ can be summarized as follows.
\begin{thm}\label{th2}
Let $s\in(\frac{1}{2},1)$, $N>2s$, $0<b<\min\{2s,\frac{N}{2}\}$, $\beta^2=\frac{2s-b}{N}$, and $V(x)$ satisfies $(V_{1})$, then
\begin{enumerate}
\item If $0\leq e(a^*)<V(0)$, there exists at least one minimizer for $e(a^{\ast})$.
\item If $V(0)=0$, there is no minimizer for $e(a^{\ast})$. Moreover, $\lim_{a\nearrow a^{\ast}}e(a)=e(a^{\ast})=0$.
\end{enumerate}
\end{thm}
Theorem \ref{th2} shows a fact that the existence and nonexistence of minimizers for $e(a^*)$ depend strongly on the value of $e(a^*)$ and $V(0)$. In brief, $V(0)$ can be regarded as a threshold of the energy $e(a^*)$ such that \eqref{e(a)} admits minimizers if $e(a^*)$ is less than $V(0)$, while \eqref{e(a)} does not admit any minimizer if $V(0)= e(a^*)=0$. In view of Theorem \ref{th2} (2), a simple analysis yields that minimizers must blow up in the sense of $\inte |(-\Delta)^{\frac{s}{2}} u_a|^2dx\to\infty$ as $a\nearrow a^*$. Therefore, we next focus on the limit behavior of minimizers $u_a$ as $a\nearrow a^*$. Note that $E_{a}(u_a)\geq E_{a}(|u_a|)$, then $|u_a|$ is also a minimizer of $e(a)$. Therefore, without loss of generality, we can restrict minimizers of $e(a)$ to nonnegative functions. We now establish the following theorem on limit behavior of nonnegative minimizers for $e(a)$.
\begin{thm}\label{th3}
Let $s\in(\frac{1}{2},1)$, $N>2s$, $0<b<\min\{2s,\frac{N}{2}\}$, $\beta^2=\frac{2s-b}{N}$, $V(x)$ satisfies $(V_{1})$ and suppose that $0<a<a^*$. For any nonnegative minimizer $u_{a}$ of (\ref{e(a)}), define
\begin{equation}\label{yp}
\varepsilon_{a}:=\Big(\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} u_{a}|^{2}dx\Big)^{-\frac{1}{2s}},
\end{equation}
and
\begin{equation}\label{xpa}
w_{a}(x)=\varepsilon^{\frac{N}{2}}_{a}u_{a}(\varepsilon_{a}x).
\end{equation}
Then we have
\begin{equation}\label{bp}
\lim\limits_{a\nearrow a^*}w_a=w_0\quad\hbox{strongly in}\ \ H^s(\R^N)\cap L^{\infty}(\R^N),
\end{equation}
where $w_0$ is an optimizer of the Gagliardo-Nirenberg inequality \eqref{GN}.
\end{thm}
Note that the limit equation \eqref{Eq} has no translation invariance, which then yields that $u_a$ must concentrate at the origin rather than any global minimum point of $V(x)$ as $a\nearrow a^*$. Therefore, the convergence of \eqref{bp} holds for the whole sequence $\{u_a\}$ as $a\nearrow a^*$ instead of the subsequence of $\{u_a\}$. Moreover, different from the proof of \cite [Theorem 1.5] {LZ}, the De Giorgi-Nash-Moser type theorem of fractional Laplacian equations cannot be used directly to prove $L^{\infty}$-convergence. In order to overcome this difficulty, we first obtain $w_a\in L^{\infty}$ by Moser iteration \cite{M1}. Stimulated by \cite{AM,AV}, we then prove that $w_a$ tends to zero at infinity. Applying the standard regularity theory, we finally obtain the $L^{\infty}$-convergence of $w_a$. Comparing with \cite{AM,AV}, there are some essential difficulties due to the singularity of the nonlinear term, which is one of the innovations and difficulties of this paper.
Finally, we investigate the uniqueness of minimizers for $e(a)$ when $a$ is small enough.
\begin{thm}\label{unique}
Let $s\in(\frac{1}{2},1)$, $N>2s$, $0<b<\min\{2s,\frac{N}{2}\}$, $\beta^2=\frac{2s-b}{N}$, and $V(x)$ satisfies $(V_{1})$, then $e(a)$ admits a unique nonnegative minimizer when $a$ is sufficiently small.
\end{thm}
Inspired by \cite{DT,GZ}, we complete the proof of Theorem \ref{unique} by implicit function theorem. However, due to the existence of singular nonlinear term $|x|^{-b}$, we need to be
more careful when verifying the differentiability of functional $g(h,\tau,t,a)$ in \eqref{d5}.
This paper is organized as follows. In Section 2, the fractional Gagliardo-Nirenberg sobolev inequality is established in Theorem \ref{pro1}. In Section 3, we shall prove Theorems \ref{th1} and \ref{th2} on the existence and nonexistence of minimizers for $e(a)$. Section 4 is devoted to proving Theorem \ref{th3} on the concentration behavior of minimizers for $e(a)$. Applying implicit function theorem, we finally prove Theorem \ref{unique} on the local uniqueness of nonnegative minimizers in Section 5. In the Appendix, we give some lemmas which are used in Sections 2-5.
\section{Fractional Gagliardo-Nirenberg-Sobolev inequality}
In this section, we complete the proof of Theorem \ref{pro1}. Motivated by \cite {M}, we consider the minimization problem
\begin{equation}\label{a1}
m:=\inf\limits_{u\in H^{s}(\R^N)\backslash\{0\}}I(u),
\end{equation}
where the ``Weinstein functional'' $I: H^{s}(\R^N)\backslash\{0\}\rightarrow \R$ is given by
\begin{equation}\label{a2}
I(u)=\frac{\|(-\Delta)^{\frac{s}{2}}u\|_{2}^{2}\|u\|_2^{2\beta^2}}{J(u)},
\end{equation}
with
\begin{equation}
J(u):=\int_{\R^N}|x|^{-b}|u(x)|^{2+2\beta^2}dx.
\end{equation}
In order to give the proof of Theorem \ref{pro1}, we first collect some estimates for the kernel of the resolvent $((-\Delta)^{s}+\lambda)^{-1}$ on $\R^N$ with $\lambda>0$ \cite [Lemma C.1] {FLS}.
\begin{lem}\label{G}
Suppose $N\geq 1$, $0<s<1$, and $\lambda>0$. Let $G_\lambda$ be the Fourier transform of $(|\xi|^{2s}+\lambda)^{-1}$. Then the following properties hold true
\begin{enumerate}
\item $G_\lambda(|x|)>0$ is radial, positive, strictly decreasing in $|x|$, and smooth for $|x|\neq 0$.
\item It holds that $\lim_{|x|\rightarrow\infty}|x|^{N+2s}G_\lambda(x)=\lambda^{-2}C_{N,s}$, where $C_{N, s}>0$ depends only on $N$ and $s$.
\item $G_\lambda\in L^{q}(\R^N)$ for all $q\in \Big[1,\frac{N}{N-2s}\Big)$.
\end{enumerate}
\end{lem}
We now give some useful knowledge about rearrangements. For any $s\in (0,1)$ and $u, v\in H^s(\R^N)$, let $u^*$ and $v^*$ be symmetric decreasing rearrangements of $u$ and $v$ respectively, it then follows from \cite[Theorem A.1]{FS} that
\begin{equation}\label{0A}
u^*\in H^s(\R^N)\ \ \ \mbox{and}\ \ \ \|(-\Delta)^{\frac{s}{2}}u^*\|_{L^2}\leq \|(-\Delta)^{\frac{s}{2}}u\|_{L^2}.
\end{equation}
Moreover, applying \cite[Theorem 3.3 and Theorem 3.4]{LE}, we deduce that
\begin{equation}\label{1A}
\|u^*\|_{L^2}=\|u\|_{L^2},
\end{equation}
and
\begin{equation}\label{2A}
\int_{\R^N}|x|^{-b}|u|^{2+2\beta^2}dx\leq \int_{\R^N}|x|^{-b}(|u|^{2+2\beta^2})^*dx=\int_{\R^N}|x|^{-b}|u^*|^{2+2\beta^2}dx.
\end{equation}
Based on the above facts, we now establish the proof of Theorem \ref{pro1}.
\vskip 0.05truein
\noindent{\bf Proof of Theorem \ref{pro1}.} Let $\{u_n\}\subset H^{s}(\R^N)\backslash\{0\}$ be a minimizing sequence for \eqref{a1}, i.e.
\begin{equation}
I(u_n)\rightarrow m:=\inf\limits_{u\in H^{s}(\R^N)\backslash\{0\}}I(u) \quad \mbox{as} \ \ \ n\rightarrow\infty.
\end{equation}
In view of \eqref{0A}-\eqref{2A} and the fact that $I(|u_n|)\leq I(u_n)$, we shall suppose that $u_n\geq0$ is radially decreasing for all $n$. Moreover, $I$ is invariant under the scaling, then we can always normalize $u_n$ such that
\begin{equation}\label{a3}
\|(-\Delta)^{\frac{s}{2}}u_n\|_{L^2}=\|u_n\|_{L^2}=1\ \ \ \mbox{for all}\ \ \ n.
\end{equation}
Hence there exists $u_*\in H^{s}(\R^N)$ such that, up to a subsequence, $u_n\rightharpoonup u_*\geq0$ weakly in $H^{s}(\R^N)$ and
\begin{equation}\label{a4}
\|(-\Delta)^{\frac{s}{2}}u_*\|_{L^2}\leq 1 \ \ \ \mbox{and}\ \ \ \|u_*\|_{L^2}\leq 1.
\end{equation}
By local compactness embedding, passing to a subsequence if necessary, we may assume that
$$ u_{n}\rightarrow u_*\,\ \hbox{strongly in}\,\ L_{loc}^{q}(\R^{N}),\,\ 2\leq q<2_s^* ,$$
where $2_{s}^{*}=\frac{2N}{N-2s}$ if $N> 2s$ and $2_s^*=+\infty$ if $N\leq 2s$.
On the other hand, for any $t\in (\frac{N}{N-b},\infty)$ and $R>0$, note that any
function $f\in L^1(\R^N)\cap L^t(\R^N)$ satisfies
\begin{align}\label{02.4}
\inte f|x|^{-b}dx
\leq& \|f\|_{L^{t}(B_R(0))}\big\||x|^{-b}\big\|_{L^{\bar t}(B_R(0))}+\frac{1}{R^b}\|f\|_{L^{1}(\R^N)} \nonumber\\
\leq& C(R)\|f\|_{L^{t}(B_R(0))}+\frac{1}{R^b}\|f\|_{L^{1}(\R^N)},
\end{align}
where $\bar t\!=\!\frac{t}{t-1}$ satisfies $1\!<\!\bar t\!<\!\frac{N}{b}$. Therefore, taking $f_n\!=\!|u_{n}(x)|^{2+2\beta^2}\!-\!|u_*(x)|^{2+2\beta^2}$, then from the Lemma \ref{A.111} in the Appendix, we have $f_n\to 0$ in $L^1((B_R(0)))\cap L^t((B_R(0)))$ for $t\in\big[1,\frac{N^2}{(N-2s)(N+2s-b)}\big)$ if $N>2s$; $t\in [1,\infty)$ if $N\leq 2s$. Let $R\rightarrow\infty$ in \eqref{02.4}, it follows that
\begin{equation}\label{a5}
\lim_{n\rightarrow\infty}\int_{\R^{N}}|x|^{-b}|u_{n}(x)|^{2+2\beta^2}dx=\int_{\R^{N}}|x|^{-b}|u_*(x)|^{2+2\beta^2}dx,
\end{equation}
we then conclude that
\begin{equation}\label{a6}
m= \lim_{n\rightarrow\infty}I(u_n)= \lim_{n\rightarrow\infty}\frac{1}{J(u_n)}\geq I(u_*)\geq m,
\end{equation}
this implies that $I(u_*)=m$ and $\|(-\Delta)^{\frac{s}{2}}u_*\|_{L^2}=\|u_*\|_{L^2}=1$, i.e. $u_n\rightarrow u_*$ strongly in $H^s(\R^N)$ and $u_*\not\equiv0$.
Since $u_*$ is a minimizer of \eqref{a1}, by variational principle, $u_*$ is a solution of the following Euler-Lagrange equation
\begin{equation}\label{a7}
(-\Delta)^s u_*+\beta^2u_*-m(1+\beta^2)|x|^{-b}u_*^{1+2\beta^2}=0.
\end{equation}
Set $Q(x)=\lambda u_*(\mu x)$, where $\lambda$ and $\mu$ satisfy the following
\begin{equation*}
\lambda=\frac{m(1+\beta^2)^{\frac{N}{4s-2b}}}{\beta^{\frac{N}{2s}}}\ \ \ \mbox{and}\ \ \ \mu=\beta^{-\frac{1}{s}}.
\end{equation*}
By some calculations, we deduce that $Q(x)$ is also a minimizer satisfying \eqref{Eq} and $m=\frac{\|Q\|^{2\beta^2}_{L^2}}{1+2\beta^2}$. Moreover, we derive from \eqref{Eq} and \eqref{a1} that
\begin{equation}\label{DS1}
\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} Q|^{2}dx=\frac{1}{\beta^2}\int_{\R^{N}}|Q|^{2}dx=\frac{1}{1+\beta^2}\int_{\R^{N}}|x|^{-b}|Q|^{2+2\beta^2}dx.
\end{equation}
We now give the decay estimate of $Q$. Recall from \cite [Proposition 5]{RS} that
\begin{equation}\label{Z1}
|Q(x)|\leq C|x|^{-N},\ \ |\nabla Q(x)|\leq C|x|^{-N-1}\ \ \ \mbox{for}\ \ \ |x|>1\ \ \mbox{and}\ \ \ Q(x)\in C^{1}(\R^N\backslash \{0\}).
\end{equation}
We shall deduce a more precise attenuation estimate of $Q$. Rewrite the equation \eqref{Eq} by
\begin{equation}\label{Eq2}
(-\Delta)^sQ+\big(1-|x|^{-b}Q^{2\beta^2}\big)Q=0,
\end{equation}
due to the decay estimate \eqref{Z1}, there exists a $R>0$ such that
\begin{equation}\label{Z2}
(-\Delta)^sQ+\frac{1}{2}Q\leq 0\ \ \ \mbox{in}\ \ B^c_{R}.
\end{equation}
We then claim that $Q(x)\leq C|x|^{-N-2s}$ in $B^c_{R}$. Inspired by \cite{FL,FLS}, we prove it by the comparison argument as follows. Applying Lemma \ref{G}, one can obtain that there exists a positive $c>0$ such that $G_{\frac{1}{2}}\geq c>0$ for $|x|\leq R$. On the other hand, recall from \cite [Proposition 4] {RS} that $Q(x)\in L^{\infty}$. Choosing $M=\|Q\|_{L^{\infty}}c^{-1}$, it holds
\begin{equation}\label{Z3}
Q(x)\leq \|Q\|_{L^{\infty}}=cM\leq M G_{\frac{1}{2}}\ \ \ \mbox{in}\ \ B_R.
\end{equation}
Next, we define the function
\begin{equation}\label{Z4}
v(x)=M G_{\frac{1}{2}}(x)-Q(x),
\end{equation}
follow \eqref{Z1}, \eqref{Z3} and Lemma \ref{G}, we deduce that $v\geq 0$ in $B_R$, $v(x)\rightarrow 0$ as $|x|\rightarrow\infty$ and $v\in C(\R\backslash \{0\})$.
We now prove that $v\geq0$ in $B_R^c$ as well. On the contrary, suppose that there exists $x\in B_R^c$ such that $v(x)<0$, since $v(x)\rightarrow 0$ as $|x|\rightarrow\infty$ and $v\geq 0$ in $B_R$, we deduce that $v$ attains its global minimum at some point $x_0\in B_R^c$ with $v(x_0)<0$, using the singular integral expression for $(-\Delta)^{s}$, we then deduce that
\begin{equation}\label{Z5}
((-\Delta)^{s}v)(x_0)<0\ \ \mbox{and}\ \ \ (-\Delta)^{s}v(x_0)+\frac{1}{2}v(x_0)<0.
\end{equation}
On the other hand, since $G_{\frac{1}{2}}$ satisfies $(-\Delta)^{s}G_{\frac{1}{2}}+\frac{1}{2}G_{\frac{1}{2}}=\delta_0$ in $\R^N$, this together with \eqref{Z2} further implies that
\begin{equation}\label{Z6}
(-\Delta)^{s}v(x)+\frac{1}{2}v(x)\geq 0\ \mbox{in}\ \ B_R^c,
\end{equation}
which contradicts \eqref{Z5}, we then derive that $v\geq 0$ in $B_R^c$, by Lemma \ref{G} and the definition of $v$, we conclude that
\begin{equation}\label{Z7}
|Q|\leq M G_{s,\frac{1}{2}}\leq \frac{C}{|x|^{N+2s}}\ \ \mbox{for any}\ \ x\in B_R^c.
\end{equation}
This combining with the fact $Q(x)\in L^{\infty}$ further implies that \eqref{ds} holds true.
Finally, we prove that $Q(x)>0$. Since $Q\geq 0$ and $Q\not\equiv 0$ solves the equation \eqref{Eq}, based on Lemma \ref{G}, using a similar argument to that in \cite{MZ}, we deduce that $Q(x)>0$. The Theorem \ref{pro1} is therefore complete.\qed
\section{Existence of minimizers}
This section is devoted to proving Theorems \ref{th1} and \ref{th2} with regard to the existence and nonexistence of minimizers for the problem (\ref{e(a)}). Motivated by \cite{GR}, we first introduce the following compactness lemma \cite[Lemma 3.2]{C}.
\begin{lem}\label{lem2.1}
Assume $V(x)\in L^{\infty}_{loc}(\R^{N})$ and $\lim_{|x|\rightarrow\infty}V(x)=\infty$, then the embedding $\mathcal{H}\hookrightarrow L^{q}(\R^{N})$ is compact for $2\leq q <2_{s}^{*}$.
\end{lem}
Due to the nonlocal nature of the operator $(-\Delta)^{s}$, in order to prove Theorems \ref{th1} and \ref{th2}, we shall also estimate the Gagliardo (semi) norm of $Q_\tau$
\begin{equation}\label{c01}
Q_{\tau}(x)=\varphi\big(\frac{x}{\tau}\big)Q(x),
\end{equation}
where $Q(x)$ satisfies \eqref{Eq}, $\varphi\in C_{0}^{\infty}(\R^{N})$ is a nonnegative cut-off function satisfying $\varphi(x)=1$ if $|x|\leq1$ and $\varphi(x)=0$ if $|x|>2$. Being inspirited by \cite[Proposition 21]{SV}, we then establish the following Lemma.
\begin{lem}\label{lem2.2}
For any $s\in(\frac{1}{2},1)$, $N> 2s$ and $Q_\tau(x)$ is defined by \eqref{c01}. Then we have the following estimate:
\begin{equation}\label{c2}
\iint_{\R^{2N}}\frac{|Q_{\tau}(x)-Q_{\tau}(y)|^2}{|x-y|^{N+2s}}dxdy\leq \iint_{\R^{2N}}\frac{|Q(x)-Q(y)|^2}{|x-y|^{N+2s}}dxdy+O(\tau^{-4s})\ \ \ \mbox{as}\ \ \tau\rightarrow\infty.
\end{equation}
\end{lem}
Since the proof of Lemma \ref{lem2.2} is rather long and standard, we leave it to the Appendix for simplicity.
Based on Lemmas \ref{lem2.1} and \ref{lem2.2}, applying the Gagliardo-Nirenberg inequality (\ref{GN}), we give the prove of Theorems \ref{th1} and \ref{th2}.
\vskip 0.1truein
\noindent\textbf{Proof of Theorem \ref{th1}.}
(1). Firstly, we prove that $e(a)$ has at least one minimizer for any $0< a< a^{\ast}=\|Q\|^{2\beta^2}_{2}$.
Indeed, for any fixed $0< a<a^{\ast}$ and $u\in \mathcal{H}$ with $\|u\|_{L^2(\R^N)}=1$, we derive from the assumption $(V_1)$ and the Gagliardo-Nirenberg inequality (\ref{GN}) that
\begin{align}\label{Eu}
E_{a}(u)&=\int_{\R^{N}}(|(-\Delta)^{\frac{s}{2}}u(x)|^{2}+V(x)|u(x)|^{2})dx-\frac{a}{1+\beta^2}\int_{\R^{N}}|u(x)|^{2+2\beta^2}|x|^{-b}dx \nonumber\\
&\geq(1-\frac{a}{a^*})\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} u(x)|^{2}dx+\int_{\R^{N}}V(x)|u(x)|^{2}dx \nonumber\\
&\geq(1-\frac{a}{a^*})\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} u(x)|^{2}dx\geq 0.
\end{align}
This implies that $e(a)\geq0$ for $0<a<a^*$.
Then we can choose a minimizing sequence $\{u_{n}\}\!\subset\!\mathcal{H}$ satisfying $\|u_{n}\|_{2}\!=\!1$ and $\lim\limits_{n\rightarrow\infty}\!\!E_{a}(u_{n})\!\!=\!\!e(a)$. Due to (\ref{Eu}), we obtain that \!$\int_{\R^{N}}\!|(-\Delta)^{\frac{s}{2}} u_{n}(x)|^{2}dx$ and \!$\int_{\R^{N}}\!\!V(x)|u_{n}|^{2}dx$ are bounded uniformly for $n$. Following Lemma \ref{lem2.1}, passing to a subsequence if necessary, we may assume that
$$u_{n}\rightharpoonup u\,\ \hbox{weakly in} \,\ \mathcal{H},\,\ u_{n}\rightarrow u\,\ \hbox{strongly in}\,\ L^{q}(\R^{N}),\,\ 2\leq q<2_s^* $$
for some $u\in \mathcal{H}$.
Thus we deduce that $\int_{\R^{N}}|u(x)|^{2}dx=1$.
For the nonlinear term, using a similiar argument to \eqref{a5}, we have
\begin{equation}\label{2.1}
\lim_{n\rightarrow\infty}\int_{\R^{N}}|x|^{-b}|u_{n}(x)|^{2+2\beta^2}dx=\int_{\R^{N}}|x|^{-b}|u(x)|^{2+2\beta^2}dx.
\end{equation}
Consequently, by weak lower semicontinuity, we deduce that
\begin{equation*}
e(a)=\lim_{n\to\infty}E_{a}(u_n)\\ \geq E_{a}(u)\geq e(a).
\end{equation*}
Therefore, $u$ must be a minimizer of $e(a)$ and Theorem \ref{th1} (1) is proved.
(2). We next show that there is no minimizer for $e(a)$ as $a>a^{\ast}$.
Let $\varphi\in C_{0}^{\infty}(\R^{N})$ be a nonnegative cut-off function satisfying $\varphi(x)=1$ if $|x|\leq1$, and $\varphi(x)=0$ if $|x|>2$. Set for all $\tau>0$,
\begin{equation}\label{st}
u_{\tau}(x)=A_{\tau}\frac{\tau^{\frac{N}{2}}}{\|Q\|_{2}}\varphi(x)Q(\tau x)=A_{\tau}\frac{\tau^{\frac{N}{2}}}{\|Q\|_{2}} Q_{\tau}(\tau x),
\end{equation}
where $A_{\tau}>0$ is chosen so that $\int_{\R^{N}}|u_{\tau}(x)|^{2}dx=1$ and $Q_{\tau}(x)$ is defined by \eqref{c01}. By scaling, we deduce from the polynomial decay of $Q$ in (\ref{ds}) that
\begin{equation}\label{A}
\frac{1}{A^{2}_{\tau}}=\frac{1}{\|Q\|^{2}_{2}}\int_{\R^{N}}Q^{2}(x)\varphi^{2}(\frac{x}{\tau })=1+O(\tau^{-N-4s}) \ \ \mbox{as}\ \ \tau\rightarrow\infty.
\end{equation}
According to (\ref{DS}), (\ref{ds}) and Lemma \ref{lem2.2}, we also obtain that
\begin{align}\label{Gj}
&\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} u_{\tau}(x)|^{2}dx-\frac{a}{1+\beta^2}\int_{\R^{N}}|x|^{-b}u_{\tau}^{2+2\beta^2}dx
\nonumber\\=&\frac{\tau^{2s}A^{2}_{\tau}}{\|Q\|^{2}_{2}}\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} Q_{\tau}|^{2}dx-\frac{a}{1+\beta^2}\int_{\R^{N}}|x|^{-b}u_{\tau}^{2+2\beta^2}dx
\nonumber\\ \leq &\frac{\tau^{2s}A^{2}_{\tau}}{\|Q\|^{2}_{2}}\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} Q|^{2}dx-\frac{a}{1+\beta^2}\frac{\tau^{2s}A^{2+2\beta^2}_{\tau}}{\|Q\|^{2+2\beta^2}_{2}}\int_{\R^{N}}|x|^{-b}Q(x)^{2+2\beta^2}dx+O(\tau^{-2s})
\nonumber\\=&\frac{\tau^{2s}A^{2}_{\tau}}{\|Q\|^{2}_{2}}\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} Q|^{2}dx-\frac{a}{1+\beta^2}\frac{\tau^{2s}A^{2+2\beta^2}_{\tau}}{\|Q\|^{2+2\beta^2}_{2}}(1+\beta^2)\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} Q|^{2}dx+O(\tau^{-2s})
\nonumber\\=&\frac{\tau^{2s}}{\|Q\|^{2}_{2}}\big(1-\frac{a}{a^*}\big)\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} Q|^{2}dx+O(\tau^{-2s})\ \ \mbox{as}\ \ \ \tau\rightarrow\infty.
\end{align}
On the other hand, since the function $V(x)\varphi^{2}(x)$ is bounded and has compact support, it follows from \cite[Theorem 1.8]{LE} that
\begin{equation}\label{jx}
\lim\limits_{\tau\rightarrow\infty}\int_{\R^{N}}V(x)|u_{\tau}(x)|^{2}dx=V(0).
\end{equation}
In view of \eqref{Gj} and \eqref{jx}, we obtain
\begin{align}\label{zh}
e(a)&\leq E_{a}(u_{\tau}(x)) \nonumber\\
&=\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} u_{\tau}(x)|^{2}dx-\frac{a}{1+\beta^2}\int_{\R^{N}}|x|^{-b}u^{2+2\beta^2}_{\tau}(x)dx+\int_{\R^{N}}V(x)|u_{\tau}(x)|^{2}dx \nonumber\\
&=\frac{\tau^{2s}}{\|Q\|^{2}_{2}}(1-\frac{a}{a^*})\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} Q|^{2}dx+\int_{\R^{N}}V(x)|u_{\tau}(x)|^{2}dx+O(\tau^{-2s})\nonumber\\
&\quad\longrightarrow-\infty\quad\quad\hbox{as}\quad \tau\to\infty.
\end{align}
Therefore, if $a>a^{\ast}$, $e(a)=-\infty$, which implies the nonexistence of minimizers as $a>a^{\ast}$.
Finally, following Theorem \ref{th1} (1) and the Gagliardo-Nirenberg inequality \eqref{GN}, it is obviously that $e(a)\!>\!0$ for $0\!<\!a\!<\!a^*$. This completes the proof of Theorem \ref{th1}.\qed
\vskip 0.1truein
\noindent\textbf{Proof of Theorem \ref{th2}.}
(1). Following the Gagliardo-Nirenberg inequality \eqref{GN}, one can check that $e(a^*)\geq 0$ is bounded from below, and thus there exists a minimizing sequence $\{u_{n}\}$ of $e(a^{\ast})$ such that $e(a^*)=\lim_{n\to\infty}E_a(u_n)$.
To prove Theorem \ref{th2} (1), similar to the proof of Theorem \ref{th1}, it is enough to prove that $\{u_{n}\}$ is bounded uniformly in $\mathcal{H}$. On the contrary, suppose that $\{u_{n}\}$ is unbounded in $\mathcal{H}$, then there exists a subsequence of $\{u_{n}\}$, still denoted by $\{u_{n}\}$, such that $\|u_{n}\|_{\mathcal{H}}\rightarrow\infty$ as $n\rightarrow\infty$. Moreover, by the Gagliardo-Nirenberg inequality, we have
\begin{equation}\label{V}
\int_{\R^{N}}V(x)|u_{n}(x)|^{2}dx\leq E_{a^{\ast}}(u_{n})\leq e(a^{\ast})+1.
\end{equation}
Since $\{u_{n}\}$ is unbounded in $\mathcal{H}$, taking a subsequence if necessary, we have
\begin{equation}\label{U}
\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} u_{n}(x)|^{2}dx\rightarrow\infty\,\ \hbox{as}\,\ n\to\infty.
\end{equation}
Now let
\begin{equation}\label{wq}
\varepsilon^{-2s}_{n}:=\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} u_{n}(x)|^{2}dx,
\end{equation}
it then follows from (\ref{U}) that $\varepsilon_{n}\rightarrow 0$ as $n\rightarrow\infty$. We next define the normalized function
\begin{equation}\label{omg}
w_{n}(x):=\varepsilon^{\frac{N}{2}}_{n}u_{n}(\varepsilon_{n}x)
\end{equation}
such that
\begin{equation}\label{2gj}
\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} w_{n}(x)|^{2}dx=\int_{\R^{N}}| w_{n}(x)|^{2}dx=1.
\end{equation}
Therefore $w_n$ is bounded uniformly for $n$ in $H^s(\R^N)$, and Sobolev embedding theorem implies that passing to a subsequence if necessary
\begin{equation}\label{s1}
w_{n}\rightharpoonup w_0\,\ \hbox{weakly in} \,\ H^s(\R^N),\,\ w_{n}\rightarrow w_0\,\ \hbox{strongly in}\,\ L_{loc}^{q}(\R^{N}),\,\ 2\leq q<2_s^*.
\end{equation}
Next, we claim that
\begin{equation}\label{2.2}
\lim_{n\to\infty}w_n=w_0\quad\hbox{strongly in $H^s(\R^N)$},
\end{equation}
where $w_0$ is an optimizer of the Gagliardo-Nirenberg inequality \eqref{GN}.
Actually, by the definition of $w_n$, we obtain from the Gagliardo-Nirenberg inequality (\ref{GN}) that
\begin{align}\label{wgx}
C&\geq e(a^*)=\lim_{n\rightarrow\infty}E_{a^*}(u_{n})
\nonumber\\&=\lim_{n\rightarrow\infty}\Big\{\int_{\R^{N}}\Big(|(-\Delta)^{\frac{s}{2}} u_{n}|^{2}-\frac{a^*}{1+\beta^2}|x|^{-b}u_{n}^{2+2\beta^2}+V(x)|u_{n}(x)|^{2}\Big)dx\Big\}
\nonumber\\
&=\lim_{n\rightarrow\infty}\Big\{\frac{1}{\varepsilon^{2s}_{n}}\int_{\R^{N}}\Big[|(-\Delta)^{\frac{s}{2}} w_{n}|^{2}-\frac{a^{\ast}}{1+\beta^2}|x|^{-b}w_{n}^{2+2\beta^2}\Big]dx+\int_{\R^{N}}V(\varepsilon_{n}x)|w_{n}(x)|^{2}dx\Big\} \nonumber\\
&\geq 0.
\end{align}
Therefore, we derive from \eqref{2gj}, the fact $\eps_n\to 0$ as $n\to\infty$ and above that
\begin{equation}\label{wnp}
\lim_{n\to\infty}\frac{a^{\ast}}{1+\beta^2}\int_{\R^{N}}|x|^{-b}w_{n}^{2+2\beta^2}(x)dx=\lim_{n\to\infty}\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} w_{n}(x)|^{2}dx=1.
\end{equation}
On the other hand, combining \eqref{02.4} with Lemma \ref{A.111} in the Appendix, and let $R\rightarrow\infty$ in \eqref{02.4} we have
\begin{equation}\label{eq2.20}
\frac{a^{\ast}}{1+\beta^2}\int_{\R^{N}}|x|^{-b}w_{0}^{2+2\beta^2}(x)dx=\lim_{n\to\infty}\frac{a^{\ast}}{1+\beta^2}\int_{\R^{N}}|x|^{-b}w_{n}^{2+2\beta^2}(x)dx=1.
\end{equation}
which further implies $w_{0}\not\equiv0$.
Moreover, by the Gagliardo-Nirenberg inequality (\ref{GN}) and the fact that $w_n\rightharpoonup w_0$ weakly in $H^s(\R^N)$, we have
\begin{align}\label{wgx1}
0&= \lim_{n\rightarrow\infty}\varepsilon_n^2e(a^*)
\nonumber\\
&\geq\lim_{n\rightarrow\infty}\int_{\R^{N}}\Big[|(-\Delta)^{\frac{s}{2}} w_{n}|^{2}-\frac{a^{\ast}}{1+\beta^2}|x|^{-b}w_{n}^{2+2\beta^2}\Big]dx
\nonumber\\&\geq\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} w_{0}(x)|^{2}dx-\frac{a^{\ast}}{1+\beta^2}\int_{\R^{N}}|x|^{-b}w_{0}^{2+2\beta^2}(x)dx
\nonumber\\&\geq\Big[1-\Big(\int_{\R^{N}}w^2_{0}(x)dx\Big)^{\beta^2}\Big]\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} w_{0}(x)|^{2}dx.
\end{align}
Since $\|w_0\|_{L^2(\R^N)}\leq 1$, the above inequality implies that
\begin{equation}\label{2.3}
\int_{\R^{N}}|w_{0}(x)|^{2}dx\!=\!1,\,\ \int_{\R^{N}}|(-\Delta)^{\frac{s}{2}} w_{0}(x)|^{2}dx\!=\!\frac{a^{\ast}}{1+\beta^2}\int_{\R^{N}}|x|^{-b}w_{0}^{2+2\beta^2}(x)dx\!=\!1.
\end{equation}
In view of the above facts, by the norm preservation, we conclude that $w_{n}$ converges to $w_{0}$ strongly in $H^{s}(\R^{N})$, where $w_0$ is an optimizer of the Gagliardo-Nirenberg inequality \eqref{GN} and \eqref{2.2} is thus proved.
Based on \eqref{2.2}, applying Fatou's lemma and Gagliardo-Nirenberg inequality \eqref{GN}, we derive that
\begin{equation}\label{md1}
e(a^{\ast})\geq\lim_{n\rightarrow\infty}\int_{\R^{N}}V(\varepsilon_{n} x)|w_{n}(x)|^{2}dx\geq \int_{\R^{N}}V(0)|w_{0}(x)|^{2}dx=V(0),
\end{equation}
which contradicts the assumption $e(a^{\ast})<V(0)$. Hence the minimizing sequence $\{u_{n}\}$ of $e(a^*)$ is bounded uniformly in $\mathcal{H}$ and Theorem \ref{th2} (1) is proved.
(2). We next consider the case $a=a^{\ast}$ and $V(0)=0$. Note that $e(a^*)\geq 0$. On the other hand, we can use the same test function as that in (\ref{st}) to derive $e(a^{\ast})\leq V(0)=0$, and thus $e(a^{\ast})=0$. Now suppose that there exists a minimizer $u\in\mathcal{H}$ satisfying $\inte |u|^2dx=1$ at $a=a^{\ast}$. Then we have
\begin{equation}\label{1}
\int_{\R^{N}}V(x)|u(x)|^{2}dx=0=\inf\limits_{x\in\R^{N}}V(x),
\end{equation}
as well as
\begin{equation}\label{2}
\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}}u(x)|^{2}dx=\frac{a^{\ast}}{1+\beta^2}\int_{\R^{N}}|x|^{-b}|u(x)|^{2+2\beta^2}dx.
\end{equation}
This is a contradiction, since the first equality implies that $u$ has compact support, while we deduce from the second that $u>0$ is an optimizer of $\eqref{GN}$ and solves the equation \eqref{Eq}. Moreover, taking the same test function as in (\ref{st}), we have $V(0)=\inf_{x\in\R^{N}}V(x)\leq\lim_{a\nearrow a^{\ast}}e(a)\leq V(0)$ and hence $\lim_{a\nearrow a^{\ast}}e(a)=V(0)=e(a^*)$. This completes the proof of Theorem \ref{th2}.\qed
\section{Mass concentration as $a\nearrow a^{\ast}$}
In this section, we shall prove Theorem \ref{th3}, which focuses on the concentration behavior of nonnegative minimizers of $e(a)$ as $a\nearrow a^{\ast}$. Let $u_{a}$ be a nonnegative minimizer of $e(a)$, by variational theory, $u_{a}$ satisfies the following Euler-Lagrange equation
\begin{equation}\label{EL}
(-\Delta)^{s} u_{a}(x)+V(x)u_{a}(x)=\mu_a u_{a}(x)+a u_{a}^{1+2\beta^2}(x)|x|^{-b}\quad \mbox{in}\ \ \R^{N},
\end{equation}
where $\mu_{a}\in\R$ is a suitable Lagrange multiplier satisfying
\begin{equation}\label{2.8}
\mu_a=e(a)-\frac{a\beta^2}{1+\beta^2}\inte |x|^{-b}|u_a|^{2+2\beta^2}dx.
\end{equation}
Define
\begin{equation}\label{yp}
\varepsilon_{a}:=\Big(\int_{\R^{N}}|(-\Delta)^{\frac{s}{2}}u_{a}|^{2}dx\Big)^{-\frac{1}{2s}},
\end{equation}
and
\begin{equation}\label{xpa}
w_{a}(x)=\varepsilon^{\frac{N}{2}}_{a}u_{a}(\varepsilon_{a}x).
\end{equation}
Based on the above facts, we then complete the proof of Theorem \ref{th3}.
\vskip 0.1truein
\noindent\textbf{Proof of Theorem \ref{th3}.}
we first claim that $\varepsilon_{a}\rightarrow 0$ as $a\nearrow a^{\ast}$.
Actually, suppose on the contrary, then there exists a sequence $\{a_{k}\}$ satisfies $a_{k}\nearrow a^{\ast}$ as $k\rightarrow\infty$ such that the sequence $\{u_{a_{k}}\}$ is bounded in $H^s(\R^N)$ uniformly for $k$. By the Gagliardo-Nirenberg inequality, we obtain that $\inte V(x)|u_{a_k}|^2dx\leq e(a_k)\leq C$ uniformly for $k$ and hence $\{u_{a_{k}}\}$ is bounded uniformly in $\mathcal{H}$.
Following Lemma \ref{lem2.1}, there exists a subsequence, still denoted by $\{a_{k}\}$, of $\{a_{k}\}$ and $u_{0}\in\mathcal{H}$ such that
$${u_{a_{k}}}\rightharpoonup u_{0}\,\ \hbox{weakly in}\,\ \mathcal{H}\,\ \hbox{and}\,\ {u_{a_{k}}}\rightarrow u_{0}\,\ \hbox{strongly in}\,\ L^{q}(\R^{N})\,(2\leq q <2_s^*).$$
Combining the above convergence with \eqref{2.1} gives that
\begin{equation*}
0=e(a^{\ast})\leq E_{a^{\ast}}(u_{0})\leq \lim\limits_{k\rightarrow\infty}E_{a_{k}}(u_{a_{k}})=\lim\limits_{k\rightarrow\infty}e(a_{k})=0,
\end{equation*}
and thus $u_{0}$ is a minimizer of $e(a^{\ast})$, which however contradicts Theorem \ref{th2} (2). Therefore we conclude that $\varepsilon_{a}\rightarrow 0$ as $a\nearrow a^{\ast}$.
We then prove that
\begin{equation}\label{2.5}
w_{a}\rightarrow w_0\,\ \hbox{strongly in}\,\ H^s(\R^N)\,\ \hbox{as}\,\ a\nearrow a^*.
\end{equation}
Note from Theorem \ref{th2} (2) that $0=e(a^*)=\lim_{a\nearrow a^*}e(a)$, thus $\{u_a\}$ is also a minimizing sequence of $e(a^*)$. Moreover, we obtain from \eqref{yp} and \eqref{xpa} that
\[
\inte |(-\Delta)^{\frac{s}{2}} w_a|^2dx=\inte |w_a|^2dx=1\,\ \hbox{for any $a\nearrow a^*$.}
\]
Hence $w_a$ is bounded in $H^s(\R^N)$ uniformly for $a$, and passing to a subsequence if necessary
$$w_{a}\rightharpoonup w_0\,\ \hbox{weakly in} \,\ H^s(\R^N),\,\ w_{a}\rightarrow w_0\,\ \hbox{strongly in}\,\ L_{loc}^{q}(\R^{N}),\,\ 2\leq q<2_s^*. $$
Note that the proof of the claim $\eqref{2.2}$ does not rely on the assumption $0\leq e(a^*)< V(0)$. Thus, the same argument of proving \eqref{2.2} yields that \eqref{2.5} holds true.
Next, we prove that
\begin{equation}\label{2.6}
w_a(x)\rightarrow w_0\,\ \hbox{strongly in}\,\ L^\infty(\R^N)\,\ \hbox{as}\,\ a\nearrow a^*.
\end{equation}
Recall from \eqref{EL} and \eqref{xpa} that $w_a$ satisfies the following equation
\begin{equation}\label{2.9}
(-\Delta )^sw_a+\eps_a^{2s}V(\eps_ax)w_a=\mu_a\eps_a^{2s}w_a+a w_a^{1+2\beta^2} |x|^{-b}\quad \hbox{in}\,\ \R^N,
\end{equation}
where $\mu_a\in\R$ is a suitable Lagrange multiplier satisfying \eqref{2.8}. We derive from \eqref{2.3} and \eqref{2.8} that
\begin{align}\label{2.10}
\eps_a^{2s}\mu_a&=\eps_a^{2s}e(a)-\eps_a^{2s}\frac{a\beta^2}{1+\beta^2}\inte |x|^{-b}|u_a|^{2+2\beta^2}dx
\nonumber\\
&=\eps_a^{2s}e(a)-\frac{a\beta^2}{1+\beta^2}\inte |x|^{-b}|w_a|^{2+2\beta^2}dx\to -\beta^2\,\ \hbox{as}\,\ a\nearrow a^*.
\end{align}
Hence for $a\nearrow a^*$, we have
\begin{equation}\label{R1}
(-\Delta)^s w_{a}-c(x)w_{a}(x)\leq0\ \ \mbox{in}\ \ \R^N,\ \ \mbox{where}\ \ c(x)=aw^{2\beta^2}_{a}|x|^{-b}.
\end{equation}
Based on the above facts, we shall prove \eqref{2.6} through the following three steps.
\noindent{\em Step 1.} We prove $w_a(x)\in L^{\infty}$.
In fact, using a Moser iteration argument \cite{M1}. For any $L>0$ and $\alpha>0$, let $\gamma(t)=tt_L^{2\alpha}$ for $t>0$, where $t_L=\min\{t,L\}$. Note that $\gamma(t)$ is a nondecreasing function, then for any $a,b\geq0$, we have
\begin{equation*}
(b-a)(\gamma(b)-\gamma(a))\geq0.
\end{equation*}
Define
\begin{equation*}
\Gamma(t)=\int_{0}^{t}(\gamma'(\tau))^{\frac{1}{2}}d\tau,
\end{equation*}
for any $a,b\geq0$ with $a<b$, applying the Schwartz inequality, we deduce that
\begin{equation}\label{2.7}
\begin{split}
(b-a)(\gamma(b)-\gamma(a))&=(b-a)\int_{a}^{b}\gamma'(t)dt\\
&=(b-a)\int_{a}^{b}(\Gamma'(t))^2dt\\
&\geq \Big(\int_{a}^{b}\Gamma'(t)dt\Big)^2=\big(\Gamma(b)-\Gamma(a)\big)^2.
\end{split}
\end{equation}
Similarly, we can verify that \eqref{2.7} also holds true for any $a\geq b$, this further implies that
\begin{equation*}
(b-a)(\gamma(b)-\gamma(a))\geq \big|\Gamma(b)-\Gamma(a)\big|^2\ \ \mbox{for any}\ \ a, b\geq 0.
\end{equation*}
In particular, by the definition of $\gamma(t)$, we then obtain that
\begin{equation}\label{02.9}
\big|\Gamma(w_a(x))-\Gamma(w_a(y))\big|^2\leq (w_a(x)-w_a(y))\big((w_a(w_a)_{L}^{2\alpha})(x)-(w_a(w_a)_{L}^{2\alpha})(y)\big),
\end{equation}
taking $\gamma(w_a)=w_a(w_a)_{L}^{2\alpha}\in \mathcal{H}$ as a test function in \eqref{R1}, it then follows from \eqref{02.9} that
\begin{equation}\label{12.9}
\begin{split}
\big[\Gamma(w_a)\big]_{s}^{2}&\leq \iint_{\R^{2N}}\frac{(w_a(x)-w_a(y))}{|x-y|^{N+2s}}\big((w_a(w_a)_{L}^{2\alpha})(x)-(w_a(w_a)_{L}^{2\alpha})(y)\big)dxdy\\
&\leq\int_{\R^N}c(x)w_a^2(w_a)_{L}^{2\alpha}(x)dx.
\end{split}
\end{equation}
On the other hand, $\Gamma(t)\geq \frac{tt_{L}^{\alpha}}{1+\alpha}$ for all $t\geq0$, applying Sobolev inequality yields that
\begin{equation}\label{c1}
\big[\Gamma(w_a)\big]_s^2\geq S_*\|\Gamma(w_a)\|^{2}_{L^{2^{*}_{s}}(\R^N)}\geq\Big(\frac{1}{1+\alpha}\Big)^{2}S_*\|w_a(w_a)_{L}^{\alpha}\|^{2}_{L^{2^{*}_{s}}(\R^N)}.
\end{equation}
This together with \eqref{12.9} further implies that
\begin{equation}\label{c2}
\Big(\frac{1}{1+\alpha}\Big)^{2}S_*\|w_a(w_a)_{L}^{\alpha}\|^{2}_{L^{2^{*}_{s}}(\R^N)}\leq \int_{\R^N}c(x)w_a^2(w_a)_{L}^{2\alpha}(x)dx=\int_{\R^N}c(x)(w_a(w_a)_{L}^{\alpha}(x))^2dx.
\end{equation}
Applying Lemma \ref{A.1}, we deduce that $c(x)\!\in\! L^{p}(\R^N)$ where $p\!\in\! \big(\frac{N}{2s},\frac{N^2}{2s(N+b-2s)}\big)$ for $N>2s$. By H\"{o}lder inequality, we obtain that
\begin{equation}\label{c3}
\int_{\R^N}c(x)(w_a(w_a)_{L}^{\alpha}(x))^2dx\leq \|c(x)\|_{L^p(\R^N)}\big\|w_a(w_a)_{L}^{\alpha}(x)\big\|^2_{L^{\frac{2p}{p-1}}(\R^N)}
\end{equation}
with $p\!\in\! \big(\frac{N}{2s},\frac{N^2}{2s(N+b-2s)}\big)$. Choose $p=\frac{N}{s}$, applying Young's inequality and interpolation inequality, we then deduce from \eqref{c2} and \eqref{c3} that
\begin{equation}\label{c4}
\begin{split}
\|uu_{L}^{\alpha}\|^{2}_{L^{2^{*}_{s}}(\R^N)}\leq& C(1+\alpha)^2\|c(x)\|_{L^{\frac{N}{s}}(\R^N)}\Big(\varepsilon\|w_a(w_a)_{L}^{\alpha}(x)\|^2_{L^{2}(\R^N)}+\frac{1}{4\varepsilon}\|w_a(w_a)_{L}^{\alpha}(x)\|^2_{L^{2^{*}_{s}}(\R^N)}\Big)\\
=&C(1+\alpha)^2\varepsilon\|c(x)\|_{L^{\frac{N}{s}}(\R^N)}\|w_a(w_a)_{L}^{\alpha}(x)\|^2_{L^{2^{*}_{s}}(\R^N)}\\
&+\frac{C}{4\varepsilon}(1+\alpha)^2\|c(x)\|_{L^{\frac{N}{s}}(\R^N)}\|w_a(w_a)_{L}^{\alpha}(x)\|^2_{L^{2}(\R^N)},
\end{split}
\end{equation}
take $\varepsilon>0$ such that
\begin{equation*}
C(1+\alpha)^2\varepsilon\|c(x)\|_{L^{\frac{N}{s}}(\R^N)}=\frac{1}{2},
\end{equation*}
it then follows from \eqref{c4} that
\begin{equation}\label{c5}
\begin{split}
\|w_a(w_a)_{L}^{\alpha}\|^{2}_{L^{2^{*}_{s}}(\R^N)}&\leq C(1+\alpha)^4\|c(x)\|_{L^{\frac{N}{s}}(\R^N)}\|w_a(w_a)_{L}^{\alpha}(x)\|^2_{L^{2}(\R^N)}\\
&:=M_{\alpha}\|w_a(w_a)_{L}^{\alpha}(x)\|^2_{L^{2}(\R^N)}.
\end{split}
\end{equation}
Now let $L\rightarrow\infty$, by the definition of $(w_a)_{L}$, we obtain
\begin{equation}\label{0c6}
\|w_{a}^{\alpha+1}\|^{2}_{L^{2^{*}_{s}}(\R^N)}\leq M_{\alpha}\|w_{a}^{\alpha+1}\|^{2}_{L^{2}(\R^N)}.
\end{equation}
Note that
\begin{equation*}
M_{\alpha}\leq C(1+\alpha)^4\leq M_{0}^{2}e^{2\sqrt{\alpha+1}},
\end{equation*}
where $M_0$ is independent of $\alpha$. This together with \eqref{0c6} further indicates that
\begin{equation}\label{c7}
\|w_a\|_{L^{2^{*}_{s}(\alpha+1)}(\R^N)}\leq M_{0}^{\frac{1}{1+\alpha}}e^{\frac{1}{\sqrt{1+\alpha}}}\|w_a\|_{L^{2(\alpha+1)}(\R^N)}.
\end{equation}
Choosing $\alpha_0=0$ and $2(\alpha_{n+1}+1)=2_s^*(\alpha_{n}+1)$, by iteration, we deduce that
\begin{equation}\label{c8}
\|w_a\|_{L^{2^{*}_{s}(\alpha_n+1)}(\R^N)}\leq M_{0}^{\sum_{i=0}^{n}\frac{1}{1+\alpha_i}}e^{\sum_{i=0}^{n}\frac{1}{\sqrt{1+\alpha_i}}}\|w_a\|_{L^{2(\alpha_0+1)}(\R^N)}.
\end{equation}
Since $1+\alpha_n=\Big(\frac{N}{N-2s}\Big)^n$, we obtain
\begin{equation}\label{c9}
\sum_{i=0}^{\infty}\frac{1}{1+\alpha_i}<\infty\ \ \ \mbox{and}\ \ \ \sum_{i=0}^{\infty}\frac{1}{\sqrt{1+\alpha_i}}<\infty,
\end{equation}
in view of the above facts, we conclude that
\begin{equation}\label{c10}
\|w_a\|_{L^\infty(\R^N)}=\lim\limits_{n\rightarrow\infty}\|w_a\|_{L^{2^{*}_{s}(\alpha_n+1)}(\R^N)}<\infty.
\end{equation}
\noindent{\em Step 2.} We claim that
\begin{equation}\label{0c12}
w_a(x)\rightarrow 0 \ \ \ \mbox{as}\ \ \ |x|\rightarrow \infty\ \ \ \mbox{and}\ \ \ a\nearrow a^*.
\end{equation}
Indeed, denote
\begin{equation}\label{c13}
g_a(x):=a w_a^{1+2\beta^2} |x|^{-b}\ \ \ \mbox{and}\ \ \ h_a(x):= g_a(x)-\varepsilon_a^{2s}V(\varepsilon_a x),
\end{equation}
we deduce from \eqref{2.9} and \eqref{2.10} that
\begin{equation}\label{0c14}
(-\Delta)^{s}w_a(x)+\eta w_a(x)=h_a(x)\ \ \ \mbox{in}\ \ \ \R^N,
\end{equation}
with $\eta=-\varepsilon_a^{2s}\mu_a >\frac{\beta^2}{2}>0$ as $a\nearrow a^*$. It then follows from \eqref{0c14} that
\begin{equation}\label{0c15}
\begin{split}
0\leq w_a(x)=G_{\eta}\ast h_a(x)&=\int_{\R^N}G_{\eta}(x-y)h_a(y)dy\\
&= \int_{\R^N}G_{\eta}(x-y)g_a(y)dy-\varepsilon_a^{2s} \int_{\R^N}G_{\eta}(x-y)V(\varepsilon_a y)dy\\
&:=B_1-B_2\leq B_1,\end{split}
\end{equation}
where the kernel $G_{\eta}(x)=\mathcal{F}^{-1}((|\xi|^{2s}+\eta)^{-1})$, recall from Lemma \ref{G} that $G_{\eta}(x)$ satisfies the following
\begin{equation}\label{c16}
G_{\eta}(x)\leq \frac{K_1}{|x|^{N+2s}}\ \ \mbox{for all} \ \ x\in \R^N\backslash \{0\}\ \ \mbox{and}\ \ \ G_{\eta}(x)\in L^q(\R^N)\ \ \mbox{for}\ \ \ q\in \Big[1,\frac{N}{N-2s}\Big).
\end{equation}
We estimate $B_1$ as follows. Motivated by \cite{AM, AV}, we define the sets
\begin{equation}\label{c17}
A_{\delta}:=\big\{y\in\R^N: |y-x|\geq \frac{1}{\delta}\big\}\ \ \ \mbox{and}\ \ \ B_{\delta}:=\big\{y\in\R^N: |y-x|< \frac{1}{\delta}\big\},
\end{equation}
then
\begin{equation}\label{c18}
\begin{split}
0\leq B_1&=\int_{A_{\delta}}G_{\eta}(x-y)g_a(y)dy+\int_{B_{\delta}}G_{\eta}(x-y)g_a(y)dy\\
&:=D_1+D_2.
\end{split}
\end{equation}
Since $w_a\in L^{\infty}(\R^N)$ and $w_a\rightarrow w_0$ in $H^s(\R^N)$, we derive that $w_a\rightarrow w_0$ in $L^{r}(\R^N)$ for all $r\in[2,\infty)$, using a similar argument to \eqref{2.1} yields that
\begin{equation}\label{c19}
g_a(x)\rightarrow a^*w_0^{1+2\beta^2}|x|^{-b}:=g(x)\ \ \ \mbox{in}\ \ \ L^{m}(\R^N)\ \ \ \mbox{with}\ \ \ \ m\in\Big[1, \frac{N}{b}\Big).
\end{equation}
In view of the above facts, applying H\"{o}lder inequality, we derive from \eqref{c16} that
\begin{equation}\label{c20}
\begin{split}
D_1&\leq K_1\int_{A_{\delta}}\frac{g_a(y)}{|x-y|^{N+2s}}dy\leq K_1 \|g_a\|_{L^2(A_{\delta})}\Big(\int_{A_{\delta}}\frac{1}{|x-y|^{2N+4s}}dy\Big)^{\frac{1}{2}}\\
&\leq K_1\delta^{2s} \|g_a\|_{L^2(A_{\delta})}\Big(\int_{A_{\delta}}\frac{1}{|x-y|^{2N}}dy\Big)^{\frac{1}{2}}\leq C \delta^{2s}.
\end{split}
\end{equation}
On the other hand,
\begin{equation}\label{c21}
D_2\leq\int_{B^{\delta}}G_{\eta}(x-y)|g_a(y)-g(y)|dy+\int_{B^{\delta}}G_{\eta}(x-y)g(y)dy.
\end{equation}
Since $\frac{b}{N}+\frac{N-2s}{N}<1$, there exist $m\in [1,\frac{N}{b})$ and $q\in[1,\frac{N}{N-2s})$ such that $\frac{1}{m}+\frac{1}{q}=1$. Applying H\"{o}lder inequality, we obtain from \eqref{c21} that
\begin{equation}\label{c22}
D_2\leq \|G_{\eta}\|_{L^q(\R^N)} \|g_a-g\|_{L^m(\R^N)}+ \|G_{\eta}\|_{L^q(\R^N)} \|g\|_{L^m(B_{\delta})},
\end{equation}
since $\|g_a-g\|_{L^m(\R^N)}\rightarrow0$ as $a\nearrow a^*$ and $\|g\|_{L^m(B_{\delta})}\rightarrow0$ as $|x|\rightarrow\infty$, for the above $\delta$, there exists $R>0$ such that
\begin{equation}\label{c23}
D_2\leq \delta\ \ \ \mbox{as}\ \ \ a\nearrow a^* \ \ \ \mbox{and}\ \ \ |x|\geq R,
\end{equation}
it then follows from \eqref{c20} that
\begin{equation}\label{c24}
B_1=\int_{\R^N}G_{\eta}(x-y)g_a(y)dy\leq C \delta^{2s}+\delta \ \ \ \mbox{as}\ \ \ a\nearrow a^* \ \ \ \mbox{and}\ \ \ |x|\geq R.
\end{equation}
Let $\delta\rightarrow0$, we deduce that $B_1\rightarrow0$ as $|x|\rightarrow\infty$ and $a\nearrow a^*$. We then derive from \eqref{0c15} that $w_a(x)\rightarrow0$ as $|x|\rightarrow\infty$ and $a\nearrow a^*$, and \eqref{0c12} is thus complete.
\noindent{\em Step 3.}
Following \eqref{ds} and \eqref{0c12}, to finish the proof of \eqref{2.6}, the rest is to show that
\begin{equation}\label{2.11}
w_a\to w_0\,\ \hbox{strongly in}\,\ L^\infty_{loc}(\R^N).
\end{equation}
Since $w_a(x)$ satisfies (\ref{2.9}), we denote
\begin{equation*}
H_a(x):=\varepsilon_a^{2s}\mu_aw_a(x)-\varepsilon_a^{2s}V(\varepsilon_ax)w_a(x)+aw^{1+2\beta^2}_{a}|x|^{-b},
\end{equation*}
so that
\begin{equation}\label{g1}
(-\Delta)^s w_a(x)=H_a(x) \ \ \mbox{in}\ \ H^s(\R^N).
\end{equation}
Because $w_a(x)$ is bounded uniformly in $H^s(\R^N)$, follow the proof of step 1, we can obtain that
\begin{equation}\label{ubl}
w_a\ \ \mbox{is bounded}\ \ \mbox{uniformly}\ \ \mbox{in} \ \ L^\infty(\R^N).
\end{equation}
Therefore, for any $r\in(1,\frac{N}{b})$, $w_{a}^{1+2\beta^2}|x|^{-b}$ is bounded in $L_{loc}^r(\R^N)$, which implies that $H_a(x)$ is bounded uniformly in $L^r_{loc}(\R^N)$. Define
\begin{equation*}
\bar{H}_a=I_sRH_a,
\end{equation*}
where $I_s$ is the Riesz potential of order $s$ and $R=DI_1$ is the vector-valued Riesz transform. Since $r\in(1,\frac{N}{b})$ and $b<2s$, there exists $\bar{r}>\frac{N}{s}$ such that $\frac{1}{r}-\frac{1}{\bar{r}}=\frac{s}{N}$ and $\| \bar{H}_a(x)\|_{L^{\bar{r}}(\R^N)}\leq C\| H_a(x)\|_{L^r(\R^N)}$, see \cite[Theorem 1.2.5]{AV}.
For any large $\bar{R}>0$, it then follows from \cite[Theorem 1.2]{SSS} that
\begin{equation}\label{wgj}
\begin{split}
\|w_a(x)\|_{W^{s,\bar{r}}(B_{\bar{R}})}
&\leq C\Big(\|w_a(x)\|_{L^{\bar{r}}(\R^N)}+\|\bar{H}_a(x)\|_{L^{\bar{r}}(\R^N)}+\|(-\Delta)^{\frac{s}{2}}w_a\|_{L^2(\R^N)}\Big)\\
&\leq C\Big(\|w_a(x)\|_{L^{\bar{r}}(\R^N)}+\|H_a(x)\|_{L^{r}(\R^N)}+\|(-\Delta)^{\frac{s}{2}}w_a\|_{L^2(\R^N)}\Big),
\end{split}
\end{equation}
where $C>0$ is independent of $a>0$. Therefore, $w_a(x)$ is also bounded in $W^{s,\bar{r}}_{loc}(\R^N)$ uniformly for $0<a<a^*$. For $\bar{r}>\frac{N}{s}$, since the embedding $W^{s,\bar{r}}(B_{\bar{R}})\hookrightarrow L^\infty(B_{\bar{R}})$ is compact, see \cite[Corollary 1.9]{BRS}, we then deduce that there exists a subsequence $\{w_{a_{k}}\}$ of $\{w_a(x)\}$ such that
\begin{equation*}
\lim\limits_{a_k\nearrow a^*}w_{a_k}(x)=\tilde{w}_0(x)\ \ \mbox{strongly in}\ \ L^\infty(B_{\bar{R}}).
\end{equation*}
In view of (\ref{2.5}) and the fact that $\bar{R}>0$ is arbitrary, we obtain that
\begin{equation}\label{lwj2}
\lim\limits_{a_k\nearrow a^*}w_{a_k}(x)=w_0\ \ \mbox{strongly in}\ \ L_{loc}^\infty(\R^N).
\end{equation}
Moreover, because the above convergence is independent of what subsequence we choose, we deduce that $w_{a}(x)\rightarrow w_0$ in $L_{loc}^{\infty}(\R^N)$ as $a \nearrow a^*$ and (\ref{2.6}) is proved in view of \eqref{0c12}. Theorem \ref{th3} is therefore complete.\qed
\section{Local uniqueness of minimizers}
This section is devoted to proving the local uniqueness of minimizers for $e(a)$. Motivated by \cite{GZ}, we prove the uniqueness of minimizers of $e(a)$ for sufficiently small $a\in[0, a^*)$. Let $\mu_1$ be the first eigenvalue of $(-\Delta)^s+V(x)$ in $\mathcal{H}$, that is
\begin{equation}\label{d1}
\mu_1=\inf\Big\{\int_{\R^N}(|(-\Delta)^{\frac{s}{2}}u|^2+V(x)u^2)dx: u\in\mathcal{H}\ \ \mbox{ and}\ \ \int_{\R^N}u^2dx=1\Big\}.
\end{equation}
Applying Lemma \ref{lem2.1}, a similar argument of \cite[Proposition 9]{SV1} gives that $\mu_1$ is simple and can be attained by nonnegative function $\phi_1\in\mathcal{H}$, where $\phi_1\geq0$ is the first eigenfunction of $(-\Delta)^s+V(x)$ in $\mathcal{H}$.
We now define
\begin{equation}\label{d2}
\mu_2=\inf\Big\{\int_{\R^N}(|(-\Delta)^{\frac{s}{2}}u|^2+V(x)u^2)dx: u\in H_1\ \ \mbox{ and}\ \ \int_{\R^N}u^2dx=1\Big\},
\end{equation}
where
\begin{equation*}
H_1=\mathrm{span}\{\phi_1\}^{\perp}=\Big\{u: u\in\mathcal{H}\ \ \mbox{ and}\ \ \int_{\R^N}u\phi_1dx=0\Big\},
\end{equation*}
then $\mu_2>\mu_1$ and $\mathcal{H}=\mathrm{span}\{\phi_1\}\oplus H_1$. Recall from \cite[Lemma A.1]{DT} that
\begin{lem}\label{lem4.1}
Suppose $V(x)$ satisfies $(V_1)$. Then we have
\begin{enumerate}
\item $\mathrm{ker}((-\Delta)^s+V(x)-\mu_1)=\mathrm{span\{\phi_1}\}$;
\item $\phi_1\notin ((-\Delta)^s+V(x)-\mu_1) H_1$;
\item $\mathrm{Im}((-\Delta)^s+V(x)-\mu_1)=((-\Delta)^s+V(x)-\mu_1) H_1$ is closed in $\mathcal{H}^*$;
\item $\mathrm{codim\ Im}((-\Delta)^s+V(x)-\mu_1)=1$,
\end{enumerate}
where $\mathcal{H}^*$ denotes the dual space of $\mathcal{H}$.
\end{lem}
Inspired by \cite[Theorem 3.2]{CB}, we establish the following lemma.
\begin{lem}\label{lem4.2}
Define the following functional $F$: $\mathcal{H}\times \R^2\rightarrow \mathcal{H}^*$.
\begin{equation}\label{d3}
F(u,\mu,a)=((-\Delta)^s+V(x)-\mu)u-a|x|^{-b}u^{1+2\beta^2},
\end{equation}
then there exist $\delta>0$ and a unique function $(u(a), \mu(a))\in C^1(B_{\delta}(0);B_{\delta}(\mu_1,\phi_1))$ such that
\begin{equation}\label{d4}
\left\{
\begin{aligned}
&\mu(0)=\mu_1,\ \ u(0)=\phi_1;\\
&F(u(a),\mu(a),a)=0; \\
& \|u(a)\|_2^2=1.
\end{aligned}
\right.
\end{equation}
\end{lem}
\noindent\textbf{ Proof.}
Let $g\in H_1\times \R^3\rightarrow\mathcal{H}^*$ be defined by
\begin{equation}\label{d5}
\begin{split}
g(h,\tau,t,a):=&F((1+t)\phi_1+h, \mu_1+\tau,a)\\
=&((-\Delta)^s+V(x)-(\mu_1+\tau))((1+t)\phi_1+h)\\
&-a|x|^{-b}[(1+t)\phi_1+h]^{1+2\beta^2}.
\end{split}
\end{equation}
It then follows from Lemma \ref{A.2} in the Appendix that $g\in C^1(H_1\times \R^3, \mathcal{H}^*)$ and
\begin{equation*}
\left\{
\begin{aligned}
g(0,0,0,0)&=F(\phi_1,\mu_1,0)=0,\\
g_t(0,0,0,0)&=F_u(\phi_1,\mu_1, 0)\phi_1=((-\Delta)^s+V(x)-\mu_1)\phi_1=0.
\end{aligned}
\right.
\end{equation*}
Moreover, for any $(\hat{h},\hat{\tau})\in H_1\times \R$, we have
\begin{equation}\label{d6}
\begin{split}
g_{(h,\tau)}(0,0,0,0)(\hat{h},\hat{\tau})&=F_u(\phi_1, \mu_1,0)\hat{h}+F_{\mu}(\phi_1,\mu_1,0)\hat{\tau}\\
&=((-\Delta)^s+V(x)-\mu_1)\hat{h}-\hat{\tau}\phi_1.
\end{split}
\end{equation}
We now claim that
\begin{equation}\label{Y1}
g_{(h,\tau)}(0,0,0,0): H_1\times \R\mapsto \mathcal{H}^*\ \mbox{ is an isomorphism}.
\end{equation}
Firstly, one can verify that $g_{(h,\tau)}(0,0,0,0)$ is linear and bounded. Assume that $(\hat{h},\hat{\tau})\in H_1\times \R$ and $g_{(h,\tau)}(0,0,0,0)(\hat{h},\hat{\tau})=0$, applying Lemma \ref{lem4.1}(3), we obtain that
\begin{equation}\label{d7}
((-\Delta)^s+V(x)-\mu_1)\hat{h}=\hat{\tau}\phi_1\in \mathrm{span}\{\phi_1\}\cap ((-\Delta)^s+V(x)-\mu_1)H_1,
\end{equation}
it then follows from Lemma \ref{lem4.1}(2) that $\hat{\tau}=0$ and $((-\Delta)^s+V(x)-\mu_1)\hat{h}=0$, this together with Lemma \ref{lem4.1}(1) further indicates that
\begin{equation*}
\hat{h}\in H_1\cap \mathrm{ker}\{(-\Delta)^s+V(x)-\mu_1\}=H_1\cap \mathrm{span}\{\phi_1\}=0,
\end{equation*}
In view of the above facts, we conclude that $(\hat{h},\hat{\tau})=0$. On the other hand, combining Lemma \ref{lem4.1} and \eqref{d6}, we deduce that
\begin{equation}\label{d8}
\begin{split}
\mathrm{Im}\ g_{(h,\tau)}(0,0,0,0)&=((-\Delta)^s+V(x)-\mu_1)H_1\oplus \mathrm{span}\{\phi_1\}\\
&=H_1\oplus\mathrm{span}\{\phi_1\}=\mathcal{H}=\mathcal{H}^*,
\end{split}
\end{equation}
and the claim \eqref{Y1} is thus proved.
Applying the implicit function theorem, we deduce that there exist $\delta_1>0$ and a unique function $(h(t,a),\tau(t,a))\in C^1(B_{\delta_1}(0,0),B_{\delta_1}(0,0))$ such that
\begin{equation}\label{d7}
\left\{
\begin{aligned}
&g(h(t,a), \tau(t,a),t,a)=F((1+t)\phi_1+h(t,a),\mu_1+\tau(t,a),a)=0,\\
& h(0,0)=0,\ \ \ \tau(0,0)=0,\\
&h_t(0,0)=-g_t(0,0,0,0)/g_{\tau}(0,0,0,0)=0.
\end{aligned}
\right.
\end{equation}
Set $u(t,a)=(1+t)\phi_1+h(t,a)$, $(t,a)\in B_{\delta_1}(0,0)$, and define
\begin{equation*}
f(t,a)=\|u(t,a)\|_2^2=(1+t)^2+\int_{\R^N}h^2(t,a)dx,\ \ \ (t,a)\in B_{\delta_1}(0,0).
\end{equation*}
We then derive from \eqref{d7} that
\begin{equation*}
f(0,0)=1,\ \ \ f_t(0,0)=2+2\int_{\R^N}h_t(0,0)h(0,0)dx=2.
\end{equation*}
Applying implicit function theorem again, there exist $0<\delta<\delta_1$ and a unique function $t=t(a)\in C^1(B_{\delta}(0,0),B_{\delta}(0,0))$ such that
\begin{equation}\label{d8}
f(t(a),a)=\|u(t(a),a)\|_2^2=f(0,0)=1,\ \ \ a\in B_{\delta}(0,0).
\end{equation}
In view of the above facts, for any $a\in B_{\delta}(0)$, we conclude that there exists a unique function $\big(u(a):=u(t(a),a),\ \ \mu_a:=\mu_1+\tau(t(a), a)\big)\in C^1(B_{\delta}(0),B_{\delta}(\phi,\mu_1))$ such that \eqref{d4} holds true and the proof of Lemma \ref{lem4.2} is therefore finished.\qed
Based on Lemma \ref{lem4.2}, we now establish the proof of Theorem \ref{unique}.
\vskip 0.1truein
\noindent\textbf{Proof of Theorem \ref{unique}.}
Let $u_a$ be a nonnegative minimizer of $e(a)$ with $a\in (0, a^*)$, then
\begin{equation}\label{d9}
e(0)=\mu_1\ \ \ \mbox{and}\ \ \ e(a)\leq e(0)=\mu_1,
\end{equation}
where $\mu_1$ is the first eigenvalue of $(-\Delta)^s+V(x)$.
Since $u_{a}$ is a nonnegative minimizer of $e(a)$, by variational theory, $u_{a}$ satisfies the following Euler-Lagrange equation
\begin{equation}\label{d01}
(-\Delta)^{s} u_{a}(x)+V(x)u_{a}(x)=\mu_a u_{a}(x)+a u_{a}^{1+2\beta^2}(x)|x|^{-b}\quad \mbox{in}\ \ \R^{N},
\end{equation}
where $\mu_{a}\in\R$ is a suitable Lagrange multiplier satisfying
\begin{equation}\label{d02}
\mu_a=e(a)-\frac{a\beta^2}{1+\beta^2}\inte |x|^{-b}|u_a|^{2+2\beta^2}dx,
\end{equation}
it then follows from $\eqref{d3}$ and $\eqref{d01}$ that $F(u_a,\mu_a,a)=0$.
Next, we claim that
\begin{equation}\label{d10}
e(a)\in C([0,a^*),\R^+)\ \ \ \mbox{and}\ \ \ \int_{\R^N}|x|^{-b}|u_a|^{2+2\beta^2}dx\leq \frac{\mu_1(1+\beta^2)}{(a^*-a)} \ \ \ \mbox{for}\ \ a\in [0,a^*).
\end{equation}
In fact, since $u_a$ is a minimizer of $e(a)$, it follows from the assumption $(V_1)$ and the Gagliardo-Nirenberg inequality (\ref{GN}) that
\begin{align}\label{d11}
e(a)=E_{a}(u_a)&=\int_{\R^{N}}(|(-\Delta)^{\frac{s}{2}}u_a(x)|^{2}+V(x)|u_a(x)|^{2})dx-\frac{a}{1+\beta^2}\int_{\R^{N}}|u_a(x)|^{2+2\beta^2}|x|^{-b}dx \nonumber\\
&\geq\frac{a^*-a}{1+\beta^2}\int_{\R^{N}}|u_a(x)|^{2+2\beta^2}|x|^{-b}dx+\int_{\R^{N}}V(x)|u_a(x)|^{2}dx \nonumber\\
&\geq\frac{a^*-a}{1+\beta^2}\int_{\R^{N}}|u_a(x)|^{2+2\beta^2}|x|^{-b}dx,
\end{align}
this together with \eqref {d9} further implies that
\begin{equation}\label{d12}
\int_{\R^{N}}|u_a(x)|^{2+2\beta^2}|x|^{-b}dx\leq \frac{e(a)(1+\beta^2)}{a^*-a}\leq\frac{\mu_1(1+\beta^2)}{a^*-a}\ \ \ \mbox{for}\ \ a\in [0,a^*).
\end{equation}
We then proof that $ e(a)\in C([0,a^*),\R^+)$. For any $a_1, a_2 \in [0, a^*)$, let $u_{a_1}$ and $u_{a_2}$ be minimizers of $e(a_1)$ and $e(a_2)$, respectively. Some calculations yield that
\begin{equation}\label{d13}
\begin{split}
e(a_1)=&E_{a_1}(u_{a_1})\\
=&\int_{\R^{N}}(|(-\Delta)^{\frac{s}{2}}u_{a_1}(x)|^{2}+V(x)|u_{a_1}(x)|^{2})dx-\frac{a_1}{1+\beta^2}\int_{\R^{N}}|u_{a_1}(x)|^{2+2\beta^2}|x|^{-b}dx \\
=&\int_{\R^{N}}(|(-\Delta)^{\frac{s}{2}}u_{a_1}(x)|^{2}+V(x)|u_{a_1}(x)|^{2})dx-\frac{a_2}{1+\beta^2}\int_{\R^{N}}|u_{a_1}(x)|^{2+2\beta^2}|x|^{-b}dx \\
&+\frac{a_2-a_1}{1+\beta^2} \int_{\R^{N}}|u_{a_1}(x)|^{2+2\beta^2}|x|^{-b}dx
\\
\geq& e(a_2)+\frac{a_2-a_1}{1+\beta^2}\int_{\R^{N}}|u_{a_1}(x)|^{2+2\beta^2}|x|^{-b}dx.
\end{split}
\end{equation}
Similarly, we obtain that
\begin{equation}\label{d14}
e(a_2)\geq e(a_1)+\frac{a_1-a_2}{1+\beta^2}\int_{\R^{N}}|u_{a_2}(x)|^{2+2\beta^2}|x|^{-b}dx.
\end{equation}
We then deduce from \eqref{d13} and \eqref{d14} that
\begin{equation}\label{d15}
\frac{a_1-a_2}{1+\beta^2}\int_{\R^{N}}|u_{a_2}(x)|^{2+2\beta^2}|x|^{-b}dx\leq e(a_2)-e(a_1)\leq \frac{a_1-a_2}{1+\beta^2}\int_{\R^{N}}|u_{a_1}(x)|^{2+2\beta^2}|x|^{-b}dx
\end{equation}
Combining this with \eqref{d12} further indicates that $\lim\limits_{a_2\rightarrow a_1}e(a_2)=e(a_1)$, that is $e(a)\in C([0,a^*),\R^+)$ and the claim \eqref{d10} is proved.
In view of \eqref{d02} and \eqref{d10}, we derive that
\begin{equation}\label{d16}
|\mu_a-\mu_1|\leq|e(a)-\mu_1|+\frac{a\beta^2}{1+\beta^2}\inte |x|^{-b}|u_a|^{2+2\beta^2}dx\leq \delta \ \ \ \mbox{for sufficiently small}\ \ a,
\end{equation}
where $\delta>0$ is same as in Lemma \ref{lem4.2}. Moreover, since
\begin{equation}\label{d17}
E_0(u_a)=e(a)+\frac{a}{1+\beta^2}\inte |x|^{-b}|u_a|^{2+2\beta^2}dx\rightarrow e(0)=\mu_1\ \ \ \mbox{as}\ \ a\searrow0,
\end{equation}
which further implies $\{u_a\}$ is a minimizing sequence of $e(0)=\mu_1$ as $a\searrow0$. Note that $\mu_1$ is a simple eigenvalue, we then deduce from Lemma \ref{lem2.1} that
\begin{equation}\label{d18}
u_a\rightarrow \phi_1\ \ \mbox{in}\ \ \mathcal{H}\ \ \mbox{as}\ \ a\searrow0.
\end{equation}
Combining the above facts with Lemma \ref{lem4.2}, we conclude that
\begin{equation}\label{d19}
\mu_a=\mu(a)\ \ \mbox{and}\ \ u_a=u(a)\ \ \mbox{as}\ \ a\searrow0,
\end{equation}
which indicates that $e(a)$ admits a unique nonnegative minimizer $u(a)$ if $a>0$ is small enough and Theorem \ref{unique} is therefore complete.\qed
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,094 |
{"url":"https:\/\/math.stackexchange.com\/questions\/3634355\/matrix-of-a-linear-transformation-on-basis","text":"# Matrix of a linear transformation on basis\n\nGiven a linear transformation on $$\\mathbb{R^3}$$ as follows: $$\\phi(x)=(x,a)a$$ where $$(x,a)$$ stands for the dot product of the vectors $$x$$ and $$a$$ ,and $$a=(1,2,3)$$. Find the matrix of this transformation on the basis $$e_1=(1,0,0),e_2=(0,1,0),e_3=(0,0,1)$$, which all the vectors above are given on, and also find the matrix on the basis $$b_1=(1,0,1),b_2=(2,0,-1),b_3=(1,1,0)$$.\n\nI have already found the matrix on the basis $$e_1,e_2,e_3$$: $$A=\\begin{bmatrix} 1 &2 &3 \\\\ 2 &4 & 6 \\\\ 3 & 6 & 9 \\end{bmatrix}$$ Also, the matrix that maps the first basis to the second: $$C=\\begin{bmatrix} 1 &2 &1 \\\\ 0 &0 & 1 \\\\ 1 & -1 & 0 \\end{bmatrix}$$ On the new basis $$a=(\\cfrac{5}{3},-\\cfrac{4}{3},2)$$. I have done some trials to find the matrix $$B$$ (the second matrix asked in the question) but none matches with the answer of the book, while $$A$$ seems to be correct.\n\nThe answer is $$B=\\begin{bmatrix} 20\/3 &-5\/3 &5 \\\\ -16\/3 &4\/3 & -4 \\\\ 8 & -2 & 6 \\end{bmatrix}$$ Any help is appreciated.\n\nYou have$$f(b_1)=(4,8,12),\\ f(b_2)=(-1,-2,-3)\\text{ and }b_3=(3,6,9).$$But, with respect to the basis $$B=\\{b_1,b_2,b_3\\}$$, you have$$f(b_1)=\\left(\\frac{20}3,-\\frac{16}3,8\\right)_B,\\, f(b_2)=\\left(-\\frac53,\\frac43,-2\\right)_B\\text{ and }f(b_3)=(5,-4,6)_B.$$So,$$C=\\begin{bmatrix}\\frac{20}3&-\\frac53&5\\\\-\\frac{16}3&\\frac43&-4\\\\8&-2&6\\end{bmatrix}.$$\n\u2022 \"$f(b_1)=\\left(\\frac{20}3,-\\frac{16}3,8\\right)_B$\" to have this, do I have to find the coordinates of $b_1 \\text{ and } a$ on the basis $B$ and then calculate $\\phi(b_1)=(b_1,a)a$? Apr 20 '20 at 8:58\n\u2022 No. You solve the system $f(b_1)=\\alpha b_1+\\beta b_2+\\gamma b_3$. The only solution is $\\alpha=\\frac{20}3$, $\\beta=-\\frac{16}3$, and $\\gamma=8$. Apr 20 '20 at 9:00","date":"2021-10-23 02:42:34","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\": 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\": 19, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.937897264957428, \"perplexity\": 82.65250956802711}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323585537.28\/warc\/CC-MAIN-20211023002852-20211023032852-00347.warc.gz\"}"} | null | null |
Victoria Larrière (born 2 May 1991) is a French former professional tennis player. As of 14 May 2012, she reached her highest singles ranking of world No. 172.
Career
Her career accelerated in the summer of 2011 when she won her first final in a $50k tournament in Istanbul.
The following week, for her first appearance in a WTA Tour tournament at the 2011 Tashkent Open, she qualified into the main draw. After winning over Zuzana Kučová in the first round, she played and beat her first top 100, seed No. 5 Magdaléna Rybáriková (6–4, 6–4) for a total of ten successive wins. She lost in the quarterfinal against Ksenia Pervak, seed No. 1 and eventual winner of the tournament, in straight sets.
Larrière lost in the first round of the doubles main-draw at the 2011 French Open.
Victoria was close to qualify for the 2012 Australian Open, leading 6–4, 3–1 in the last qualification round, but lost 6–4, 4–6, 3–6 to Chang Kai-chen. She was awarded a wildcard for the main draw of the 2012 French Open but lost in the first round to the 16th seed Maria Kirilenko, in two sets.
ITF Circuit finals
Singles: 15 (10 titles, 5 runner-ups)
Doubles: 12 (10 titles, 2 runner-ups)
External links
1991 births
Living people
French female tennis players | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,221 |
Gli Spargo sono un gruppo musicale olandese formatosi ad Amsterdam nel 1975 specializzato nel genere disco.
Storia
I loro leader fondatori sono Ellert Driessen (voce maschile e tastiere), Jef Nassenstein (basso), Leander Lammertink (batteria) e Ruud Mulder (chitarra). Alla fine degli anni settanta si aggiunse la cantante statunitense Lilian Day Jackson (voce femminile). Furono conosciuti dal grande pubblico con la loro hit You and Me del 1980 che raggiunse in Italia la posizione numero due della Hit Parade e si piazzò al nono posto nella graduatoria dei singoli più venduti di quell'anno. Altri singoli che ottennero successo internazionale furono One Night Affair (1981), Just for You (1981) e Hip Hap Hop (1982).
Scioltisi nel 1985, si sono riformati nel 1997 e sono tuttora in attività.
Formazione
Discografia
Collegamenti esterni | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,140 |
\section{Introduction}\label{s:intro}
Let $G=G_{n}=GL(n)$ or $ SO(n)$ and let $B_{n-1}$ be the standard upper triangular Borel subgroup of
$G_{n-1}\subset G$. In this paper, we continue our study of the $B_{n-1}$-orbits on the flag variety $\mathcal{B}_{n}$ of
$G$ using the results of the accompanying paper ``$B_{n-1}$-bundles on the flag variety, I". We obtain a combinatorial model for the set of orbits $B_{n-1}\backslash\mathcal{B}_{n}$ and use this model to develop a canonical set of representatives for the orbits in terms of flags. We then use these representatives
along with our results from \cite{CE21I} to show that every $B_{n-1}$-orbit arises from a zero dimensional orbit using an extended monoid action by simple roots of $\mbox{${\mathfrak k}$}:=\mbox{${\mathfrak g}$}_{n-1}$ and $\mbox{${\mathfrak g}$}$. Given this result, we show using a theorem of Richardson and Springer in \cite{RS} that the closure ordering on $B_{n-1}\backslash\mathcal{B}_{n}$ is given by the standard order (Corollary \ref{c:bruhatisstandard}). In the general linear case, $B_{n-1}$-orbits are described in \cite{Hashi} and in \cite{MWZ}. In a subsequent paper \cite{Magyar}, Magyar gives a combinatorial description of the closure relations. Our approach is more geometric and has the advantage that both the general linear and orthogonal cases can be described in an essentially uniform manner. We also establish a complete picture of the extended monoid action. It would be interesting to understand the relations between the different descriptions of the orbits in the general linear case. We note that the orthogonal case does not seem to be accessible using the previous approaches.
In the future, we plan to use the closure relations for these orbits to understand the category of $(\mbox{${\mathfrak g}$}, B_{n-1})$-modules, i.e., $U(\mbox{${\mathfrak g}$})$-modules with a locally finite action of the group $B_{n-1}$. Such modules can be constructed using local systems on $B_{n-1}$-orbits on $\mathcal{B}_{n}$ and the Beilinson-Bernstein correspondence.
The bundle description of orbits from \cite{CE21I} and our extended monoid action should both be essential ingredients in describing the $(\mbox{${\mathfrak g}$}, B_{n-1})$-modules. The category of $(\mbox{${\mathfrak g}$}, B_{n-1})$-modules is closely related to the category of Gelfand-Zeitlin (GZ) modules which quantize the complex GZ integrable systems. GZ modules were first introduced by Drozd, Futorny, and Ovsienko in \cite{DFO} and are increasingly becoming a broad area of research.
In more detail, in the case $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$, we develop a
bijection between $B_{n-1}\backslash\B_{n}$ and the set of
all partitions of $\{1,\dots, n\}$ into ordered subsets (Theorem \ref{thm:counttypeA}).
We refer to any such partition as a \emph{PIL} (partition into lists) of the set $\{1,\dots, n\}$.
In Theorem \ref{thm:orthocount}, we extend this result to the orthogonal case, associating to each $B_{n-1}$-orbit on $\mathcal{B}_{n}$ a partition into certain signed lists (\emph{SPIL}) of the set $\{1,\dots, \ell\}$ where $\ell=\mbox{rank}(\mathfrak{so}(n))$. These combinatorial models allow us to compute explicit
formulas and exponential generating functions for the sequence $\{|B_{n-1}\backslash\B_{n}|\}_{n\in\mathbb{N}}$ in the various cases. When $\mbox{${\mathfrak g}$}$ is a type A or D Lie algebra these formulas can be expressed succinctly in terms of the classical Lah numbers, which play an important role in enumerative and applied combinatorics (Propositions \ref{p:formulaA} and \ref{p:formulaD}). In type B a variant of Lah numbers is required.
We then use the combinatorial models to develop explicit representatives for the $B_{n-1}$-orbits
in terms of flags. We call these representatives flags in standard form and note that they depend on the type of $\mbox{${\mathfrak g}$}$. We show that any $B_{n-1}$-orbit contains a unique flag in standard form by first using the parameterization of
$B_{n-1}\backslash\B_{n}$ by PILs and SPILs to show that $|B_{n-1}\backslash\B_{n}|$ is the same as the cardinality of
the set of all flags in standard form. We then show that any two flags in standard form contained in a given
$B_{n-1}$-orbit must coincide. The key ingredient in this last step is the classification of the $B_{n-1}$-orbits on the Grassmannian of (isotropic) $i$-planes in $\mbox{${\mathbb C}$}^{n}$.
The representatives of $B_{n-1}\backslash\B_{n}$ in standard form facilitate easy computation of certain instances of the monoid action that are not covered by the results of \cite{CE21I} (Section \ref{s:monoid}). These computations along with the results of \emph{loc.cit.} allow us to prove that the closure ordering on $B_{n-1}\backslash\B_{n}$ is given by the standard order (Corollary \ref{c:bruhatisstandard}).
The paper is organized as follows. In Section \ref{s:Prelim}, we review some standard facts about the Lie
algebras $\mathfrak{gl}(n)$ and $\mathfrak{so}(n)$ and discuss the parameterization of $K:=G_{n-1}$-orbits on $\mathcal{B}_{n}$ using flags and isotropic flags. In Section \ref{s:PILS}, we develop the combinatorial models for $B_{n-1}\backslash\B_{n}$ by PILs and SPILs and prove that our models classify the orbits. In \ref{ss:formulae}, we give explicit formulas for the sequence $\{|B_{n-1}\backslash\B_{n}|\}_{n\in\mathbb{N}}$ in the various cases and compute the corresponding exponential generating functions. Section \ref{s:std} is devoted to proving that every element of $B_{n-1}\backslash\B_{n}$ contains a unique flag in standard from. The various types are discussed separately. In Section \ref{s:monoid}, after reviewing the monoid action on both $K\backslash \mathcal{B}_{n}$ and $B_{n-1}\backslash\B_{n}$ via simple roots of $\mbox{${\mathfrak g}$}$, we use the representatives of $B_{n-1}$-orbits in standard form to compute certain monoid actions on $B_{n-1}\backslash\B_{n}$ that are needed later. The results of Section \ref{s:monoid} along with the results of \emph{loc.cit.} are then used in Section \ref{s:closure} to prove that closure ordering on $B_{n-1}\backslash\B_{n}$ coincides with the standard ordering. These results use crucially the extended monoid action and provide an answer to a conjecture posed by Hashimoto in the Introduction and Section 4 of \cite{Hashi}. Section \ref{s:closure} begins with a review of the work of Richardson and Springer and then we prove that the minimal elements for the extended monoid action are the zero dimensional orbits. Finally, in Section \ref{s:graphs}, we give examples of Bruhat graphs for the set $B_{n-1}\backslash\B_{n}$ in all types in low rank, labelling the different monoid actions and relations in the standard order that cannot be obtained from the weak order.
We would like to thank Jeb Willenbring and David Galvin for helpful discussions on the material in Section \ref{s:PILS}. We would also like to thank Jacopo Gandini, Guido Pezzini, and Friedrich Knop for discussions relevant to the material in this paper, and thank Michael Finkelberg for bringing the work of Magyar in \cite{Magyar} to our attention.
During the preparation of this paper, the first author was supported in part by the National Security Agency grant H98230-16-1-0002 and the second author was supported in part by the Simons Foundation grant 359424.
\section{Preliminaries}\label{s:Prelim}
In this paper, we study the complex general linear and orthogonal Lie algebras.
We let $G=G_{n}=GL(n)$ (resp. $SO(n)$) and let $\mbox{${\mathfrak g}$}=\mbox{${\mathfrak g}$}_{n}=\mathfrak{gl}(n)$ (resp. $\mathfrak{so}(n)$) be
the corresponding Lie algebras. The group $G$ acts on its Lie algebra $\mbox{${\mathfrak g}$}$ via
the adjoint action ${\rm Ad}(g)X=gXg^{-1}$ for $g\in G$, $X\in \mbox{${\mathfrak g}$}$.
\subsection{Realizations of Lie algebras}\label{ss:realization}
We denote the standard basis of $\mbox{${\mathbb C}$}^{n}$ by
$\{e_{1},\dots, e_{n}\}$. The Lie algebra $\mathfrak{gl}(n)$ is
the Lie algebra of $n\times n$ complex matrices. To realize
the orthogonal Lie algebra, $\mathfrak{so}(n)$, we consider the non-degenerate,
symmetric bilinear form $\beta$ on $\mbox{${\mathbb C}$}^{n}$ given by
\begin{equation}\label{eq:beta}
\beta(x,y)=x^{T} S_{n} y,
\end{equation}
where $x, y$ are $n\times 1$ column vectors and $S_{n}$ is the permutation matrix mapping $e_i$ to $e_{n+1-i}$ for $i=1, \dots, n$.
The special orthogonal group is
$$
SO(n):=\{g\in SL(n): \, \beta(gx, gy)=\beta(x,y)\; \forall\; x,\, y \in \mbox{${\mathbb C}$}^{n}\}
$$
and its Lie algebra is
$$
\mathfrak{so}(n)=\{Z\in\mathfrak{gl}(n):\, \beta(Zx, y)=-\beta(x,Zy)\,\forall\; x, \, y\in\mbox{${\mathbb C}$}^{n}\}.
$$
It follows that $\mathfrak{so}(n)$ is the Lie algebra of all $n\times n$ complex matrices
which are skew-symmetric about the skew-diagonal.
For $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$ or $\mathfrak{so}(n)$,
let $\mbox{${\mathfrak h}$}$ be the Cartan subalgebra of diagonal matrices in $\mbox{${\mathfrak g}$}$. We denote the rank of the Lie algebra $\mbox{${\mathfrak g}$}$ by
$\mbox{rk}(\mbox{${\mathfrak g}$})=\dim\mbox{${\mathfrak h}$}$. If $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$, then $\mbox{rk}(\mbox{${\mathfrak g}$})=n$, and
$\mbox{${\mathfrak h}$}=\{\mbox{diag}[x_{1},\dots, x_{n}], \, x_{i}\in\mbox{${\mathbb C}$}\}$. We let
$\epsilon_{i}\in\mbox{${\mathfrak h}$}^{*}$ be the linear functional $\epsilon_{i}(\mbox{diag}[x_{1},\dots, x_{n}])=x_{i}$.
Then the standard simple roots for $\mbox{${\mathfrak g}$}$ are $\Pi_{\mbox{${\mathfrak g}$}}=\{\alpha_{1},\dots, \alpha_{n-1}\}$, with
$\alpha_{i}=\epsilon_{i}-\epsilon_{i+1}$.
For $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)$ (type D), $\mbox{rk}(\mbox{${\mathfrak g}$})=\ell$.
In this case, it is convenient to relabel part of the basis of $\mbox{${\mathbb C}$}^{2\ell}$ as $e_{-j}:=e_{2\ell+1-j}$ for
$j=1,\dots, \ell$. Then the Cartan subalgebra $\mbox{${\mathfrak h}$}=\{\mbox{diag}[x_{1},\dots, x_{\ell}, -x_{\ell},\dots, -x_{1}],\, x_{i}\in\mbox{${\mathbb C}$}\}$,
and we let $\epsilon_{i}\in\mbox{${\mathfrak h}$}^{*}$ be $\epsilon_{i}(\mbox{diag}[x_{1},\dots, x_{\ell}, -x_{\ell},\dots, -x_{1}])=x_{i}$ for
$i=1,\dots, \ell$. The standard simple roots of $\mbox{${\mathfrak g}$}$ are
$\Pi_{\mbox{${\mathfrak g}$}}=\{\alpha_{1},\dots, \alpha_{\ell-1}, \alpha_{\ell}\}$ with
$\alpha_{i}=\epsilon_{i}-\epsilon_{i+1}$, $i=1,\dots, \ell-1$, and $\alpha_{\ell}=\epsilon_{\ell-1}+\epsilon_{\ell}$.
For $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell + 1)$ (type B), $\mbox{rk}(\mbox{${\mathfrak g}$})=\ell$. In this case, we relabel the basis
of $\mbox{${\mathbb C}$}^{2\ell+1}$ as $e_{-j}:=e_{2\ell+2-j}$ for $j=1,\dots, \ell$ and $e_{0}:=e_{\ell+1}$.
The Cartan subalgebra $\mbox{${\mathfrak h}$}=\{\mbox{diag}[x_{1},\dots, x_{\ell}, 0, -x_{\ell},\dots, -x_{1}], x_{i}\in\mbox{${\mathbb C}$}\}$ and
$\epsilon_{i}\in\mbox{${\mathfrak h}$}^{*}$ is given by $\epsilon_{i}(\mbox{diag}[x_{1},\dots, x_{\ell}, 0, -x_{\ell},\dots, -x_{1}])=x_{i}$.
The standard simple roots for $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)$ are
$\Pi_{\mbox{${\mathfrak g}$}}=\{\alpha_{1},\dots, \alpha_{\ell-1}, \alpha_{\ell}\}$ with $\alpha_{i}=\epsilon_{i}-\epsilon_{i+1}$ for
$i=1,\dots, \ell-1$ and $\alpha_{\ell}=\epsilon_{\ell}$.
\begin{rem}\label{r:beta}
The form $\beta$ in Equation (\ref{eq:beta}) with respect to the standard
bases of $\mbox{${\mathbb C}$}^{2\ell}$ and $\mbox{${\mathbb C}$}^{2\ell+1}$ is determined by the property that $\beta(e_{j}, e_{k})=\delta_{j,-k}$.
\end{rem}
Let $H\subset G$ be the Cartan subgroup of diagonal matrices with Lie algebra $\mbox{${\mathfrak h}$}$.
Let $W=W_{G}=N_{G}(H)/H$ be the Weyl group of $G$ with respect to $H$.
\begin{nota}\label{nota:Weyl}
For an element $w\in W$, let $\dot{w}\in N_{G}(H)$ be a representative of $w$.
If $\mbox{${\mathfrak m}$}\subset\mbox{${\mathfrak g}$}$ is a Lie subalgebra which is normalized by $H$, then ${\rm Ad}(\dot{w})\mbox{${\mathfrak m}$}$ is independent of the choice of representative of $w$,
and we denote it by $w(\mbox{${\mathfrak m}$})$.
\end{nota}
\subsection{Borel subalgebras and flag varieties}\label{ss:Borels}
We denote the standard Borel subalgebra of upper triangular matrices
in $\mathfrak{gl}(n)$ by $\mbox{${\mathfrak b}$}_{n}$. For $\mbox{${\mathfrak g}$}=\mathfrak{so}(n)$, we let $\mbox{${\mathfrak b}$}_{n}$ denote the upper triangular matrices in $\mbox{${\mathfrak g}$}$ with respect to the ordered basis $e_1, \dots, e_{\ell}, e_{-\ell}, \dots, e_{-1}$ when $n=2\ell$ is even, and with respect to the ordered basis $e_1, \dots, e_{\ell}, e_0, e_{-\ell}, \dots, e_{-1}$ when $n=2\ell + 1$ is odd. Note that $\mbox{${\mathfrak h}$}\subset\mbox{${\mathfrak b}$}_{n}$ and the standard simple roots $\Pi_{\mbox{${\mathfrak g}$}}$ given above are simple roots for $\mbox{${\mathfrak b}$}_{n}$. We let $\mathcal{B}_{n}:=\mathcal{B}_{\mbox{${\mathfrak g}$}}$ be the variety of all
Borel subalgebras of $\mbox{${\mathfrak g}$}$.
When $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$, the variety $\mathcal{B}_{n}$ is $G$-equivariantly isomorphic to the
variety of all full flags on $\mbox{${\mathbb C}$}^{n}$, i.e., flags of the form
$$
\{\mathcal{F}=(V_{1}\subset\dots\subset V_{i}\subset\dots\subset V_{n}) |\, \dim V_{i}=i,\, V_{i}\subset \mbox{${\mathbb C}$}^{n}\}.
$$
When $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)$, the variety
$\mathcal{B}_{2\ell+1}$ is $G$-equivariantly isomorphic to the variety of all maximal isotropic flags in $\mbox{${\mathbb C}$}^{2\ell+1}$, i.e., partial flags of the form
$$
\mathcal{F}=( V_{1}\subset\dots\subset V_{i}\subset\dots\subset V_{\ell}),
$$
with $\dim V_i=i$ and $\beta(u,w)=0$ for all $u,w \in V_i.$
In the type D case, the variety
$\mathcal{B}_{2\ell}$ is $G$-equivariantly isomorphic to the variety of all partial isotropic flags in $\mbox{${\mathbb C}$}^{2\ell}$ of the form:
$$
\mathcal{F}=( V_{1}\subset\dots\subset V_{i}\subset\dots\subset V_{\ell-1}).
$$
This is a different realization of $\mathcal{B}_{2\ell}$ than the one used in \cite{CE21I}.
We make heavy use of the following shorthand notation for flags throughout the paper.
\begin{nota} \label{nota:standard}
Let
$$
\mathcal{F}=(V_{1}\subset V_{2}\subset\dots\subset V_{i}\subset V_{i+1}\subset \dots)
$$
be a flag in $\mbox{${\mathbb C}$}^{n}$, with $\dim V_{i}=i$ and $V_{i}=\mbox{span}\{v_{1},\dots, v_{i}\}$, with each $v_{j}\in\mbox{${\mathbb C}$}^{n}$. We will denote this flag $\mathcal{F}$
by
$$
\mathcal{F}= (v_{1}\subset v_{2}\subset\dots\subset v_{i}\subset v_{i+1}\subset\dots ).
$$
\end{nota}
\begin{nota}\label{note:uppertriangular}
Identifying $\mathcal{B}_{n}$ with various flag varieties as above, the standard Borel subalgebra of
upper triangular matrices is identified with the flags
\begin{equation}\label{eq:upper}
\mathcal{F}_{+}:=\left\lbrace\begin{array}{ll} (e_{1}\subset e_{2}\subset \dots \subset e_{n}) &\mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{gl}(n)\\
(e_{1}\subset\dots\subset e_{\ell}) &\mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)\\
(e_{1}\subset \dots\subset e_{\ell-1}) &\mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)\end{array}\right\rbrace_{.}
\end{equation}
\end{nota}
\subsection{$K$-orbits on $\mathcal{B}_{n}$}\label{ss:Korbits}
We recall that $\mbox{${\mathfrak k}$}:=\mbox{${\mathfrak g}$}_{n-1}=\mathfrak{gl}(n-1)$ or $\mathfrak{so}(n-1)$ can be embedded
in $\mbox{${\mathfrak g}$}$ as a symmetric subalgebra (up to centre in $\mathfrak{gl}(n)$ case).
For more details, see Section 2.3 of \cite{CE21I}. The
corresponding algebraic group $K=GL(n-1)$ or $SO(n-1)$ acts on $\mathcal{B}_{n}$ via the adjoint action with
finitely many orbits. These are classified in Propositions 2.8-2.10 of \emph{loc. cit.}, and we
follow the notation used there. For our work here, it will be useful to have
explicit representatives of $K$-orbits in terms of flags.
For $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$, these representatives are given in Equations (2.6) and (2.9) of \emph{loc. cit.}.
We restate these here for the convenience of the reader. There are $n$ closed $K$-orbits on $\mathcal{B}_{n}$ which
we denote by $Q_{i}$ for $i=1,\dots, n$. The orbit $Q_{i}$ contains the flag
\begin{equation}\label{eq:typeAflagclosed}
\mathcal{F}_{i}:=(e_{1}\subset\dots \subset e_{i-1}\subset\underbrace{e_{n}}_{i}\subset e_{i}\subset \dots \subset e_{n-1}).
\end{equation}
There are ${n\choose 2}$ non-closed $K$-orbits on $\mathcal{B}_{n}$ which we denote by $Q_{i,j}$ for $1\leq i<j\leq n$.
The orbit $Q_{i,j}$ contains the flag
\begin{equation}\label{eq:typeAflag}
\mathcal{F}_{i,j}:=(e_{1}\subset\dots\subset e_{i-1} \subset \underbrace{e_{j-1}+e_{n}}_{i}\subset e_{i}\subset\dots\subset e_{j-2}\subset\underbrace{e_{n}}_{j}\subset e_{j}\subset\dots\subset e_{n-1}).
\end{equation}
For ease of notation, we sometimes denote the closed $K$-orbit $Q_{i}$ by $Q_{i,i}$, so that
the $K$-orbits on $\mathcal{B}_{n}$ are denoted by $Q_{i,j}$ with $1\leq i\leq j\leq n$.
For $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)$, the closed $K$-orbits are $Q_{+}$ and $Q_{-}$ (see Part (2) of Proposition 2.9 of \emph{loc. cit.}) and are represented by the maximal isotropic flags
$\mathcal{F}_{+}$, and
$\mathcal{F}_{-}:=(e_{1}\subset \dots\subset e_{\ell-1}\subset e_{-\ell})$ respectively.
We denote the non-closed $K$-orbits by $Q_{i}$ with $i=0,\dots, \ell-1$ (see Part (3) of Proposition 2.9 of \emph{loc. cit.}) and can be represented by the maximal isotropic flags
\begin{equation}\label{eq:typeBflag}
\mathcal{F}_{i}=(e_{1}\subset \dots \subset e_{i}\subset\underbrace{ e_{\ell}+\sqrt{2}e_{0}-e_{-\ell}}_{i+1-position}\subset e_{i+1}\subset \dots\subset e_{\ell-1}) \mbox{ for } i=0, \dots, \ell-1.
\end{equation}
This can be verified using Equation (2.11) and Remark 2.11 in \emph{loc. cit.}.
For $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)$, the unique closed $K$-orbit, $Q_{+}$ contains the
partial isotropic flag $\mathcal{F}_{+}$ (see
Part (2) of Proposition 2.10 of \emph{loc. cit.}). The non-closed orbits are denoted by $Q_{i}$ with $i=1,\dots, \ell-1$ and
can be represented by the partial isotropic flags
\begin{equation}\label{eq:typeDflag}
\mathcal{F}_{i}=(e_{1}\subset\dots\subset e_{i-1}\subset\underbrace{ e_{\ell}}_{i-position}\subset e_{i}\subset \dots\subset e_{\ell-2}) \mbox{ for } i=1,\dots, \ell-1.
\end{equation}
This can be verified using Equation (2.13) of \emph{loc. cit.}.
We also recall the notion of a length of a $K$-orbit.
\begin{dfn}\label{d:length}
Let $Q_{K}$ be a $K$-orbit on $\mathcal{B}_{n}$. We define the \emph{length} of $Q_{K}$,
$\ell(Q_{K})$, by
\begin{equation}\label{eq:Klength}
\ell(Q_{K}):=\dim Q_{K}-\dim \mathcal{B}_{\mbox{${\mathfrak k}$}},
\end{equation}
where $\mathcal{B}_{\mbox{${\mathfrak k}$}}$ denotes the flag variety of $\mbox{${\mathfrak k}$}$.
\end{dfn}
\begin{rem}\label{r:Korbitlength}
For $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$, $\ell(Q_{i,j})=j-i$. For $\mbox{${\mathfrak g}$}=\mathfrak{so}(n)$, $\ell(Q_{\pm})=0$ and
$\ell(Q_{i})=\ell-i$. These assertions can be verified using Part (3) of Propositions 2.8-2.10 of
\emph{loc. cit.} and the well-known fact that if $Q_{K}$ is closed then $Q_{K}\cong \mathcal{B}_{\mbox{${\mathfrak k}$}}$ ( \cite{CEexp} for example).
\end{rem}
\begin{nota}\label{note:orbitnote}
Let $H$ be an algebraic group and $X$ an $H$-variety. We denote the
set of $H$-orbits on $X$ by $H\backslash X$.
\end{nota}
In this paper, we study $B_{n-1}\backslash\B_{n}$, where $B_{n-1}:=K\cap B_{n}$ and $B_{n}\subset G$ is the standard
upper triangular Borel subgroup of $G$ which stabilizes the flag $\mathcal{F}_{+}$ in (\ref{eq:upper}). It follows from Section 2.2 of \cite{CE21I} that $B_{n-1}\subset K$ is the standard Borel subgroup of upper triangular matrices in $K$.
\section{Combinatorics of $B_{n-1}$-orbits on $\mathcal{B}_{n}$}\label{s:PILS}
In this section, we introduce sets $PIL(n)$ and $SPIL(n)$ which count the number of $B_{n-1}$-orbits on $\mathcal{B}_n$ in the general linear and orthogonal cases.
As a consequence, we obtain formulas counting the number of $B_{n-1}$-orbits on
$\mathcal{B}_n$ and study the corresponding exponential generating functions. It will be convenient to declare $B_{n}$ to be the trivial group
for $n<0$. In particular, $|B_{-1}\backslash \mathcal{B}_{0}|=1$.
\subsection{$PIL(n)$ and the $GL(n)$ case}\label{ss:gl}
We first consider the case where $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$ and $K=GL(n-1)$.
\begin{dfn}\label{dfn:lists}
\begin{enumerate}
\item We define a list on a subset $\{a_{1},\dots, a_{k}\}$ of the non-negative integers to be a $k$-tuple $\sigma=(a_{i_{1}},\dots, a_{i_{k}}) \in \mathbb{Z}_{\geq 0}^k$. We regard a list as an ordering on the corresponding subset. For the list $\sigma$ above, we say
${\rm supp}(\sigma)=\{ a_{i_1}, \dots, a_{i_k} \}$, the length $\ell(\sigma)=k$,
and $\sigma(j)=a_{i_j}$ for $1 \le j \le k$.
\item Let $A\subset \mathbb{Z}_{\geq 0}$ be any finite subset. We define a PIL (partition into lists) of the set $A$ to be a partition of $A$ into lists.
We shall denote a PIL consisting of $k$ lists $\sigma_{1},\dots, \sigma_{k}$ by $\Sigma=\{\sigma_{1},\, \dots, \, \sigma_{k}\}$.
\item For a finite subset $A\subset\mathbb{Z}_{\geq 0}$, we denote the set consisting of all PIL's of $A$ by $PIL(A)$.
In the case where $A=\{1,\dots, n\}$, we denote $PIL(A)$ by $PIL(n)$.
We also denote the one-element set $PIL(\{0\})$ by $PIL(0)$.
\end{enumerate}
\end{dfn}
\begin{exam}\label{ex:lists}
If $n=2$, then $|PIL(2)|=3$. The three elements of $PIL(2)$ are $\{(1,2)\},\, \{(2,1)\}, \,$ and $\{(1), (2)\}$.
If $n=3$, then $|PIL(3)|=13$. There are six PIL's of the form $\{(i_1, i_2, i_3 )\; \}$,
six of the form $\{(i_{1} i_{2}), (i_{3})\}$, and lastly, the PIL $\{(1), \, (2),\, (3)\}$.
\end{exam}
\begin{thm}\label{thm:counttypeA}
The number of $B_{n-1}$-orbits on the flag variety $\mathcal{B}_n$ of $\mathfrak{gl}(n)$ is $|PIL(n)|$.
\end{thm}
\begin{proof} For the proof, we adopt the convention that if $\Sigma = \{ \sigma_1, \dots, \sigma_k \} \in PIL(n)$ then $n \in {\rm supp}(\sigma_1)$, which is no loss of generality. Recall from Section \ref{ss:Korbits} that the $K$-orbit decomposition may be written as $\mathcal{B}_n = \sqcup_{1 \le i \le j \le n} Q_{i,j}$. Since $B_{n-1} \subset K$, it follows that $B_{n-1}\backslash \mathcal{B}_n = \sqcup_{1 \le i \le j \le n} B_{n-1} \backslash Q_{i,j}$. The subset of $PIL(n)$ corresponding to the $B_{n-1}$-orbits in $Q_{i,j}$ is
\begin{equation}\label{e.qij}
PIL(n)_{i,j}:= \{ \Sigma = \{ \sigma_1, \dots, \sigma_k \} \in PIL(n) : \sigma_1(i)=n \mbox{ and } \ell(\sigma_1)=n-(j-i)\}.
\end{equation}
The reader can check easily that $PIL(n)=\sqcup_{1\le i\le j \le n} PIL(n)_{i,j}.$
Hence, to prove the theorem, it suffices to verify that $|B_{n-1}\backslash Q_{i,j} |=|PIL(n)_{i,j}|.$ By Theorem 3.1 of \cite{CE21I}, for each $K$-orbit $Q_{i,j}$ in $\mathcal{B}_n$, there is a parabolic subgroup $R_{i,j}$ of $G$ such that
$K\cap R_{i,j}$ is a parabolic subgroup of $K$ with Levi factor
$GL(j-i) \times (GL(1))^{n-(j-i)-1}$. Further, by Theorem 3.5 and Notation 3.6 as well as Theorem 3.8 of \cite{CE21I}, the $B_{n-1}$-orbits on $Q_{i,j}$ are classified by
$\mathcal{O}(Q_{\fr},Q_{\fl})$ as $Q_{\mbox{${\mathfrak r}$}}$ varies over $B_{n-1}$-orbits on $K/K\cap R_{i,j}$
and $Q_{\mbox{${\mathfrak l}$}}$ varies over $B_{j-i-1}$-orbits in $\mathcal{B}_{j-i}$. Thus,
\begin{equation}\label{eq:BinKcount}
|B_{n-1} \backslash Q_{i,j} | = |B_{n-1}\backslash K /K\cap R_{i,j} | \cdot |B_{j-i-1}\backslash \mathcal{B}_{j-i} |.
\end{equation}
To compute $|PIL(n)_{i,j}|$, we first consider the set of lists $$\mathfrak{S}_{i,j}:= \{ \mbox { lists } \sigma_1 : \ell(\sigma_1)=n-(j-i), \sigma_1(i)=n, \mbox { and }{\rm supp}(\sigma_1) \subset \{ 1, \dots, n \} \}.$$
We note that $|\mathfrak{S}_{i,j}|=|B_{n-1}\backslash K/K\cap R_{i,j}|.$ Indeed, the Bruhat decomposition implies that
$|B_{n-1}\backslash K/K\cap R_{i,j}|=|W_K|/|W_{K\cap R_{i,j}}|,$ while
$|\mathfrak{S}_{i,j}|=(n-1)!/(j-i)!$ since $\mathfrak{S}_{i,j}$ parametrizes the numbers of ways to choose an ordered subset of cardinality $n-(j-i)-1$ from a set with $n-1$ elements. Since $W_K$ is the symmetric group on $n-1$ letters and $W_{K\cap R_{i,j}}$ is the symmetric group on $j-i$ letters, the assertion follows.
From the definition of $PIL(n)_{i,j}$ in (\ref{e.qij}), we have a surjective map
$$
\pi: PIL(n)_{i,j}\to \mathfrak{S}_{i,j}\mbox{ given by } \{\sigma_{1},\sigma_{2},\dots, \sigma_{n}\}\to \sigma_{1}.
$$
For any $\sigma_{1}\in\mathfrak{S}_{i,j}$, the fibre $\pi^{-1}(\sigma_{1})$ is $PIL(\{1,\dots, n\}\setminus \mbox{supp}(\sigma_{1}))$. Since
$\ell(\sigma_{1})=n-(j-i)$, the set $\{1,\dots, n\}\setminus \mbox{supp}(\sigma_{1})$ has cardinality $j-i$. Thus,
$|\pi^{-1}(\sigma_{1})|=|PIL(j-i)|$. By induction, we may assume that
$|PIL(j-i)|=|B_{j-i-1}\backslash \mathcal{B}_{j-i}|$. Thus,
$$|PIL(n)_{i,j}|=|\mathfrak{S}_{i,j}||PIL(j-i)|= |B_{n-1}\backslash K /K\cap R_{i,j} | \cdot |B_{j-i-1}\backslash \mathcal{B}_{j-i} |,$$
and the result now follows from Equation (\ref{eq:BinKcount}).
\end{proof}
\subsection{Orthogonal Case}\label{ss:orthogonal}
To parameterize the $B_{n-1}$-orbits on $\mathcal{B}_{n}$ in the orthogonal case, we need to introduce the concept of a signed PIL which we
abbreviate by the acronym SPIL. We begin with the definition of a signed list.
\begin{dfn}\label{d:signedlistsB}
Let $A=\{a_{1},\dots, a_{k}\}\subset \mathbb{Z}_{\geq 0}$ be a finite set. We define a signed list of the set
$A$ to be an ordered subset $(\lambda_{1},\dots, \lambda_{r})$ of the set $\{\pm a_{1}, \dots, \pm a_{k}\}$ with the property that
$\lambda_{m}\neq \pm \lambda_{n}$ for $m\neq n$.
\end{dfn}
\noindent For any signed list $\sigma=(\lambda_{1},\dots, \lambda_{r})$, let $|\sigma|=(|\lambda_{1}|, \dots, |\lambda_{r}|).$
\begin{dfn}\label{d:SPILS}
For any set $A\subset\mathbb{Z}_{\geq 0}$, we define a \emph{signed} $PIL$ (abbreviated SPIL) of $A$ to be a collection
$\Sigma$ of signed lists of $A$ with $\Sigma=\{\sigma_{1},\dots, \sigma_{k}\}$
such that $|\Sigma|:=\{|\sigma_{1}|,\dots, |\sigma_{k}|\}\in PIL(A)$ and $\Sigma$ satisfying the following two conditions:
\begin{equation}\label{eq:Sigmaconds}
\begin{split}
& (1)\mbox{ The last entry of any signed list } \sigma_{i} \mbox{ is non-negative.}\\
& (2) \mbox{ If }0\in\sigma_{i}, \mbox{ then }0 \mbox{ is the last entry of } \sigma_{i}.
\end{split}
\end{equation}
\end{dfn}
\begin{nota}
As for PILs, we denote the set of SPILs of the set $\{1,\dots,\ell\}$ by
$SPIL(\ell)$ and the set of SPILs of $\{0, 1,\dots, \ell\}$ by
$SPIL(\ell\cup\{0\})$. For convenience, we denote the one-element set $SPIL(\{0\})$ by $SPIL(0)$.
\end{nota}
\begin{exam}\label{ex:spils}
First note that $|SPIL(1)|=1$ and $|SPIL(1 \cup \{ 0 \})|=3.$ Indeed,
$SPIL(1 \cup \{ 0 \})$ consists of $\{(\pm 1, 0)\}$ and $\{ (1), (0) \}.$
While we saw above that $|PIL(2)|=3,$
there are
five elements in SPIL(2). They are $\{(\pm 1, 2)\},\, \{(\pm 2, 1)\},\, \mbox{and }\{(1), (2)\}$.
There are seventeen elements of $SPIL(2\cup\{0\})$. Indeed, for $a,\, b\in \{1,\, 2\}$ with $a\neq b$, we have
eight SPIL's of the form $\{(\pm a, \pm b, 0)\}$, four of the form $\{(\pm a, 0), (b)\}$,
and five of the form $\{(0), \Sigma\}$ with $\Sigma\in SPIL(2)$. One can also
compute that $|SPIL(3)|=37$, $|SPIL(4)|=361$, $|SPIL(3\cup\{0\})|=139$, and
$|SPIL(4\cup\{0\})|=1473.$
\end{exam}
To prove the main result of this section, we first require a technical lemma.
Let $A=\{a_{1},\dots, a_{k}\}\subset \mathbb{N}$. For any $x\in A$, we define a subset $SPIL_{x}(A)$ of $SPIL(A)$ by
$$
SPIL_{x}(A):=\{\Sigma\in SPIL(A)|\, \pm x \mbox{ occurs at the beginning of a signed list in $\Sigma$}\}.
$$
\begin{lem}\label{l:shift}
There is a bijection between the sets
$$
SPIL_{x}(A)\leftrightarrow SPIL(A\setminus\{x\} \cup \{0\}).
$$
\end{lem}
\begin{proof}
We first define a map $\Lambda:SPIL(A\setminus\{x\} \cup \{0\})\to SPIL_{x}(A)$ by
$$
\Lambda(\{(\lambda_{1},\dots ,\lambda_{j-1}, \lambda_{j},0), \sigma_{2},\dots, \sigma_{k}\})=\{(\mbox{sgn}(\lambda_{j})x, \lambda_{1},\dots \lambda_{j-1}, |\lambda_{j}|), \sigma_{2},\dots, \sigma_{k}\}.
$$
To define the map $\Gamma$ in the other direction, consider $\Sigma\in SPIL_{x}(A)$
with\\ $\Sigma=\{(\pm x,\mu_{1},\dots, \mu_{r}), \sigma_{2},\dots, \sigma_{k}\}$. We then define
$$
\Gamma(\Sigma):=\{(\mu_{1},\dots, \mu_{r-1}, \pm \mu_{r}, 0), \, \sigma_{2},\dots, \sigma_{k} \}.
$$
We leave it the reader to check that $\Lambda$ and $\Gamma$ are inverse mappings.
\end{proof}
We can now prove the main result of this section.
\begin{thm}\label{thm:orthocount}
\begin{enumerate}
\item The number of $B_{SO(2\ell-1)}$-orbits on $\mathcal{B}_{\mathfrak{so}(2\ell)}$ is $|SPIL(\ell)|$.
\item The number of $B_{SO(2\ell)}$-orbits on $\mathcal{B}_{\mathfrak{so}(2\ell+1)}$ is $|SPIL(\ell\cup\{0\})|$.
\end{enumerate}
\end{thm}
\begin{proof}
We prove by induction that the number of $B_{SO(n-1)}$-orbits on $\mathcal{B}_{\mathfrak{so}(n)}$ is given by $SPIL(\frac{n-1}{2} \cup \{ 0 \})$ when $n$ is odd and by $SPIL(\frac{n}{2})$ when $n$ is even. The cases $n=1$ and $n=2$ are both trivial.
The inductive argument depends on whether $n$ is even or odd. We begin with the case when $n=2\ell + 1$ is odd. In this case, the $K=SO(2\ell)$-orbits are parametrized in Section \ref{ss:Korbits} as $Q_0, \dots, Q_{\ell-1}, Q_+,$ and $Q_-$. Abusing notation, we define $Q_{\ell}:=Q_{+}\cup Q_{-}$. Since $B_{SO(2\ell)} \subset K$, it follows that the number of $B_{SO(2\ell)}$-orbits on
$\mathcal{B}_{\mathfrak{so}(2\ell + 1)}$ equals $\sum_{i=0}^{\ell} |B_{SO(2\ell)}\backslash Q_i|$. First, we compute $|B_{SO(2\ell)}\backslash Q_{\ell}|$. By Remark \ref{r:Korbitlength}, each orbit
$Q_{\pm}$ is $K$-equivariantly isomorphic to the flag variety of $K$, so that $|B_{SO(2\ell)}\backslash Q_{\pm}|=|W_{K}|=2^{\ell-1} \ell !$, whence
\begin{equation}\label{eq:closedcount}
|B_{SO(2\ell)}\backslash Q_{\ell}|=2^{\ell} \ell !.
\end{equation}
Now to compute $|B_{SO(2\ell)}\backslash Q_i|$ for $i\leq \ell-1$, note that in Equations (3.4) and (3.5) and Theorem 3.1 of \cite{CE21I}, we associate to each $Q_i$ a parabolic subgroup $R_i\subset G$ with Levi factor $L$. The Lie algebra $\mbox{${\mathfrak l}$}$ of $L$ is isomorphic to $\mathfrak{so}(2(\ell -i)+1) \oplus \mathfrak{gl}(1)^i$ and $\mbox{${\mathfrak l}$} \cap \mbox{${\mathfrak k}$}$ is the Lie algebra of a Levi factor of the parabolic subgroup $K\cap R_i$ of $K$, with $\mbox{${\mathfrak l}$} \cap \mbox{${\mathfrak k}$} \cong \mathfrak{so}(2(\ell -i)) \oplus \mathfrak{gl}(1)^i.$ Then using Theorem 3.5, Notation 3.6, and Theorem 3.8 of {\it loc. cit.}, $B_{SO(2\ell)}$-orbits in $Q_i$ are parametrized by pairs $(Q_{\mbox{${\mathfrak r}$}}, Q_{\mbox{${\mathfrak l}$}})$, where $Q_{\mbox{${\mathfrak r}$}}$ runs through $B_{SO(2\ell)}$-orbits in $K/K\cap R_i$ and $Q_{\mbox{${\mathfrak l}$}}$ runs through $B_{SO(2(\ell -i)-1)}$-orbits on $\mathcal{B}_{\mathfrak{so}(2(\ell-i))}.$ By induction using the case (1) where $n$ is even, the number of orbits $Q_{\mbox{${\mathfrak l}$}}$ that arise is $|SPIL(\ell - i)|.$ The number of orbits $Q_{\mbox{${\mathfrak r}$}}$ that arise in this parametrization is $$\frac{|W_{\mbox{${\mathfrak k}$}}|}{|W_{\mbox{${\mathfrak k}$}\cap \mbox{${\mathfrak l}$}}|} = \frac{2^{\ell-1} \cdot {\ell}!}{2^{\ell - i - 1}\cdot (\ell - i)!} = \frac{2^i \cdot {\ell}! }{(\ell - i)!}.$$
Using these observations along with (\ref{eq:closedcount}), we have
\begin{equation}\label{e.qiorbits}
|B_{SO(2\ell)}\backslash Q_i | =
|SPIL(\ell - i)| \cdot \frac{2^i \cdot {\ell}! }{(\ell - i)!} \mbox{ for } i=0,\dots, \ell.
\end{equation}
To show $|B_{SO(2\ell)} \backslash \mathcal{B}_{\mathfrak{so}(2\ell + 1)}|$ coincides with $|SPIL(\ell \cup \{ 0 \} )|$, we give an analogous partition of $SPIL(\ell \cup \{ 0 \}).$ For convenience, we assume that if $\Sigma = \{ \sigma_1, \dots, \sigma_k \} \in SPIL(\ell \cup \{ 0 \}),$ then $0 \in \sigma_1.$
For $i=0, \dots, \ell$, we let $$SPIL(\ell \cup \{ 0 \})^i = \{ \Sigma = \{ \sigma_1, \dots, \sigma_{k} \} \in SPIL(\ell \cup \{ 0 \}) : \ell(\sigma_1)=i+1 \}.$$
We note that
$$
{SPIL(\ell \cup \{ 0 \})}^{\ell} = \{ \sigma_1 = (b_1, \dots, b_{\ell}, 0) : \mbox{supp}(|\sigma_{1}|)=\{1,\dots, \ell\} \}.
$$
\noindent It is clear that $SPIL(\ell \cup \{ 0 \}) = \sqcup_{i=0}^{\ell} {SPIL(\ell \cup \{ 0 \})}^i$ . Hence, to complete the case when $n=2\ell + 1$, it suffices to show that
$|{SPIL(\ell \cup \{ 0 \})}^{i}|=|B_{SO(2\ell)}\backslash Q_i|$ for $i=0, \dots, \ell $.
Let $SLI(i, \ell)$ denote the set of signed lists on an $i$-tuple of distinct integers chosen from $\{ 1, \dots, \ell \}.$
We have a surjective map
\begin{equation}\label{eq:mappi}
\pi: SPIL(\ell \cup \{ 0 \})^{i}\to SLI(i,\ell)\mbox{ given by } \pi:\{ \sigma_1, \dots, \sigma_k \}\to (b_1, \dots, b_i), \mbox{where } \sigma_1=(b_1, \dots, b_i, 0).
\end{equation}
For a signed list $(b_1, \dots, b_i)\in SLI(i,\ell)$, the fibre $\pi^{-1}((b_1, \dots, b_i))$ has cardinality $|SPIL(\ell-i)|$.
Since $|SLI(i, \ell)| = \frac{2^i\cdot \ell !}{(\ell -i)!}$, it follows that
\begin{equation}\label{eq:countSPILi}
|{SPIL(\ell \cup \{ 0 \})}^{i}|= \frac{2^i \cdot \ell !}{(\ell -i)!} \cdot |SPIL(\ell - i)|,
\end{equation} and this coincides with
$|B_{SO(2\ell)}\backslash Q_i |$ by Equation \eqref{e.qiorbits}.
It remains to establish the inductive step for the even case $n=2\ell$, and this follows the same outline as in the odd case, although some features of the calculation are different. On the orbit side, the $K=SO(2\ell-1)$-orbits on
$\mathcal{B}_{\mathfrak{so}(2\ell)}$ are parametrized in Section \ref{ss:Korbits} as $Q_i$, $i=1, \dots, \ell-1$, and the closed orbit $Q_+$. For convenience, denote $Q_+$ by $Q_{\ell}$. On the combinatorial side, we adopt the convention that for an element $\Sigma = \{ \sigma_1, \dots, \sigma_k \}$ in $SPIL(\ell)$, the elements $\pm \ell$ occur in $\sigma_1$. For $i=1, \dots, \ell$, let ${SPIL(\ell)}^i := \{ \Sigma = \{ \sigma_1, \dots, \sigma_k \} : \sigma_1(i)=\pm \ell \}.$ To establish the even case, it suffices to show that $|B_{SO(2\ell - 1)}\backslash Q_i| = |{SPIL(\ell)}^i|$ for $i=1, \dots, \ell.$ On the geometric side, in Equation (3.7) of \cite{CE21I}, we associate to the orbit $Q_i$ a parabolic subgroup $R_i\subset G$ with Levi factor $L$ whose Lie algebra $\mbox{${\mathfrak l}$} \cong \mathfrak{so}(2(l-i)+2) \oplus \mathfrak{gl}(1)^{i-1}$
such that $K\cap R_i$ is a parabolic subgroup of $K$ with Levi factor $K\cap L$ with $\mbox{Lie}(K\cap L)=\mbox{${\mathfrak k}$} \cap \mbox{${\mathfrak l}$} \cong \mathfrak{so}(2(l-i)+1) \oplus \mathfrak{gl}(1)^{i-1}$. Further, by Theorem 3.5, Notation 3.6, and Theorem 3.8 of {\it loc.cit.}, the $B_{SO(2\ell-1)}$-orbits on $Q_{i}$ are parametrized by pairs $(Q_{\mbox{${\mathfrak r}$}}, Q_{\mbox{${\mathfrak l}$}})$ where $Q_{\mbox{${\mathfrak r}$}}$ runs through $B_{SO(2\ell - 1)}$-orbits on $K/K\cap R_i$ and $Q_{\mbox{${\mathfrak l}$}}$ runs through
$B_{SO(2(\ell-i))}$-orbits on $\mathcal{B}_{\mathfrak{so}(2(\ell - i)+1)}.$ By induction, the latter number is equal to $|SPIL(\ell - i \cup \{ 0 \})|.$ The number of $B_{SO(2\ell - 1)}$-orbits on $K/K\cap R_i$ is
$\frac{|W_K|}{|W_{K\cap L}|}=\frac{2^{i - 1}\cdot (\ell -1)!}{(\ell - i)!},$ as follows easily by the above description of $\mbox{${\mathfrak k}$} \cap \mbox{${\mathfrak l}$}$. Hence,
\begin{equation}\label{e.Bevencaseorbits}
|B_{SO(2\ell - 1)}\backslash Q_i|=\frac{2^{i - 1}\cdot (\ell -1)!}{(\ell - i)!}\cdot |SPIL(\ell - i \cup \{ 0 \})|.
\end{equation}
To count the elements on the combinatorial side, for $\Sigma = \{ \sigma_1, \dots, \sigma_k \} \in {SPIL(\ell)}^i,$ let $\sigma_1 =(b_1, \dots, b_{i-1}, \pm \ell, b_i, \dots, b_{\ell(\sigma_1)})$. We consider the surjective map
$$
\pi: SPIL(\ell)^{i}\to SLI(i-1,\ell-1) \mbox{ given by } \pi(\Sigma)=(b_{1},\dots, b_{i-1}).
$$
As we observed above in the case $n=2\ell+1$, $|SLI(i-1,\ell-1)|=\frac{2^{i-1} (\ell-1) !}{(\ell-i) !}.$
Further, the fibre $\pi^{-1}(\pi(\Sigma))$ is in bijection with the set $SPIL_{\ell}(\{1,\dots, \ell\}\setminus \{b_{1},\dots, b_{i-1}\})$.
It now follows from Lemma \ref{l:shift} that
\begin{equation} \label{e:evencombinatorics}
|{SPIL(\ell)}^i|=\frac{2^{i - 1}\cdot (\ell -1)!}{(\ell - i)!} \cdot
|SPIL(\ell - i \cup \{ 0 \}) |.
\end{equation}
The even case now follows by Equations \eqref{e.Bevencaseorbits} and \eqref{e:evencombinatorics}, and this completes the proof.
\end{proof}
\subsection{Formulas and Exponential Generating Functions for $B_{n-1}$-orbits} \label{ss:formulae}
To find formulas for $|B_{n-1}\backslash \mathcal{B}_{n}|$ in the different cases
using Theorems \ref{thm:counttypeA} and \ref{thm:orthocount}, we introduce the
\emph{Lah numbers} which play an important role in enumerative combinatorics and applied mathematics (see \cite{daboullah} and other references).
\begin{dfn}\label{d:Lahnumbers}
Given $n\in \mathbb{N}$ and $1\leq k\leq n$, the $(n,k)$ Lah number, $L(n,k)$, is defined by the formula
\begin{equation}\label{eq:Lahnumber}
L(n,k)=\frac{n !}{k!}{n-1\choose k-1}.
\end{equation}
It is well known that the number $L(n,k)$ is the number of ways to partition a set of
$n$ elements into $k$ lists, so that $|PIL(n)|=\sum_{k=1}^n L(n,k)$.
\end{dfn}
\noindent The following result follows immediately from Definitions \ref{dfn:lists} and \ref{d:Lahnumbers} and
Theorem \ref{thm:counttypeA}.
\begin{prop}\label{p:formulaA}
Let $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$.
A formula for the sequence $\{|B_{n-1}\backslash \mathcal{B}_{n}|\}_{n\in \mathbb{N}}$ is
\begin{equation}\label{eq:typeAformula}
|B_{n-1}\backslash \mathcal{B}_{n}|= \displaystyle\sum_{k=1}^{n} L(n,k)=\displaystyle\sum_{k=1}^{n}\frac{n!}{k!}{n-1\choose k-1}.
\end{equation}
\end{prop}
Recall that if $\{ f(n) \}_{n\in \mathbb{Z}_{\ge 0}}$ is a sequence of complex numbers, the corresponding exponential generating function $E_f(x)$ is the formal power series $\sum \frac{f(n) }{n!} x^n.$
For functions $f, g:{\mathbb{Z}}_{\ge 0} \to \mbox{${\mathbb C}$}$, define $s=s(f,g, \cdot):{\mathbb{Z}}_{\ge 0} \to \mbox{${\mathbb C}$}$ by $s(n)=\sum_{k=0}^{n}{n\choose k} f(k)g(n-k)$. Then the multiplication principle for exponential generating functions asserts that $E_s(x)=E_f(x)\cdot E_g(x)$ (Proposition 5.1.3 and its proof in \cite{Stanley99}).
Let $P_k(n)$ denote the set of partitions $\lambda_1 + \dots + \lambda_k = n$ of $n$ into $k$ parts. Now for functions $f, g:{\mathbb{Z}}_{\ge 0} \to \mbox{${\mathbb C}$}$, assume $g(0)=1$ and $f(0)=0$, and define a new function $h=h(f,g, \circ):{\mathbb{Z}}_{\ge 0} \to \mbox{${\mathbb C}$}$ by $h(0)=1$ and $h(n)=\sum_{k=1}^n \sum_{\lambda \in P_k(n)} g(k)\cdot \prod_{i=1}^k f(\lambda_i).$ Then the composition principle of exponential generating functions asserts that $E_h(x)=E_g(E_f(x))$ (see Theorem 5.1.4 in \cite{Stanley99}).
We can now obtain the exponential generating function for the sequence in (\ref{eq:typeAformula}). Let $f(n) = |PIL(n)|$ for $n\in\mathbb{Z}_{\geq 0}$.
\begin{prop}\label{p:egf}
The exponential generating function for the sequence
$\{|B_{n-1}\backslash \mathcal{B}_{n}|\}_{n\in{\mathbb{Z}}_{\ge 0}}$
is
$e^{\frac{x}{1-x}}$.
\end{prop}
\begin{proof}
By Theorem \ref{thm:counttypeA}, the sequence $\{|B_{n-1}\backslash \mathcal{B}_{n}|\}_{n\in\mathbb{Z}_{\geq 0}}$ coincides
with the sequence $\{|PIL(n)|\}_{n\in \mathbb{Z}_{\geq 0}}$. The reader can easily check that $|PIL(n)|=\sum_{k=1}^n \sum_{\lambda \in P_k(n)} \prod_{i=1}^k \lambda_i !$ for $n\geq 1$. Thus, if we take $f(n)=n!$ for $n > 0$ and $f(0)=0$ and $g(n)=1$ for all $n$, then $h(f,g, \circ)(n)=|PIL(n)|$ by an easy argument.
Since $E_f(x)= \frac{x}{1-x}$ and $E_g(x)= e^x$, the assertion follows by the composition principle.
\end{proof}
\begin{rem}\label{r.anrecursion}
It is well-known that the sequence $f(n)=|PIL(n)|=\sum_{k=1}^{n} L(n,k)$ satisfies the two-term
recursion relation
$$
f(n+1)=(2n+1)f(n)-(n^2-n)f(n-1).
$$
To verify this relation, let $f(x)=e^{\frac{x}{1-x}} = \sum \frac{f(n)}{n!}x^n$. By calculus, $(x-1)^2 f^{\prime}(x) = f(x)$ and if we compare the $x^n$ coefficients in the power series representing each side, we obtain the recursion relation.
Theorem \ref{thm:counttypeA} then implies that the sequence $\{|B_{n-1}\backslash \mathcal{B}_n|\}_{n\in \mathbb{N}}$ satisfies this recursion as well.
This is the assertion made without proof in the footnote on page 18 of \cite{Hashi}.
\end{rem}
We can also use Lah numbers to develop formulas for the number of $B_{n-1}$-orbits on $\mathcal{B}_n = \mathcal{B}_{\mathfrak{so}(n)}$
in the orthogonal cases. We begin with the type $D$ case, $n=2\ell$. Let
$SPIL(\ell,k) = \{ \Sigma = \{ \sigma_1, \dots, \sigma_k \} \in SPIL(\ell) \}.$
Note that $|SPIL(\ell,k)|=2^{\ell-k}L(\ell,k)$ using Property (1) from Equation \eqref{eq:Sigmaconds} in the definition of $SPIL(\ell).$
\begin{prop}\label{p:formulaD}
For $\ell \in\mathbb{N}$,
\begin{equation}\label{eq:formulaD}
|B_{SO(2\ell-1)}\backslash \mathcal{B}_{\mathfrak{so}(2\ell)}|=\displaystyle\sum_{k=1}^{\ell} 2^{\ell-k} L(\ell,k)=\displaystyle\sum_{k=1}^{\ell} 2^{\ell-k} \frac{\ell !}{k !} {\ell-1 \choose k-1}.
\end{equation}
\end{prop}
\begin{proof}
Equation (\ref{eq:formulaD}) follows from Part (1) of Theorem \ref{thm:orthocount}, and the above formula for $|SPIL(\ell, k)|.$
\end{proof}
As in the type $A$ case, we can also obtain a generating function for the sequence $\{|B_{SO(2\ell-1)}\backslash \mathcal{B}_{\mathfrak{so}(2\ell)}|\}_{\ell\in\mathbb{Z}_{\geq 0}}$.
\begin{prop}\label{p:typeDgenfun}
The exponential generating function for the sequence
$$\{|B_{SO(2\ell-1)}\backslash \mathcal{B}_{\mathfrak{so}(2\ell)}|\}_{\ell\in\mathbb{Z}_{\geq 0}}\mbox{ is }e^{\frac{x}{1-2x}}.$$
\end{prop}
\begin{proof}
By Part (1) of Theorem \ref{thm:orthocount}, for each $\ell\in {\mathbb{Z}}_{\geq 0}$, $|SPIL(\ell)|=|B_{SO(2\ell - 1)}\backslash \mathcal{B}_{\mathfrak{so}(2\ell)}|.$
Note that $|SPIL(\ell)| = \sum_{k=1}^\ell \sum_{\lambda \in P_k(\ell)} 2^{\lambda_i - 1}\cdot \lambda_i !,$ for $\ell \geq 1.$
We let $f(\ell)=2^{\ell-1}\cdot \ell!$ and $f(0)=0$ and let $g(\ell)=1$ for all $\ell$, and note that if $h=h(f,g, \circ)$, then $h(\ell)=|SPIL(\ell)|.$ By the composition principle, we conclude that $E_h(x)=E_g(E_f(x)).$ Since $\frac{x}{1-2x} = \sum_{\ell \in {\mathbb N}} 2^{\ell-1}\cdot x^\ell,$ $E_f(x)=\frac{x}{1-2x}$ and the proposition follows.
\end{proof}
The type $B$ case is slightly more involved than the other cases.
\begin{prop}\label{p:formulaB}
For $\ell \in\mathbb{N}$,
\begin{equation}\label{eq:formulaB}
|B_{SO(2\ell)}\backslash \mathcal{B}_{\mathfrak{so}(2\ell + 1)}|=\displaystyle\sum_{k=1}^{\ell+1}\frac{\ell !}{(k-1) !} {\ell\choose k-1} 2^{\ell-k+1}.
\end{equation}
\end{prop}
\begin{proof}
By Part (2) of Theorem \ref{thm:orthocount}, $|B_{SO(2\ell)}\backslash \mathcal{B}_{\mathfrak{so}(2\ell + 1)}|=|SPIL(\ell\cup\{0\})|$.
Let
$$
SPIL(\ell\cup\{0\},k):=\{\Sigma\in SPIL(\ell\cup\{0\}):\, \Sigma=\{\sigma_{1},\dots, \sigma_{k}\}\}.
$$
Of course,
\begin{equation}\label{eq:SPILcount}
|SPIL(\ell\cup\{0\})|=\sum_{k=1}^{\ell+1} |SPILS(\ell\cup\{0\},k)|.
\end{equation}
To compute $|SPIL(\ell\cup\{0\},k)|$, we note that we can construct an element in $SPIL(\ell \cup \{ 0 \}, k)$ in steps as follows. First choose a list
$(i_1, \dots, i_{\ell})$ on the set $\{ 1, \dots, \ell \}$ and identify it with the list $(i_1, \dots, i_{\ell}, 0)$ on the set $\{ 0, 1, \dots, \ell \}$ satisfying
Condition (2) of Equation \eqref{eq:Sigmaconds}. We next choose $k-1$ elements $\{ j_1, \dots, j_{k-1} \}$ from $\{ 1, \dots, \ell \}$ and let
$\mbox{$\tilde{\sigma}$}_r = (i_{j_{r-1} + 1}, \dots, i_{j_r})$ for $r=1, \dots, k-1$ with $j_{0}=0$. Let $\mbox{$\tilde{\sigma}$}_k = (i_{j_{k-1} + 1}, \dots, i_\ell, 0 ).$ There are $\ell ! \cdot {\ell \choose k-1 }$ ways to choose an ordered sequence of lists $\tilde{\Sigma} = (\mbox{$\tilde{\sigma}$}_1, \dots, \mbox{$\tilde{\sigma}$}_{k-1},\mbox{$\tilde{\sigma}$}_{k})$ in this way.
The sequence of lists $\tilde{\Sigma}$ defines an element of $PIL(\ell\cup\{0\})$ by simply forgetting the
ordering of the lists $\tilde{\sigma_{i}}$. The reader can verify that another sequence of $k$ ordered lists $\Sigma^{\prime}=(\sigma_{1}^{\prime},\dots, \sigma_{k-1}^{\prime}, \sigma_{k}^{\prime})$
constructed in this fashion defines the same element of $PIL(\ell\cup\{0\})$ if and only if $\sigma_{i}^{\prime}=\tilde{\sigma}_{w(i)}$, $i\leq k-1$ for some permutation
$w$ of the set $\{1,\dots, k-1\}$ and $\sigma_{k}^{\prime}=\tilde{\sigma}_{k}$.
Thus, we can construct exactly $\frac{\ell ! {\ell \choose k-1}}{(k-1) !}$ elements of $PIL(\ell\cup\{0\})$ in this way.
From each of the $\frac{\ell ! {\ell \choose k-1}}{(k-1) !}$ such $PILs$, we can construct an element of $SPIL(\ell\cup \{0\}, k)$ by
assigning a sign to all of the non-final elements in each of the lists of the $PIL$ . There
are evidently $2^{\ell-k+1}$ ways to assign these signs to the $PIL$. It follows that
\begin{equation}\label{eq:SPILkcount}
|SPIL(\ell\cup\{0\},k)|= 2^{\ell-k+1}\frac{\ell !}{(k-1) !}{\ell\choose k-1}.
\end{equation}
Equation \eqref{eq:formulaB} now follows from Equations \eqref{eq:SPILcount} and \eqref{eq:SPILkcount}.
\end{proof}
We can also obtain an exponential generating function for the sequence $\{|B_{SO(2\ell)}\backslash \mathcal{B}_{\mathfrak{so}(2\ell+1)}|\}_{\ell\in\mathbb{Z}_{\geq 0}}.$
\begin{prop}\label{p:typeBgenfun}
The exponential generating function for the sequence
$$\{|B_{SO(2\ell)}\backslash \mathcal{B}_{\mathfrak{so}(2\ell + 1)}|\}_{\ell\in\mathbb{Z}_{\geq 0}}\mbox{ is } \frac{e^{\frac{x}{1-2x}}}{1-2x}.$$
\end{prop}
\begin{proof}
We observed in (\ref{eq:countSPILi}) that
\begin{equation}\label{eq:long}
|SPIL(\ell\cup\{0\})|=\displaystyle\sum_{i=0}^{\ell} |SPIL(\ell\cup \{0\})^{i}|=\displaystyle\sum_{i=0}^{\ell} \frac{2^{i} \ell ! } {(\ell-i) !} |SPIL(\ell-i)|=\displaystyle\sum_{i=0}^{\ell}{\ell\choose i} 2^{i} i! |SPIL(\ell-i)|.
\end{equation}
Now let $f:\mathbb{Z}_{\geq 0}\to \mathbb{N}$ be the sequence $f(i)=2^{i} i !$, and let $g:\mathbb{Z}_{\geq 0}\to \mathbb{N}$ be the
sequence $g(i)=|SPIL(i)|$. Then $E_{f}(x)=\frac{1}{1-2x}$, and $E_{g}(x)=e^{\frac{x}{1-2x}}$ by Proposition \ref{p:typeDgenfun} and Part (2) of Theorem \ref{thm:orthocount}.
The result now follows from Equation \ref{eq:long} and the multiplication principle for
exponential generating functions.
\end{proof}
\begin{rem}\label{r.bdrecursions}
For $n\in\mathbb{Z}_{\geq 0}$, let $d_n = |B_{SO(2n-1)}\backslash \mathcal{B}_{\mathfrak{so}(2n)}|$, and let $b_n = |B_{SO(2n)}\backslash \mathcal{B}_{\mathfrak{so}(2n+1)}|$. Then the sequences $\{ d_n \}$ and $\{ b_n \}$ satisfy the recursion relations
\[
d_{n+1}=(1+4n)d_n - 4(n^2 - n)d_{n-1} \mbox{ and } b_{n+1}=(3+4n) b_n - 4n^2 b_{n-1}.
\]
To verify these formulas, let $f(x)=\sum_{n=0} \frac{d_n}{n!} x^n = e^{\frac{x}{1-2x}}$ and verify that $(2x-1)^2 f^{\prime}(x)=f(x).$ Comparison of the $x^n$ coefficient gives the $d_n$-relation. For the $b_n$-relation, let $f(x)=\sum_{n=0} \frac{b_n}{n!} x^n = \frac{e^{\frac{x}{1-2x}}}{1-2x}$, and observe that $(2x-1)^2 f^{\prime}(x)=(3-4x) f(x)$. Now compare $x^n$ coefficients.
\end{rem}
\begin{rem}\label{r:Lahtransform}
Given a sequence $\{a_{n}\}_{n\in\mathbb{Z}_{\geq 0}}$, we define its Lah transform to be
the sequence $\{b_{n}\}_{n\in \mathbb{Z}_{\geq 0}}$ with $b_{n}:=\sum_{k=1}^{n} L(n,k) a_{k}$, and $b_{0}=a_{0}$ where
$L(n,k)$ is the $(n,k)$ Lah number defined in Equation (\ref{eq:Lahnumber}). It follows immediately
from Proposition \ref{p:formulaA} that the sequence $\{|B_{\mathfrak{gl}(n-1)}\backslash \mathcal{B}_{\mathfrak{gl}(n)}|\}_{n\in\mathbb{Z}_{\geq 0}}$ is the
Lah transform of the constant sequence $\{1\}_{n\in\mathbb{Z}_{\geq 0}}$.
We also claim that the sequence $\{|B_{\mathfrak{so}(2n-1)}\backslash \mathcal{B}_{\mathfrak{so}(2n)}|\}_{n\in\mathbb{Z}_{\geq 0}}$ is the Lah transform of the sequence
$\{|B_{\mathfrak{gl}(n-1)}\backslash \mathcal{B}_{\mathfrak{gl}(n)}|\}_{n\in\mathbb{Z}_{\geq 0}}$.
This follows from the following general fact concerning Lah transforms and exponential generating functions.
If $f(n)=a_{n}$ is a sequence and $g(n)=b_{n}$ is a sequence, then
$\{b_{n}\}_{n\in\mathbb{Z}_{\geq 0}}$ is the Lah transform of $\{a_{n}\}_{n\in\mathbb{Z}_{\geq 0}}$ if and only
if $E_{g}(x)=E_{f}(x/1-x)$.
This assertion can be demonstrated using the well-known recursion relation $L(n+1, k)=(n+k) L(n,k)+L(n,k-1)$ for
Lah numbers to show that for any smooth function $h(x)$,
$$
\frac{d^{n}}{(dx)^{n}} h\left( \frac{x}{1-x}\right)\Bigr |_{x=0}=\displaystyle\sum_{k=1}^{n} L(n,k) h^{(n)}(0),
$$
for $n\geq 1$.
\end{rem}
\section{Representatives for $B_{n-1}$-orbits}\label{s:std}
In this section, we give explicit representatives for $B_{n-1}$-orbits on the flag variety $\mathcal{B}_n.$ The constructions and proofs rely on the results on $PIL(n)$ and $SPIL(\ell)$ from the previous section. The cases of $GL(n), SO(2\ell)$, and $SO(2\ell + 1)$ are discussed separately.
\subsection{Representatives in the case of $GL(n)$}\label{ss:glreps}
We first describe the form of our standard representatives.
\begin{dfn-nota}\label{d:std}
\begin{enumerate}
\item For a standard basis vector $e_{i}\in\mbox{${\mathbb C}$}^{n}$ with $i\leq n-1$, we define $\hat{e}_{i}:=e_{i}+e_{n}$ and refer to $\hat{e}_{i}$ as a hat vector of index $i$.
\item We say that a flag
\begin{equation}\label{eq:basicflag}
\mathcal{F}:=(v_{1}\subset \dots \subset v_{i}\subset\dots\subset v_{n})
\end{equation}
in the flag variety $\mathcal{B}_n$ for $GL(n)$
is in \emph{standard form} if $v_{i}=e_{j_{i}}$ or $v_{i}=\hat{e}_{j_{i}}$ for all $i=1,\dots, n$, and
$\mathcal{F}$ satisfies the following three conditions:
\begin{enumerate}
\item $v_i = e_n$ for some $i.$
\item If $v_{i}=e_{n}$, then $v_{k}=e_{j_{k}}$ for all $j>i$.
\item If $i<k$ with $v_{i}=\hat{e}_{j_{i}}$ and $v_{k}=\hat{e}_{j_{k}}$, then $j_{i}>j_{k}$.
\end{enumerate}
\end{enumerate}
\end{dfn-nota}
\begin{rem}\label{r.glstandard}
If $\mathcal{F}=(v_{1}\subset \dots \subset v_{i}\subset\dots\subset v_{n})$ is a flag in standard form, then it follows easily that if $v_i = e_{j_i}$ or $\hat{e}_{j_i}$, then $\{ j_1, \dots, j_n \} = \{ 1, \dots, n \}$ consists of $n$ distinct indices.
\end{rem}
\begin{rem}\label{r.schubert} Let $B=B_n$ be the upper triangular Borel subgroup of $G=GL(n)$. Then it follows from the Bruhat decomposition that every $B$-orbit on the Grassmannian ${\rm Gr}(k,n)$ of $k$-planes in $\mbox{${\mathbb C}$}^n$ can be written as $B\cdot \mbox{${\rm span}$}\{e_{j_1}, \dots, e_{j_k}\}$ for a unique subset $\{ j_1, \dots, j_k \}$ of $\{ 1, \dots, n \}.$ Furthermore, every $B$-orbit on a partial flag variety can be written uniquely as the $B$-orbit through a collection of nested subspaces, where each subspace is a span of the vectors of the form $e_{j_i}$.
\end{rem}
It is useful for our purposes to classify $B_{n-1}$-orbits on ${\rm Gr}(k,n)$. Recall from Section 2.2 of \cite{CE21I} the automorphism on $GL(n)$, $\theta(g)=tgt^{-1}$, where $t=\mbox{diag}[1,\dots, 1,-1]$ so that $G_{n-1}=G^{\theta}$ (up to centre). Consider the $G_{n-1}$-stable decomposition $\mbox{${\mathbb C}$}^n = U_1 \oplus U_2$, where $U_1 = (\mbox{${\mathbb C}$}^{n})^{t}$ and $U_2=(\mbox{${\mathbb C}$}^{n})^{-t}$ are the $n-1$ and $1$ dimensional subspaces consisting of $t$ and $-t$ fixed spaces on $\mbox{${\mathbb C}$}^n.$
\begin{lem} \label{l:AGrass} Let $Q=B_{n-1}\cdot W$ be the $B_{n-1}$-orbit through a subspace $W \subset {\rm Gr}(k,n)$.
\begin{enumerate}
\item If $W\subset U_1$, then $Q={\mathcal{O}}_{j_1, \dots, j_k} := B_{n-1}\cdot \mbox{${\rm span}$}\{e_{j_1}, \dots, e_{j_k}\}$ for a unique subset $\{ j_1, \dots, j_k \}$ of $\{ 1, \dots, n-1 \}.$
\item If $\dim(W \cap U_1)=k-1$ and $U_2 \subset W$, then $Q={\mathcal{O}}_{j_1, \dots, j_{k-1}, n} := B_{n-1}\cdot \mbox{${\rm span}$}\{e_{j_1}, \dots, e_{j_{k-1}}, e_n \}$ for a unique subset $\{ j_1, \dots, j_{k-1} \}$ of $\{ 1, \dots, n-1 \}.$
\item If $\dim(W \cap U_1)=k-1$ and $U_2 \not\subset W$, then
$Q= {\mathcal{O}}_{j_1, \dots, j_{k-1}, \hat{j}_k} := B_{n-1}\cdot \mbox{${\rm span}$}\{e_{j_1}, \dots, e_{j_{k-1}}, \hat{e}_{j_k} \}$ for a unique subset
$\{ j_1, \dots, j_k \}$ of $\{ 1, \dots, n-1\}.$
\end{enumerate}
\end{lem}
\begin{proof}
By linear algebra, the integers $(\dim(W \cap U_1), \dim(W \cap U_2))$ are
either $(1) \ (k, 0)$, $ (2) \ (k-1, 1)$, or $(3) \ (k-1, 0)$ and these conditions are evidentally invariant under the $B_{n-1}$-action. The classification of $B_{n-1}$-orbits on planes $W$ satisfying condition (1) is the same as the classification of $B_{n-1}$-orbits on ${\rm Gr}(k,n-1)$, and follows from Remark \ref{r.schubert}. The classification of $B_{n-1}$-orbits on planes $W$ satisfying condition (2) is the same as the classification of $B_{n-1}$-orbits on ${\rm Gr}(k-1,n-1)$, and again follows from Remark \ref{r.schubert}. Lastly, the classification of $B_{n-1}$-orbits on planes $W$ satisfying condition (3) reduces easily to the classification of $B_{n-1}$-orbits of partial flags $(W\cap U_1 \subset p_{1}(W))$ in ${\rm Gr}(k-1, n-1) \times {\rm Gr}(k,n-1)$, where $p_{1}:\mbox{${\mathbb C}$}^n \to U_1$ is projection off the subspace $U_2.$ By Remark \ref{r.schubert}, we may assume $W \cap U_1$ is the span of vectors $e_{j_1}, \dots, e_{j_{k-1}}$ with each $j_i < n$ and $p_{1}(W)$ is given by adjoining another vector $e_{j_k}$ with $j_k < n.$ The assertion now follows easily.
\end{proof}
\begin{prop}\label{p:AflagsandPILS}
There is a bijection
\begin{equation}\label{eq:AGamma}
\Gamma: PIL(n) \longleftrightarrow \{\mbox{Complete flags in standard form in $\mbox{${\mathbb C}$}^n$}\}.
\end{equation}
\end{prop}
\begin{proof}
Let $\Sigma\in PIL(n)$ with $\Sigma=\{\sigma_{1},\, \sigma_{2},\,\dots, \, \sigma_{t}\},$ let $\ell(\sigma_j)=k_j$ and let $\sigma_{j}=(i_{j,1},\dots, i_{j, k_{j}}).$
The lists $\sigma_j$ in $\Sigma$ may be ordered uniquely so that $i_{1,k_{1}}>i_{2,k_{2}}>\dots>i_{t-1, k_{t-1}}$ and $n\in\sigma_{t}$. If we order $\Sigma$ in this way,
and define $\Gamma(\Sigma)$ to be the flag
\begin{equation}\label{eq:Gammadef}
\begin{split}
\Gamma(\Sigma)=&(e_{i_{1,1}}\subset e_{i_{1,2}}\subset e_{i_{1,k_{1}-1}}\subset\hat{e}_{i_{1,k_{1}}}\subset e_{i_{2,1}}\subset\dots\subset \hat{e}_{i_{2,k_{2}}}\subset\dots\\
&\dots\subset e_{i_{t-1,1}}\dots\subset \dots \subset \hat{e}_{i_{t-1,k_{t-1}}}\subset e_{i_{t,1}}\subset \dots\subset e_{i_{t,k_{t}}}),
\end{split}
\end{equation}
then the flag $\Gamma(\Sigma)$ is in standard form. We now define a map $\Lambda:\{\mbox{Complete flags in standard form}\}\to PIL(n)$ inverse to $\Gamma.$ Let
$\mathcal{F}$ be a flag in standard form with $\mathcal{F}=(v_{1}\subset \dots \subset v_{n})$. Let $1\leq k_{1}<\dots< k_{r}< n$ be the subsequence of
$\{1,\dots, n\}$ such that $\{v_{k_{1}},\dots, v_{k_{r}}\}$ consists of all the hat vectors in the given flag. It follows that each $v_{k_{i}}=\hat{e}_{i_{k_{i}}}$ and $v_{j}=e_{i_{j}}$ for $j\notin\{k_{1},\dots, k_{r}\}$.
Then we define
\begin{equation}\label{eq:Lambdadefn}
\Lambda(\mathcal{F}):=\{(i_{1},\dots ,i_{k_{1}-1}, i_{k_{1}}), (i_{k_{1}+1},\dots ,i_{k_{2}}),\dots, (i_{k_{1}+\dots+k_{r-1}+1},\dots ,i_{k_{r}}),(i_{k_{1}+\dots+k_{r}+1}, \dots, i_{n})\}.
\end{equation}
It is routine to check that $\Lambda$ and $\Gamma$ are mutual inverses.
\end{proof}
We need a preliminary result concerning the span of vectors in a flag in standard form. For $\mathcal{F}=(v_1 \subset \dots \subset v_n)$, let $V_m = \mbox{${\rm span}$}\{ v_1, \dots, v_m \}.$ If ${\pi}_m:\mathcal{B}_n \to {\rm Gr}(m,n)$ is the natural projection, then $\pi_m(\mathcal{F})=V_m.$ We say $j_i$ is the index of $v_i$ if $v_i = e_{j_i}$ or $\hat{e}_{j_i}$.
\begin{lem}\label{l:spanstandard}
Let $\mathcal{F}=(v_1 \subset \dots \subset v_n)$ be a flag in standard form.
\par\noindent (i) If $v_{i}=e_{j_{i}}$ with $j_{i}\leq n$ for all $i=1,\dots,m$,
then $V_{m}=\mbox{span}\{e_{j_{1}},\dots, e_{j_{m}}\}$.
\par\noindent (ii) If $v_i=e_n$ for some $i$, then for all $m \ge i$, the space $V_m = \mbox{${\rm span}$}\{e_{r_1}, \dots, e_{r_{m-1}}, e_{n}\}$ where $\{ r_1, \dots, r_{m-1}, n \}$ are the indices of $v_1, \dots, v_m.$
\par\noindent (iii) Let $k_1 >\dots > k_s$ be the indices of the hat vectors appearing in the first $m$ vectors in $\mathcal{F}$ and let $r_1, \dots, r_{m-1}\in \{1,\dots, n-1\}$ be the indices of $v_i$ for $1\le i \le m$ besides $k_s$. Then $B_{n-1}\cdot V_m = {\mathcal{O}}_{r_1, \dots, r_{m-1}, \hat{k}_{s}}.$
\end{lem}
\begin{proof} The proof of (i) is trivial. The proof of (ii) is based on the observation that $\mbox{${\rm span}$} \{ \hat{e}_j , e_n\} = \mbox{${\rm span}$}\{ e_j, e_n \}.$ To prove (iii), note that
by part (c) of Definition \ref{d:std}, $k_i > k_s$ for $i < s$. Then the span of
$\hat{e}_{k_i}$ and $\hat{e}_{k_s}$ coincides with the space $\mbox{${\rm span}$} \{e_{k_i}-e_{k_s}, \hat{e}_{k_s}\}$, and this is $B_{n-1}$-conjugate to $\mbox{${\rm span}$}\{e_{k_i}, \hat{e}_{k_s}\}$ without altering any of the other vectors in $\mathcal{F}.$ Assertion (iii) follows by repeated application of this assertion.
\end{proof}
\begin{thm}\label{thm:std}
The map
\begin{equation}\label{eq:flagassoc}
\Psi:\mathcal{F} \to B_{n-1}\cdot \mathcal{F}
\end{equation}
is a bijection between flags in standard form and $B_{n-1}$-orbits on $\mathcal{B}_n$.
\end{thm}
\begin{proof}
By Theorem \ref{thm:counttypeA}, the set $PIL(n)$ has the same cardinality as
the set of $B_{n-1}$-orbits on $\mathcal{B}_n$, and by Proposition \ref{p:AflagsandPILS},
it follows that the number of flags in standard form coincides with the number of $B_{n-1}$-orbits on $\mathcal{B}_n.$ Thus, it suffices to show that the map $\Psi$ in (\ref{eq:flagassoc}) is injective.
To this effect, let $Q=B_{n-1}\cdot \mathcal{F}$, and $Q^{\prime}=B_{n-1}\cdot \mathcal{F}^{\prime}$ where $\mathcal{F}=(v_{1}\subset v_{2}\subset \dots\subset v_{i}\subset \dots \subset v_n )$,
and $\mathcal{F}^{\prime}=(v_{1}^{\prime}\subset v_{2}^{\prime}\subset \dots\subset v_{i}^{\prime}\subset \dots v_n^{\prime})$ are flags in standard form.
Suppose that $Q=Q^{\prime}$. We prove that $v_{i}=v_{i}^{\prime}$ for all $i$. The proof proceeds by induction on $i$ using the classification
of $B_{n-1}$-orbits on ${\rm Gr}(i, n)$ given in Lemma \ref{l:AGrass}.
Since $Q=Q^{\prime}$, we conclude that
$B_{n-1}\cdot V_{i}=B_{n-1}\cdot V_{i}^{\prime}$ for all $i$.
To begin the induction, consider the orbit $\mathcal{O}_{1}=B_{n-1}\cdot V_{1}=B_{n-1}\cdot V_{1}^{\prime}$. Then we must be in one of the three cases of Lemma \ref{l:AGrass}. In case (1), $v_1=e_{j_1}$ and $v_1^{\prime}=e_{k_1}$ with $j_1, k_1 < n$, and by Remark \ref{r.schubert}, $j_1=k_1$. In case (2), $v_1=e_n=v_1^{\prime}$. In case (3), $v_1 = \hat{e}_{j_1}$ and $v_1^{\prime}=\hat{e}_{k_1}$ with $j_1, k_1 < n$, and since the $B_{n-1}$-orbits through the lines $p_{1}(V_1)$ and $p_{1}(V_1^{\prime})$ coincide, we conclude by Remark \ref{r.schubert} that $j_1=k_1.$ Thus, in any case $v_1=v_1^{\prime}.$ For the inductive step, we may assume
that $v_{i}=v_{i}^{\prime}$ for $i=1,\dots, m-1$, so that $V_{m-1}=V_{m-1}^{\prime}$.
We prove that $v_m = v_m^{\prime}$ using our assumption that $B_{n-1}\cdot V_m = B_{n-1}\cdot V_m^{\prime}.$ To prove this, we argue based on the case of
$B_{n-1}\cdot V_{m-1}$ described in Lemma \ref{l:AGrass}. In case (1), $V_{m-1}\subset U_1$ and $V_{m-1}=\mbox{${\rm span}$}\{e_{j_1}, \dots, e_{j_{m-1}}\}$. If $v_m = e_{j_m}$ with $1 \le j_m \le n$, then $V_m = \mbox{${\rm span}$}\{e_{j_1}, \dots, e_{j_m}\}$ and $B_{n-1}\cdot V_m = {\mathcal{O}}_{j_1, \dots, j_m}$ or ${\mathcal{O}}_{j_1, \dots, j_{m-1}, n}.$ If $v_m = \hat{e}_{j_m}$, then $V_m = \mbox{${\rm span}$}\{e_{j_1}, \dots, e_{j_{m-1}}, \hat{e}_{j_m}\}$ and
$B_{n-1}\cdot V_m = {\mathcal{O}}_{j_1, \dots, j_{m-1}, \hat{j}_m}.$
Thus, we can recover $v_m$ from $V_{m-1}$
and $B_{n-1}\cdot V_m,$ whence $v_{m}=v_{m}^{\prime}$. In case (2), $B_{n-1}\cdot V_{m-1}=\mathcal{O}_{j_{1},\dots, j_{m-2}, n}$. By Lemma \ref{l:spanstandard}, it follows that $v_i = e_n$ for some $i < m$, and hence by the definition of a standard flag, $v_m = e_{j_m}$ for some $j_m < n.$ Another application of Lemma \ref{l:spanstandard} yields $V_m = \mbox{${\rm span}$}\{e_{j_1}, \dots, e_{j_m}\}$ and $j_{m}$ is the unique index that appears in ${\mathcal{O}}_{j_1, \dots, j_{m-2}, j_{m}, n} = B_{n-1}\cdot V_m$ that does not appear in $B_{n-1}\cdot V_{m-1}.$ In case (3), $B_{n-1}\cdot V_{m-1}=\mathcal{O}_{j_{1},\dots, j_{m-2}, \hat{k}_{s}}$, so by Lemma \ref{l:spanstandard}, the vector $\hat{e}_{k_s}$ must be $v_r$ for some $r \le m-1$ and $v_i \not= e_n$ for any $i \le m-1.$ Then if $v_m = e_{j_m}$ with $j_m < n$, then $B_{n-1}\cdot V_m=\mathcal{O}_{j_{1},\dots, j_{m-2}, j_{m}, \hat{k}_{s}}$, and we can recover $j_m$ from $V_{m-1}$ and $B_{n-1}\cdot V_m.$ If $v_m = e_n$, then $V_m$ is the span of $\{ e_{j_i} : i \le m-2 \},$ $e_n$, and $e_{k_s}$ and we can recover $e_n$ from $V_{m-1}$ and $V_m.$ If $v_m = \hat{e}_{j_m}$, then by the definition of a flag in standard form, we know that $j_m < k_s$. Using Lemma \ref{l:spanstandard}, we see easily that $B_{n-1}\cdot V_m={\mathcal{O}}_{j_1, \dots, j_{m-2}, k_s,\hat{j}_m,}.$ Hence, $v_m=\hat{e}_{j_m}$ is the hat index in the label of $B_{n-1}\cdot V_m$ which replaces $\hat{k}_s$ in $B_{n-1}\cdot V_{m-1}$ and thus is uniquely determined by $B_{n-1}\cdot V_m$ and $V_{m-1}.$ Thus in any case, $v_m$ is uniquely determined by $B_{n-1}\cdot V_m$ and $V_{m-1}$, and this establishes the theorem in the final case.
\end{proof}
\begin{rem}\label{r:pilorbit}
By composing the bijections $\Gamma$ and $\Psi$ from Proposition \ref{p:AflagsandPILS} and Theorem \ref{thm:std}, we obtain a bijection $\Psi \circ \Gamma: PIL(n) \to B_{n-1}\backslash \mathcal{B}_n.$ This bijection improves on the numerical equality of Theorem \ref{thm:counttypeA}, and in particular, reflects the twisting aspect of the bundle structure of orbits in a better way. It would be interesting to see whether this equivalence between elements of $PIL(n)$ and orbits is useful in understanding the geometry of orbit closures. We note that similar remarks apply in the orthogonal cases discussed later in this section, but we will omit them.
\end{rem}
\subsection{Representatives in the case of $SO(2\ell)$}\label{ss:Dreps}
In this subsection, we give explicit representatives for $B_{n-1}$-orbits on $\mathcal{B}_n$ in the case where $G=SO(2\ell).$ We omit some arguments which are similar to the case of $GL(n)$. Recall the description of $\mathcal{B}_{2\ell}$ in terms of isotropic flags from Section \ref{ss:Borels}.
\begin{dfn-nota}\label{d:stdD}
\begin{enumerate}
\item For $i=1,\dots, \ell-1$, we define $\hat{e}_{i}:=e_{-i}+e_{-\ell}$, and $\widetilde{e}_{i}:=e_{-i}+e_{\ell}$, which we refer to as hat vectors and tilde vectors respectively in $\mbox{${\mathbb C}$}^{2\ell}.$
\item We say that the isotropic flag
\begin{equation}\label{eq:basicflagD}
\mathcal{F}:=(v_{1}\subset \dots \subset v_{i}\subset\dots\subset v_{\ell-1})
\end{equation}
is in \emph{standard form} if $v_{i}$ is either a standard basis vector, a tilde vector, or a hat vector,
and $\mathcal{F}$ satisfies the following conditions:
\begin{enumerate}
\item If $v_{i}=e_{\pm\ell}$, then $v_{k}=e_{j_{k}}$ for $k>i$.
\item If $\mathcal{F}$ contains a tilde vector, then $e_{\ell}$ must also occur in $\mathcal{F}$.
\item If $v_{i}=\hat{e}_{j_{i}}$ and $v_{k}=\hat{e}_{j_{k}}$ for $i<k$, then $j_{i}<j_{k}$, and the analogous condition holds for tilde vectors.
\item The vectors $\hat{e}_{i}$ and $e_{-i}$ (respectively $\widetilde{e}_{i}$ and $e_{-i}$) do not both occur in $\mathcal{F}$.
\end{enumerate}
\end{enumerate}
We call such an isotropic flag a $SO(2\ell)$-flag in standard form.
If $v_i = e_{j_i}, \hat{e}_{j_i},$ or $\widetilde{e}_{j_i}$, then we say the index of $v_i$ is $|j_i|.$
\end{dfn-nota}
\begin{rem}\label{r.standardD}
It follows from definitions and the isotropic nature of the flag that the set of indices of $v_1, \dots, v_{\ell-1}$ consists of $\ell - 1$ distinct indices from $1$ to $\ell$. Further, hat vectors and tilde vectors cannot occur in the same flag in standard form, and if some hat vector $\hat{e}_i$ (resp. tilde vector $\widetilde{e}_i$) occurs, then $e_{\ell}$ (resp. $e_{-\ell}$) cannot also occur.
\end{rem}
\begin{rem}\label{r.outerD}
In Section 2.2 of \cite{CE21I}, we discuss an element $\sigma_{2\ell}$ of the orthogonal group $O(2\ell)$ which interchanges $e_{\ell}$ and $e_{-\ell}.$ The automorphism $\theta$ induced by conjugation by $\sigma_{2\ell}$ defines $SO(2\ell-1)$ in $SO(2\ell)$ and stabilizes $B_{2\ell-1}.$ If we considered orbits of the semidirect product of $B_{2\ell-1}$ and $\theta$, then we would not need tilde vectors.
\end{rem}
\begin{prop}\label{p:flagsandPILSD}
There is a bijection
\begin{equation}\label{eq:GammaD}
\Gamma:\{SPIL(\ell)\}\longleftrightarrow \{ SO(2\ell)-\mbox{Flags in standard form}\}.
\end{equation}
\end{prop}
\begin{proof}
Let $\Sigma=\{\sigma_{1},\, \sigma_{2},\,\dots, \, \sigma_{t}\},$ let $\ell(\sigma_j)=k_j$ and let $\sigma_{j}=(i_{j,1},\dots, i_{j, k_{j}}).$ We may choose the ordering of the $\sigma_j$ in a unique way so that
$i_{1,k_{1}}<\dots <i_{t-1,k_{t-1}}$ and $\pm \ell \in \sigma_{t}$. We say $\Sigma$ with this ordering is in case 1 if either $i_{t,k_{t}}=\ell$ or $-\ell\in\sigma_{t}$, and if so,
then $\Gamma(\Sigma)$ is given by Equation \eqref{eq:Gammadef} with the last vector $e_{i_{t,k_{t}}}$ omitted.
We say $\Sigma$ is in case 2 if $\ell\in \sigma_{t}$ and $\ell\neq i_{t,k_{t}}$, then we define $\Gamma(\Sigma)$ by (\ref{eq:Gammadef}), but with the hat vectors replaced by tilde vectors, and again omit the final vector $e_{i_{t,k_{t}}}$. Note that in case 1, the vector $e_{\ell}$ does not occur in $\Gamma(\Sigma)$ and in case 2, the vector $e_{\ell}$ does occur in $\Gamma(\Sigma)$. We note that in either case $\Gamma(\Sigma)$ is in standard form, as follows from the definition and Remark \ref{r.standardD}. We define the inverse map $\Lambda$ as follows. For a $SO(2\ell)$-flag $\mathcal{F}$ in standard form, then exactly one index in $\{ 1, \dots, \ell \}$ does not occur in $\mathcal{F}$ by Remark \ref{r.standardD}. If the vector $e_{\ell}$ does not occur in $\mathcal{F}$, then we use the formula of Equation \eqref{eq:Lambdadefn}, except the last index $i_{\ell}$ is the index in $\{ 1, \dots, \ell \}$ not appearing among the indices in $\mathcal{F}$. If the vector $e_{\ell}$ does occur in $\mathcal{F}$, then we use the same prescription as in the last case, but with tilde vectors replacing hat vectors. It is routine to check that $\Lambda$ and $\Gamma$ are inverse bijections.
\end{proof}
As in the type A case, we need to describe $B_{n-1}$-orbits on the space
$\mbox{OGr}(i,n)$ consisting of isotropic $i$-planes on $\mbox{${\mathbb C}$}^{n}$ for $1\le i \le n- 1.$ Let $B=B_{n}$ consist of the upper triangular matrices in $SO(n)$.
\begin{rem}\label{r:schubertD}
Let $n=2\ell$ or $2\ell + 1$. By the Bruhat decomposition, the distinct $B$-orbits on $\mbox{OGr}(i,n)$ are given by the
orbits through the planes $\mbox{${\rm span}$} \{ e_{j_1}, \dots, e_{j_i} \}$ where $\{j_{1},\dots, j_{i-1}, \, j_{i}\}\subset \{\pm 1,\dots, \pm \ell \}$,
with $j_{k}\neq \pm j_{m}$.
\end{rem}
In the case where $n=2\ell$, for $j=1, \dots, \ell$, we let $V_{< j}=\mbox{${\rm span}$}\{e_{1},\dots, e_{j-1}\}$
and for $j=0, \dots, \ell-2$, let $V_{<-j}=\mbox{${\rm span}$}\{ e_{-(j+1)},\dots, e_{-(l-1)} \}.$ Let $V_{+}=V_{<\ell}$ and $V_{-}=V_{<0}.$
\begin{rem}\label{r:bvectororbit}
Let $N_{2\ell-1}$ be the derived subgroup of $B_{2\ell-1}.$
\begin{enumerate}
\item For $j=1, \dots, \ell,$ the affine set $e_j + V_{<j} = N_{2\ell-1}\cdot e_j$ and $e_{-\ell} + V_{+} = N_{2\ell-1}\cdot e_{-\ell}.$
\item For $j=1, \dots, \ell -1,$ the set $$I_{-j}:=\{ v \in e_{-j} + V_{<-j} + \mbox{${\mathbb C}$}(e_{\ell} + e_{-\ell}) + V_{+}: \beta(v,v)=0 \} = N_{2\ell-1}\cdot e_{-j}.$$
\end{enumerate}
Indeed, to prove the second assertion, we first note that $I_{-j}$ is irreducible of dimension $2\ell - j - 2$. The variety $I_{-j}$ is clearly a quadratic hypersurface in the irreducible $2\ell-j-1$ dimensional affine set $e_{-j} + V_{<-j} + \mbox{${\mathbb C}$}(e_{\ell} + e_{-\ell}) + V_{+}$. To see that $I_{-j}$ is irreducible, we compute the equation $\beta(v,v)=0$. For $v\in I_{-j}$, we write
$v=e_{-j}+\sum_{k=j+1}^{\ell-1} c_{-k}e_{-k}+\lambda(e_{\ell}+e_{-\ell})+\sum_{k=1}^{\ell-1} c_{k}e_{k}$. Then
$$
\beta(v,v)=0 \Leftrightarrow \displaystyle \sum_{k=j+1}^{\ell-1} c_{k}c_{-k}+2\lambda^{2}+c_{j}=0.
$$
The polynomial on the right-hand side is clearly irreducible.
Now note that $N_{2\ell-1}$ maps $I_{-j}$ to itself. By computing the tangent space of the $N_{2\ell-1}$-orbit $N_{2\ell-1}\cdot e_{-j}$ on $I_{-j}$, we can see that $\dim(N_{2\ell-1}\cdot e_{-j})=\dim(I_{-j}).$ It follows that $N_{2\ell-1}\cdot e_{-j}=I_{-j}$ since orbits of unipotent groups on affine varieties are closed. The proof of the first assertion follows by a simpler version of this argument.
\end{rem}
\begin{lem}\label{l:GrassD}
For $i \in \{ 1, \dots, \ell -1 \}$, the distinct $B_{2\ell-1}$-orbits on $\mbox{OGr}(i,2\ell)$ are given by the following list:
\noindent
\begin{equation}\label{eq:firstsubspaceD}
\mathcal{O}_{j_1, \dots, j_i}:=B_{2\ell-1}\cdot \mbox{span}\{e_{j_{1}},\dots, e_{j_{i}}\}.
\end{equation}
\begin{equation}\label{eq:secondsubspaceD}
\mathcal{O}_{j_1, \dots, j_{i-1}, \ell } :=B_{2\ell-1}\cdot \mbox{span}\{e_{j_{1}},\dots, e_{j_{i-1}}, e_{\ell}\}.
\end{equation}
\begin{equation}\label{eq:thirdsubspaceD}
\mathcal{O}_{j_1, \dots, j_{i-1}, -\ell } :=B_{2\ell-1}\cdot \mbox{span}\{e_{j_{1}},\dots, e_{j_{i-1}}, e_{-\ell}\}.
\end{equation}
\begin{equation}\label{eq:fourthsubspaceD}
\mathcal{O}_{j_1, \dots, j_{i-1}, \tilde{|j_i|}}:=B_{2\ell-1}\cdot \mbox{span}\{e_{j_{1}},\dots, e_{j_{i-1}}, \widetilde{e}_{|j_{i}|}\},
\end{equation}
where $\{j_{1},\dots, j_{i-1}, \, j_{i}\}\subset \{\pm 1,\dots, \pm (\ell-1)\}$,
with $j_{k}\neq \pm j_{m}$.
\end{lem}
\begin{proof}
We must show each orbit is one of the listed orbits, and no two of the listed orbits coincide.
We first decompose $\mbox{${\mathbb C}$}^{2\ell}=U_{1}\oplus U_{2}$, where $U_{1}=\mbox{span}\{e_{\pm 1},\dots, e_{\pm(\ell-1)}, e_{\ell}+e_{-\ell}\}$ is the fixed set of the involution $\sigma_{2\ell}$ from Section 2.2 of \cite{CE21I}, and $U_{2}=\mbox{span}\{e_{\ell}-e_{-\ell}\}$ is the $-1$-eigenspace of $\sigma_{2\ell}.$ For a plane $V\in \mbox{OGr}(i, 2\ell)$, then either
\begin{equation}\label{eq:2conds}
\begin{split}
&(AD)\; V\subset U_{1} \mbox{ or }\\
&(BD)\; \dim V\cap U_{1}=i-1. \\
\end{split}
\end{equation}
Note that both of these conditions are $B_{2\ell-1}$-stable.
First, suppose that $U$ satisfies (AD). We recall that $K=SO(2\ell-1)$ is
realized as determinant $1$ orthogonal transformations of the space
$U_{1}$ (see Remark 2.1 of \cite{CE21I}). Thus, the classification of $B_{2\ell-1}-$orbits on the space of $V$ in $\mbox{OGr}(i, 2\ell)$ satisfying condition (AD) is equivalent to the classification of $B_{2\ell-1}$-orbits on $\mbox{OGr}(i, 2\ell - 1)$. By Remark \ref{r:schubertD}, this is given by the list in Equation \eqref{eq:firstsubspaceD}.
We now consider orbits on the set of $V$ satisfying condition (BD). For each such $V$, the subspace $V \cap U_1 \in \mbox{OGr}(i-1, 2\ell -1 )$, and so by Remark \ref{r:schubertD}, we may conjugate it by $B_{2\ell-1}$ to the span of $e_{j_1}, \dots, e_{j_{i-1}}$ where each $j_k \in \{ \pm 1, \dots, \pm (\ell - 1) \}$ and the absolute values of the $j_k$ are distinct. Hence, up to $B_{2\ell-1}$-conjugation
$U=\mbox{span}\{e_{j_{1}},\dots, e_{j_{i-1}}, \, u\}$ for $\{j_{1},\dots, j_{i-1}\}\,$ as above and $u\notin V_{1}$. We can write $u$ as
\begin{equation}\label{eq:udecomp}
u=v_{+}+\mu e_{\ell}+\lambda e_{-\ell} +v_{-},
\end{equation}
where $v_{+}\in V_{+},$
$v_{-}\in V_{-},$
and $\mu\neq \lambda$. Further, since the subspace $V$ is isotropic, we can assume that the coefficient of any $e_{\pm j_{k}}$ is zero in $v_{+}$ and $v_{-}$.
Suppose that $v_{-}=0$. Then since $u$ is an isotropic vector, at least
one of $\mu$ or $\lambda$ must be equal to zero. If $\lambda=0$,
then by Remark \ref{r:bvectororbit} there is $b\in B_{2\ell-1}$ such $b\cdot e_{\ell}=e_{\ell} + v_+$ and $b\cdot e_{j_{k}}=e_{j_{k}}$
for $k=1,\dots, i-1$. Thus, $b\cdot U=\mbox{${\rm span}$}\{e_{j_{1}},\dots, e_{j_{i-1}}, e_{\ell}\}$ is one of
the orbits in Equation (\ref{eq:secondsubspaceD}). If $\mu=0$, we can show similiarly that
$B_{2\ell-1}\cdot U$ is one of the orbits in (\ref{eq:thirdsubspaceD}).
Now suppose that $v_{-}\neq 0$ in Equation (\ref{eq:udecomp}), and let us assume that $\mu\neq 0$.
Since $\beta(u, u)=0$, it follows that $\beta(v_{+}, v_{-})=-\lambda\mu$.
Let $v_{-} = \sum c_j e_{-j}$ and let $s$ be minimal so $c_s\not= 0.$
We claim that there is $b\in B_{2\ell-1}$ such that $b\cdot u$ is a nonzero scalar multiple of $ e_{-s} + e_{\ell}$
and $b$ fixes each $e_{j_k}$ in our basis of $U\cap V_1.$ Let $SO(2\ell - 2)$ be the subgroup of $SO(2\ell)$ fixing pointwise the subspace spanned by $e_{\ell}$ and $e_{-\ell}$, and let $B_{2\ell-2} = B_{2\ell-1} \cap SO(2\ell - 2).$ By Remark \ref{r:bvectororbit}, there is $b_1\in B_{2\ell-2}$ such that $b_1\cdot v_- = e_{-s}.$ By the same remark, there is $b_2$ in $N_{2\ell-1}$ such that $b_2 \cdot e_{-s} = e_{-s} - \lambda(e_{\ell} + e_{-\ell}) + \lambda^2 e_s.$ Then $b_2\cdot b_1\cdot u=w_+ + (\mu - \lambda)e_{\ell} + e_{-s}$ for some $w_+ \in V_{+}.$
Again by Remark \ref{r:bvectororbit}, there is $b_3 \in B_{2\ell-2}$ such that
$b_3 \cdot e_{-s} =e_{-s} - w_+.$ Then there is an element $h$ in the diagonal torus of $B_{2\ell-1}$ so that $b=h b_3b_2b_1$ satisfies the claim, and we may assume $b$ stabilizes each $e_{j_k}$ in our basis of $U \cap V_1$ by working in the special orthogonal group of the span of the $e_k$ with $k \not= \pm j_r$ for $r=1, \dots, i-1$.
If we had assumed instead that $\lambda\neq 0$ and $\mu=0$, then we can argue similarly
to obtain $B_{2\ell-1}\cdot U=B_{2\ell-1}\cdot\mbox{span}\{e_{j_{1}},\dots, e_{j_{i-1}}, \hat{e}_{s}\}$. Using again Remark \ref{r:bvectororbit},
is easy to see that
\begin{equation}\label{eq:hattildeorbit}
B_{2\ell-1}\cdot \mbox{span}\{e_{j_{1}},\dots, e_{j_{i-1}}, \tilde{e}_{s}\}=B_{2\ell-1}\cdot \mbox{span}\{e_{j_{1}},\dots, e_{j_{i-1}}, \hat{e}_{s}\}.
\end{equation}
For uniqueness, note that for each $i$ element subset $\{ r_1, \dots, r_i \}$ of
$\{ \pm 1, \dots, \pm l \}$ with distinct absolute values, each of the $B_{2\ell-1}$-orbits $\mathcal{O}_{r_1, \dots, r_i}$ is contained in $B\cdot \mbox{${\rm span}$} \{ e_{r_1}, \dots, e_{r_i} \}.$ Further, the $B_{2\ell-1}$-orbit $\mathcal{O}_{j_1, \dots, j_{i-1}, \tilde{|j_i|}}$ is contained in $B\cdot \mbox{${\rm span}$} \{ e_{j_1}, \dots, e_{j_{i-1}}, e_{-|j_i|}\}.$ From Remark \ref{r:schubertD}, the only possible coincidences are between orbits $\mathcal{O}_{j_1, \dots, j_{i-1}, \tilde{|j_i|}}$ and $\mathcal{O}_{j_1, \dots, j_{i-1},-|j_i|}$ with $j_1, \dots, j_i$ elements with distinct absolute values in $\{ \pm 1, \dots, \pm (\ell - 1) \}.$ But the first orbit is of type (BD) and the second is of type (AD), so they cannot coincide.
\end{proof}
\begin{lem}\label{l:spanstandardD}
Let $\mathcal{F}=(v_1 \subset \dots \subset v_{\ell-1})$ be a $SO(2\ell)$-flag in standard form and let $V_{m}=\mbox{${\rm span}$}\{v_{1},\dots, v_{m}\}$.
\par\noindent (i) If for all $i \le m$, $v_i = e_{j_i}$ with $j_i \in \{ \pm 1, \dots, \pm \ell \}$, then $V_m = \mbox{${\rm span}$}\{ e_{j_1}, \dots, e_{j_m} \}.$
\par\noindent (ii) Suppose $v_{i}=e_{-\ell}$ (resp. $v_{i}=e_{\ell}$) for some $i$. Then for all $m\geq i$,
$V_{m}=\mbox{${\rm span}$}\{\overline{v_{1}},\dots, \overline{v_{m}}\}$, where $\overline{v_{k}}=v_{k}$
if $v_{k}=e_{j_{k}}$ is a standard basis vector, and $\overline{v_{k}}=e_{-j_{k}}$ if $v_{k}=\hat{e}_{j_{k}}$
(resp. if $v_{k}=\tilde{e}_{j_{k}}$) for $k=1,\dots, m$.
\par\noindent (iii) Suppose that for all $j\leq m$, $v_{j}\neq e_{\pm \ell}$ and at least one
of the vectors $v_{1},\dots, v_{m}$ is a tilde or hat vector. Let $1\leq k_{1}<\dots <k_{r}\leq m$ be
the subsequence of $\{1,\dots, m\}$ such that $v_{k_{i}}=\hat{e}_{i_{k_{i}}}$ or $v_{k_{i}}=\tilde{e}_{i_{k_{i}}}.$
Let $s_{1}<\dots <s_{m-r}$ be the complementary subsequence with $v_{s_{i}}=e_{i_{s_{i}}}$. Then
\begin{equation}\label{eq:hatandtilde}
B_{2\ell-1}\cdot V_{m}=B_{2\ell-1}\cdot\mbox{span}\{e_{i_{s_{1}}},\dots, e_{i_{s_{m-r}}}, e_{-i_{k_{1}}},\dots, e_{-i_{k_{r-1}}}, \tilde{e}_{i_{k_{r}}}\}.
\end{equation}
\end{lem}
\begin{proof}
Assertions (i) and (ii) are similar to the proof of Lemma \ref{l:spanstandard}, as is the proof of (iii) when $v_{j_m}$ is a tilde vector. In case $v_{j_m}$ is a hat vector, a similar argument proves Equation \eqref{eq:hatandtilde} with $\tilde{e}_{j_m}$ replaced with $\hat{e}_{j_m}$. By Equation \eqref{eq:hattildeorbit}, the Remark follows.
\end{proof}
\begin{thm}\label{thm:stdD}
The map
\begin{equation}\label{eq:flagassocD}
\Psi:\mathcal{F} \to B_{2\ell-1}\cdot \mathcal{F}
\end{equation}
is a bijection between $SO(2\ell)$-flags in standard form and $B_{2\ell-1}$-orbits on $\mathcal{B}_{2\ell}$.
\end{thm}
\begin{proof}
By the same reasoning as in the proof of Theorem \ref{thm:std}, and using Theorem \ref{thm:orthocount} (i) and Proposition \ref{p:flagsandPILSD}, it suffices to show that the map $\Psi$ is injective. As in that proof, we let $Q=B_{2\ell-1}\cdot \mathcal{F}$, and $Q^{\prime}=B_{2\ell-1}\cdot \mathcal{F}^{\prime}$ where $\mathcal{F}=(v_{1}\subset v_{2}\subset \dots\subset v_{i}\subset \dots \subset v_{\ell - 1} )$,
and $\mathcal{F}^{\prime}=(v_{1}^{\prime}\subset v_{2}^{\prime}\subset \dots\subset v_{i}^{\prime}\subset \dots v_{\ell - 1}^{\prime})$ are $SO(2\ell)$-flags in standard form. We prove by induction on $i$ that $v_i = v_{i}^{\prime}$ for $i=1, \dots, \ell - 1.$
To begin the induction, consider the orbit $\mathcal{O}_{1}=B_{2\ell-1}\cdot V_{1}=B_{2\ell-1}\cdot V_{1}^{\prime}$. In the case the orbit is one of those from Equations
\eqref{eq:firstsubspaceD}, \eqref{eq:secondsubspaceD}, or \eqref{eq:thirdsubspaceD}, it follows from Lemma \ref{l:GrassD} and the definition of standard form that $v_{1} = v_{1}^{\prime}.$ The remaining case is when $\mathcal{O}_1=\mathcal{O}_{\widetilde{e}_{j_1}}.$ In this case, by using Lemma \ref{l:GrassD},
it suffices to show that assuming that $v_1=\widetilde{e}_{j_1}$ and $v_{1}^{\prime}=\hat{e}_{j_1}$ leads to a contradiction. By the definition of standard form, some $v_k=e_{\ell}$ for $k > \ell$. By Lemma \ref{l:spanstandardD},
it follows that $B_{2\ell-1}\cdot V_k$ is one of the orbits appearing in Equation \eqref{eq:secondsubspaceD}. Since $\hat{e}_{j_i}$ occurs in $\mathcal{F}^{\prime}$, then $e_{\ell}$ does not occur in $\mathcal{F}^{\prime}$ by Remark \ref{r.standardD}. Thus, either $e_{-\ell}$ occurs in $\mathcal{F}^{\prime}$ or neither of $e_{\pm \ell}$ occurs in $\mathcal{F}^{\prime}.$ But then we can use Lemma \ref{l:spanstandardD} to see that we cannot obtain one of the orbits in Equation \eqref{eq:secondsubspaceD}, and this is a contradiction. Hence, $v_1 = v_1^{\prime}.$
For the inductive step, we may assume
that $v_{i}=v_{i}^{\prime}$ for $i=1,\dots, m-1$, so that $V_{m-1}=V_{m-1}^{\prime}$.
We prove that $v_m = v_m^{\prime}$ using our assumption that $B_{2\ell-1}\cdot V_m = B_{2\ell-1}\cdot V_m^{\prime}.$ To prove this, we argue based on the case of
$B_{2\ell-1}\cdot V_{m-1}$ described in Lemma \ref{l:GrassD}. If we are in the case of Equation \eqref{eq:firstsubspaceD}, then recovering $v_m$ from $B_{2\ell-1}\cdot V_m$ is similar to the $m=1$ case. If we are in the case of Equation \eqref{eq:secondsubspaceD}, then by Lemma \ref{l:spanstandardD}, one of the vectors $v_k = e_{\ell}$ for $k \le m-1$. Thus, from the definition of standard form, we see that $v_m = e_{j_m}$ with $j_m \not= \pm \ell$, and then by computing $V_{m-1} + \mbox{${\mathbb C}$} v_m$ we see that $v_m = v_m^{\prime}.$ If we are in the case of Equation \eqref{eq:thirdsubspaceD}, then we argue similarly using $e_{-\ell}$ in place of $e_{\ell}.$
Finally, suppose that
$B_{2\ell-1}\cdot V_{m-1}$ is one of the orbits in (\ref{eq:fourthsubspaceD}). Then by Lemma \ref{l:spanstandardD} some vectors $v_{k}$
with $k\leq m-1$ are either tilde vector or hat vectors and $v_{k}\neq e_{\pm \ell}$ for all $k\leq m-1$. Let $B_{2\ell-1}\cdot V_{m-1}=\mbox{span}\{e_{j_{1}},\dots, e_{j_{m-2}}, \tilde{e}_{j_{m-1}}\}$. If $v_{m}=e_{j_{m}}$ or $e_{\pm \ell}$, then $v_{m}=v_{m}^{\prime}$ by Lemmas \ref{l:GrassD} and \ref{l:spanstandardD}.
If $v_{m}=\tilde{e}_{j_{m}}$ or $v_{m}=\hat{e}_{j_{m}}$, then condition (c) in the definition of the standard form and Equation (\ref{eq:hatandtilde}) yield
$B_{2\ell-1}\cdot V_{m}=\mbox{span}\{e_{j_{1}},\dots, e_{j_{m-2}}, \, e_{-j_{m-1}}, \tilde{e}_{j_{m}}\}.$ Since tilde and
hat vectors cannot both occur in the standard form, we are forced to have $v_{m}=v_{m}^{\prime}$ in this case as well.
\end{proof}
\subsection{Representatives in the case of $SO(2\ell + 1)$}\label{ss:Breps}
In this subsection, we give explicit representatives for $B_{n-1}$ on $\mathcal{B}_n$ in the case where $G=SO(n)$ with $n=2\ell + 1$ odd. We omit most proofs, since they are generally simpler versions of the proofs in the type D case in Section \ref{ss:Dreps}. Recall the description of $\mathcal{B}_n$ in terms of isotropic flags from Section \ref{ss:Borels}.
\begin{dfn-nota}\label{d:stdB}
\begin{enumerate}
\item For $i=1,\dots, \ell$, define $\hat{e}_{i}:=e_{i}+\sqrt{2}e_{0}-e_{-i}$. For $1\leq j<i\leq \ell$, define
$\hat{e}_{i,-j}:=\hat{e}_{i}+e_{-j}$. We refer to a vector of the form $\hat{e}_{i}$ as a hat vector of the first kind
and a vector of the from $\hat{e}_{i,-j}$ as a hat vector of the second kind. We say that the index of both $\hat{e}_i$ and of the standard basis vector $e_{i}$ is $|i|$, and the index of a hat vector of the second kind $\hat{e}_{i,-j}$ is $j.$
\item We say that the isotropic flag
\begin{equation}\label{eq:basicflagB}
\mathcal{F}:=(v_{1}\subset \dots \subset v_{i}\subset\dots\subset v_{\ell})
\end{equation}
is in \emph{standard form} if $v_{i}$ is either a standard basis vector, a hat vector of the first kind, or a
hat vector of the second kind, and $\mathcal{F}$ satisfies the following conditions:
\begin{enumerate}
\item If $v_{i}=\hat{e}_{j_{i}}$ is a hat vector of the first kind, then $v_{k}=e_{j_{k}}$ for all $k > i$.
\item If $i < k$, $v_{i}=\hat{e}_{a,-j_{i}}$ and $v_{k}=\hat{e}_{a, -j_{k}}$, then $j_{i}<j_{k}$.
\item Each integer in $\{ 1, \dots, \ell\}$ is the index of exactly one vector $v_i$ occurring in $\mathcal{F}.$
\end{enumerate}
\end{enumerate}
\end{dfn-nota}
\begin{rem}\label{r:firstkind}
We assume that a hat vector of the second kind $\hat{e}_{a,-j}$ occurs in a $SO(2\ell + 1)$-standard flag $\mathcal{F}.$ Then the hat vector of the first kind $\hat{e}_a$ must occur in $\mathcal{F}$, and if $\hat{e}_{b,-k}$ is another hat vector of the second kind in $\mathcal{F}$, then $b=a$. Indeed, assume that $\hat{e}_{a,-j}$ occurs in $\mathcal{F}$. Then the vectors $e_{\pm a}$ does not occur in $\mathcal{F}$ since $\mathcal{F}$ is isotropic, and for the same reason, $\hat{e}_{b, -a}$ does not occur. By property (c) in the definition of a $SO(2\ell+1)$-standard flag, the index $a$ must occur, and hence $\hat{e}_a$ occurs in $\mathcal{F}$. If $b\not= a$, then the vector $\hat{e}_b$ cannot occur in our flag since it is isotropic, and hence by the first observation, $\hat{e}_{b,-k}$ cannot occur in $\mathcal{F}$ for any $k$.
\end{rem}
\begin{prop}\label{p:flagsandPILSB}
There is a bijection
\begin{equation}\label{eq:GammaB}
\Gamma:SPIL(\ell \cup \{ 0 \})\longleftrightarrow \{SO(2\ell + 1)-\mbox{Flags in standard form}\}.
\end{equation}
\end{prop}
\begin{proof}
For $\Sigma=\{\sigma_{1},\, \sigma_{2},\,\dots, \, \sigma_{t}\} \in SPIL(\ell \cup \{ 0 \}),$ let $\ell(\sigma_j)=k_j$ and let $\sigma_{j}=(i_{j,1},\dots, i_{j, k_{j}}).$ We may choose the ordering of the $\sigma_j$ uniquely so that
$i_{1,k_{1}}<\dots <i_{t-1,k_{t-1}}$ and $0 \in \sigma_{t}$. Let $a:=i_{t-1,k_{t-1}}.$ Then we define
\begin{equation}\label{eq:GammaBdef}
\begin{split}
\Gamma(\Sigma):=
&(e_{i_{1,1}}\subset e_{i_{1,2}}\subset\dots\subset \hat{e}_{a,-i_{1,k_{1}}}\subset e_{i_{2,1}}\subset\dots\subset \hat{e}_{a, -i_{2,k_{2}}}\subset\dots\\
&\subset e_{i_{t-1,1}}\subset \dots \subset \hat{e}_{a}
\subset e_{i_{t,1}}\subset\dots\subset e_{i_{t,k_t - 1}}).
\end{split}
\end{equation}
By construction, this is a $SO(2\ell + 1)$-flag in standard form.
To define the inverse $\Lambda$, note that for a $SO(2\ell + 1)$-flag $(v_1\subset \dots\subset v_{\ell})$ in standard form, if we let $k_1 < \dots < k_r$ be the subsequence consisting of hat vectors, then by Remark \ref{r:firstkind} it follows that
$v_{k_{i}}=\hat{e}_{a, i_{k_{i}}}$ for $i=1,\dots, r-1$ and $v_{k_{r}}=\hat{e}_{a}$.
We define $\Lambda(\mathcal{F}) \in SPIL(\ell \cup \{ 0 \})$ by Equation (\ref{eq:Lambdadefn}) with zero adjoined at the end of the last list, and it is routine to check that $\Gamma$ and $\Lambda$ are inverse bijections.
\end{proof}
\begin{lem}\label{l:GrassB}
Let $i \in \{ 1, \dots, \ell \}$. The distinct $B_{2\ell}$-orbits on $\mbox{OGr}(i,2\ell+1)$ are given by the orbits
\begin{equation}\label{eq:firstsubspaceB}
\mathcal{O}=B_{n-1}\cdot \mbox{span}\{e_{j_{1}},\dots, e_{j_{i}}\}
\end{equation}
\begin{equation}\label{eq:secondsubspaceB}
\mathcal{O}=B_{n-1}\cdot \mbox{span}\{e_{j_{1}},\dots, e_{j_{i-1}}, \hat{e}_{|j_{i}|}\}
\end{equation}
where $\{j_{1},\dots, j_{i}\}\subset \{\pm 1,\dots, \pm \ell\}$, and with $j_{k}\neq \pm j_{m}$.
\end{lem}
To prove this lemma, it is useful to recall that $K=SO(2\ell)$ is realized in $G$ as the elements fixing $e_0$ (\cite{CE21I}, Remark 2.1) and to prove the following analogue of Remark \ref{r:bvectororbit}. Recall that $N_{2\ell}$ is the derived subgroup of $B_{2\ell}.$
First, for $1 \le j \le \ell$, $N_{2\ell}\cdot e_j = e_j + \sum_{k < j} \mbox{${\mathbb C}$} e_k$ and
\begin{equation}\label{eq:odd4.13one}
N_{2\ell}\cdot e_{-j} = \{ v\in e_{-j} +\sum_{k > j} \mbox{${\mathbb C}$} e_{-k} + \sum_{r=1}^{\ell} \mbox{${\mathbb C}$} e_r : \beta(v,v)=0\}.
\end{equation}
Second, for $1 \le j \le \ell$,
$$
N_{2\ell}\cdot (e_{-s} - e_s) = \{ v\in e_{-s} + \sum_{k > s} \mbox{${\mathbb C}$} e_{-k} + \sum_{r=1}^{\ell} \mbox{${\mathbb C}$} e_r : \beta(v,v)=-2\}.
$$
These assertions follow similarly to the proof of Remark \ref{r:bvectororbit}, and the proof of the Lemma is similar to the proof of Lemma \ref{l:GrassD}.
\begin{thm}\label{thm:stdB}
The map
\begin{equation}\label{eq:flagassocB}
\Psi:\mathcal{F} \to B_{2\ell}\cdot \mathcal{F}
\end{equation}
is a bijection between $SO(2\ell+ 1)$-flags in standard form and $B_{2\ell}$-orbits on $\mathcal{B}_{2\ell + 1}$.
\end{thm}
To prove this theorem, it is useful to compute $V_{m-1} + \mbox{${\mathbb C}$} v_m$ when
$(v_1 \subset \dots \subset v_\ell)$ is a $SO(2\ell+1)$-flag in standard form and $V_k=\mbox{${\rm span}$} \{ v_1, \dots, v_k \}.$ In particular, it is useful to note the following assertions. First, $B_{2\ell} \cdot \hat{e}_{a,-j}=B_{2\ell}\cdot \hat{e}_{j}$ for $1 \le j \le \ell$. Secondly, if $k_j > k_i$, then
$B_{2\ell} \cdot \mbox{${\rm span}$}\{ \hat{e}_{a,-k_i}, v_2 \} = B_{2\ell}\cdot \mbox{${\rm span}$} \{ e_{-k_i}, v_2 \}$ when $v_2 = \hat{e}_{a,-k_j}$ or $\hat{e}_a.$ Given these assertions, the proof follows the same steps as the proof of Theorem \ref{thm:stdD}.
\section{Monoid action on standard forms}\label{s:monoid}
An essential aspect of the geometry of closures of $B_{n-1}$-orbits in $\mathcal{B}_n$ is an understanding of the action of the monoid given by simple roots of $\mbox{${\mathfrak g}$}$ and of $\mbox{${\mathfrak k}$}=\mbox{${\mathfrak g}$}_{n-1}$, which gives information about the relation between different orbits. In this section, we compute the monoid action for roots of $\mbox{${\mathfrak g}$}.$
\subsection{Monoid Action by simple $\mbox{${\mathfrak g}$}$-roots}\label{ss:monoid}
Let $R$ be a complex, reductive algebraic group, let $\mathcal{B}=\mathcal{B}_{R}$ be the flag
variety of $R$, and let $M$ be an algebraic subgroup of $R$ acting on $\mathcal{B}$ with finitely many orbits.
Let $S$ be the simple reflections of the Weyl group of $R$, and recall the operator $m(s)$ on $M\backslash \mathcal{B}$ from \cite{RS} and other sources. For this, let $s=s_{\alpha}$ for a simple root $\alpha$ and let $\pi_{\alpha}:\mathcal{B} \to {\mathcal{P}}_{\alpha}$ be the canonical projection from the flag variety to the variety of parabolics of $R$ of type $\alpha.$ Then for $Q_{M}\in M\backslash \mathcal{B}$, recall that
$m(s)*Q_{M}$ is the unique $M$-orbit open and dense in $\pi_{\alpha}^{-1}(\pi_{\alpha}(Q_{M})).$ Further, $Q_{M} \not= m(s)*Q_{M}$ if and only if $\dim(m(s)*Q_{M})=\dim(Q_{M})+1.$
If $\alpha$ is a simple root of $\mbox{${\mathfrak r}$}$, recall that $\alpha$ can be either real, non-compact imaginary, compact imaginary, or complex for $Q_{M}$, depending on how $Q_{M}$ and $m(s)*Q_{M}$ meet a fibre $\pi_{\alpha}^{-1}(\pi_{\alpha}(\mbox{${\mathfrak b}$}))$ for $\mbox{${\mathfrak b}$} \in Q_{M}$ (see Section 2.3 of \cite{CE21I} for details).
For the remainder of this section, we let $M=K=G_{n-1}$ or $M=B_{n-1}$ and $R=G$ with $G=GL(n)$ or $SO(n).$ To compute the monoid action explicitly, it is useful to make the following standard observations, which may be taken to be the definition of the monoid action in these cases.
Let $\mathcal{F}_{+}\in \mathcal{B}_{n}$ be the standard upper triangular flag given in Equation (\ref{eq:upper}).
\begin{prop}\label{prop:monoid}
Let $Q_M=M\cdot {\rm Ad}(v)\mathcal{F}_{+}$ be an $M$-orbit, where $v\in G$, and let $\alpha\in \Pi_{\mbox{${\mathfrak g}$}}$ be a standard simple root.
Let $s_{\alpha}\in W$ be the simple reflection determined by $\alpha$, and let $u_{\alpha}\in G$ be the Cayley transform with respect to the root $\alpha$ defined in Notation 2.5 of \cite{CE21I}.
\begin{enumerate}
\item The root $\alpha$ is non-compact imaginary or real for $Q_{M}$ if the variety
$\pi_{\alpha}^{-1}(\pi_{\alpha}(Q_{M}))
consists of exactly three orbits. The root $\alpha$ is non-compact imaginary if $\dim (m(s_{\alpha})*Q_{M}) = \dim(Q_{M})+1$ and
real if $m(s_{\alpha})*Q_{M}=Q_{M}$. If $\alpha$ is non-compact imaginary then
$m(s_{\alpha})*Q_{M}=M\cdot {\rm Ad}(vu_{\alpha})\mathcal{F}_{+}$.
\item We say $\alpha$ is complex for $Q_{M}$ if the variety
$$\pi_{\alpha}^{-1}(\pi_{\alpha}(Q_{M}))=Q_{M}\cup M\cdot {\rm Ad}(v)s_{\alpha}(\mathcal{F}_{+}).$$
The root $\alpha$ is \emph{complex stable} if $m(s_{\alpha})*Q_{M}\neq Q_{M}$ and \emph{complex unstable} if
$m(s_{\alpha})*Q_{M}=Q_{M}$.
\item For $M=K$, we say that $\alpha$ is compact imaginary for $Q_{K}$ if
$$
\pi_{\alpha}^{-1}(\pi_{\alpha}(Q_{K}))=Q_{K}.
$$
\end{enumerate}
\end{prop}
The following observation will be useful for computing the monoid action on standard forms.
\begin{lem}\label{l:cplxvncpt}
Let $Q_{M}=M\cdot {\rm Ad}(v)\mathcal{F}_{+}$ for $v\in G$ and let $\alpha\in\Pi_{\mbox{${\mathfrak g}$}}$ be a simple root
with $m(s_{\alpha})*Q_{M}\neq Q_{M}$. Then $\alpha$ is non-compact for $Q_{M}$ if and only if $M\cdot {\rm Ad}(vu_{\alpha})\mathcal{F}_{+}\neq M\cdot {\rm Ad}(v)s_{\alpha}(\mathcal{F}_{+})$.
\end{lem}
\begin{proof}
Since the variety $\pi_{\alpha}^{-1}(\pi_{\alpha}(Q_{M}))\mapsto \pi(Q_{M})$ is an $M$-homogeneous $\mathbb{P}^{1}=\mathcal{B}_{\mbox{${\fs\fl}$}(2)}$-bundle, it suffices to prove the statement when $G=SL(2)$ and $M\subset SL(2)$ is a subgroup with finitely many orbits on $\mathcal{B}_{\mbox{${\fs\fl}$}(2)}$, which is an easy computation.
\end{proof}
\begin{nota}
If $Q=B_{n-1}\cdot\mathcal{F}$ with $\mathcal{F}$ a flag in standard form and $\alpha\in\Pi_{\mbox{${\mathfrak g}$}}$, then we denote by $m(s_{\alpha})*\mathcal{F}$ the unique flag in standard form contained in $m(s_{\alpha})*Q$.
\end{nota}
\subsection{Computing monoid actions}\label{ss:monoidcompute}
Let $Q$ be a $B_{n-1}$-orbit contained in a $K$-orbit $Q_{K}\in \mathcal{B}_{n}$.
In Theorems 4.11 and 4.12 of \cite{CE21I}, we describe the monoid action on $B_{n-1}\backslash\B_{n}$ by roots $\alpha\in \Pi_{\mbox{${\mathfrak g}$}}$ for which $\alpha$ is compact imaginary for $Q_{K}$ as defined in Part (3) of Proposition \ref{prop:monoid}.
We now compute the monoid action by roots $\alpha\in \Pi_{\mbox{${\mathfrak g}$}}$ on orbits $Q\inB_{n-1}\backslash\B_{n}$ such that $m(s_{\alpha})*Q_{K}\neq Q_{K}$. It follows from Proposition 4.8 of \emph{loc.cit} that for such an $\alpha$, $m(s_{\alpha})*Q\neq Q$.
We being with the type $A$ case. Recall our labelling of the elements of $K\backslash\mathcal{B}_{n}$ by $Q_i$ or $Q_{i,j}$ from Section \ref{ss:Korbits}.
Recall the $K$-stable decomposition of $\mbox{${\mathbb C}$}^{n}$,
$\mbox{${\mathbb C}$}^{n}=U_{1}\oplus U_{2}$ where $U_{1}=\mbox{span}\{e_{1},\dots, e_{n-1}\}$
and $U_{2}=\mbox{span}\{e_{n}\}$ given after Remark \ref{r.schubert}. Let
$p_{1}:\mbox{${\mathbb C}$}^{n}\to U_{1}$ be the projection onto $U_{1}$ off of $U_{2}$.
Let $\mathcal{F} =(v_1 \subset \dots\subset v_n)\in\mathcal{B}_{n}$ be a flag in standard form. By Remark \ref{r.glstandard}, exactly one vector $p_{1}(v_i)=0$ and
if we let $p_1(\mathcal{F})$ be the sequence $(p_{1}(v_1) \subset \dots\subset p_{1}(v_n))$ with $p_{1}(v_i)$ omitted, then $p_1(\mathcal{F})$ is in $\mathcal{B}_{n-1}$
and is stabilized by the standard diagonal Cartan subalgebra of $\mbox{${\mathfrak k}$}$.
\begin{lem}\label{l:5.1}
Let $\mathcal{F}=(v_{1}\subset v_{2}\subset\dots\subset v_{n})$ be a flag in standard form.
\begin{enumerate}
\item The flag $\mathcal{F}\in Q_{j}$ if and only if $\mathcal{F}$ contains no hat vectors and $v_{j}=e_{n}$.
\item The flag $\mathcal{F}\in Q_{i,j}$ with $i<j$ if and only if $v_{i}$ is a hat vector,
$v_{k}$ is a standard basis vector for all $k<i$, and $v_{j}=e_{n}$.
\end{enumerate}
\end{lem}
\begin{proof}
We first prove the sufficiency of both (1) and (2). Suppose that $\mathcal{F}$ contains no hat vectors and that $v_{j}=e_{n}$. Since $W_K$ acts on $\mathcal{B}_n$ as permutation matrices fixing $e_n$, there exists a $w\in W_{K}$ such that $w(p_{1}(\mathcal{F}))=\mathcal{F}_{+,n-1}$
where $\mathcal{F}_{+,n-1}$ is the standard upper triangular flag in $\mbox{${\mathbb C}$}^{n-1}$ (see Equation (\ref{eq:upper})).
Since the map $p_{1}$ is $K$-equivariant it follows that $w(\mathcal{F})=\mathcal{F}_{j}$, where $\mathcal{F}_{j}$ is the flag in Equation (\ref{eq:typeAflagclosed}) with $i=j$.
Now suppose that $\mathcal{F}=(v_{1}\subset \dots\subset v_{i}\subset\dots \subset v_{j}\subset \dots\subset v_{n})$ with $v_{i}$ a hat vector, $v_{k}$ a standard basis vector for all $k<i$, and $v_{j}=e_{n}$. Then arguing as above, we can find a $\sigma\in W_{K}$ such that $\sigma(p_{1}(\mathcal{F}))=\mathcal{F}_{i,j}^{\prime}$, where
$$
\mathcal{F}_{i,j}^{\prime}=(e_{1}\subset \dots \subset e_{i-1}\subset \underbrace{e_{j-1}}_{i}\subset e_{i}\subset \dots \subset \underbrace{e_{j-2}}_{j-1}\subset\underbrace{e_{j}}_{j}\subset \dots \subset e_{n-1}).
$$
As above, it follows that
$$
{\rm Ad}(\dot{\sigma})\mathcal{F}=(e_{1}\subset \dots\subset e_{i-1}\subset\underbrace{\hat{e}_{j-1}}_{i}\subset v_{i+1}^{\prime}\subset \dots \subset v_{j-1}^{\prime}\subset \underbrace{e_{n}}_{j}\subset e_{j}\subset\dots\subset e_{n-1}),
$$
where $v_{t}^{\prime}=e_{t-1}$ or $\hat{e}_{t-1}$ for all $t=i+1, \dots, j-1$. Now if $v_{t}^{\prime}=e_{t-1}$ for all $t$, then
${\rm Ad}(\dot{\sigma})\mathcal{F}=\mathcal{F}_{i,j}$, where $\mathcal{F}_{i,j}$ is the flag in Equation (\ref{eq:typeAflag}) whence $\mathcal{F}_{i,j}\in Q_{i,j}$.
If, on the other hand, $v_{t}^{\prime}=\hat{e}_{t-1}$ for some $t$, then consider the space
$\mbox{span}\{\hat{e}_{j-1}, \, \hat{e}_{t-1}\}=\mbox{span}\{\hat{e}_{j-1}, e_{t-1}-e_{j-1}\}.$
This space is $K$-conjugate to $\mbox{span}\{\hat{e}_{j-1}, e_{t-1}\}$ without altering any other vectors
in ${\rm Ad}(\dot{\sigma})\mathcal{F}$. Thus, there exists $k\in K$ such that ${\rm Ad}(k \dot{\sigma})\mathcal{F}=\mathcal{F}_{i,j}$ and $\mathcal{F}_{i,j}\in Q_{i,j}$ and this completes the proof of sufficiency. Necessity now follows since every flag in standard form satisfies exactly one of the sufficient conditions in the Lemma.
\end{proof}
Let $\alpha \in \Pi_{\mbox{${\mathfrak g}$}}.$ Note that if $Q_K=Q_i$ is a closed $K$-orbit in $\mathcal{B}_n$, then by Proposition 4.9 of \cite{CE21I}, $m(s_{\alpha})*Q_i\not= Q_i$ if and only if $\alpha=\alpha_{i-1}$ or $\alpha_i$. By the same result, if $Q_K=Q_{i,j}$ is a non-closed $K$-orbit in $\mathcal{B}_n$, then $m(s_{\alpha})*Q_{i,j} \not= Q_{i,j}$ if and only if $\alpha=\alpha_{i-1}$ or $\alpha_j.$
\begin{prop}\label{p:monoidactiononPILS}
Let $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$ and $Q=B_{n-1}\cdot \mathcal{F}$ and let $Q$ be in the $K$-orbit $Q_{K}$.\\
\noindent Case I: Suppose $Q_{K}$ is not closed so that $Q_{K}=Q_{i,j}$ with $1\leq i<j\leq n$. Then $\mathcal{F}$ has the form
\begin{equation}\label{eq:baseflagmonoid}
\mathcal{F}=(e_{\ell_{1}}\subset e_{\ell_{2}}\subset \dots\subset e_{\ell_{i-1}}\subset\underbrace{\hat{e}_{\ell_{i}}}_{i}\subset v_{i+1}\subset\dots \subset v_{j-1}\subset\underbrace{e_{n}}_{j}\subset e_{\ell_{j+1}}\subset\dots\subset e_{\ell_{n-1}}).
\end{equation}
\begin{enumerate}
\item For the simple root $\alpha_{i-1},$
\begin{enumerate}
\item if $\ell_{i-1}<\ell_{i}$, then $\alpha_{i-1}$ is complex stable for $Q$ and
\begin{equation}\label{eq:i-1cplx}
m(s_{\alpha_{i-1}})*\mathcal{F}=(e_{\ell_{1}}\subset\dots\subset e_{\ell_{i-2}}\subset\underbrace{\hat{e}_{\ell_{i}}}_{i-1}\subset \underbrace{e_{\ell_{i-1}}}_{i}\subset v_{i+1}\subset\dots\subset v_{j-1}\subset e_{n}\subset \dots \subset e_{\ell_{n-1}}).
\end{equation}
\item If $\ell_{i-1}>\ell_{i}$, then $\alpha_{i-1}$ is non-compact for $Q$ and
\begin{equation}\label{eq:i-1nc}
m(s_{\alpha_{i-1}})*\mathcal{F}=(e_{\ell_{1}}\subset\dots\subset e_{\ell_{i-2}}\subset\underbrace{\hat{e}_{\ell_{i-1}}}_{i-1}\subset\underbrace{\hat{e}_{\ell_{i}}}_{i}\subset v_{i+1}\subset \dots\subset v_{j-1}\subset e_{n}\subset \dots\subset e_{\ell_{n-1}}).
\end{equation}
\end{enumerate}
\item For the simple root $\alpha_{j}$,
let $k:=\min(\{\ell_{i}\}\cup\{t_{m}|\, v_{m}=\hat{e}_{t_{m}}, \, m=i+1,\dots, j-1.\}).$
\begin{enumerate}
\item If $\ell_{j+1}>k$, then $\alpha_{j}$ is complex stable for $Q$ and
\begin{equation}\label{eq:jcplx}
m(s_{\alpha_{j}})*\mathcal{F}=(e_{\ell_{1}}\subset \dots\subset e_{\ell_{i-1}} \subset \hat{e}_{\ell_{i}}\subset v_{i+1}\subset\dots\subset v_{j-1}\subset \underbrace{e_{\ell_{j+1}}}_{j}\subset\underbrace{e_{n}}_{j+1}\subset \dots\subset e_{\ell_{n-1}}).
\end{equation}
\item If $k>\ell_{j+1}$, then $\alpha_{j}$ is non-compact for $Q$ and
\begin{equation}\label{eq:jnc}
m(s_{\alpha_{j}})*\mathcal{F}=(e_{\ell_{1}}\subset \dots\subset e_{\ell_{i-1}}\subset\hat{e}_{\ell_{i}}\subset v_{i+1}\subset \dots \subset v_{j-1} \subset\underbrace{\hat{e}_{\ell_{j+1}}}_{j}\subset \underbrace{e_{n}}_{j+1} \subset\dots\subset e_{\ell_{n-1}}).
\end{equation}
\end{enumerate}
\end{enumerate}
\noindent Case II: Let $Q_{K}$ be closed, so $Q_{K}=Q_{i}$ for $i=1,\dots, n$.
Then
$$
\mathcal{F}=(e_{\ell_{1}}\subset\dots\subset e_{\ell_{i-1}}\subset \underbrace{e_{n}}_{i} \subset e_{\ell_{i+1}}\subset\dots\subset e_{\ell_{n-1}}).
$$
The roots $\alpha_{i-1}$ and $\alpha_{i}$ are both non-compact for $Q$ and
\begin{equation}\label{eq:typeAclosed}
\begin{split}
m(s_{\alpha_{i-1}})*\mathcal{F}&=(e_{\ell_{1}}\subset\dots\subset \underbrace{\hat{e}_{\ell_{i-1}}}_{i-1}\subset \underbrace{e_{n}}_{i} \subset e_{\ell_{i+1}}\subset\dots\subset e_{\ell_{n-1}}), \\ m(s_{\alpha_{i}})*\mathcal{F}&=(e_{\ell_{1}}\subset\dots\subset e_{\ell_{i-1}}\subset \underbrace{\hat{e}_{\ell_{i+1}}}_{i}\subset \underbrace{e_{n}}_{i+1} \subset e_{\ell_{i+2}}\subset\dots\subset e_{\ell_{n-1}}).
\end{split}
\end{equation}
\end{prop}
\begin{proof}
We prove the statements when $Q_{K}=Q_{i,j}$.
Equation (\ref{eq:baseflagmonoid}) follows from Lemma \ref{l:5.1}.
Let $\mathcal{F}= {\rm Ad}(v)\mathcal{F}_{+}$ for some $v\in G$. By Proposition 4.8 of \emph{loc. cit.},
we know that $m(s_{\alpha_{j}})*Q\neq Q.$
We need only determine whether $\alpha_{j}$ is non-compact or complex stable for $Q$.
For this, it suffices by Lemma \ref{l:cplxvncpt} to compare the orbits $Q_{1}:=B_{n-1}\cdot{\rm Ad}(v) s_{\alpha_{j}}(\mathcal{F}_{+})$ and $Q_{2}:=B_{n-1}\cdot {\rm Ad}(v){\rm Ad}(u_{\alpha_{j}})\mathcal{F}_{+}$. Let $\mathcal{F}_{1}$ and $\mathcal{F}_{2}$ be the unique flags in standard form in the orbits $Q_{1}$ and $Q_{2}$ respectively.
Then straightforward computations with flags show that $\mathcal{F}_{1}$ is the flag in (\ref{eq:jcplx})
and $Q_{2}$ contains the flag in (\ref{eq:jnc}) (though this flag need not be in standard form). Let $k$ be given as in Part (2) of Case I of the Proposition.
Now if $\ell_{j+1}>k$, then as in the proof of Lemma \ref{l:spanstandard}, the space $\mbox{span}\{\hat{e}_{k}, \hat{e}_{\ell_{j+1}}\}$ is $B_{n-1}$-conjugate to $\mbox{span}\{\hat{e}_{k}, e_{\ell_{j+1}}\}$, where the conjugation leaves all other vectors in the flag unchanged. Thus, $\mathcal{F}_{2}=\mathcal{F}_{1}$, so $Q_{2}=Q_{1}$.
Lemma \ref{l:cplxvncpt} now implies $\alpha_{j}$ is complex stable for $Q$ and $m(s_{\alpha_{j}})*\mathcal{F}=\mathcal{F}_{1}$
is given by (\ref{eq:jcplx}) by Proposition \ref{prop:monoid}.
On the other hand, if $\ell_{j+1}<k$ then the flag in (\ref{eq:jnc}) is in standard form
so that $\mathcal{F}_{2}$ is given by (\ref{eq:jnc}). Thus, $\mathcal{F}_{1}\neq \mathcal{F}_{2}$, and it follows
from Theorem \ref{thm:std} that $Q_{1}\neq Q_{2}$.
Now Lemma \ref{l:cplxvncpt} implies that $\alpha_{j}$ is non-compact for $Q$
and $m(s_{\alpha_{j}})*\mathcal{F}=\mathcal{F}_{2}$ is given by (\ref{eq:jnc}) by Proposition \ref{prop:monoid}.
Now we consider the simple root $\alpha_{i-1}$. Let $Q_{1}:=B_{n-1}\cdot{\rm Ad}(v) s_{\alpha_{i-1}}(\mathcal{F}_{+})$ and $Q_{2}:=B_{n-1}\cdot {\rm Ad}(v){\rm Ad}(u_{\alpha_{i-1}})\mathcal{F}_{+}$ and let $\mathcal{F}_{1}$ and $\mathcal{F}_{2}$ be as above. In this case,
$\mathcal{F}_{1}$ is the flag in Equation (\ref{eq:i-1cplx}) and $Q_{2}$ contains the flag (not in standard form)
\begin{equation}\label{eq:helperflag}
(e_{\ell_{1}}\subset\dots\subset e_{\ell_{i-2}}\subset\underbrace{e_{\ell_{i-1}}+\hat{e}_{\ell_{i}}}_{i-1}\subset\underbrace{\hat{e}_{\ell_{i}}}_{i}\subset v_{i+1}\subset \dots\subset v_{j-1}\subset e_{n}\subset \dots\subset e_{\ell_{n-1}}).
\end{equation}
Now if $\ell_{i}>\ell_{i-1}$, then the flag in (\ref{eq:helperflag}) is $B_{n-1}$-conjugate to the flag
in (\ref{eq:i-1cplx}) where the conjugation maps $e_{\ell_{i}}$ to $e_{\ell_{i}}-e_{\ell_{i-1}}$ and fixes all other vectors. So $Q_{1}=Q_{2}$ and Lemma \ref{l:cplxvncpt} implies that the root $\alpha_{i-1}$ is complex stable for $Q$. The flag $m(s_{\alpha_{i-1}})*\mathcal{F}$ is then given by (\ref{eq:i-1cplx}) by Proposition \ref{prop:monoid}.
If, on the other hand, $\ell_{i}< \ell_{i-1}$, then the flag in (\ref{eq:helperflag}) is
$B_{n-1}$-conjugate to the flag in Equation (\ref{eq:i-1nc}), which is in standard form.
It follows that $Q_{1}\neq Q_{2}$, so that $\alpha_{i-1}$ is non-compact for $Q$ by Lemma \ref{l:cplxvncpt}, and
$m(s_{\alpha_{i-1}})*\mathcal{F}$ is given by Equation (\ref{eq:i-1nc}) by Proposition \ref{prop:monoid}. The proof when $Q_{K}$ is closed is simpler and we leave the details to the reader.
\end{proof}
\noindent We now state the analogues of Proposition \ref{p:monoidactiononPILS} for
types D and B. The proofs are analogous to the type A case.
The analogue of Lemma \ref{l:5.1} can be proven using Equation (\ref{eq:typeDflag}) in the type D case
and Equation (\ref{eq:typeBflag}) in the type B case. The assertions about the monoid action are proven using Lemma \ref{l:cplxvncpt} and computations with isotropic flags using Remark \ref{r:bvectororbit} in the type D case and Equation (\ref{eq:odd4.13one}) in the type B case. The details are left to the reader.
Let $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)$ and $\alpha\in\Pi_{\mbox{${\mathfrak g}$}}$. If $Q_{K}=Q_{+}$ is the unique closed $K$-orbit,
then by Proposition 4.9 of \cite{CE21I}, $m(s_{\alpha})*Q_{+}\neq Q_{+}$ if and only if $\alpha=\alpha_{\ell-1},\, \alpha_{\ell}$. If $Q_{K}=Q_{i}$ with $i=1,\dots, \ell-1$ is not closed, then the same result implies
that $m(s_{\alpha})*Q_{i}\neq Q_{i}$ if and only if $\alpha=\alpha_{i-1}$.
\begin{prop}\label{p:monoidactiononPILSD}
Let $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)$ and $Q=B_{2\ell-1}\cdot \mathcal{F}$ with $Q\subset Q_{K}$.\\
\noindent Case I: $Q_{K}=Q_{i}$, $i=1, \dots, \ell-1$ is not closed.
In this case, $\mathcal{F}$ has the form:
$$
\mathcal{F}=(e_{j_{1}}\subset \dots \subset e_{j_{i-1}}\subset v_{i}\subset \dots\subset v_{\ell-1}),
$$
where $v_{i}=e_{\ell},\, e_{-\ell},\, \hat{e}_{j_{i}},\, \mbox{or } \widetilde{e}_{j_{i}}$.
There are two cases to consider:
\begin{enumerate}
\item $v_{i}=e_{\pm\ell}$.
\begin{enumerate}
\item If $j_{i-1}>0$, then $\alpha_{i-1}$ is complex stable for $Q$, and
\begin{equation}\label{eq:cplxDroot}
m(s_{\alpha_{i-1}})*\mathcal{F}=(e_{j_{1}}\subset \dots \subset e_{j_{i-2}}\subset\underbrace{e_{\pm \ell}}_{i-1}\subset e_{j_{i-1}} \subset v_{i+1}\subset \dots\subset v_{\ell-1}).
\end{equation}
\item If $j_{i-1}<0$, then $\alpha_{i-1}$ is non-compact for $Q$, and
\begin{equation}\label{eq:noncptDroot}
m(s_{\alpha_{i-1}})*\mathcal{F}=(e_{j_{1}}\subset \dots \subset e_{j_{i-2}}\subset\underbrace{v_{i-1}}_{i-1}\subset v_{i} \subset v_{i+1}\subset \dots\subset v_{\ell-1}),
\end{equation}
where $v_{i-1}=\widetilde{e}_{|j_{i-1}|}$ if $v_{i}=e_{\ell}$ and $v_{i-1}=\hat{e}_{|j_{i-1}|}$ if $v_{i}=e_{-\ell}.$
\end{enumerate}
\item Let $v_{i}=\widetilde{e}_{j_{i}} \mbox{ or } \hat{e}_{j_{i}}$.
\begin{enumerate}
\item If $j_{i-1}>0$ or $|j_{i-1}|>j_{i}$, then $\alpha_{i-1}$ is complex stable for $Q$ and $m(s_{\alpha_{i-1}})*\mathcal{F}$ is given by replacing $e_{\pm \ell}$ with $v_i$ in Equation (\ref{eq:cplxDroot}).
\item If $j_{i-1}<0$ and $|j_{i-1}|<j_{i}$, then $\alpha_{i-1}$ is non-compact and $m(s_{\alpha_{i-1}})*\mathcal{F}$ is given by (\ref{eq:noncptDroot}),
where $v_{i-1}=\widetilde{e}_{|j_{i-1}|}$ if $v_{i}=\widetilde{e}_{j_{i}}$ and $v_{i-1}=\hat{e}_{|j_{i-1}|}$ if $v_{i}=\hat{e}_{j_{i}}.$
\end{enumerate}
\end{enumerate}
\noindent Case II: Suppose that $Q_{K}=Q_{+}$ is the unique closed $K$-orbit on $\mathcal{B}$.
In this case, $\mathcal{F}$ is of the form
$$
\mathcal{F}=(e_{j_{1}}\subset e_{j_{2}}\subset\dots\subset e_{j_{\ell-1}}),
$$
where $j_{k}\neq \pm \ell$ for $k=1,\dots,\ell-1$.
\begin{enumerate}
\item If $j_{\ell-1}>0$, then $\alpha_{\ell-1}$ and $\alpha_{\ell}$ are complex stable for $Q$. However, their monoid actions are different.
We have
\begin{equation}\label{eq:closedD1}
m(s_{\alpha_{\ell-1}})*\mathcal{F}=(e_{j_{1}}\subset \dots \subset e_{j_{\ell-2}}\subset e_{\ell})
\end{equation}
and
\begin{equation}\label{eq:closedD2}
m(s_{\alpha_{\ell}})*\mathcal{F}=(e_{j_{1}}\subset\dots\subset e_{j_{\ell-2}}\subset e_{-\ell}).
\end{equation}
\item If $j_{\ell-1}<0$, then the roots $\alpha_{\ell-1}$ and $\alpha_{\ell}$ are both non-compact, and
$$
m(s_{\alpha_{\ell-1}})*\mathcal{F}=m(s_{\alpha_{\ell}})*\mathcal{F}=(e_{j_{1}}\subset \dots\subset e_{j_{\ell-2}}\subset\hat{e}_{|j_{\ell-1}|} ).
$$
\end{enumerate}
\end{prop}
Let $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)$ and $\alpha\in\Pi_{\mbox{${\mathfrak g}$}}$. If $Q_{K}=Q_{+}$ or $Q_{-}$ is a closed $K$-orbit,
then by Proposition 4.9 of \cite{CE21I}, $m(s_{\alpha})*Q_{K}\neq Q_{K}$ if and only if $\alpha=\alpha_{\ell}$. If $Q_{K}=Q_{i}$ with $i=0,\dots, \ell-1$ is not closed, then the same result implies
that $m(s_{\alpha})*Q_{i}\neq Q_{i}$ if and only if $\alpha=\alpha_{i}$.
\begin{prop}\label{p:monoidactiononPILSB}
Let $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)$ and let $Q=B_{2\ell}\cdot \mathcal{F}$ with $Q\subset Q_{K}$.
\noindent Case I: $Q_{K}=Q_{i}$, $i=0,\dots, \ell-1$ is not closed.
In this case, $\mathcal{F}$ is of the form
\begin{equation}\label{eq:typeBflagi}
\mathcal{F}=(e_{j_{1}}\subset \dots \subset e_{j_{i}}\subset v_{i+1}\subset \dots\subset v_{\ell}),
\end{equation}
where $v_{i+1}=\hat{e}_{j_{i+1}}$ or $v_{i+1}=\hat{e}_{a,-j_{i+1}}$.
\begin{enumerate}
\item If $j_{i}>0$ or $|j_{i}|> j_{i+1}$, then $\alpha_{i}$ is complex stable and $m(s_{\alpha_{i}})*\mathcal{F}$ is given by changing the sequence $e_{j_i} \subset v_{i+1}$
to $v_{i+1} \subset e_{j_i}.$
\item If $j_{i}<0$ and $|j_{i}|<j_{i+1}$, then $\alpha_{i}$ is non-compact and
$$
m(s_{\alpha_{i}})*\mathcal{F}=(e_{j_{1}}\subset\dots\subset e_{j_{i-1}}\subset\ v_{i}\subset v_{i+1}\subset\dots\subset v_{\ell}),
$$
\end{enumerate}
where $v_{i}=\hat{e}_{j_{i+1}, \,j_{i}}$ if $v_{i+1}=\hat{e}_{j_{i+1}}$, and $v_{i}=\hat{e}_{a,\,j_{i}}$ if $v_{i+1}=\hat{e}_{a,-j_{i+1}}$.
\noindent Case II: $Q_{K}=Q_{+}\mbox{ or } Q_{-}$ is closed.
In this case,
$$
\mathcal{F}=(e_{j_{1}}\subset \dots \subset e_{j_{\ell}}).
$$
consists entirely of standard basis vectors. For $Q\subset Q_{K}$, the root $\alpha_{\ell}$ is non-compact for $Q$ and
\begin{equation}\label{eq:closedB}
m(s_{\alpha_{\ell}})*\mathcal{F}= (e_{j_{1}}\subset \dots \subset e_{j_{\ell-1}}\subset \hat{e}_{|j_{\ell}|}).
\end{equation}
\end{prop}
\noindent We note that the computation of Remark 2.11 of \cite{CE21I} is useful in the proof of (\ref{eq:closedB}).
To fully describe the monoid action by simple roots of $\mbox{${\mathfrak g}$}$ it remains to compute $m(s_{\alpha})*Q$ when
$Q\subset Q_{K}$ and $\alpha$ is either real or complex unstable for $Q_{K}$. This can be done
using Proposition \ref{prop:monoid} along with Propositions \ref{p:monoidactiononPILS}, \ref{p:monoidactiononPILSD}, and \ref{p:monoidactiononPILSB}. We omit the calculations because we will not require these monoid actions in this paper.
\section{The Monoid action and the closure ordering on $B_{n-1}\backslash\mathcal{B}_{n}$}\label{s:closure}
In this section, we prove one of the main results of the paper which states that the closure ordering coincides with a certain standard order defined by Richardson and Springer in \cite{RS}. This result enables us to determine the closure ordering in terms of a monoid action using simple roots both of $\mbox{${\mathfrak g}$}$ and $\mbox{${\mathfrak k}$}$.
\subsection{The monoid action and the standard order}\label{ss:RS}
Recall from Section 5.1 the action of a subgroup $M$ of a group $R$ on the flag variety $\mathcal{B}:=\mathcal{B}_{R}$ with finitely many orbits and the monoid action by a simple reflection $s\in S$ from the Weyl group of $R$ on $M\backslash \mathcal{B}$. Given a sequence $\vec{s}=(s_{1},\dots, s_{k})$ of elements in $S$ and
an $M$-orbit $Q\inM\backslash \B$, we let
\begin{equation} \label{eq:Ssequence}
m(\vec{s})*Q:=m(s_{k})*\dots *m(s_{1})*Q \mbox{ if } k > 0, m(\vec{s})*Q=Q \mbox{ if } k = 0.
\end{equation}
Then $\mathfrak{M}:=\{ m(\vec{s}): \vec{s} \mbox{ a sequence} \} $ is a finite monoid with $1$, which follows from the well-known fact that the operators $m(s)$ satisfy both braid relations and $m(s)^{2}=m(s)$.
The \emph{weak order } $\leq_w$ is defined by the property that if $Q, Q^{\prime} \in M\backslash \mathcal{B}$, then $Q \leq_w Q^{\prime}$ if and only if $Q^{\prime}=m(\vec{s})*Q$ for some sequence $\vec{s}$ as above. It is the weakest partial order such that $Q$ is less than or equal to $m(s)*Q$ for each $s\in S$ and $Q \in M\backslash \mathcal{B}.$
\begin{dfn}\label{dfn:minimal}
We say $Q\inM\backslash \B$ is minimal if $Q\in \mathfrak{M}*Q^{\prime}$ implies
$Q=Q^{\prime}$ for every $Q^{\prime}\inM\backslash \B$.
\end{dfn}
The minimal orbits are the minimal elements of $M\backslash \B$ in the weak order. We need the following assumption about minimal elements in $M\backslash \B.$
\begin{equation}\label{eq:minimalcond}
\mbox{The minimal elements } Q \in M\backslash \B \mbox{ are exactly the orbits of minimal dimension } d.
\end{equation}
Given the assumption in (\ref{eq:minimalcond}), we define a length function $\ell: M\backslash \B\to \mathbb{Z}_{\geq 0}$ by
\begin{equation}\label{eq:lengthfn}
\ell(Q):=\dim Q-d
\end{equation}
so the minimal orbits are exactly the orbits of length $0.$
There are two other partial orderings that we consider on $M\backslash \B$ called the closure order and the standard order.
The closure order (sometimes called the Bruhat order) is defined by
$$
Q^{\prime}\leq Q\mbox{ if and only if } Q^{\prime}\subset \overline{Q}.
$$
The standard order is denoted by $\preceq$ and is defined in stages.
We first define a relation $\dashv$ on $M\backslash \B$ as follows.
Let $Q,\, Q^{\prime}\inM\backslash \B$. We say that $Q^{\prime}\dashv Q$ if
there exists a sequence $\vec{s}=(s_{1},\dots, s_{k})$ of elements of $S$, $t\in S$, and
$Q^{\prime\prime}\in M\backslash \B$ such that the following two conditions hold:
\begin{equation}\label{eq:stdconditions}
\begin{split}
&(i)\; Q^{\prime}=m(\vec{s})*Q^{\prime\prime} \mbox{ and } \ell(Q^{\prime})=\ell(Q^{\prime\prime})+k.\\
&(ii) \; Q=m(\vec{s})*(m(t)*Q^{\prime\prime}) \mbox{ and } \ell(Q)=\ell(Q^{\prime\prime})+k+1.
\end{split}
\end{equation}
\noindent The conditions in (\ref{eq:stdconditions}) can be easily visualized in the following diamond diagram:
\begin{center}
\begin{tikzpicture} [scale=1.5,auto=center,every node/.style={rectangle,fill=white!20}]
\node (a1) at (0,5) {$Q^{\prime\prime}$}; \node (a2) at (-1,4) {$m(t)*Q^{\prime\prime}$}; \node (a3) at (1,4) {$Q^{\prime} $};
\node (a4) at (0,3) {$ Q$}; \draw [-stealth] (a1) -- (a2) node[midway, above] {$t$}; \draw [-stealth] (a1) -- (a3) node[midway, above] {$\vec{s}$}; \draw [-stealth] (a2) -- (a4) node[midway, above] {$\vec{s}$}; \draw [-stealth] [dashed](a3) -- (a4) node[near start, below] {$\vdash$};
\end{tikzpicture} \end{center}
The standard order is defined by the property that
$Q^{\prime}\preceq Q$ if there exists a sequence $\vec{Q}=(Q_{0},\dots, Q_{k})$, $k\geq 0$,
with $Q_{0}=Q^{\prime}$ and $Q_{k}=Q$ such that $Q_{i-1}\dashv Q_{i}$ for all $i=1,\dots, k$.
Assuming Equation (\ref{eq:minimalcond}), a partial order $\leq_O$ is said to be compatible with the
action of the monoid $\mathfrak{M}$ on $M\backslash \B$ if for all $s\in S$ and $Q, Q^{\prime} \in M\backslash \B$, we have
\begin{equation}\label{eq:compatible}
\begin{split}
&\; (1)\; Q\leq_{O} m(s)*Q.\\
&\; (2) \mbox{ If } Q^{\prime}\leq_{O} Q, \mbox{ then } m(s)*Q^{\prime}\leq_{O} m(s) *Q.\\
& \;(3) \mbox{ If } Q^{\prime}\leq_{O} Q \mbox{ and } \ell(Q^{\prime})\geq \ell(Q),\, \mbox{then } Q^{\prime}=Q.
\end{split}
\end{equation}
It follows easily from definitions that the closure order is compatible with the $\mathfrak{M}$-action.
\begin{thm}\label{thm:closureorder}[Theorem 7.11 in \cite{RS}]
Under the assumption in (\ref{eq:minimalcond}) the closure order on
$M\backslash \B$ coincides with the standard order.
\end{thm}
\begin{rem}\label{r:rsthm711}
To be precise, this theorem is only proved in \cite{RS} in the case where $M$ is the fixed points $H$ of an algebraic involution of $R$. However, the proof given in \cite{RS} applies in the more general situation of Theorem \ref{thm:closureorder}. In more detail, Richardson and Springer introduce a property on a partial order on $M\backslash \B$ called the one-step property which in the setting of Theorem \ref{thm:closureorder} means the following. For a $M$-orbit $Q$ and $s\in S$ corresponding to a simple root $\alpha$, let $p(s,Q)=\{ Q^{\prime} \in M\backslash \mathcal{B} : Q^{\prime} \subset \pi_{\alpha}^{-1}(\pi_{\alpha}(Q))\}.$ Then the one-step property is said to hold if $$\overline{m(s)*Q}=\displaystyle\bigcup_{ Q^{\prime} \leq Q} p(s, Q^{\prime})$$ for all $s\in S$ and $Q\in M\backslash \B.$ The one-step property is shown to hold for the closure order when $M=H$ in Lemmas 7.5 and 7.6 of \cite{RS}. The same proof applies in our more general context. In Propositions 6.3, 6.4, and 6.5 and Lemma 6.1 of \cite{RS}, the authors prove that if we consider a partial order compatible with the $\mathfrak{M}$-action and with a length function such that the minimal elements are precisely the elements of length $0$, then if the partial order satisfies the one-step property, then it coincides with the standard order. This proves the theorem.
\end{rem}
\subsection{Applications to $B_{n-1}\backslash\B_{n}$}\label{ss:Bmonoid}
We require an extended monoid action to study $B_{n-1}\backslash\B_{n}.$ For this, let
$K_{\Delta}=\{ (x,x) \in K \times G \}$ and note that the map $B_{n-1}\backslash\B_{n} \to
K_{\Delta}\backslash (\mathcal{B}_{\mbox{${\mathfrak k}$}}\times \mathcal{B}_{n})$ given by
$Q\mapsto K_{\Delta}\cdot (\mbox{${\mathfrak b}$}_{n-1}, Q)$
is bijective. Further, $\dim(K_{\Delta}\cdot (\mbox{${\mathfrak b}$}_{n-1}, Q))=\dim(\mathcal{B}_{\mbox{${\mathfrak k}$}}) + Q$ and this bijection preserves the closure order. If we let the group $R=K\times G$ in Section \ref{ss:monoid}, then we have a monoid action by simple roots from
$\Pi_{\mbox{${\mathfrak k}$} \oplus \mbox{${\mathfrak g}$}} = \Pi_{\mbox{${\mathfrak k}$}} \cup \Pi_{\mbox{${\mathfrak g}$}}$ on the orbits in
$K_{\Delta}\backslash (\mathcal{B}_{\mbox{${\mathfrak k}$}}\times \mathcal{B}_{n}).$ We use the above bijection to obtain monoid actions of $\Pi_{\mbox{${\mathfrak k}$}}$ and $\Pi_{\mbox{${\mathfrak g}$}}$ on $B_{n-1}\backslash\B_{n}.$ We refer
to this monoid action by $\Pi_{\mbox{${\mathfrak k}$}}$ and $\Pi_{\mbox{${\mathfrak g}$}}$ as the \emph{extended monoid action}. In particular, if $\alpha \in \Pi_{\mbox{${\mathfrak k}$}}$, and $Q \in B_{n-1}\backslash\B_{n}$, then
$m(s_{\alpha})*Q$ is the $B_{n-1}$-orbit in $\mathcal{B}_n$ such that
$K_{\Delta}\cdot (eB_{n-1}, m(s_{\alpha})*Q)$ is the orbit given by
$m(s_{\alpha})*K_{\Delta} \cdot (eB_{n-1}, Q)$ where $\alpha$ is regarded as a simple root for $\mbox{${\mathfrak k}$}\oplus \mbox{${\mathfrak g}$}$.
We will prove in this section that the collection of $B_{n-1}$-orbits in $\mathcal{B}_n$ satisfies the minimal condition in Equation (\ref{eq:minimalcond}) for this extended monoid action. On the other hand, even in the case of $GL(3)$, the $B_{n-1}$-orbits do not satisfy this minimal condition if we only use the simple roots of $\Pi_{\mbox{${\mathfrak g}$}}$ (see Example \ref{exam:bigone} below).
Let $Q=B_{n-1}\cdot {\rm Ad}(v)\mathcal{F}_{+}$ be an orbit in $B_{n-1}\backslash\B_{n}.$ Let $\alpha \in \Pi_{\mbox{${\mathfrak k}$}}.$ By Equation (4.1) of \cite{CE21I},
\begin{equation}\label{eq:leftmonoid}
m(s_{\alpha})*Q \mbox{ is the unique open $B_{n-1}$-orbit in } P_{K, \alpha}\cdot {\rm Ad}(v) \mathcal{F}_{+},
\end{equation}
where $P_{K, \alpha}\supset B_{n-1}$ is the standard parabolic subgroup of $K$ determined by the root $\alpha$. We refer to this monoid action as ``the left monoid action.'' Let $\alpha \in \Pi_{\mbox{${\mathfrak g}$}}.$ By Equation (4.2) of \cite{CE21I},
\begin{equation}\label{eq:rightmonoidagain}
m(s_{\alpha})*Q\mbox{ is the unique open $B_{n-1}$-orbit in }
B_{n-1}\cdot{\rm Ad}(v P_{\alpha})\mathcal{F}_{+},
\end{equation}
where $P_{\alpha}\supset B_{n}$ is the standard parabolic subgroup of $G$ determined by the root $\alpha$. We refer to this monoid action as ``the right monoid action'' and note that it coincides with the monoid action by $m(s_{\alpha})$ on $B_{n-1}\backslash\B_{n}$ from Section \ref{ss:monoid}.
\begin{rem}\label{r:kexplicit}
An analogue of Proposition \ref{prop:monoid} also holds for the left monoid action except in this case the simple reflection $s_{\alpha}$ and the Cayley transform $u_{\alpha}$ act on the left of the representative of the orbit $Q$ instead of on the right. That is to say that if $Q=B_{n-1}\cdot {\rm Ad}(v)\mathcal{F}_{+}$ for $v\in G$ and $\alpha\in\Pi_{\mbox{${\mathfrak k}$}}$ is complex stable (resp. non-compact) for $Q$ then $m(s_{\alpha})*Q=B_{n-1}\cdot {\rm Ad}(\dot{s}_{\alpha}v)\mathcal{F}_{+}$ (resp $m(s_{\alpha})*Q=B_{n-1}\cdot {\rm Ad}(u_{\alpha}^{-1}v)\mathcal{F}_{+})$.
\end{rem}
\begin{rem}\label{r:kmodpright}
Let $P^{\prime}$ be a parabolic subgroup of $K$ containing $B_{n-1}.$
By a construction similar to the one above, there is a left monoid action by roots in $\Pi_{\mbox{${\mathfrak k}$}}$ on $B_{n-1}\backslash K/P^{\prime}$ (see Part (1) of Remark 4.5 from \cite{CE21I}). It is determined by the property that for $\alpha \in \Pi_{\mbox{${\mathfrak k}$}}$ and an orbit $Q \in B_{n-1}\backslash K/P^{\prime}$,
\begin{equation}\label{eq:monoidpartial}
m(s_{\alpha})*Q \mbox{ is the unique open $B_{n-1}$-orbit in } P_{\alpha}\cdot Q.
\end{equation}
By fundamental properties of the Weyl group, the only minimal orbit for the monoid action by $\Pi_{\mbox{${\mathfrak k}$}}$ on $B_{n-1}\backslash K/P^{\prime}$ is the one point orbit
$eP^{\prime}=B_{n-1}\cdot eP^{\prime}.$
\end{rem}
In the notation
of Section \ref{ss:RS}, let $S:=\{s_{\alpha}:\, \alpha\in \Pi_{\mbox{${\mathfrak k}$}}\cup\Pi_{\mbox{${\mathfrak g}$}}\},$ and let $\mathfrak{M}=\{ m(\vec{s})|\, \vec{s}=(s_{1},\dots, s_{k}),\,s_{i}\in S,\, k\geq 0\}$.
Then $\mathfrak{M}$ acts on $B_{n-1}\backslash\B_{n}$ via the extended monoid action described above.
It then follows that Theorem \ref{thm:closureorder} holds
for $B_{n-1}\backslash\B_{n}$ as long as (\ref{eq:minimalcond}) holds for the action of the monoid $\mathfrak{M}$. To that effect, we prove
\begin{thm}\label{thm:bigthm}
The minimal elements for the action of the monoid $\mathfrak{M}$ on $B_{n-1}\backslash\B_{n}$
(see Definition \ref{dfn:minimal}) are precisely the zero dimensional $B_{n-1}$-orbits.
\end{thm}
We review some results about the fibre bundle structure of
the $B_{n-1}$-orbits on $\mathcal{B}_{n}$ developed in \cite{CE21I} which will be needed in the proof of this Theorem, beginning with results concerning the $K$-orbits $Q_K.$ Let $Q\inB_{n-1}\backslash\B_{n}$ and let $Q_K = K\cdot Q$ be the $K$-orbit containing $Q$.
In Theorem 3.1 and Remark 3.3 of \cite{CE21I}, we
associate to the $K$-orbit $Q_{K}$ a parabolic subgroup $R\subset G$ with a Levi factor
$L$ containing the standard Cartan subgroup of diagonal matrices $H$.
In more detail, we denote by $\mbox{${\mathfrak p}$}_{S}\supset\mbox{${\mathfrak b}$}_{n}$ the standard
parabolic subalgebra of $\mbox{${\mathfrak g}$}$ given by a subset $S\subset\Pi_{\mbox{${\mathfrak g}$}}$ of standard simple roots. Recall the explicit description of $K$-orbits on $\mathcal{B}_n$ given in Section \ref{ss:Korbits}.
Then $\mbox{${\mathfrak r}$}=\mbox{Lie}(R)=\tilde{w}(\mbox{${\mathfrak p}$}_{S})$ where $S\subset \Pi_{\mbox{${\mathfrak g}$}}$ and $\tilde{w}\in W$ depend on $Q_K$ according to the formulas
\begin{equation}\label{eq:rootsforLevi}
S=\left\lbrace\begin{array}{lll} \{\alpha_{i},\dots, \alpha_{j-1}\} & \mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{gl}(n), & Q_{K}=Q_{i,j},\, i<j\\
\{\alpha_{i+1},\dots, \alpha_{\ell}\} & \mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1), & Q_{K}=Q_{i}\\
\{\alpha_{i},\dots , \alpha_{\ell}\} & \mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell), & Q_{K}=Q_{i}\\
\emptyset &\mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{gl}(n) \mbox{ or }\mathfrak{so}(n), &Q_{K}\mbox{ closed} \end{array}\right\rbrace_{,}
\end{equation}
and
\begin{equation}\label{eq:guyinW}
\tilde{w}=\left\lbrace\begin{array}{llll} w_{i}=(n, n-1, \dots , i+1, i) & \mbox{ if } \mbox{${\mathfrak g}$}=\mathfrak{gl}(n), &\mbox { and } &Q_{K}=Q_{i,j} \mbox{ or } Q_{i}\\
\mbox{ e }& \mbox{ if } \mbox{${\mathfrak g}$}=\mathfrak{so}(n), &\mbox{ and }& Q_{K}=Q_{i} \mbox{ or } \,Q_{+}\\
s_{\alpha_{l}}& \mbox{ if } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1),& \mbox{ and } &Q_{K}=Q_{-}\end{array}\right\rbrace_{.}
\end{equation}
To describe a Levi factor $\mbox{${\mathfrak l}$}$ of $\mbox{${\mathfrak r}$}$, consider the index
\begin{equation}\label{eq:km}
k(m):=\left\lbrace\begin{array}{ll} m & \mbox{if } \mbox{${\mathfrak g}$}=\mathfrak{gl}(n)\\
2m & \mbox{if } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)\\
2m+1 & \mbox{if } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)\end{array}\right.
\end{equation}
Let $\mbox{${\mathfrak g}$}_{k(m)}=\mathfrak{gl}(k(m))$ or $ \mathfrak{so}(k(m))$ in the general linear and orthogonal cases respectively. Then $\mbox{${\mathfrak l}$}\cong \mbox{${\mathfrak g}$}_{k(m)+1}+ \mbox{${\mathfrak z}$}(\mbox{${\mathfrak l}$}),$
where $\mbox{${\mathfrak z}$}(\mbox{${\mathfrak l}$})$ is the centre of $\mbox{${\mathfrak l}$}$.
In addition, the group $K\cap R$ is a standard parabolic subgroup of $K$ with Levi factor $K\cap L=G_{k(m)}\cdot Z$ where $Z$ is the connected group with Lie algebra $\mbox{${\mathfrak k}$}\cap\mbox{${\mathfrak z}$}(\mbox{${\mathfrak l}$})$. Under these identifications, in the $GL(n)$-case, $G_{k(m)+1}$ is identified as the group of all invertible linear transformations of the space spanned by $\{e_{i}, \dots, e_{j-1}, e_{n}\}$.
In the $SO(2\ell+1)$-case (resp. $SO(2\ell)$-case), $G_{k(m)+1}$ is identified with the group of
all orthogonal transformations of determinant one of the space spanned by $\{ e_{\pm (i+1)}, \dots, e_{\pm \ell}, e_0 \}$ (resp. $\{ e_{\pm i}, \dots, e_{\pm \ell}\}$) with respect to the restriction of the form $\beta$ defined in Equation (\ref{eq:beta}). Then the subgroup $G_{k(m)}=G_{k(m)+1}\cap K$ is embedded in $G_{k(m)+1}$ as in Section \ref{ss:Korbits}. Note that $\mathcal{B}_{\mbox{${\mathfrak l}$}}\cong \mathcal{B}_{k(m)+1}$ and $\mathcal{B}_{\mbox{${\mathfrak l}$}\cap\mbox{${\mathfrak k}$}}\cong \mathcal{B}_{k(m)}$ and $B_{n-1}\cap L$ is a Borel subgroup of $K\cap L$. Thus, the $K\cap L$-action and $B_{n-1}\cap L$-actions on $\mathcal{B}_{\mbox{${\mathfrak l}$}}$ may be identified with the $G_{k(m)}$ and $B_{k(m)}$-actions on $\mathcal{B}_{k(m) + 1}$ and we use these identifications freely in the future. We let $\tilde{Q}_{K\cap L}$ denote the open $K\cap L$-orbit on $\mathcal{B}_{\mbox{${\mathfrak l}$}}$, which we identify with the open $G_{k(m)}$-orbit on $\mathcal{B}_{k(m)+1}.$ In Theorem 3.8 of \cite{CE21I}, we prove that there is a point ${\mathcal{F}}_{\mbox{${\mathfrak l}$}}$ in $\tilde{Q}_{K\cap L}$ with stabilizer in $K\cap L$ corresponding to the upper triangular matrices $B_{k(m)-1}$ in $G_{k(m)-1},$ where,
in the $GL(n)$-case, $G_{k(m)-1}\subset G_{k(m)}$ is the subgroup preserving the subspace spanned by
$\{e_{i},\dots, e_{j-2}\}$ and fixing the vectors $e_{j-1}$ and $e_{n}$, and in the orthogonal cases the embedding of $G_{k(m)-1}$ as a subgroup of
$G_{k(m)}$ is described in Remark 2.1 of \emph{loc.cit.} Explictly, in Equation (4.22) of \emph{loc.cit.}, we note that
\begin{equation}\label{eq:basepoint}
\mathcal{F}_{\mbox{${\mathfrak l}$}}:=\left\lbrace\begin{array}{lll} (\hat{e}_{j-1}\subset e_{i}\subset e_{i+1}\subset\dots\subset e_{j-2}\subset e_{n}) & \mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{gl}(n), & Q_{K}=Q_{i,j}, i<j\\
(\hat{e}_{\ell}\subset e_{i+1}\subset \dots\subset e_{\ell-1})& \mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1), & Q_{K}=Q_{i}\\
(e_{\ell}\subset e_{i}\subset\dots\subset e_{\ell-2}) & \mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell), & Q_{K}=Q_{i}\end{array}\right\rbrace_{,}
\end{equation}
so that $B_{k(m)-1}$ stabilizes the flag in $\mbox{${\mathfrak g}$}_{k(m)-1}$ given by
\begin{equation*
\mathcal{F}_{+,k(m)-1}:=\left\lbrace\begin{array}{lll} (e_{i}\subset e_{i+1}\subset \dots \subset e_{j-2}) & \mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{gl}(n), & Q_{K}=Q_{i,j}, i<j\\
(e_{i+1}\subset\dots\subset e_{\ell-1}) & \mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1), & Q_{K}=Q_{i}\\
(e_{i}\subset \dots\subset e_{\ell-2})& \mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell), & Q_{K}=Q_{i}\end{array}\right\rbrace_{.}
\end{equation*}
We now discuss the $B_{n-1}$-orbit structure. By
Theorem 3.5 and Notation 3.6 of \cite{CE21I}, the canonical projection
$\pi_{R}:\mathcal{B}_{n}\to G/R$ makes $Q$ into a $B_{n-1}$-equivariant fibre bundle, $Q=\mathcal{O}(Q_{\mbox{${\mathfrak r}$}}, Q_{\mbox{${\mathfrak l}$}})$ with base a $B_{n-1}$-orbit $Q_{\mbox{${\mathfrak r}$}}=\pi_{R}(Q)\cap \mbox{${\mathfrak k}$}$ on the partial flag variety $K/K\cap R$ of $\mbox{${\mathfrak k}$}$ and fibre a $B_{n-1}\cap L$-orbit $Q_{\mbox{${\mathfrak l}$}}$ contained in the above open orbit $\tilde{Q}_{K\cap L}$ on $\mathcal{B}_{\mbox{${\mathfrak l}$}}.$ Since $B_{n-1}$ is a Borel subgroup of $K$, the orbits $Q_{\mbox{${\mathfrak r}$}}$ are Schubert cells in $K/K\cap R$, and we denote them by $X_w^{K\cap R}=B_{n-1}w K\cap R$ in $K/K\cap R$. To understand the orbits $Q_{\mbox{${\mathfrak l}$}}$, given the above comments about the stabilizer of the point ${\mathcal{F}}_{\mbox{${\mathfrak l}$}}$, we note that $B_{n-1}\cap L$-orbits on
$\tilde{Q}_{K\cap L}$ correspond to double cosets in $B_{k(m)}\backslash G_{k(m)}/B_{k(m)-1}$, and the map $B_{k(m)}\ell B_{k(m)-1} \mapsto B_{k(m)-1}\ell^{-1} B_{k(m)}$ is a bijection on double cosets. In this correspondence,
\begin{equation}\label{eq:op}
Q_{\mbox{${\mathfrak l}$}}=B_{k(m)}\cdot {\rm Ad}(\ell) {\mathcal{F}}_{\mbox{${\mathfrak l}$}} \Leftrightarrow Q_{\mbox{${\mathfrak l}$}}^{op} := B_{k(m)-1}\cdot {\rm Ad}(\ell^{-1}) {\mathcal{F}}_{+, k(m)},
\end{equation}
where
${\mathcal{F}}_{+,k(m)}$ is the flag stabilized by the upper triangular matrices $B_{k(m)}$ in $G_{k(m)}$.
\begin{rem}\label{r:Borelintersect}
We can make this correspondence more explicit as follows. Let $Q=\mathcal{O}(X_w^{K\cap R},Q_{\mbox{${\mathfrak l}$}})$. The following assertions are restatements of Remark 3.7 of \cite{CE21I}.
\par\noindent Type A: Consider the point ${\mathcal{F}}_{\mbox{${\mathfrak l}$}} \in \mathcal{B}_{\mbox{${\mathfrak l}$}}$ in the case whre $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$ where $Q_K=Q_{i,j}$ from Equation \eqref{eq:basepoint}. Suppose that $Q_{\mbox{${\mathfrak l}$}}=(B_{n-1}\cap L)\cdot {\rm Ad}(\ell){\mathcal{F}}_{\mbox{${\mathfrak l}$}}$ for $\ell \in K\cap L.$ Then $Q=B_{n-1}\cdot {\rm Ad}(\dot{w}\ell){\mathcal{F}}_{i,j}$, where ${\mathcal{F}}_{i,j}$ is from Equation \eqref{eq:typeAflag}.
\par\noindent Type B: Consider the point ${\mathcal{F}}_{\mbox{${\mathfrak l}$}} \in \mathcal{B}_{\mbox{${\mathfrak l}$}}$ in the case $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell + 1)$ and $Q_K=Q_i$ from Equation \eqref{eq:basepoint}. Suppose that $Q_{\mbox{${\mathfrak l}$}}=(B_{n-1}\cap L)\cdot {\rm Ad}(\ell){\mathcal{F}}_{\mbox{${\mathfrak l}$}}$ for $\ell \in K\cap L.$ Then $Q=B_{n-1}\cdot {\rm Ad}(\dot{w}\ell){\mathcal{F}}_{i}$, where ${\mathcal{F}}_{i}$ is from Equation \eqref{eq:typeBflag}.
\par\noindent Type D: Consider the point ${\mathcal{F}}_{\mbox{${\mathfrak l}$}} \in \mathcal{B}_{\mbox{${\mathfrak l}$}}$ in the case $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)$ where $Q_K=Q_i$ from Equation \eqref{eq:basepoint}. Suppose that $Q_{\mbox{${\mathfrak l}$}}=(B_{n-1}\cap L)\cdot {\rm Ad}(\ell){\mathcal{F}}_{\mbox{${\mathfrak l}$}}$ for $\ell \in K\cap L.$ Then $Q=B_{n-1}\cdot {\rm Ad}(\dot{w}\ell){\mathcal{F}}_{i}$, where ${\mathcal{F}}_{i}$ is from Equation \eqref{eq:typeDflag}.
\end{rem}
\begin{rem}\label{r:opencorrespondence}
When $Q_{K}$ is the open $K$-orbit on $\mathcal{B}_{n}$, the parabolic subalgebra $\mbox{${\mathfrak r}$}$ coincides with $\mbox{${\mathfrak g}$}$, so that $\mbox{${\mathfrak l}$}=\mbox{${\mathfrak g}$}$ and the partial flag variety $K/K\cap R$ is a point. In this case, the orbit $\tilde{Q}_{K\cap L}=Q_{K}$
and any $Q\in B_{n-1}\backslash \tilde{Q}_{K}$ corresponds to a unique $Q^{op}\in B_{n-2}\backslash \mathcal{B}_{n-1}$.
In the examples in Section \ref{s:graphs}, we will demonstrate how the Bruhat graph of $ B_{n-2}\backslash \mathcal{B}_{n-1}$ can be realized as a subgraph of the Bruhat graph of $B_{n-1}\backslash \mathcal{B}_{n}$ using this correspondence.
\end{rem}
To discuss the action of the monoid $\mathfrak{M}$ on orbits $\mathcal{O}(X_w^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})$, we recall the left monoid action by roots of
$\Pi_{\mbox{${\mathfrak k}$}}$ on $B_{n-1}\backslash K/K\cap R$ from Remark \ref{r:kmodpright}.
Suppose $\alpha\in\Pi_{\mbox{${\mathfrak k}$}}$ is a root of the Levi subalgebra $w(\mbox{${\mathfrak l}$}\cap\mbox{${\mathfrak k}$}).$
It follows by (\ref{eq:monoidpartial}) that
$m(s_{\alpha})*X_w^{K\cap R}=X_w^{K\cap R}$. Hence, if $\alpha\in\Pi_{\mbox{${\mathfrak k}$}}$ is a root such that $m(s_{\alpha})*X_w^{K\cap R}\neq X_w^{K\cap R}$,
then $\alpha$ is not a root of $w(\mbox{${\mathfrak k}$}\cap\mbox{${\mathfrak l}$})$. Combining this observation with Equation (4.7) of Theorem 4.7 of \cite{CE21I} we obtain
\begin{equation}\label{eq:baseaction}
\mbox{If } m(s_{\alpha})*X_w^{K\cap R}\neq X_w^{K\cap R},\mbox{ then } m(s_{\alpha})*\mathcal{O}(X_w^{K\cap R},Q_{\mbox{${\mathfrak l}$}})=\mathcal{O}(m(s_{\alpha})*X_w^{K\cap R}, Q_{\mbox{${\mathfrak l}$}}).
\end{equation}
We now study the extended monoid action on the orbits in the fibre. In particular, we explain how the
results of \cite{CE21I} may be applied to transfer monoid actions on the orbit $Q_{\mbox{${\mathfrak l}$}}^{op}$ in $B_{k(m)-1}\backslash \mathcal{B}_{k(m)}$ to monoid actions on the orbit $Q_{\mbox{${\mathfrak l}$}}$ in $(B_{n-1}\cap L)\backslash\tilde{Q}_{K\cap L}$. The set of orbits $B_{k(m)-1}\backslash\mathcal{B}_{k(m)}$ has a right monoid action via
the simple roots of $\Pi_{\mbox{${\mathfrak g}$}_{k(m)}}$ and a left monoid action via the simple roots
$\Pi_{\mbox{${\mathfrak g}$}_{k(m)-1}}.$ Explicitly,
\begin{equation}\label{eq:smallerroots}
\Pi_{\mbox{${\mathfrak g}$}_{k(m)-1}}=\left\lbrace\begin{array}{lll} \{\alpha_{i},\dots, \alpha_{j-3}\} &\mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{gl}(n), & Q_{K}=Q_{i,j}, \, i<j\\
\{\alpha_{i+1},\dots , \alpha_{\ell-2}, \alpha_{\ell-1}\} &\mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1), & Q_{K}=Q_{i}\\
\{\alpha_{i},\dots, \alpha_{\ell-2}, \alpha_{\ell-1}\} &\mbox{ for } \mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell), & Q_{K}=Q_{i}\end{array}\right\rbrace_{.}
\end{equation}
Let $S^{\prime}\subset \Pi_{\mbox{${\mathfrak g}$}}$ be the subset of simple roots
\begin{equation}\label{eq:Sprime}
S^{\prime}:=\{\alpha_{k+1}: \, \alpha_{k}\in \Pi_{\mbox{${\mathfrak g}$}_{k(m)-1}}\}.
\end{equation}
Then $S^{\prime}\subset S$ where $S$ is given in (\ref{eq:rootsforLevi}), and
Proposition 4.9 of \cite{CE21I} implies that $S^{\prime}$ consists of precisely the roots in $S$ which are compact
imaginary for the $K$-orbit $Q_{K}$ (see Part (3) of Proposition-Definition \ref{prop:monoid}.).
Then Equation (4.24) of \emph{loc.cit.} implies that
\begin{equation}\label{eq:transfer}
\mbox{for } \alpha_{k}\in\Pi_{\mbox{${\mathfrak g}$}_{k(m)-1}},\, m(s_{\alpha_{k}})*Q_{\mbox{${\mathfrak l}$}}^{op}=(m(s_{\tilde{w}(\alpha_{k+1})})*Q_{\mbox{${\mathfrak l}$}})^{op},
\end{equation}
where $\tilde{w}$ is given by Equation (\ref{eq:guyinW}). The monoid action
on the left-hand side of (\ref{eq:transfer}) is a left monoid action and the monoid action on the right-hand
side is a right monoid action. Note that on the right-hand side of
(\ref{eq:transfer}) we think of $\alpha_{k+1}\in S^{\prime}\subset S$, so that $\tilde{w}(\alpha_{k+1})\in \Pi_{\mbox{${\mathfrak l}$}}$ and
$\tilde{w}(\alpha_{k+1})$ is compact imaginary for the $K\cap L$-orbit $\tilde{Q}_{K\cap L}$, whence $m(s_{\tilde{w}(\alpha_{k+1})})*Q_{\mbox{${\mathfrak l}$}}$ is a well-defined right monoid action on the space $(B_{n-1}\cap L)\backslash\tilde{Q}_{K\cap L}$. By Equation (4.23) of \emph{loc. cit.} we know that
\begin{equation}\label{eq:lefttoright}
\mbox{for } \alpha\in\Pi_{\mbox{${\mathfrak g}$}_{k(m)}},\; m(s_{\alpha})*Q_{\mbox{${\mathfrak l}$}}^{op}=(m(s_{\alpha})*Q_{\mbox{${\mathfrak l}$}})^{op},
\end{equation}
where the left-hand side is a right monoid
action and the right-hand side is a left monoid action.
We will apply these observations in the following situation. Let $Q^{\prime}=\mathcal{O}(Q_{\mbox{${\mathfrak r}$}}, Q_{\mbox{${\mathfrak l}$}}^{\prime})$ and $Q=\mathcal{O}(Q_{\mbox{${\mathfrak r}$}}, Q_{\mbox{${\mathfrak l}$}})$ with
$Q_{\mbox{${\mathfrak r}$}}=X_{e}^{K\cap R}$ the unique zero dimensional $B_{n-1}$-orbit on $K/K\cap R$.
We claim that
\begin{equation}\label{eq:weakorderclaim}
(Q_{\mbox{${\mathfrak l}$}}^{\prime})^{op}\leq_{w} Q_{\mbox{${\mathfrak l}$}}^{op}\Rightarrow Q^{\prime}\leq_{w} Q.
\end{equation}
By definition of the weak order, it suffices to consider the case where
$Q_{\mbox{${\mathfrak l}$}}^{op}=m(s_{\alpha})*(Q_{\mbox{${\mathfrak l}$}}^{\prime})^{op}$, where
$\alpha\in \Pi_{\mbox{${\mathfrak g}$}_{k(m)-1}}\cup\Pi_{\mbox{${\mathfrak g}$}_{k(m)}}$.
First, consider $\alpha\in \Pi_{\mbox{${\mathfrak g}$}_{k(m)}}$. It follows from (\ref{eq:lefttoright}) that the orbit $Q_{\mbox{${\mathfrak l}$}}=m(s_{\alpha})*Q_{\mbox{${\mathfrak l}$}}^{\prime}$. If we take $w=e$ in Equation (4.6) of Theorem 4.7 of \cite{CE21I}, we obtain
$$
m(s_{\alpha})*Q^{\prime}=m(s_{\alpha})*\mathcal{O}(X_{e}^{K\cap R}, Q_{\mbox{${\mathfrak l}$}}^{\prime})=\mathcal{O}(X_{e}^{K\cap R}, m(s_{\alpha})*Q_{\mbox{${\mathfrak l}$}}^{\prime})=\mathcal{O}(X_{e}^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})=Q,
$$
yielding (\ref{eq:weakorderclaim}) in this case. For $\alpha=\alpha_{k}\in \Pi_{\mbox{${\mathfrak g}$}_{k(m)-1}}$, Equation (\ref{eq:transfer}) implies $Q_{\mbox{${\mathfrak l}$}}=m(s_{\tilde{w}(\alpha_{k+1})})*Q_{\mbox{${\mathfrak l}$}}^{\prime}$. Since $\alpha_{k+1}\in S^{\prime}\subset S$ where $S^{\prime}$ is given in (\ref{eq:Sprime}), we can apply Equation (4.14) of Part (1) of Theorem 4.11 of \cite{CE21I} to obtain
$$
m(s_{\alpha_{k+1}})*Q^{\prime}=m(s_{\alpha_{k+1}})*\mathcal{O}(X_{e}^{K\cap R}, Q_{\mbox{${\mathfrak l}$}}^{\prime})=\mathcal{O}(X_{e}^{K\cap R}, m(s_{\tilde{w}(\alpha_{k+1})})*Q_{\mbox{${\mathfrak l}$}}^{\prime})=\mathcal{O}(X_{e}^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})=Q,
$$
establishing (\ref{eq:weakorderclaim}) in this case as well.
\begin{lem}\label{l:zerodim}
Each closed $K$-orbit in $\mathcal{B}_n$ has a unique $B_{n-1}$-fixed point, and every $B_{n-1}$-fixed point in $\mathcal{B}_n$ is contained in a unique closed $K$-orbit.
\end{lem}
\begin{proof}
Let $Q_K$ be a closed $K$-orbit. By the Borel fixed-point theorem, the Borel
subgroup $B_{n-1}$ of $K$ has a unique fixed point on $Q_K.$ Conversely, any $B_{n-1}$-fixed point in $\mathcal{B}_n$ is in a closed $K$-orbit.
\end{proof}
\begin{rem}\label{r:numberclosed}
It follows from Lemma \ref{l:zerodim} and our description of $K\backslash\mathcal{B}_{n}$ in Section \ref{ss:Korbits}
that there are $n$ zero dimensional $B_{n-1}$-orbits on $\mathcal{B}_{n}$ for $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$, two for $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)$,
and one for $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)$. By Theorem 4.10 of \cite{CEexp}, these orbits are all of the form $B_{n-1}\cdot w(\mathcal{F}_{+})$ where $w\in W$ is given as follows. For $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$, $w$ is a representative of the cycle $w=(n, n-1, \dots, i)$ for some $i=1,\dots, n$. For
$\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)$, $w=e$ or $w=s_{\alpha_{\ell}}$, and for $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)$, $w=e$.
\end{rem}
\begin{proof}[Proof of Theorem \ref{thm:bigthm}]
Let $Q$ be a $B_{n-1}$-orbit on $\mathcal{B}_n$. We must show that there is a zero dimensional orbit $Q_0$ with $Q_0 \leq_{w} Q.$ We prove the result by induction on $n$. In the initial cases $n=2$ when
$\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$ and $n=3$ when $\mbox{${\mathfrak g}$}=\mathfrak{so}(n)$, the group $B_{n-1}=\mbox{${\mathbb C}$}^{\times}$ and
$\mathcal{B}_{n}=\mathbb{P}^{1}$ and the assertion is elementary. For the inductive step,
we use a second induction on $m=\ell(Q_K)$ where $Q_K=K\cdot Q$. In the case $m=0$, $Q_K$ is closed, and by Equation (\ref{eq:rootsforLevi}), $K\cap L$ is abelian, $Q_{\mbox{${\mathfrak l}$}}$ is a point, $Q\cong Q_{\mbox{${\mathfrak r}$}}$ and $K/K\cap R \cong \mathcal{B}_{\mbox{${\mathfrak k}$}}.$ By Theorem 4.7 of \cite{CE21I}, it follows that for $\alpha\in\Pi_{\mbox{${\mathfrak k}$}}$,
\begin{equation}\label{eq:leftequiv}
m(s_{\alpha})*Q\cong m(s_{\alpha})*Q_{\mbox{${\mathfrak r}$}},
\end{equation}
where the action on the right-hand side is the action of the monoid $\mathfrak{M}_{\mbox{${\mathfrak k}$}}$ generated by simple roots of $\mbox{${\mathfrak k}$}$ on $B_{n-1}\backslash \mathcal{B}_{\mbox{${\mathfrak k}$}}$ in (\ref{eq:monoidpartial}). By Remark \ref{r:kmodpright}, there is a unique minimal element in $B_{n-1}\backslash \mathcal{B}_{\mbox{${\mathfrak k}$}}$ for the $\mathfrak{M}_{\mbox{${\mathfrak k}$}}$-action, and the minimal orbit is the zero dimensional orbit corresponding to $\mbox{${\mathfrak b}$}_{n-1}.$ It follows easily that this orbit is minimal for the action of the full monoid $\mathfrak{M}.$
Now suppose that $m>0$ and let $Q=\mathcal{O}(Q_{\mbox{${\mathfrak r}$}},Q_{\mbox{${\mathfrak l}$}}).$ By Remark
\ref{r:kmodpright}, there is a sequence $\vec{s}=(s_{\alpha_{i_{1}}}, \dots, s_{\alpha_{i_{k}}})$ with
$\alpha_{i_{j}}\in\Pi_{\mbox{${\mathfrak k}$}}$ and a sequence of distinct
$B_{n-1}$-orbits in $K/K\cap R$, $\vec{Q}_{\mbox{${\mathfrak r}$}}=(Q_{0, \mbox{${\mathfrak r}$}},\dots, Q_{k,\mbox{${\mathfrak r}$}})$ with
$Q_{0,\mbox{${\mathfrak r}$}}= X_e^{K\cap R}$, $Q_{k,\mbox{${\mathfrak r}$}}=Q_{\mbox{${\mathfrak r}$}}$ such that $m(s_{\alpha_{i_{j}}})*Q_{j-1, \mbox{${\mathfrak r}$}}=Q_{j,\mbox{${\mathfrak r}$}}$, so that $m(\vec{s})*(X_{e}^{K\cap R})=Q_{\mbox{${\mathfrak r}$}}$ (see Equation \eqref{eq:Ssequence}). Applying (\ref{eq:baseaction}) iteratively, we obtain
$$
m(\vec{s})*\mathcal{O}(X_e^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})=\mathcal{O}(m(\vec{s})*(X_e^{K\cap R}), Q_{\mbox{${\mathfrak l}$}})=\mathcal{O}(Q_{\mbox{${\mathfrak r}$}}, Q_{\mbox{${\mathfrak l}$}}),
$$
so $\mathcal{O}(X_e^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})\leq_{w} Q$.
By our above remarks, $Q_{\mbox{${\mathfrak l}$}}$ corresponds to a $B_{k(m)-1}$-orbit $Q_{\mbox{${\mathfrak l}$}}^{op}$ on $\mathcal{B}_{k(m)}$ where $k(m)$ is given in (\ref{eq:km}). By induction on $n$, there exists
a zero dimensional $B_{k(m)-1}$-orbit $\{\mbox{${\mathfrak b}$}_{k(m)}\}\subset \mathcal{B}_{k(m)}$ with
$\{\mbox{${\mathfrak b}$}_{k(m)}\}\leq_{w} Q_{\mbox{${\mathfrak l}$}}^{op}$. Let $Q_{\mbox{${\mathfrak l}$}}^{\prime}$ be the unique $B_{k(m)}$-orbit in $\tilde{Q}_{K\cap L}$ such that $(Q_{\mbox{${\mathfrak l}$}}^{\prime})^{op}=\mbox{${\mathfrak b}$}_{k(m)}$ and let $Q^{\prime}=\mathcal{O}(X_e^{K\cap R},Q_{\mbox{${\mathfrak l}$}}^{\prime}).$
Equation (\ref{eq:weakorderclaim}) now implies
$\mathcal{O}(X_e^{K\cap R}, Q_{\mbox{${\mathfrak l}$}}^{\prime})\leq_{w}\mathcal{O}(X_e^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})$, whence $Q^{\prime}\leq_{w} Q$
Thus, it suffices to prove the Theorem for orbits $Q=\mathcal{O}(X_{e}^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})$ with $\dim Q_{\mbox{${\mathfrak l}$}}^{op}=0$. For this, we claim that there is a $B_{n-1}$-orbit $Q^{\prime}$ such that $Q^{\prime}\leq_{w} Q$ where $Q^{\prime}\subset Q_{K}^{\prime}$ with
$\ell(Q_{K}^{\prime})<m$.
It then follows by induction on $m$ that there exists a Borel subalgebra
$\mbox{${\mathfrak b}$}\in\mathcal{B}_{n}$ with $\mbox{${\mathfrak b}$}_{n-1}\subset \mbox{${\mathfrak b}$}$ and $\{\mbox{${\mathfrak b}$}\}\leq_{w} Q^{\prime}$, whence
$\{\mbox{${\mathfrak b}$}\}\leq_{w} Q$ and the proof is complete. The $B_{n-1}$-orbit $Q^{\prime}$ is constructed
on a case-by-case basis using the results of Section \ref{s:monoid}.
The first step is to describe the flag in standard form $\mathcal{F}$ contained
in an orbit $Q=\mathcal{O}(X_{e}^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})$ with $\dim Q_{\mbox{${\mathfrak l}$}}^{op}=0$.
We begin with the case $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n)$.
Since $m=\ell(Q_K)>0$, then by Remark \ref{r:Korbitlength}, the orbit
$Q_{K}=Q_{i,j}$ with $i<j$.
We claim that $Q=B_{n-1}\cdot \mathcal{F}$, where
\begin{equation}\label{eq:closedflag}
\mathcal{F}=(e_{1}\subset \dots\subset e_{i-1}\subset\underbrace{\hat{e}_{k}}_{i}\subset e_{i}\subset \dots\subset e_{k-1} \subset e_{k+1}\subset\dots\subset e_{j-1}\subset\underbrace{e_{n}}_{j}\subset e_{j}\subset\dots\subset e_{n-1})
\end{equation}
for some $k=i,\dots, j-1.$ Recall in this case the index $k(m)=m$. The orbit $Q_{\mbox{${\mathfrak l}$}}=(B_{n-1}\cap L)\cdot {\rm Ad}(\ell)\mathcal{F}_{\mbox{${\mathfrak l}$}}$
for some $\ell\in K\cap L$ and where $\mathcal{F}_{\mbox{${\mathfrak l}$}}$ is the flag in Equation (\ref{eq:basepoint}). Since $Q=\mathcal{O}(X_e^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})$, then by Remark \ref{r:Borelintersect}, the orbit $Q=B_{n-1}\cdot {\rm Ad}(\ell) \mathcal{F}_{i,j}$ with $\mathcal{F}_{i,j}$ the flag in Equation (\ref{eq:typeAflag}). Then by Equation \eqref{eq:op}, the orbit $Q_{\mbox{${\mathfrak l}$}}^{op}=B_{m-1}\cdot {\rm Ad}(\ell^{-1}){\mathcal{F}}_{+,m}.$ By Lemma \ref{l:zerodim} and Remark \ref{r:numberclosed}, we may assume that $\ell^{-1}$ is a representative for the cycle $ (j-1, j-2,\dots, k+1, k)$ for
some $k\in \{ i, \dots, j-1 \}.$ But then $Q = B_{n-1}\cdot {\rm Ad}(\ell){\mathcal{F}}_{i,j}$, so by Equation (\ref{eq:typeAflag}), the orbit $Q$ contains the flag in Equation \eqref{eq:closedflag}. By Theorem \ref{thm:std}, this flag $\mathcal{F}$ is the unique flag in standard form in the orbit $Q$.
Using this result, we now
use our results in Section \ref{s:monoid} to construct a $B_{n-1}$-orbit $Q^{\prime}\subset Q_{K}^{\prime}$
with $\ell(Q_{K}^{\prime})<m$ and $m(s_{\alpha})*Q^{\prime}=Q$ for some $\alpha\in \Pi_{\mbox{${\mathfrak g}$}}$.
First, suppose that $m>1$, so that $j>i+1$. There are two subcases to consider.
\noindent Case I: $i\leq k<j-1$: Let $Q^{\prime}:=B_{n-1}\cdot \mathcal{F}^{\prime}$, where
$$
\mathcal{F}^{\prime}=(e_{1}\subset \dots\subset e_{i-1}\subset\underbrace{\hat{e}_{k}}_{i}\subset e_{i}\subset \dots\subset e_{k-1} \subset e_{k+1}\subset\dots\subset\underbrace{e_{n}}_{j-1}\subset e_{j-1}\subset e_{j}\subset\dots\subset e_{n-1}).
$$
By Lemma \ref{l:5.1}, the orbit
$Q_{K}^{\prime}=Q_{i,j-1}$, so $\ell(Q_{K}^{\prime})=m-1$. Further, it follows from Proposition \ref{p:monoidactiononPILS} that $\alpha_{j-1}$ is complex stable for $Q^{\prime}$ and $m(s_{\alpha_{j-1}})*Q^{\prime}=Q$ (see Equation (\ref{eq:jcplx})).
\noindent Case II: $k=j-1$. In this case,
we let $Q^{\prime}=B_{n-1}\cdot \mathcal{F}^{\prime}$, where
$$
\mathcal{F}^{\prime}=(e_{1}\subset \dots\subset e_{i-1}\subset e_{i}\subset\underbrace{\hat{e}_{j-1}}_{i+1}\subset e_{i+1}\subset \dots\subset e_{j-2}\subset\underbrace{e_{n}}_{j}\subset e_{j}\subset \dots\subset e_{n-1}).
$$
Again by Lemma \ref{l:5.1}, the orbit $Q_{K}^{\prime}=Q_{i+1,j}$. Since $i<j-1$, Proposition \ref{p:monoidactiononPILS} implies $\alpha_{i}$ is complex stable for $Q^{\prime}$ and $m(s_{\alpha_{i}})*Q^{\prime}=Q$ (see Equation \eqref{eq:i-1cplx}).
Lastly, suppose $m=1$, so that $j=i+1$. Then
$$
\mathcal{F}=(e_{1}\subset \dots\subset e_{i-1}\subset\underbrace{\hat{e}_{i}}_{i}\subset e_{n}\subset e_{i+1}\subset\dots\subset e_{n-1}).
$$
Let $Q^{\prime}=B_{n-1}\cdot\mathcal{F}^{\prime}$ where
$$
\mathcal{F}^{\prime}=(e_{1}\subset \dots \subset e_{i-1}\subset e_{n}\subset e_{i}\subset \dots\subset e_{n-1}).
$$
Then $Q^{\prime}$ is closed and $Q^{\prime}\subset Q_{K}^{\prime}$, where
$Q_{K}^{\prime}=Q_{i}$ is a closed $K$-orbit on $\mathcal{B}$. Case II of Proposition \ref{p:monoidactiononPILS} implies that $\alpha_{i}$ is non-compact for $Q$ and
$m(s_{\alpha_{i}})* Q^{\prime}=Q$.
This establishes the claim in each of the three cases, which proves the Theorem for $\mbox{${\mathfrak g}$}=\mathfrak{gl}(n).$
Now we consider the case $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)$. Since $m=\ell(Q_K)>0$, then by Remark \ref{r:Korbitlength}, the $K$-orbit $Q_K = Q_i$ with $i \in \{ 1, \dots, \ell - 1 \}.$ We first consider the case when $m > 1$
so that $Q_{K}=Q_{i}$ with
$i<\ell-1$. In this case, we claim that our $B_{2\ell-1}$-orbit $Q$ in $Q_K$ contains one of the two flags
\begin{equation}\label{eq:closedflagD}
\mathcal{F}_{\pm, i}:=(e_{1}\subset\dots\subset e_{i-1}\subset e_{\pm \ell} \subset e_{i} \subset \dots \subset e_{\ell-2}).
\end{equation}
Indeed, $Q=\mathcal{O}(X_e^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})$ and $k(m)=2m+1$, so that our
$B_{2m+1}$-orbit $Q_{\mbox{${\mathfrak l}$}}$ corresponds to a zero dimensional $B_{2m}$-orbit $Q_{\mbox{${\mathfrak l}$}}^{op}$ in $\mathcal{B}_{2m+1}.$ By Lemma \ref{l:zerodim} and Remark \ref{r:numberclosed}, there are exactly two such orbits. If we let $\mathcal{F}_{+,2m+1}$ be the flag in $\mathcal{B}_{2m+1}$ stabilized by upper triangular matrices in $G_{2m+1}\cong SO(2m+1)$, then the two zero dimensional orbits are the points $\mathcal{F}_{+,2m+1}$ and $s_{\alpha_{\ell}}s_{\alpha_{\ell-1}} (\mathcal{F}_{+,2m+1})$ (note that $s_{\alpha_{\ell}}s_{\alpha_{\ell-1}}\in W_{K\cap L}\cong W_{G_{2m+1}}$ by Proposition 2.22 of \cite{CEspherical} and is a representative of the simple reflection determined by the short simple root of $\mbox{${\mathfrak g}$}_{2m+1}= \mbox{${\mathfrak g}$}_{2m+2}\cap \mbox{${\mathfrak k}$}$). It now follows as in the $\mathfrak{gl}(n)$-case using Remark \ref{r:Borelintersect}, Equation \eqref{eq:op}, and Equation \eqref{eq:typeDflag} that our orbit $Q$ contains one of the two standard flags ${\mathcal{F}}_{\pm, i}.$
To complete the proof for $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell)$ when $m > 1$, consider the $SO(2\ell)$-standard flag
$$
\mathcal{F}^{\prime}=(e_{1}\subset\dots\subset e_{i-1}\subset e_{i} \subset e_{\pm \ell} \subset \dots \subset e_{\ell-2}).
$$
Then it follows from Proposition \ref{p:monoidactiononPILSD} that $\alpha_{i}$ is complex stable
for $Q^{\prime}=B_{2\ell-1}\cdot \mathcal{F}^{\prime}\subset Q_{i+1}$ and $m(s_{\alpha_{i}})*Q^{\prime}=Q$ (see Equation (\ref{eq:cplxDroot})).
Now suppose that $m=1$, so that $Q_{K}=Q_{\ell-1}$. In this case, by reasoning as in the previously discussed cases, we can prove that our $B_{2\ell-1}$-orbit $Q=\mathcal{O}(X_e^{K\cap R},Q_{\mbox{${\mathfrak l}$}})$ contains exactly one of the standard flags
\begin{equation}\label{eq:length1Dflag}
\mathcal{F}_{\pm}=(e_{1}\subset\dots\subset e_{i} \subset \dots \subset e_{\ell-2}\subset e_{\pm \ell}).
\end{equation}
Now we take $\mathcal{F}^{\prime}=\mathcal{F}_{+}$. By Proposition \ref{p:monoidactiononPILSD}, if the last vector in (\ref{eq:length1Dflag}) is $e_{\ell}$,
then $m(s_{\alpha_{\ell-1}})*\mathcal{F}_{+}=\mathcal{F}$ (by Equation (\ref{eq:closedD1})), and if the last vector is $e_{-\ell}$, then $m(s_{\alpha_{\ell}})*\mathcal{F}_{+}=\mathcal{F}$ (by Equation (\ref{eq:closedD2})).
Finally, we consider the case $\mbox{${\mathfrak g}$}=\mathfrak{so}(2\ell+1)$, which turns out to be the easiest of the three cases.
First, note that if $m>1$, then $Q_{K}=Q_{i}$ with $i=0,\dots,\ell-2$. In this case, similar analysis shows that our $B_{2\ell}$-orbit $Q=\mathcal{O}(X_e^{K\cap R}, Q_{\mbox{${\mathfrak l}$}})$ contains the standard flag
\begin{equation}\label{eq:closedflagB}
\mathcal{F}=(e_{1}\subset\dots\subset e_{i}\subset\underbrace{ \hat{e}_{\ell} }_{i+1}\subset e_{i+1}\subset\dots\subset e_{\ell-1}).
\end{equation}
The key point is that there is exactly one closed $B_{2m-1}$-orbit on $\mathcal{B}_{2m}$ for any $m$ by Lemma \ref{l:zerodim} and Remark \ref{r:numberclosed}. We take as our $\mathcal{F}^{\prime}$ the flag
$$
\mathcal{F}^{\prime}=(e_{1}\subset\dots\subset e_{i}\subset e_{i+1}\subset \hat{e}_{\ell}\subset\dots \subset e_{\ell-1})
$$
and again let $Q^{\prime}=B_{2\ell}\cdot \mathcal{F}^{\prime}.$
Then $Q^{\prime}\subset Q_{i+1}$ and by Proposition \ref{p:monoidactiononPILSB}, $m(s_{\alpha_{i}})*Q^{\prime}=Q$.
If $m=1$, i.e. $Q_{K}=Q_{\ell-1}$, then we take $\mathcal{F}^{\prime}=\mathcal{F}_{+}$. In this case, $m(s_{\alpha_{\ell}})*Q^{\prime}=Q$ by Equation (\ref{eq:closedB}).
\end{proof}
By Theorem \ref{thm:closureorder}, Theorem \ref{thm:bigthm} has the following consequence.
\begin{cor}\label{c:bruhatisstandard}
The Bruhat order on $B_{n-1}\backslash \mathcal{B}_n$ coincides with the standard action for the extended monoid action by simple roots from $\mbox{${\mathfrak k}$}$ and $\mbox{${\mathfrak g}$}$.
\end{cor}
\newpage
\section{Examples of Bruhat graphs}\label{s:graphs}
We present the Bruhat graphs for $B_{\mathfrak{gl}(2)}\backslash\mathcal{B}_{\mathfrak{gl}(3)}$, $B_{\mathfrak{so}(3)}\backslash \mathcal{B}_{\mathfrak{so}(4)}$, and $B_{\mathfrak{so}(4)}\backslash \mathcal{B}_{\mathfrak{so}(5)}$. Each orbit
is represented by the unique flag in standard form contained in the orbit. The
first row of orbits are zero dimensional, the second row of orbits are the one dimensional orbits, and so
on. A blue line connecting two orbits indicates
that the lower orbit is obtained from the upper orbit via the monoid action of the specified root and
that the given root is complex stable for the upper orbit.
A red line, on the other hand, indicates that the given root is non-compact for the upper orbit.
A solid red or blue line denotes a right monoid action by a simple root of $\mbox{${\mathfrak g}$}$ as in (\ref{eq:rightmonoidagain}) and
a dashed line denotes a left monoid action by a simple root of $\mbox{${\mathfrak k}$}$ as in (\ref{eq:leftmonoid}). When $\mbox{rank}(\mbox{${\mathfrak k}$})=1$, we do not label the dashed line. Note that we do not exhibit all the non-trivial monoid actions, but we instead exhibit a path from a zero dimensional orbit to any orbit. In the case where a monoid action via either a simple root of $\mbox{${\mathfrak k}$}$ or $\mbox{${\mathfrak g}$}$ can be used to move between orbits, the dashed line is omitted and the root of $\mbox{${\mathfrak k}$}$ does not appear as a label except to illustrate Equations (\ref{eq:transfer}) and (\ref{eq:lefttoright}) in the correspondence between $B_{n-1}$-orbits contained in the open $K$-orbit on $\mathcal{B}_{n}$ and $B_{n-2}\backslash \mathcal{B}_{n-1}$ described in Remark \ref{r:opencorrespondence}. Finally, a solid green line indicates that the two orbits are related in the standard order, but not the weak order. The explicit computations of the monoid actions can be performed using Propositions \ref{p:monoidactiononPILS}, \ref{p:monoidactiononPILSD}, \ref{p:monoidactiononPILSB}, Proposition
\ref{prop:monoid}, and Remark \ref{r:kexplicit}.
\newpage
\begin{exam}\label{exam:bigone}
It follows from Example \ref{ex:lists} and Theorem \ref{thm:counttypeA} that $|B_{\mathfrak{gl}(2)}\backslash\mathcal{B}_{\mathfrak{gl}(3)}|=13.$ We label the simple roots of $\mathfrak{gl}(3)$ as $\alpha=\alpha_{1}=\epsilon_{1}-\epsilon_{2}$ and
$\beta=\alpha_{2}=\epsilon_{2}-\epsilon_{3}$ (see Section \ref{ss:realization}).
\begin{center}
\begin{tikzpicture}
[scale=2.0,auto=center,every node/.style={rectangle,fill=white!20}]
\node (a1) at (-1,5) {$(e_{1}\subset e_{2}\subset e_{3})$};
\node (a2) at (1,5) {$(e_{1}\subset e_{3}\subset e_{2})$};
\node (a3) at (3,5) {$(e_{3}\subset e_{1}\subset e_{2}) $};
\node (a4) at (-2,3) {$(e_{2}\subset e_{1}\subset e_{3})$};
\node (a5) at (-0.5,3) {$(e_{1}\subset \hat{e}_{2}\subset e_{3})$};
\node (a6) at (1,3) {$(e_{2}\subset e_{3}\subset e_{1})$};
\node (a7) at (2.5,3) {$(\hat{e}_{1}\subset e_{3}\subset e_{2})$};
\node (a8) at (4,3) {$(e_{3}\subset e_{2}\subset e_{1})$};
\node (a9) at (-2,1) {$(e_{2}\subset \hat{e}_{1}\subset e_{3})$};
\node (a10) at (0,1) {$(\hat{e}_{2}\subset e_{1}\subset e_{3})$};
\node (a11) at (2,1){$(\hat{e}_{1}\subset e_{2}\subset e_{3})$} ;
\node (a12) at (4,1) {$(\hat{e}_{2}\subset e_{3}\subset e_{1})$} ;
\node (a13) at (1,-1) {$(\hat{e}_{2}\subset \hat{e}_{1}\subset e_{3})$};
\draw [blue] (a1) -- (a4) node[midway, above] {$\alpha$};
\draw [red] (a1) -- (a5) node[midway, above] {$\beta$};
\draw [red] (a2) -- (a5) node[midway, above] {$\beta$};
\draw [dashed] [blue] (a2)--(a6);
\draw [red] (a2)--(a7) node[midway, above] {$\alpha$};
\draw [red] (a3)--(a7) node[midway, above] {$\alpha$};
\draw [blue] (a3)--(a8) node[midway, above] {$\beta$};
\draw [red] (a4)--(a9) node[midway, above] {$\beta$};
\draw[green] (a4)--(a10);
\draw[dashed][blue] (a5)--(a9);
\draw[blue] (a5) --(a10) node[near end, below] {$\alpha$};
\draw[green] (a5)--(a11);
\draw[red] (a6)--(a9) node[near end, above] {$\beta$};
\draw[red](a6)--(a12) node[near end, above] {$\alpha$};
\draw[green] (a7)--(a10);
\draw[dashed][blue] (a7)--(a12);
\draw [blue] (a7)--(a11) node[near end, below] {$\beta$};
\draw [red] (a8)--(a12)node[near end, above] {$\alpha$};
\draw[green] (a8)--(a11);
\draw[red](a9)--(a13) node[near end, above] {$\alpha$};
\draw[dashed][red](a10)--(a13);
\draw[dashed][red](a11)--(a13) ;
\draw[red](a12)--(a13)node[near end, above] {$\beta$};
\end{tikzpicture}
\end{center}
We examine a few portions of the above graph in more detail. The orbit
$Q_{0}=B_{\mathfrak{gl}(2)}\cdot (e_{2}\subset e_{3}\subset e_{1})$ is minimal if we do not
use the simple roots of $\mbox{${\mathfrak k}$}$, but not minimal for the extended monoid action from Section \ref{ss:Bmonoid}. This is illustrated since there are no solid lines ending in $Q_{0}$, but there is a dotted line ending in $Q_{0}$.
Consider the orbit $Q^{\prime}=B_{\mathfrak{gl}(2)}\cdot(e_{2}\subset e_{1}\subset e_{3})$ in the first entry
of the second row of the graph. Let $Q^{\prime\prime}=B_{\mathfrak{gl}(2)}\cdot (e_{1}\subset e_{2}\subset e_{3})$,
and let $Q=B_{\mathfrak{gl}(2)}\cdot(\hat{e}_{2}\subset e_{1}\subset e_{3}).$ In the notation of (\ref{eq:stdconditions}), let $t=s_{\beta}$ and $\vec{s}=s_{\alpha}$.
We see that $Q^{\prime}\preceq Q$ in the standard order. However,
$Q^{\prime}$ and $Q$ are not related in the weak order.
Indeed, the root $\alpha$ is complex unstable for $Q^{\prime}$ and so
is the root $\epsilon_{1}-\epsilon_{2}\in\Pi_{\mathfrak{gl}(2)}$ (see Proposition \ref{prop:monoid}.)
The root $\beta$ is non-compact for $Q^{\prime}$ with $m(s_{\beta})*Q^{\prime}=B_{\mathfrak{gl}(2)}\cdot (e_{2}\subset \hat{e}_{1}\subset e_{3}).$ The other green lines in the graph can be analyzed in a similar fashion.
Consider the following subgraph in the third and fourth rows:
\begin{center}
\begin{tikzpicture}
[scale=2.0,auto=center,every node/.style={rectangle,fill=white!20}]
\node (a1) at (-1,4) {$(\hat{e}_{2}\subset e_{1}\subset e_{3})$};
\node (a2) at (1,4) {$(\hat{e}_{1}\subset e_{2}\subset e_{3})$};
\node (a3) at (0,3) {$ (\hat{e}_{2}\subset\hat{e}_{1}\subset e_{3})$};
\draw[dashed][red](a1)--(a3);
\draw[dashed][red](a2)--(a3);
\end{tikzpicture}
\end{center}
This is the Bruhat graph for the $B_{2}$-orbits contained in the open $GL(2)$-orbit on $\mathcal{B}_{\mathfrak{gl}(3)}$.
Taking $\mbox{${\mathfrak l}$}=\mbox{${\mathfrak g}$}=\mathfrak{gl}(3)$ as in Remark \ref{r:opencorrespondence} above, these orbits correspond with $B_{1}\cong \mbox{${\mathbb C}$}^{\times}$-orbits on $\mathcal{B}_{\mathfrak{gl}(2)}$ with Bruhat graph:
\begin{center}
\begin{tikzpicture}
[scale=2.0,auto=center,every node/.style={rectangle,fill=white!20}]
\node (a1) at (-1,4) {$(e_{1}\subset e_{2})$};
\node (a2) at (1,4) {$(e_{2}\subset e_{1})$};
\node (a3) at (0,3) {$ (\hat{e}_{1}\subset e_{2})$};
\draw[red](a1)--(a3);
\draw[red](a2)--(a3);
\end{tikzpicture}
\end{center}
Note that the left monoid actions by the single root of $\mbox{${\mathfrak k}$}=\mathfrak{gl}(2)$ in the first graph correspond to
right monoid actions in the second graph as predicted by Equation (\ref{eq:lefttoright}).
\end{exam}
\begin{exam}\label{ex:smallone}
It follows from Part (1) of Theorem \ref{thm:orthocount} and Example \ref{ex:spils} that $|B_{\mathfrak{so}(3)}\backslash \mathcal{B}_{\mathfrak{so}(4)}|=5$. We label the simple roots of $\mathfrak{so}(4)$ as $\alpha=\alpha_{1}=\epsilon_{1}-\epsilon_{2}$ and
$\beta=\alpha_{2}=\epsilon_{1}+\epsilon_{2}$.
\begin{center}
\begin{tikzpicture}
[scale=2.0,auto=center,every node/.style={rectangle,fill=white!20}]
\node (a1) at (0,5) {$(e_{1})$};
\node (a2) at (-1,4) {$(e_{2})$};
\node (a3) at (0,4) {$(e_{-1})$};
\node (a4) at (1,4) {$(e_{-2}) $};
\node (a5) at (0,3) {$ (\hat{e}_{1})$};
\draw [dashed] [blue] (a1)--(a3);
\draw [blue] (a1) -- (a2) node[midway, above] {$\alpha$};
\draw [blue] (a1) -- (a4) node[midway, above] {$\beta$};
\draw[dashed] [red] (a2) -- (a5) ;
\draw [red] (a3) -- (a5) node[near end, above] {$\alpha, \beta$};
\draw[dashed] [red] (a4) -- (a5);
\end{tikzpicture}
\end{center}
We observe that the orbit $B_{\mathfrak{so}(3)}\cdot (e_{-1})$ is minimal
with respect to the right monoid action and one dimensional. Thus, the left monoid action is also necessary in the orthogonal setting for Theorem \ref{thm:bigthm}
to hold.
\end{exam}
\begin{exam}\label{ex:bigorthoexam}
It follows from Part (2) of Theorem \ref{thm:orthocount} and Example \ref{ex:spils} that
$|B_{\mathfrak{so}(4)}\backslash \mathcal{B}_{\mathfrak{so}(5)}|=17$. We label the simple roots of $\mbox{${\mathfrak g}$}=\mathfrak{so}(5)$
as $\alpha=\alpha_{1}=\epsilon_{1}-\epsilon_{2}$ and $\beta=\alpha_{2}=\epsilon_{2}$. We label the simple
roots of $\mbox{${\mathfrak k}$}=\mathfrak{so}(4)$ as $\tilde{\alpha}_{1}=\epsilon_{1}-\epsilon_{2}$ and $\tilde{\beta}=\epsilon_{1}+\epsilon_{2}$.
\begin{center}
\begin{tikzpicture}
[scale=2.0,auto=center,every node/.style={rectangle,fill=white!20}]
\node (a1) at (0,5) {$(e_{1}\subset e_{2})$};
\node (a2) at (3,5) {$(e_{1}\subset e_{-2})$};
\node (a3) at (-1,3) {$(e_{-2}\subset e_{-1} )$};
\node (a4) at (0.25,3) {$(e_{2}\subset e_{1})$};
\node (a5) at (1.5,3) {$(e_{1}\subset \hat{e}_{2})$};
\node (a6) at (2.75,3) {$(e_{-2}\subset e_{1})$};
\node (a7) at (4,3) {$(e_{2}\subset e_{-1})$};
\node (a8) at (-1,1) {$(e_{-1}\subset e_{-2})$};
\node (a9) at (0.25,1) {$(e_{-2}\subset \hat{e}_{1})$};
\node (a10) at (1.5,1) {$(\hat{e}_{2}\subset e_{1})$};
\node (a11) at (2.75,1){$(e_{2}\subset \hat{e}_{1})$} ;
\node (a12) at (4,1) {$(e_{-1}\subset e_{2})$} ;
\node (a13) at (-1,-1) {$(e_{-1}\subset \hat{e}_{2})$};
\node (a14) at (0.25,-1) {$(\hat{e}_{1}\subset e_{2})$};
\node (a15) at (1.5, -1) {$(\hat{e}_{2}\subset e_{-1})$};
\node (a16) at (2.75, -1) {$(\hat{e}_{1}\subset e_{-2})$};
\node (a17) at (1.5,-3) {$(\hat{e}_{2,-1}\subset \hat{e}_{2})$};
\draw [dashed][blue] (a1)--(a3) node[midway, above]{$\tilde{\beta}$};
\draw [blue] (a1)--(a4) node[midway, above]{$\alpha$};
\draw [red] (a1)--(a5) node[midway, above]{$\beta$};
\draw [red] (a2)--(a5) node[midway, above]{$\beta$};
\draw [blue] (a2)--(a6) node[midway, above]{$\alpha$};
\draw [dashed][blue] (a2)--(a7) node[midway, above]{$\tilde{\alpha}$};
\draw [blue] (a3)--(a8) node[midway, above]{$\alpha$};
\draw [red] (a3)--(a9) node[near end, below]{$\beta$};
\draw [dashed][blue] (a4)--(a8) node[near end, above]{$\tilde{\beta}$};
\draw [red] (a4)--(a11) node[near end, below]{$\beta$};
\draw [green] (a4)--(a10) ;
\draw [dashed][blue] (a5)--(a9) node[near end, above]{$\tilde{\beta}$};
\draw [dashed][blue] (a5)--(a11) node[near end, above]{$\tilde{\alpha}$};
\draw [blue] (a5)--(a10) node[near end, above]{$\alpha$};
\draw [dashed] [blue] (a6)--(a12) node[near end, above]{$\tilde{\alpha}$};
\draw[green] (a6)--(a10);
\draw [red] (a6)--(a9) node[near end, below]{$\beta$};
\draw [red] (a7)--(a11) node[near end, below]{$\beta$};
\draw [blue] (a7)--(a12) node[midway, above]{$\alpha$};
\draw [red] (a8)--(a13) node[near end, below]{$\beta$};
\draw [green] (a8)--(a16);
\draw [dashed][blue] (a9)--(a13) node[near end, above]{$\tilde{\alpha}$};
\draw [blue] (a9)--(a16) node[near end, above]{$\alpha$};
\draw[green] (a9)--(a15);
\draw [dashed][blue] (a11)--(a13) node[near end, above]{$\tilde{\beta}$};
\draw [blue] (a11)--(a14) node[near end, above]{$\alpha$};
\draw [green] (a11)--(a15);
\draw [dashed][blue] (a10)--(a14) node[near start, above]{$\tilde{\alpha}$};
\draw [blue] (a10)--(a15) node[near start, above]{$\beta$};
\draw [dashed][blue] (a10)--(a16) node[near start, above]{$\tilde{\beta}$};
\draw [red] (a12)--(a13) node[near end, below]{$\beta$};
\draw[green] (a12)--(a14);
\draw [red] (a13)--(a17) node[midway, above]{$\alpha$};
\draw [red] (a14)--(a17) node[midway, above]{$\beta$};
\draw [dashed][red] (a15)--(a17) node[midway, above]{$\tilde{\alpha},\tilde{\beta}$};
\draw [red] (a16)--(a17) node[midway, above]{$\beta$};
\end{tikzpicture}
\end{center}
Consider the orbits $Q=B_{\mathfrak{so}(4)}\cdot (\hat{e}_{1}\subset e_{-2})$ and
$Q^{\prime}=B_{\mathfrak{so}(4)}\cdot (e_{-1}\subset e_{-2})$ (the last orbit in the fourth row and the first orbit in the third row respectively). We claim
$Q^{\prime}\preceq Q$ in the standard order, but $Q^{\prime}\not \leq_{w} Q$.
Indeed, if we let $Q_{+}=B_{\mathfrak{so}(4)}\cdot (e_{1}\subset e_{2})$, then
$Q^{\prime}=m(\vec{s})*Q_{+}$, where $\vec{s}$ is the sequence
$\vec{s}=(s_{\alpha},\, s_{\tilde{\beta}})$ (see Equation (\ref{eq:Ssequence})).
The orbit $Q$ is $Q=m(\vec{s})*m(s_{\beta})*Q_{+}$. So it follows
from the definition of the standard order (\ref{eq:stdconditions}) that
$Q^{\prime}\preceq Q$, but from the diagram it is clear that $Q^{\prime}\not\leq_{w} Q$.
Consider the subgraph in the bottom right corner:
\begin{center}
\begin{tikzpicture}
[scale=2.0,auto=center,every node/.style={rectangle,fill=white!20}]
\node (a1) at (0,5) {$(\hat{e}_{2}\subset e_{1})$};
\node (a2) at (-1,3.5) {$(\hat{e}_{1}\subset e_{2})$};
\node (a3) at (0,3.5) {$(\hat{e}_{2}\subset e_{-1})$};
\node (a4) at (1,3.5) {$(\hat{e}_{1}\subset e_{-2})$};
\node (a5) at (0,2) {$ (\hat{e}_{2,-1}\subset \hat{e}_{1})$};
\draw [dashed] [blue] (a1) -- (a2) node[midway, above] {$\tilde{\alpha}$};
\draw [blue] (a1)--(a3) node[midway, above] {$\beta$};
\draw [dashed] [blue] (a1) -- (a4) node[midway, above] {$\tilde{\beta}$};
\draw [red] (a2) -- (a5) node[midway, below] {$\beta$};
\draw [dashed] [red] (a3) -- (a5) node[near end, above] {$\tilde{\alpha},\tilde{ \beta}$};
\draw [red] (a4) -- (a5) node[midway, below] {$\beta$};
\end{tikzpicture}
\end{center}
This graph is the graph of the weak order
for $B_{\mathfrak{so}(4)}$-orbits contained in the open $K=SO(4)$-orbit on $\mathcal{B}_{\mathfrak{so}(5)}$.
By Remark \ref{r:opencorrespondence}, these orbits are in one-to-one correspondence with
$B_{\mathfrak{so}(3)}\backslash \mathcal{B}_{\mathfrak{so}(4)}$ whose Bruhat graph is given in Example \ref{ex:smallone}.
But notice that the right monoid actions in Example \ref{ex:smallone} correspond to left monoid actions here,
and the left monoid actions in Example \ref{ex:smallone} correspond to right monoid actions in this graph.
This is precisely the phenomenon described in Equations (\ref{eq:transfer}) and (\ref{eq:lefttoright}) where in this example $\mbox{${\mathfrak l}$}=\mbox{${\mathfrak g}$}$ and the element $\tilde{w}\in W$ in (\ref{eq:guyinW}) is the identity. Note that we also see the shift from the root $\epsilon_{1}-\epsilon_{2}$ of $\mathfrak{so}(3)$ in Example \ref{ex:smallone} to the root $\beta$ here described in Equation (\ref{eq:transfer}).
\end{exam}
\bibliographystyle{amsalpha.bst}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,111 |
Level: The Forgotten Grave
Author(s): Lin Fu
Bene 7 7 6 7
Ceamonks890 5 5 6 5
Duncan 5 6 6 6
dya1403 6 6 6 6
eTux 4 5 5 4
Jay 5 5 7 7
Moonpooka 7 7 7 7
Raiderfan 5 6 5 6
Sash 5 4 6 5
Sutekh 6 7 6 5
"This is a nice little potboiler in an Egyptian setting that takes a little more than a half hour to play. Strictly for something to do in between the more complex levels, but enjoyable nevertheless. Dutchy has provided one of his earlier walks, and it's interesting to see how his style has developed over the years. I'm sure the same is true of my walks, as I cringe now when I read some of them. If I thought people were still playing those older levels on a regular basis, I'd probably take the time to streamline the language a bit. Anyway, there's nothing very taxing in Forgotten Grave, the gameplay flows smoothly and in linear fashion, and the level ends rather unceremoniously as Lara goes down some stairs into the darkness. The flare bug kicked in near the end, but everything is so well lighted that this created no problem at all." - Phil (12-Jun-2019)
"Traditional, classic Egyptian raiding, much like what was being experienced back in 2001/2002. Nothing here that will set your world alight. But taken on its own merits, it's actually pretty well done and provided me with an undemanding but sufficiently enjoyable experience for just short of half an hour. The texturing is standard Egyptian but nicely presented, the lighting is creative in a couple of places (the red deadly pool and the fact that for once, crawlspaces aren't shrouded in darkness) and the gameplay, while sequential, displays a couple of neat touches (like the Eye Piece hidden behind some treasure) which I quite liked. Simple, relaxing raiding, and enjoyable for all that." - Ryan (16-Mar-2019)
"A perfectly average debut level that uses a portion of TR4's assets competently from beginning to end. Sure, rooms may feel generally samey & empty, the enemies(consisting of scorpions and white-clothed ninjas) don't pose much of a threat and the gameplay is far too easily choreographed beforehand. But overall, you could play far worse things for 20 minutes. So give this one a go, if you're looking at something more comfortably approachable to go through." - Ceamonks890 (17-Mar-2018)
"This just goes to show how spoilt we've all become.What we have here is a perfectly decent Egyptian level with extremely competant construction (no stretched textures anywhere),decent lighting,a few well-placed enemies,simple but pleasing design,fluent and eventful gameplay,and a really neat 'hidden in full view' key pick-up (which took me two attempts to locate).The puzzles and traps are standard but solidly crafted and the whole is perfectly enjoyable. As yet,there are no further levels from this builder;something which,one hopes,will soon be rectified." - Orbit Dream (05-May-2008)
"A good Egyptian level built with the Tut1 stuff except for some static objects in the treasure room. Ah if all the tutorial levels had at least the quality of this one. I could not fault anything except for the flares bug in the final area. The lighting lacks depth too. Aside from that , a well made level , not very original and fairly easy but which is very pleasant to play for 30 minutes. I like the placement of some pickups and the author knows to trigger the right audio tracks , also the fact that this is not a dark level which suits me fine." - eRIC (26-Aug-2007)
"The clasical egyptian adventure with the over used pieces to collect that I have seen so many times before.But I have seen this is the author first level, so I hope he will specialize." - dya1403 (02-Mar-2007)
"This is a solidly built tut level that gets you from the start to the finish with no real hassles in 25 minutes. The texturing was extremely plain and monochromatic, though this helped hide some crawlspaces well as they blended in almost seamlessly, and the game itself held nothing to get the thrills bubbling, but there is an air of delightful familiarity that let's you be reminded of the early days of custom levels and this makes them very much worthwhile to play. This for me is one of them. If this is a debut then all power to the author, but more thought should go into the texturing and gameplay of any follow up levels. There is one secret to find, made that little harder with one of those well blended crawlspaces, and the game should take you around 30 minutes." - Sash (26-May-2005)
"A level easy to play. This level was made using the textures, wads, objects, enemies, cameras, default,... from Tomb Raider Level Editor. But this is not a bad level. Is a level with no bugs (only the flare bug in the final rooms!) but definitively is a good level for me which has to be played if you want to have an entertaining time. You find the same old textures, the same old objects, the same old enemies (few) and the same old puzzles. But is a level which can be played. If you want to entertainment a little, you can play this level." - Jose (18-May-2005)
"We are adventuring in Egyptian milieu, in a temple. Our goal is to get the Amulet of Horus. Meanwhile we have to solve puzzles, and collect the Ba Cartouche, the two Eye Pieces, and the two The Hand of Orions. In the meantime scorpions, mummies and some gunmen disturb us. We have to run away from rolling stones, moving among hidden spikes and sloped parts. The only secret of the level was hard to find. Or to be more precise, the lever that opens the door. The camera changes view exactly in the big water room, so I could only hardly notice the crawlspace, where it was hidden. The textures suit the level, and the added sounds were also a fantastic selection from the creator. I propose it. There are no really hard parts, and the gameplay is quite linear, except of course getting the secret. :) You can find a Hungarian walkthrough (as we don't have English version), savegames and pictures here: http://www.treditor.hu/15/the_forgotten_grave.htm " - Obig (25-Mar-2005)
"This is traditional and straightforward, with easy, linear gameplay, perfect for the younger and/or inexperienced raider. Enemies are mummies, scorpions and a brace of ninjas right at the end and there are a cartouche, two hands, an eye of Horus and an amulet to find. You really won't need all the weaponry so generously provided, but it's always nice to have a full backpack, isn't it? For a first time level, it seemed to me to be very competently built and I think this builder has real potential." - Jay (20-Mar-2005)
"This pleasant and easy journey through familiar surroundings shows the author has done their homework and can work with the editor. There are some fun bits here, and I liked the underwater pyramid. Let's hope we see more work from this author, and it gets spicier now that the recipe is mastered." - Duncan (24-Feb-2005)
"I loved this little level. It really made my night to sit and play some good old fashioned TR. Lara starts below ground, and what I liked first of all was you actually go back from the start to get your first bunch of goodies, goodies, ah, yes all so nicely placed throughout the level, in fact I think the uzi in particular should have been made a secret, it was that sneakily placed, but then I did manage to miss the only secret of the level, doh! Make your way through this Tut level, with its usual old style textures (that the spoilt brat players will no doubt gripe about, lol) and collect the whole cartouche piece, hand, two halves of the eye piece and ankh, the ankh, Lara gets to take home. There are levers to use but not overly done, a small spike trapped floor, and a boulder run to do. Enemies are Ninjas, mummies and scorpions. This is by no means a hard level, I found it more enjoyable to take the straight route through without anything too taxing, but there are a few sneaky things about, like a carefully hidden room below ground which I ran past I don't know how many times, and one half of the eye piece, which took me two treks back for a re look only to find it was right there looking at me all the time, one of those, 'no that's too obvious' things you know? I thought this was an adorable level, and apart from the flare bug I had no problems with gameplay." - Moonpooka (21-Feb-2005)
"There are some nice touches to this builder's first level. Yes, the sameness is a bit tiring as it's an Egyptian level without contrast but the author has already mastered the art of 'hide in plain sight' - crawl spaces concealed by a blend of coloring instead of a light/dark interplay and the second half of the Eye Piece in amongst other gold pieces and urns. Very nice beginning with shotgun, ammo and medipack pickup. All that's needed is a bit of exploration and the level is off to a good start. Enemies are the conventional ones: scorpions, ninjas, with one sneaky ninja out to grab an ammo pickup if Lara doesn't get it in time. Well done secret area and for me, a personal hunt for the crossbow seen early on - of course it's a pickup that comes later but not too much later as this is a short level with maybe 45 minutes of game time. I had fun with the Grenade Gun but would have liked to see a real use for it. There was, unfortunately, the binocular bug that caused my computer to crash and the flare glitch also. All in all, this builder shows a lot of promise and I'm hoping there are more levels in the future." - Bene (21-Feb-2005)
"Nice level, but very short. The builder managed to avoid most of the beginner's bugs, which is a good thing. No stretched or missing textures, I couldn't find any illegal slope, quite nice and linear gameplay and some well-placed enemies. But there's also some room for improvement. Rooms could sometimes be smaller, and some hallways are way too long. Lightning is quite plain. The flare bug appeared near the end. Overall, everything is done quite well. The (german) readme says there's one secret, but I couldn't find it. You included all triggered audio files in the download, which is unnecessary." - Raiderfan (21-Feb-2005)
"For a beginner this is worth while to play. This is a solid level and apart from the second Eye Piece that is hidden very clever between more treasures, you sail through it. The lighting in this level could use some work though. And the almighty flare bug kicks in, not that one needs a flare but sometimes they are rather handy. Slobodan shows great potential so I would say, keep on building. 16-02-2005" - Gerty (21-Feb-2005)
"A debut level and one that shows all the classic tutorial elements and clearly demonstrated that the builder has worked his way through the manual. This is a good clean half hour of standard raiding which will hardly have Lara break into a sweat along the way, but is still fun while it lasts. Clearly a builder with solid potential for future levels as the experience with the editor keeps growing." - Michael (20-Feb-2005)
"A nice little level, of average quality, my main beef with it being its uniformity, visually speaking. It's not ugly, and I haven't found any stretched texture or so, but you often see the same texture being applied over a whole room, combined with a very flat lighting. As a side effect, research is made more difficult insofar as you might very well totally miss an opening because they sometimes so perfectly blend in with the walls that they become invisible. Apart from that it's a very easy level, with some pretty well-placed enemies (I did give a start once or twice). I did have some trouble with flares that would give light only once dropped, but other than that, I didn't notice any bug. It's rather short, but it was fun while it lasted, so it might be a nice break between two more difficult ones." - Sutekh (18-Feb-2005)
"A solid, short tutorial adventure as you would've expected them in the old days. Despite my ratings being more on the low side - this is actually a rather good and enjoyable level, but there's just... just... erm... lots of place for improvement! Yes, that's it! It's quite short, and with not so much to do really - but the odd jump sequence and trap avoiding is quite fun, and the eye piece among the treasure confused me at first. The good thing is that there aren't that many beginners mistakes, which is always a plus, but the looks are a bit on the dull side - ie. technically done well more or less (lighting could've used more work - like a sun bulb in every room, but I'll forgive this time, as the author couldn't have known), but nothing that makes you go 'wow' really. Also the flare bug (when 32+ flame emitters are triggered at the same time, flares and binocular lights don't work) kicked in by the end, so something for the builder to watch out in the future. But as said - for a first effort - well done, and I'm sure if author keeps expanding his horizons, we can expect lots of great levels from him! So keep building :)" - eTux (18-Feb-2005)
"This is a good effort but with few enemies that pose much of a threat and somehow it rather was nice as a level. I can't say it has original puzzles, just a hand, a cartouche and the Eye of Horus pieces. The setting is definitely Egyptian with rooms full of deadly water and one with jumps on slopes. It lasted twenty five minutes for me and Lara dealt with mummies, ninjas and scorpions but they weren't placed so well but possibly randomly. The one secret I got was with help from Obig as I overlooked the crawlspace at first due to the broken camera. I hope the next level will have a bit of challenge in it and the outside areas will be designed better so we don't get the 'end of the world' bug." - Kristina (18-Feb-2005) | {
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} | 7,976 |
(string) One of: 'wpcom' or 'email'. Default: 'wpcom'.
(int) The number of results to return per page. Defaults to 20. Maximum 100. Default: 20.
(string) Returns followers with matching email addresses. Only works in combination with type="email". | {
"redpajama_set_name": "RedPajamaC4"
} | 4,480 |
Peak 10's Atlanta data center 2 is located at 2775 Northwoods Parkway NW, Norcross, GA 30071. The data center offers colocation, cloud services, managed services, and disaster recovery services.
Peak 10 offers comprehensive colocation solutions with half and full cabinet space, customized cage space, and private suites. The data center provides 10,000 square feet of 24 inches raised floor space for subfloor cable management and power distribution. The data center is regularly audited in accordance with SSAE 16 SOC 1 and SOC 3, ISO 27001, ISAE 3402, and AT-101 requirements; and can help customers meet the requirements of regulatory compliance acts such as Sarbanes-Oxley (SOX), HIPAA/HITECH, PCI DSS and Gramm-Leach-Bliley (GLBA). The data center security features onsite trained staff, 24x7x365 video surveillance, combination lock access for cabinets, biometric fingerprint readers, and proximity card access with PIN code. The facility has clean agent fire suppression system for any fire spark.
Atlanta data center 2 offers a reliable and fault tolerant power infrastructure with all critical power components in redundant configurations. The critical infrastructure is protected by redundant UPS system on the loss of utility power that is backed up by redundant 2.4 MW diesel generators. The data center provides the power density of 200 watts per square feet. The cooling and humidity in the data center is maintained through multiple Liebert CRAC units. The facility has raised floor cooling with cold aisle containment to help reduce energy costs.
Peak 10's 2775 Northwoods Parkway NW data center is a carrier neutral facility with multiple Tier I providers. The data center has dual fiber entry points providing over 20Gb of Internet capacity. The facility has multiple physical connectivity options including 100 Mbps, 1 Gbps, and 10 Gbps network ports. The data center has Cisco service provider network architecture with ASR 9000 and 7600 series routers providing core routing functionalities, and Nexus 7000 and Catalyst 6500 switches at distribution layer. The data center provides 100 % network uptime, and offers burstable services to accommodate unforeseen or seasonal demand. The facility also provides carrier neutral telecom services, including T1, PRI, MPLS etc., and Metro Ethernet at 10/100/1000 Mbps. 24x7x365 NOC technical staff provides the support and helpdesk services, and monitoring services.
View all Peak 10 data center locations. You may also view all data centers in Norcross, or expand your search to all Georgia data centers.
I would like a quote from Peak 10 - Atlanta Data Center #2. | {
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{"url":"https:\/\/testbook.com\/question-answer\/when-sampling-is-done-without-replacement-then-sta--5feafbf1c605c99d67ea51bc","text":"# When sampling is done without replacement then standard error of mean is:\n\nFree Practice With Testbook Mock Tests\n\n## Options:\n\n1. $$SE_{\\bar{X}}=\\dfrac{\\sigma}{\\sqrt{n}}$$\n\n2. $$SE_{\\bar{X}} = \\dfrac{\\sigma}{\\sqrt{n}} \\sqrt{\\dfrac{N-n}{N-1}}$$\n\n3. $$SE_{\\bar{X}} = \\dfrac{\\sigma}{\\sqrt{n}} \\sqrt{\\dfrac{N-1}{N-n}}$$\n\n4. $$SE_{\\bar{X}} = \\dfrac{\\sigma}{\\sqrt{n}}\\sqrt{1-\\dfrac{n}{N}}$$\n\n### Correct Answer: Option 2 (Solution Below)\n\nThis question was previously asked in\n\nUGC Paper 2: Commerce_17th Oct 2020 Shift 1\n\n## Solution:\n\nStandard Error:\n\n1. The standard error of the mean is the standard deviation of the sampling distribution of the mean.\n2. In other words, it is the standard deviation of a large number of sample means of the same sample size drawn from the same population.\n3. The term standard error of the mean is commonly (though imprecisely) shortened to just standard error.\n4. The \"standard error of the mean\" refers to the standard deviation of the distribution of sample means taken from a population.\n5. The smaller the standard error, the more representative the sample will be of the overall population.\n\nIn sampling without replacement, the formula for the standard deviation of all sample means for samples of size n must be modified by including a finite population correction.\u00a0 The formula becomes:\u00a0\u00a0where N is the population size.\n\nThus, option 2 is the correct answer.\n\nWhen sampling with replacement the standard deviation of all sample means equals the standard deviation of the population divided by the square root of the sample size when sampling with replacement.","date":"2021-08-03 21:41:42","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\": 0.8490199446678162, \"perplexity\": 419.6155390938823}, \"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-2021-31\/segments\/1627046154471.78\/warc\/CC-MAIN-20210803191307-20210803221307-00109.warc.gz\"}"} | null | null |
Govt says will use less lethal plastic bullets in JK
By Guest on 2:30 am March 21, 2018 No Comment
New Delhi: Less lethal plastic bullets will be used to tackle law and order situations in Jammu and Kashmir, the Lok Sabha was informed Tuesday.
Union Minister of State for Home Hansraj Gangaram Ahir also said the government has no plans for enhanced use of bunkers to protect security forces from stone throwers after the annual shift of the capital from Jammu to Srinagar in the next few days.
"The government has decided to introduce less lethal plastic bullets also to be used in tackling law and order situations in Jammu and Kashmir," he said in reply to a written question.
The minister said the government has appointed Dineshwar Sharma, former Director of the Intelligence Bureau, as its representative to initiate and carry forward dialogue with the elected representatives, organisations and individuals concerned in Jammu and Kashmir.
"The response from the people of Jammu and Kashmir has been very positive. A large number of delegations and individuals representing various sections of society and particularly youths have already interacted with the Government of India representative," he said. (PTI)
Govt says will use less lethal plastic bullets in JK added by Guest on 2:30 am March 21, 2018 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,417 |
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UWindsor chemist John Trant has received a grant from the American Chemical Society Petroleum Research Fund to design molecular tubes that can self-destruct on command.
UWindsor chemist designing molecular tubes for biomedical applications
Imagine a nanoscopic device that can be implanted in your body to slowly release medication and that self-destructs when it's done.
A UWindsor chemist is working on such a breakthrough, thanks to a $110,000 US grant from the American Chemical Society Petroleum Research Fund.
John Trant proposes making molecular tubes from organic petroleum byproducts. A biomedical chemistry researcher, he aims to design nanotubes that can be inserted into bacteria or cancer cells in the body.
"The idea here is to make a tube your body can degrade," Dr. Trant said. "It could lead to new pharmaceuticals that could maybe kill bacteria or can be used for delivering drugs."
Trant and his team of researchers will delve into the world of rotaxanes, a field pioneered by UWindsor professor Steven Loeb whose research was cited in the work of the winners of the 2016 Nobel Prize in Chemistry.
A rotaxane is a nanoscopic tubular structure made of a series of a rings assembled around a barbell-shaped rod with balls on each end. Pseudo-rotaxanes are similar structures without the balls and where the rings must be strongly attracted to the rod to avoid falling off.
If the rings could be attached to one another, they would form a tube once the rod in the middle is removed. The problem is that the rings are strongly bound to the rod or thread that runs through them. The longer the tube, the harder it is to remove the rod.
Trant said his research will involve designing these structures where, instead of removing the rod, it will just breakdown in place on command.
"No current approach allows for that," he said. "It sidesteps the entire problem in accessing this type of structure."
The nanotubes he is developing offer a promising alternative to carbon nanotubes which don't degrade in the body and are possibly toxic.
Earlier this year, the province identified Trant as a rising star in the world of biomedical research, awarding him an Early Researcher Award grant to help offset his work in chemistry, materials science and molecular biology for the next five years.
"Chemistry gives us the tools to design and build specific solutions to solve unmet problems in medicine and materials science. It's like playing with the world's largest and most diverse Lego kit," Trant said.
"It's awesome that funding agencies recognize the promise of this approach."
In addition to authoring recent research on lab safety, Trant is also an executive member of the Windsor Cancer Research Group. He and WCRG colleague, UWindsor biologist Lisa Porter, are developing new drugs to target the proteins that protect cells from mutating into tumours.
He is also working on innovations that could lead to anti-cancer vaccines, and new drugs to treat rheumatoid arthritis and other autoimmune diseases.
—Sarah Sacheli
John Trant
Lisa Porter
Strategic Priority:
Engage in community partnerships
Pursue strengths in research and graduate education
Academic Area:
Project Notifications
Chrysler Hall Tower-CHT 3rd Flr. Women's & Men's Washroom - Domestic Cold and Hot Water Shutdown for Valve/Faucet Replacements, January 20, 2020, 7:30am-12:00pm
Leddy Library (East) Main Building-W100 Baby Changing Station, January 14, 2020, 8:00am-1:00pm
Lambton Tower-CS3 AHU Upgrades-Heating Coils Replacement, January 7-February 29, 2020, 7:00am-12:00pm
Chrysler Hall Tower-3rd Floor Women's Bathroom (Shutdown for 1 hour), January 13, 2020, 8:00am-2:00pm | {
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Revista: Seizure : The Journal Of The British Epilepsy Association.
Purpose: To analyse the methods of reasoning with regard to patients' experiences of living with psychogenic nonepileptic seizures (PNES) in Buenos Aires, Argentina. Method: A qualitative approach using semi-structured interviews was used to gain an in-depth and contextual understanding of the perspectives of five patients with PNES. Data collection and analysis were followed by an inductive and interpretive approach informed by the principles of thematic analysis. Results: Explanatory models and prototypes were identified from the patients' narratives. Four patients related their suffering regarding psychosocial causes –family conflicts, sexual harassment, and life changes, among others-. Hereditary and organic hypotheses appeared to be unspecific. Folk explanations were common to all participants (magic, witchcraft, energetic causes). Four patients used the term epilepsy as an illness prototype, focusing on seizures and the use of antiepileptic drugs. Three of them also compared their illness to other people's "attacks" (heart attacks, panic attacks, nervous breakdown). Only one of them referred to someone who was suspected of having epilepsy. Conclusion: Patients' psychosocial explanatory models are different from the results of previous studies because these studies indicate that most patients support somatic explanations. Patients also use folk explanations related to traditional medicine, which highlights the interpersonal aspects of the disease. Doctor-patient communication is essential for a correct understanding of PNES, resulting in better outcomes. It could also help to reduce the cultural distance between professionals and patients, leading to narrowing inequalities present in multicultural healthcare services. | {
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Q: Disable this week and future dates Jquery I have modified the calendar to select weeks and show in a textbox which works great.
I am trying to disable the current week as well as future dates but don't know how to, I tried this but it doesnt work
$("#selector").datepicker({
maxDate: 0
});
My fiddle is below
$(function() {
var startDate;
var endDate;
var selectCurrentWeek = function() {
window.setTimeout(function () {
$('.ui-datepicker-current-day a').addClass('ui-state-active')
}, 1);
}
$('.week-picker').datepicker( {
showOtherMonths: true,
selectOtherMonths: true,
changeMonth: true,
changeYear: true,
onSelect: function(dateText, inst) {
var date = $(this).datepicker('getDate');
startDate = new Date(date.getFullYear(), date.getMonth(), date.getDate() - date.getDay());
endDate = new Date(date.getFullYear(), date.getMonth(), date.getDate() - date.getDay() + 6);
var dateFormat = inst.settings.dateFormat || $.datepicker._defaults.dateFormat;
$("#txtWeekPicker").val($.datepicker.formatDate( dateFormat, startDate, inst.settings )+" - "+$.datepicker.formatDate( dateFormat, endDate, inst.settings ));
selectCurrentWeek();
},
beforeShowDay: function(date) {
var cssClass = '';
if(date >= startDate && date <= endDate)
cssClass = 'ui-datepicker-current-day';
selectCurrentWeek();
return [true, cssClass];
},
onChangeMonthYear: function(year, month, inst) {
selectCurrentWeek();
}
});
$('.ui-datepicker-calendar tr').live('mousemove', function() { $(this).find('td a').addClass('ui-state-hover'); });
$('.ui-datepicker-calendar tr').live('mouseleave', function() { $(this).find('td a').removeClass('ui-state-hover'); });
});
<link href="https://ajax.googleapis.com/ajax/libs/jqueryui/1.8.14/themes/base/jquery-ui.css" rel="stylesheet" />
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.4.1/jquery.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jqueryui/1.8.14/jquery-ui.min.js"></script>
<div class="week-picker"></div>
<br /><br />
<input type="text" id="txtWeekPicker" class="week-picker" />
A: You could try the new HTML5 week input type.
<input type="week" max="week number">
However, it's hard to style and you would also have to figure out the JS to calculate current week. Also, no Firefox support or pre-IE 12.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,912 |
Find the best local Furnace Repair Service Pros in Union Bridge, MD. Get fast responses from on demand pros in your area.
We are your source for prompt, courteous, and reliable heating services in Arizona.
We service and repair all brands. Including forced air furnaces, wall heaters, and floor furnaces. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,614 |
Q: Voronoi cells - remove boundary lines I would really appreciate it if someone can help me with the code below. I am trying to plot Voronoi cells for some random data points and I want to assign some colours. The to reproduce my work is provided below. As you can see in the plot, there are thick lines. I completely want to eliminate those lines. Is there any way to get rid of them? I want to fill the polygon but not have the line. Any recommendation is greatly appreciated.
I took most of the code from here
import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial import Voronoi
import pandas as pd
def voronoi_finite_polygons_2d(vor, radius=None):
"""
Reconstruct infinite voronoi regions in a 2D diagram to finite
regions.
Parameters
----------
vor : Voronoi
Input diagram
radius : float, optional
Distance to 'points at infinity'.
Returns
-------
regions : list of tuples
Indices of vertices in each revised Voronoi regions.
vertices : list of tuples
Coordinates for revised Voronoi vertices. Same as coordinates
of input vertices, with 'points at infinity' appended to the
end.
"""
if vor.points.shape[1] != 2:
raise ValueError("Requires 2D input")
new_regions = []
new_vertices = vor.vertices.tolist()
center = vor.points.mean(axis=0)
if radius is None:
radius = vor.points.ptp().max()
# Construct a map containing all ridges for a given point
all_ridges = {}
for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices):
all_ridges.setdefault(p1, []).append((p2, v1, v2))
all_ridges.setdefault(p2, []).append((p1, v1, v2))
# Reconstruct infinite regions
for p1, region in enumerate(vor.point_region):
vertices = vor.regions[region]
if all(v >= 0 for v in vertices):
# finite region
new_regions.append(vertices)
continue
# reconstruct a non-finite region
ridges = all_ridges[p1]
new_region = [v for v in vertices if v >= 0]
for p2, v1, v2 in ridges:
if v2 < 0:
v1, v2 = v2, v1
if v1 >= 0:
# finite ridge: already in the region
continue
# Compute the missing endpoint of an infinite ridge
t = vor.points[p2] - vor.points[p1] # tangent
t /= np.linalg.norm(t)
n = np.array([-t[1], t[0]]) # normal
midpoint = vor.points[[p1, p2]].mean(axis=0)
direction = np.sign(np.dot(midpoint - center, n)) * n
far_point = vor.vertices[v2] + direction * radius
new_region.append(len(new_vertices))
new_vertices.append(far_point.tolist())
# sort region counterclockwise
vs = np.asarray([new_vertices[v] for v in new_region])
c = vs.mean(axis=0)
angles = np.arctan2(vs[:,1] - c[1], vs[:,0] - c[0])
new_region = np.array(new_region)[np.argsort(angles)]
# finish
new_regions.append(new_region.tolist())
return new_regions, np.asarray(new_vertices)
# make up data points
np.random.seed(1234)
points = np.random.rand(12, 2)
df = pd.DataFrame(points, columns=list('XY'))
df[["Name"]] = [chr(i+65) for i in df.index]
# compute Voronoi tesselation
vor = Voronoi(points)
# plot
regions, vertices = voronoi_finite_polygons_2d(vor)
cluster_color_dit = {
"A": "orange",
"B": "red",
"C": "red",
"D": "red",
"E": "blue",
"F": "blue",
"G": "blue",
"H": "blue",
"I": "red",
"J": "red",
"K": "purple",
"L" : "blue"
}
fig, ax = plt.subplots()
cluster_color_dit[df.Name[0]]
for j, region in enumerate(regions):
polygon = vertices[region]
color = cluster_color_dit[df.Name[j]]
plt.fill(*zip(*polygon), alpha=0.4, color = color)
plt.plot(points[:,0], points[:,1], 'ko')
plt.xlim(vor.min_bound[0] - 0.1, vor.max_bound[0] + 0.1)
plt.ylim(vor.min_bound[1] - 0.1, vor.max_bound[1] + 0.1)
plt.show()
A: You can pass linewidth=0 to plt.fill() to get rid of the lines.
| {
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var express = require('express'),
http = require('http'),
httpProxy = require('http-proxy'),
workDir = process.cwd();
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proxies = [], self = this, app;
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// if (err) throw err;
socket.close();
});
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var url = req.url, urlMatched = false;
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res.writeHead(502);
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RunnerServer.prototype.constructor = RunnerServer;
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} | 3,914 |
Q: What can be done to add the Lambdalabs repository to Ubuntu 19.04? This Err: 6 has stopped my attempt to install "Lambda Stack". What is the work around to install lambdalabs.com repository?
Err:6 . . . lambdalabs.com/ubuntu disco Release
404 Not Found [IP: 52.218.209.43 80]
. . .
Reading package lists... Done
E: The repository '. . . disco Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.
A: If you look at their website they have a universal installation method that is supported for LTS releaes:
LAMBDA_REPO=$(mktemp) && \
wget -O${LAMBDA_REPO} https://lambdalabs.com/static/misc/lambda-stack-repo.deb && \
sudo dpkg -i ${LAMBDA_REPO} && rm -f ${LAMBDA_REPO} && \
sudo apt-get update && sudo apt-get install -y lambda-stack-cuda
For 19.04 you would get the 18.04 version and this will circumvent your problem with the PPA.
Regarding the PPA: if a release is not supported the general idea is to change the version to install. Example:
And then you can use the regular
sudo apt-get update && sudo apt-get install -y lambda-stack-cuda
A: For anyone who finds this answer in the future - I'm running Pop 20.10 and had the exact same issue with the repo. I changed the version from "groovy" (20.10) to "focal" (20.04), since Lambda Stack only supports LTS versions.
My /etc/apt/sources.list.d/lambda-repository.list looks like this:
deb http://archive.lambdalabs.com/ubuntu focal main
# deb-src http://archive.lambdalabs.com/ubuntu groovy main
Then, simply installing lambda-stack-cuda works.
| {
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} | 3,044 |
Théo St-Cyr est un des personnages principaux de la série québécoise Tactik. Son interprète est Benjamin Chouinard.
Sur le site de Tactik: Ce joueur de défense pour l'Épik a finalement trouvé sa véritable passion : la course. Et ce n'est pas parce qu'il ne joue plus au soccer qu'il n'est plus actif pour autant. Entre son amour de la bande dessinée où il a trouvé le moyen de s'exprimer librement et la garde partagée de la maison, notre rêveur n'a pas le temps de s'ennuyer. En effet, les parents de Théo ont eu la bonne idée de venir habiter dans le loft, chacun leur tour. Bien qu'elle fasse le bonheur de Théo, cette « nouvelle » solution risque d'être la source de « nouveaux » ennuis...
Biographie
Théo St-Cyr vit seul avec son père Jeff, qui est un comédien, dans un loft en bagarre, tandis que sa mère, qui est productrice de spectacle, se déplace dans les quatre coins du monde. Les parents de Théo se sont séparés quand Théo avait au moins cinq ans. Théo souhaite après, le retour de ses parents. Théo fait partie d'un club d'échecs, mais fait aussi partie de l'Épik, même si Théo n'aime pas les sports.
Saison 1
Théo est déprimé: il est pressé d'aller s'inscrire dans le club d'échecs, mais il est retenu chez lui par un journaliste qui veut écrire un article sur son père. Finalement, il fait partie de l'Épik, et aussi du club d'échecs.
Saison 2
Depuis que Vallières a fait l'échange d'entraîneur, Théo lâche l'équipe, mais il n'est pas le seul: Dalie part avec lui. Finalement, au retour de Reda, Théo reprend l'équipe, et Dalie aussi reprend l'équipe. Quelques semaines plus tard, Théo a pris une décision : il lâche l'Épik une fois pour toutes, même si sa mère est contre. Heursement, la mère de Théo accepte qu'il lâche l'équipe, grâce à Béa. Il trouve sa véritable passion, la course à pied, et développe aussi une passion pour la bande dessinée. Théo y fait aussi la rencontre de Philémon, qui lui as fait sa passion pour la BD et Clémentine, la petite sœur de Philémon, et aussi une coureuse.
Saison 3
Reda (coach de course de Théo) lui apprend qu'il ne peut plus l'entraîner pour la course. Alors, Théo décide d'être solitaire pour la course. Finalement, grâce à Clémentine, il fait partie d'un club d'athlétisme, dirigé par Axel McDuff, un pince-sans-rire. Pour sa famille, Jeff et Sophie décide de faire une garde partagée: il s'installe dans le loft pendant une semaine chacun leur tour, au grand bonheur de Théo, mais pas tellement celui de ses parents.
Saison 5
Théo sort avec Audrey une fille de Valmont, mais il est en fait en amour avec un ami qui lui tourne le dos lorsqu'il lui avoue. Dans le tout dernier épisode, qui présente les personnages quelques mois après, Théo est en couple avec un gars.
Caractère
Théo est un poème sur deux pattes, un rêveur, un philosophe et un rassembleur. Il ne s'intéresse vraiment pas a l'amour. Il porte des chandails avec des signes de récupération, de vélo ou de sécurité.
Personnage de Tactik | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,250 |
\section{Introduction}
The fluctuation-dissipation theorem (FDT)
relates nonequilibrium transport coefficients to equilibrium fluctuations,
and plays a pivotal role in statistical mechanics.
It dates back to Einstein's theory of Brownian motion \cite{Einstein1905}
and the Nyquist relation between resistance and a thermal noise in voltage
\cite{Nyquist1928}, culminating in linear response theory \cite{Kubo1957}
(for a review, see, e.g., Ref.~\cite{Marconi2008}).
The FDT establishes the relationship between the expectation values of the commutator and the anticommutator,
\begin{align}
C_{[A,B]}(t,t')
&\equiv
\langle [\hat A(t),\hat B(t')]\rangle,
\\
C_{\{A,B\}}(t,t')
&\equiv
\langle \{\hat A(t),\hat B(t')\}\rangle,
\end{align}
of arbitrary (bosonic or fermionic\footnote{We call an operator $\hat A$ bosonic (fermionic)
if $\hat A$ is a linear combination of operators,
each of which contains an even (odd) number of fermion creation and/or annihilation operators.})
Heisenberg operators $\hat A(t)=e^{\frac{i}{\hbar}\hat H t}\hat A e^{-\frac{i}{\hbar}\hat H t}$
and $\hat B(t)=e^{\frac{i}{\hbar}\hat H t}\hat B e^{-\frac{i}{\hbar}\hat H t}$.
Here $\hat H$ is the Hamiltonian of the system, $\hbar$ is the Planck constant,
$\langle \cdot \rangle\equiv {\rm Tr}(\hat\rho\, \cdot \,)$,
and $\hat\rho=e^{-\beta\hat H}/Z$ ($Z={\rm Tr}e^{-\beta\hat H}$)
with $\beta=(k_B T)^{-1}$ being the inverse temperature ($k_B$ is the Boltzmann constant).
In the Fourier representation [i.e., $C_{\{A,B\}}(\omega)=\int_{-\infty}^{\infty} dt\, e^{i\omega t}C_{\{A,B\}}(t,0)$, etc.],
the FDT is expressed as
\begin{align}
C_{\{A,B\}}(\omega)
&=
\coth\left(\frac{\beta\hbar\omega}{2}\right)
C_{[A,B]}(\omega).
\label{FDT}
\end{align}
If either $\hat A$ or $\hat B$ is bosonic, then
$C_{\{A,B\}}(\omega)$ represents thermal fluctuations and $C_{[A,B]}(\omega)$ represents
dissipation (and vice versa if both $\hat A$ and $\hat B$ are fermionic) \cite{Kubo1957,KuboBook,noneqDMFTreview}.
What is the law that governs higher-order fluctuations beyond the FDT (\ref{FDT}) and beyond the linear response regime?
The generalization of the FDT has led to deeper understanding of nonequilibrium statistical mechanics.
The prime examples are the fluctuation theorem \cite{EvansCohenMorriss1993,EvansSearles1994} and the Jarzynski equality \cite{Jarzynski1997},
which are valid in arbitrary far off-equilibrium situations,
reproduce the FDT (\ref{FDT}) at zero frequency if applied to near thermal equilibrium, and place constraints
on higher-order fluctuations \cite{Gallavotti1996,AndrieuxGaspard2007,SaitoUtsumi2008,EspositoHarbolaMukamel2009,Campisi2011}.
Here we pursue a different direction of generalization of the FDT by
considering the second moments of fluctuation and dissipation such as
$\langle \{\hat A(t),\hat B(t')\}^2\rangle$ and $\langle [\hat A(t),\hat B(t')]^2\rangle$.
They involve the operator sequences $\hat A(t)\hat B(t')\hat A(t)\hat B(t')$ and $\hat B(t')\hat A(t)\hat B(t')\hat A(t)$
that constitute out-of-time-ordered correlators (OTOCs) \cite{LarkinOvchinnikov1969}.
The OTOC has attracted growing attention as a measure to characterize chaotic behavior in quantum systems \cite{Kitaev2015}.
The relation to chaos can be seen in the semiclassical approximation:
If $\hat A$ and $\hat B$ form a canonically conjugate pair, then $\langle [\hat A(t),\hat B(0)]^2\rangle
\sim -\hbar^2 \langle\!\langle \{A(t),B(0)\}_P^2\rangle\!\rangle
=-\hbar^2\langle\!\langle \big(\frac{\partial A(t)}{\partial A(0)}\big)^2 \rangle\!\rangle$,
where $\langle\!\langle \cdot \rangle\!\rangle$ is the classical phase-space average with respect to the Gibbs ensemble,
and $\{,\}_P$ is the Poisson bracket. This quantity indicates the sensitivity of the time-evolving quantity $A(t)$
to its initial value $A(0)$ and is expected to grow exponentially in time for chaotic systems (``butterfly effect'')
as $\sim e^{\lambda t}$, where $\lambda$ is an analog of the Lyapunov exponent in classical chaotic systems
(see also Ref.~\cite{Rozenbaum2016}).
The interest in OTOCs has recently surged in various contexts
including the Sachdev-Ye-Kitaev model \cite{SachdevYe1993,Kitaev2015,MaldacenaStanford2016},
black holes and the holography principle \cite{ShenkerStanford2014b,ShenkerStanford2015,MaldacenaShenkerStanford2016},
quantum information \cite{Hosur2016,Swingle2016,Campisi2016},
many-body localization \cite{Huang2016,Fan2016,Chen2016,He2016}, and
strongly correlated systems \cite{Shen2016,Aleiner2016,TsujiWernerUeda2016,Dora2016,Bohrdt2016}.
The OTOC has recently been observed in experiments \cite{Garttner2017,Li2016,Wei2016,Meier2017}.
In this paper, we show that a generalized fluctuation-dissipation theorem holds for a certain class of OTOCs
with an arbitrary frequency.
The theorem describes a universal relation between chaotic properties in quantum systems and a nonlinear response function
for a perturbation involving a time-reversed process. To be more precise, there is a difference in operator ordering between
OTOCs defined by the usual statistical average [$\langle \hat A(t)\hat B(t')\hat A(t)\hat B(t')\rangle
={\rm Tr}(\hat\rho \hat A(t)\hat B(t')\hat A(t)\hat B(t'))$] and those that do obey the out-of-time-order FDT.
This difference can be expressed in terms of the Wigner-Yanase skew information \cite{WignerYanase1963}
which is known in the context of quantum information theory and serves as a measure of information contents contained in quantum fluctuations
of observables.
Within the difference of the skew information, the out-of-time-order FDT relates the chaotic behavior and the nonlinear
response function.
The rest of this paper is organized as follows. In Sec.~\ref{main results},
we present the statement of one of the main results in the paper, the out-of-time-order FDT.
In Sec.~\ref{physical meaning}, we discuss the physical meaning of the out-of-time-order FDT.
We prove the out-of-time-order FDT in Sec.~\ref{proof}.
In Sec.~\ref{generalization}, we generalize the theorem to higher-order OTOCs as well as other operator ordering of OTOCs.
In Sec.~\ref{conclusion}, we conclude the paper.
In Appendix, we present the proofs of some relations among OTOCs used in the main text.
\section{Main results}
\label{main results}
The FDT is generalized for OTOCs not in a straightforward manner
but in a twisted form. Namely,
we should split $\hat\rho$ into two $\hat\rho^{\frac{1}{2}}$'s, one of which is inserted
in between commutators and/or anticommutators
of $\hat A(t)$ and $\hat B(t')$ and the other is placed in front of them.
To be specific, we define a {\it bipartite} OTOC (also called a regularized OTOC)
\cite{MaldacenaShenkerStanford2016,Stanford2016,Yao2016,PatelSachdev2016} as
\begin{align}
C_{AB}^{\alpha_1\alpha_2}(t,t')
&\equiv
C_{[A,B]_{\alpha_1}[A,B]_{\alpha_2}}(t,t')
\notag
\\
&\equiv
{\rm Tr}\left(
\hat\rho^{\frac{1}{2}}[\hat A(t),\hat B(t')]_{\alpha_1}
\hat\rho^{\frac{1}{2}}[\hat A(t),\hat B(t')]_{\alpha_2}
\right),
\label{bipartite OTOC}
\end{align}
where $\alpha_1, \alpha_2=\pm$, and $[, ]_{-(+)}$ represents the (anti) commutator.
Note that (\ref{bipartite OTOC}) is different from an ordinary OTOC which takes the form of
the expectation value [${\rm Tr}(\hat\rho\cdots)$] of products of (anti)commutators for a given state $\hat\rho$,
\begin{align}
C_{AB}^{{\rm phys}, \alpha_1\alpha_2}(t,t')
&\equiv
C_{[A,B]_{\alpha_1}[A,B]_{\alpha_2}}^{\rm phys}(t,t')
\notag
\\
&\equiv
{\rm Tr}\left(
\hat\rho[\hat A(t),\hat B(t')]_{\alpha_1}
[\hat A(t),\hat B(t')]_{\alpha_2}
\right).
\label{physical OTOC}
\end{align}
Since this quantity is written in the form of the expectation value
that allows for a direct physical interpretation,
we shall refer to (\ref{physical OTOC}) as a {\it physical} OTOC.
Depending on $\alpha_1,\alpha_2=\pm$, Eq.~(\ref{bipartite OTOC}) introduces four types of bipartite OTOCs,
of which $C_{\{A,B\}[A,B]}$ and $C_{[A,B]\{A,B\}}$ are equal due to the cyclic invariance of the trace.
Hence there are three independent bipartite OTOCs for a given pair of $\hat A$ and $\hat B$.
One of the main results in this paper is that for {\it any} quantum system in thermal equilibrium
the three bipartite OTOCs are related via
\begin{align}
C_{\{A,B\}^2}(\omega)+C_{[A,B]^2}(\omega)
&=
2\coth\left(\frac{\beta\hbar\omega}{4}\right)C_{\{A,B\}[A,B]}(\omega),
\label{FDT2}
\end{align}
which we call the out-of-time-order FDT.
If we ignore the difference in operator ordering between (\ref{bipartite OTOC}) and (\ref{physical OTOC})
(the physical meaning of this is explained in Sec.~\ref{physical meaning}),
then the equality (\ref{FDT2}) implies a universal relation among the second moments of fluctuation and dissipation, and their cross-correlation.
In this sense, the equality (\ref{FDT2}) can be viewed as a second-order extension of the FDT (\ref{FDT}).
\section{Physical meaning of the out-of-time-order fluctuation-dissipation theorem}
\label{physical meaning}
To see the physical meaning of the equality (\ref{FDT2}),
let us first note that the difference between $C_{AB}^{\alpha_1\alpha_2}(t,t')$ (\ref{bipartite OTOC})
and $C_{AB}^{{\rm phys},\alpha_1\alpha_2}(t,t')$ (\ref{physical OTOC})
takes a form reminiscent of
the Wigner-Yanase (WY) skew information\footnote{There is a one-parameter generalization of the WY skew information due to Dyson, i.e.,
$I_\alpha(\hat\rho,\hat O)={\rm Tr}(\hat\rho\hat O^2)-{\rm Tr}(\hat\rho^\alpha\hat O \rho^{1-\alpha}\hat O)$ ($0\leqslant \alpha \leqslant 1$).} \cite{WignerYanase1963} defined by
\begin{align}
I_{\frac{1}{2}}(\hat\rho,\hat O)
&\equiv
-\frac{1}{2}{\rm Tr}([\hat\rho^{\frac{1}{2}},\hat O]^2)
\notag
\\
&=
{\rm Tr}(\hat\rho \hat O^2)
-{\rm Tr}(\hat\rho^{\frac{1}{2}} \hat O \hat\rho^{\frac{1}{2}}\hat O)
\end{align}
for a Hermitian operator $\hat O$.
It serves as a measure of information contents concerning quantum fluctuations.
Here by quantum fluctuations we mean the following \cite{Luo2005}.
Let us consider the variance of $\hat O$, $\langle (\Delta\hat O)^2\rangle$,
where $\Delta\hat O\equiv\hat O-\langle\hat O\rangle$.
The variance $\langle (\Delta\hat O)^2\rangle$ generally contains
classical mixing and quantum uncertainty, so that
we are tempted to decompose the variance
as
\begin{align}
\langle (\Delta\hat O)^2\rangle
&=
C(\hat\rho,\hat O)+Q(\hat\rho,\hat O).
\end{align}
If $C(\hat\rho,\hat O)$ and $Q(\hat\rho,\hat O)$
satisfy the following conditions, we call them the classical and quantum fluctuations of $\hat O$:
\begin{enumerate}
\renewcommand{\labelenumi}{(\alph{enumi})}
\item $C(\hat\rho,\hat O), Q(\hat\rho,\hat O)\geqslant 0$.
\item If $\hat\rho$ is pure, then $C(\hat\rho,\hat O)=0$ and $Q(\hat\rho,O)=\langle(\Delta\hat O)^2\rangle$.
\item If $\hat\rho$ and $\hat O$ commute, then $C(\hat\rho,O)=\langle(\Delta\hat O)^2\rangle$ and
$Q(\hat\rho,\hat O)=0$.
\item $C(\hat\rho,\hat O)$ is concave and $Q(\hat\rho,O)$ is convex as functions of $\hat\rho$,
i.e.,
\begin{align}
C(\lambda\hat\rho_1+(1-\lambda)\hat\rho_2,\hat O)\geqslant \lambda C(\hat\rho_1,\hat O)+(1-\lambda)C(\hat\rho_2,\hat O),
\notag
\\
Q(\lambda\hat\rho_1+(1-\lambda)\hat\rho_2,\hat O)\leqslant \lambda Q(\hat\rho_1,\hat O)+(1-\lambda)Q(\hat\rho_2,\hat O),
\notag
\end{align}
for $0\leqslant\lambda\leqslant 1$.
\end{enumerate}
The condition (d) means that classical fluctuations should increase and quantum fluctuations should decrease by a classical mixing of states.
These conditions are in accordance with our intuition of quantum fluctuations.
Although such a decomposition is not unique \cite{Hansen2008}, the WY skew information provides one realization
of the measure of quantum fluctuations [$Q(\hat\rho,\hat O)=I_{\frac{1}{2}}(\hat\rho,\hat O)$]. In fact, it satisfies the inequalities
\begin{align}
0\leqslant I_{\frac{1}{2}}(\hat\rho,\hat O)
\leqslant \langle (\Delta\hat O)^2\rangle.
\label{WYD inequality}
\end{align}
The equality on the left-hand side
of (\ref{WYD inequality}) is satisfied when $[\hat\rho,\hat O]=0$,
and the one on the right-hand side is met when $\hat\rho$ is
a pure state.
Furthermore, the WY skew information is convex as a function of a quantum state \cite{Lieb1973},
\begin{align}
I_{\frac{1}{2}}(\lambda\hat\rho_1+(1-\lambda)\hat\rho_2,\hat O)
\leqslant
\lambda I_{\frac{1}{2}}(\hat\rho_1,\hat O)+(1-\lambda)I_{\frac{1}{2}}(\hat\rho_2,\hat O),
\label{convexity}
\end{align}
for $0\leqslant \lambda \leqslant 1$. That is,
it decreases under a classical mixing of quantum states,
justifying [with (\ref{WYD inequality})] the use of $I_{\frac{1}{2}}(\hat\rho,\hat O)$ as an information-theoretic measure of quantum fluctuations.
If $\hat A$ and $\hat B$ are Hermitian, then
$C_{AB}^{\alpha_1\alpha_2}(t,t')$ and $C_{AB}^{{\rm phys},\alpha_1\alpha_2}(t,t')$ are related
to the WY skew information via
\begin{align}
C_{\{A,B\}^2}(t,t')
&=
C_{\{A,B\}^2}^{\rm phys}(t,t')-I_{\frac{1}{2}}\!\left(\hat\rho, \{\hat A(t),\hat B(t')\}\right),
\label{difference1}
\\
C_{[A,B]^2}(t,t')
&=
C_{[A,B]^2}^{\rm phys}(t,t')+I_{\frac{1}{2}}\!\left(\hat\rho, i[\hat A(t),\hat B(t')]\right),
\label{difference2}
\\
C_{\{A,B\}[A,B]}(t,t')
&=
\frac{1}{2}[C_{\{A,B\}[A,B]}^{\rm phys}(t,t')+C_{[A,B]\{A,B\}}^{\rm phys}(t,t')]
\notag
\\
&\quad
+\frac{i}{4}I_{\frac{1}{2}}\!\left(\hat\rho,\{\hat A(t),\hat B(t')\}+i[\hat A(t),\hat B(t')]\right)
\notag
\\
&\quad
-\frac{i}{4}I_{\frac{1}{2}}\!\left(\hat\rho,\{\hat A(t),\hat B(t')\}-i[\hat A(t),\hat B(t')]\right).
\label{difference3}
\end{align}
Note that $\{\hat A(t),\hat B(t')\}$, $i[\hat A(t),\hat B(t')]$, and $\{\hat A(t),\hat B(t')\}\pm i[\hat A(t),\hat B(t')]$ are Hermitian.
We thus find that the difference between the bipartite (\ref{bipartite OTOC}) and physical OTOCs (\ref{physical OTOC})
can be expressed in terms of the skew information.
Within this difference, which is negligible when quantum fluctuations are small,
Eq.~(\ref{FDT2}) shows the relation among
the second moments of fluctuation and dissipation, and their cross-correlation.
We can explicitly express this by rewriting Eq.~(\ref{FDT2}) in terms of the physical OTOCs,
\begin{align}
&
C_{\{A,B\}^2}^{\rm phys}(\omega)+C_{[A,B]^2}^{\rm phys}(\omega)
\notag
\\
&=
\coth\left(\frac{\beta\hbar\omega}{4}\right)
[C_{\{A,B\}[A,B]}^{\rm phys}(\omega)+C_{[A,B]\{A,B\}}^{\rm phys}(\omega)]
+I_{AB}(\omega),
\label{FDT2 physical}
\end{align}
where
\begin{align}
I_{AB}(\omega)
&=
\int_{-\infty}^{\infty} dt e^{i\omega t}\bigg\{
I_{\frac{1}{2}}\!\left(\hat\rho, \{\hat A(t),\hat B(0)\}\right)
-I_{\frac{1}{2}}\!\left(\hat\rho, i[\hat A(t),\hat B(0)]\right)
\notag
\\
&\quad
+\frac{i}{2}\coth\left(\frac{\beta\hbar\omega}{4}\right)
I_{\frac{1}{2}}\!\left(\hat\rho,\{\hat A(t),\hat B(0)\}+i[\hat A(t),\hat B(0)]\right)
\notag
\\
&\quad
-\frac{i}{2}\coth\left(\frac{\beta\hbar\omega}{4}\right)
I_{\frac{1}{2}}\!\left(\hat\rho,\{\hat A(t),\hat B(0)\}-i[\hat A(t),\hat B(0)]\right)
\bigg\}
\end{align}
is a linear combination of the skew information.
The physical meaning of Eq.~(\ref{FDT2}) [or Eq.~(\ref{FDT2 physical})] is as follows.
The right-hand side of (\ref{FDT2}) is related to a certain type of a nonlinear-response function (Fig.~\ref{protocol}).
To see this, let us consider the following experimental protocol.
The initial state is set to be in thermal equilibrium with $\hat\rho$.
At time $t=0$, we perturb the system with a variation of the Hamiltonian $\delta \hat H(t)=\hbar\varepsilon_B \delta(t)\hat B$
($\varepsilon_B\in\mathbb R$).
Then we let the system evolve from $t=0$ to $t_0$ with the Hamiltonian $+\hat H$. At $t=t_0$ $(>0)$,
we perturb the system with
$\delta\hat H(t)=\hbar\varepsilon_A \delta(t-t_0)\hat A$ ($\varepsilon_A\in\mathbb R$). Then we let the system
evolve from $t=t_0$ to $2t_0$ with the inverted Hamiltonian $-\hat H$
(as in spin echo, Loschmidt echo, or ultracold atom \cite{TsujiWernerUeda2016} experiments),
i.e., the time propagation is effectively reversed.
Finally, we measure $\hat B$ at $t=2t_0$.
Let us suppose that $\varepsilon_A$
and $\varepsilon_B$ are sufficiently small,
which allows us to expand $\langle \hat B(2t_0)\rangle$ with respect to $\varepsilon_A$ and $\varepsilon_B$,
\begin{align}
\langle \hat B(2t_0)\rangle
&=
\sum_{m,n=0}^\infty \varepsilon_A^m \varepsilon_B^n
[\delta_{A^mB^n}^{m+n}\langle \hat B(2t_0)\rangle].
\end{align}
Here $\delta_{A^mB^n}^{m+n}\langle \hat B(2t_0)\rangle$ represents the expansion coefficient
at the $m$th and $n$th orders with respect to the perturbation strength $\varepsilon_A$ and $\varepsilon_B$.
The lowest order at which OTOCs appear is the third order ($m+n=3$).
We define a nonlinear response function $L_{(AB)^2}^{(3)}(t_0,0)$
as a coefficient of the third-order variation of $\langle \hat B(2t_0)\rangle$
that is proportional to $\varepsilon_A^2 \varepsilon_B$, i.e.,
\begin{align}
\delta_{A^2B}^3\langle \hat B(2t_0)\rangle
&=:
\frac{1}{2}L_{(AB)^2}^{(3)}(t_0,0).
\label{B(2t)}
\end{align}
The density matrix at $t=2t_0$ is given by
\begin{align}
\hat\rho(2t_0)
&=
e^{\frac{i}{\hbar}\hat Ht_0}e^{-i\varepsilon_A\hat A}e^{-\frac{i}{\hbar}\hat Ht_0}e^{-i\varepsilon_B\hat B}
\hat\rho e^{i\varepsilon_B\hat B}e^{\frac{i}{\hbar}\hat Ht_0}e^{i\varepsilon_A\hat A}e^{-\frac{i}{\hbar}\hat Ht_0}.
\end{align}
By expanding $\langle \hat B(2t_0)\rangle={\rm Tr}[\hat\rho(2t_0)\hat B]$
with respect to $\varepsilon_A$ and $\varepsilon_B$, and collecting terms proportional to $\varepsilon_A^2\varepsilon_B$,
we obtain
\begin{align}
L_{(AB)^2}^{(3)}(t_0,0)
&=
-i[C_{\{A,B\}[A,B]}^{\rm phys}(t_0,0)+C_{[A,B]\{A,B\}}^{\rm phys}(t_0,0)]
\notag
\\
&\quad
+iC_{[A^2,B^2]}(t_0,0).
\label{L_(AB)^2}
\end{align}
The two terms in the square bracket in Eq.~(\ref{L_(AB)^2}) coincide with those in
the square bracket in Eq.~(\ref{difference3}) (with $t=t_0$ and $t'=0$)\footnote{The present protocol measures $L_{(AB)^2}^{(3)}(t_0,0)$ for $t_0>0$. The remaining part ($t_0<0$)
can be obtained by changing the protocol such that the system evolves with $-H$ from $t=0$ to $t_0$ and with $+H$ from $t=t_0$ to $2t_0$.},
while the last term in Eq.~(\ref{L_(AB)^2}), $L_{A^2B^2}^{(1)}(t_0,0)\equiv -iC_{[A^2,B^2]}(t_0,0)$,
is a linear-response function with respect to $\hat A^2$ and $\hat B^2$
(i.e., a linear response of $\langle \hat A(t_0)^2\rangle$
against a perturbation $\delta\hat H(t)=\hbar\varepsilon_B\delta(t)\hat B^2$),
which can be measured independently.
One can see that the right-hand side of (\ref{FDT2}), $2C_{\{A,B\}[A,B]}(t,t')$, is related to the response function
$i[L_{(AB)^2}^{(3)}(t,t')+L_{A^2B^2}^{(1)}(t,t')]$
within the difference of the WY skew information,
\begin{align}
2C_{\{A,B\}[A,B]}(t,t')
&=
i[L_{(AB)^2}^{(3)}(t,t')+L_{A^2B^2}^{(1)}(t,t')]
\notag
\\
&\quad
+\frac{i}{4}I_{\frac{1}{2}}\!\left(\hat\rho,\{\hat A(t),\hat B(t')\}+i[\hat A(t),\hat B(t')]\right)
\notag
\\
&\quad
-\frac{i}{4}I_{\frac{1}{2}}\!\left(\hat\rho,\{\hat A(t),\hat B(t')\}-i[\hat A(t),\hat B(t')]\right).
\label{RHS FDT2}
\end{align}
\begin{figure}[t]
\includegraphics[width=8.5cm]{protocol.pdf}
\caption{Measurement protocol for the nonlinear response function $L_{(AB)^2}^{(3)}(t_0,0)$.
The system is perturbed by the pulsed fields at $t=0$ and $t=t_0$. The system evolves with the Hamiltonian $+\hat H$
from $t=0$ to $t=t_0$ and then with $-\hat H$ from $t=t_0$ to $t=2t_0$. The measurement of $\hat B$ is performed
at $t=2t_0$.}
\label{protocol}
\end{figure}
The protocol has advantages
that it can be applied to arbitrary thermal initial states and avoids multiple measurements that cause
measurement back action.
This is in contrast to the protocols described in Refs.~\cite{TsujiWernerUeda2016,Garttner2017},
where the initial state is set to be an eigenstate of the operator $\hat A$ or $\hat B$ to readout the OTOC.
This is equivalent to making a projection measurement at the initial time, which causes measurement back actions.
A Loschmidt-echo-type protocol similar to the one shown in Fig.~\ref{protocol} has been proposed in Ref.~\cite{Swingle2016}.
The difference is that in the former one measures the nonlinear response function $L_{(AB)^2}(t,0)$
to reconstruct ${\rm Re}\langle \hat A(t)\hat B(0)\hat A(t)\hat B(0)\rangle
=\frac{1}{4}[C_{\{A,B\}^2}^{\rm phys}(t,0)+C_{[A,B]^2}^{\rm phys}(t,0)]$
for Hermitian operators $\hat A$ and $\hat B$
via the out-of-time-order FDT (\ref{FDT2}),
while in the latter one measures
$|\langle\psi|\hat W^\dagger(t)\hat V^\dagger(0)\hat W(t)\hat V(0)|\psi\rangle|^2$ for unitary operators $\hat V$ and $\hat W$.
The latter also requires the projection onto the initial state $|\psi\rangle$.
We note that there are various other types of protocols which have been proposed
to measure OTOCs \cite{Swingle2016,Yao2016,Zhu2016,Bohrdt2016,YungerHalpern2017,YungerHalpernSwingleDressel2017}.
The left-hand side of (\ref{FDT2}), on the other hand, is related to chaotic behavior in quantum many-body systems \cite{Kitaev2015,MaldacenaShenkerStanford2016}.
As we have mentioned, if $\hat A$ and $\hat B$ are a canonically conjugate pair, then
$C_{[A,B]^2}^{\rm phys}(t,0)\sim -\hbar^2 \langle\!\langle \big(\frac{\partial A(t)}{\partial A(0)}\big)^2\rangle\!\rangle$
in the semiclassical regime, indicating an initial-value sensitivity of $A(t)$.
In chaotic systems, $-\hbar^2 \langle\!\langle \big(\frac{\partial A(t)}{\partial A(0)}\big)^2\rangle\!\rangle$
is expected to grow exponentially in time ($\sim e^{\lambda t}$),
where $\lambda$ is an analog of the Lyapunov exponent.
The exponential growth in $C_{[A,B]^2}^{\rm phys}(t,0)$ arises from
its out-of-time-ordered part $\langle (\hat A(t)\hat B(0))^2\rangle+\langle (\hat B(0)\hat A(t))^2\rangle$
\cite{MaldacenaShenkerStanford2016},
which is equal to $\frac{1}{2}[C_{\{A,B\}^2}^{\rm phys}(t,0)+C_{[A,B]^2}^{\rm phys}(t,0)]$.
Therefore, the left-hand side of Eq.~(\ref{FDT2}) represents an initial-value sensitivity of a time-evolving observable
(within the difference of the WY skew information).
Based on these observations, we are led to a general principle that the nonlinear response defined in Eq.~(\ref{B(2t)}) is related
to chaotic behavior in quantum systems through the out-of-time-order FDT (\ref{FDT2}).
This allows one to access the exponentially growing part of
the OTOC $\langle [\hat A(t),\hat B(0)]^2\rangle$ in chaotic systems by the nonlinear-response experiment.
As far as the exponential growth of $\langle [\hat A(t),\hat B(0)]^2\rangle$ is concerned,
the difference of the WY skew information, a measure of quantum fluctuations,
is suppressed in the semiclassical regime of our interest.
In the strictly classical limit with $\hbar\to 0$,
the out-of-time-order FDT (\ref{FDT2}) can be expressed as
\begin{align}
\partial_t \langle\!\langle A(t)^2 B(t')^2\rangle\!\rangle
&=
k_BT\langle\!\langle \{A(t)^2,B(t')^2\}_P\rangle\!\rangle.
\label{classical limit}
\end{align}
We can see that the classical limit of (\ref{FDT2}) reduces to that of the conventional FDT (\ref{FDT})
with $A(t)$ and $B(t)$ replaced by $A(t)^2$ and $B(t)^2$, respectively.
\section{Proof of the out-of-time-order fluctuation-dissipation theorem}
\label{proof}
We now prove the equality (\ref{FDT2}). To this end, we introduce a representation of the bipartite OTOCs
different from (\ref{bipartite OTOC}):
\begin{align}
C_{AB}^{\mu_1\mu_2}(t,t')
&\equiv
{\rm Tr}\left(
\hat\rho^{\frac{1}{2}}(\hat A(t)\hat B(t'))^{\mu_1}
\hat\rho^{\frac{1}{2}}(\hat A(t)\hat B(t'))^{\mu_2}
\right),
\label{bipartite OTOC2}
\end{align}
where $\mu_1,\mu_2=\;>,<$, and
\begin{align}
(\hat A(t)\hat B(t'))^{\mu_i}
&\equiv
\begin{cases}
\hat A(t)\hat B(t') & \mbox{for} \quad \mu_i=\;>, \\
\hat B(t')\hat A(t) & \mbox{for} \quad \mu_i=\;<.
\end{cases}
\end{align}
In the above definition, we do not include the minus sign for $\mu_i=\;<$
when both $\hat A$ and $\hat B$ are fermionic.
However, all the arguments below can equally be applied to this case without any change.
Again we have $C_{AB}^{><}=C_{AB}^{<>}$
due to the cyclic invariance of the trace.
The two representations (\ref{bipartite OTOC}) and (\ref{bipartite OTOC2}) are connected
by a linear transformation
\begin{align}
L
\begin{pmatrix}
C_{AB}^{>>} & C_{AB}^{><} \\
C_{AB}^{<>} & C_{AB}^{<<}
\end{pmatrix}
L^T
&=
\frac{1}{2}
\begin{pmatrix}
C_{[A,B]^2} & C_{[A,B]\{A,B\}} \\
C_{\{A,B\}[A,B]} & C_{\{A,B\}^2}
\end{pmatrix},
\label{matrix transformation}
\end{align}
where
\begin{align}
L
&\equiv
\frac{1}{\sqrt{2}}
\begin{pmatrix}
1 & -1 \\
1 & 1
\end{pmatrix}
\end{align}
is an orthogonal matrix and $L^T$ is the transpose of $L$.
For convenience, we use notations $C_{(AB)^2}(t,t')\equiv C_{AB}^{>>}(t,t')$
and $C_{(BA)^2}(t',t)\equiv C_{AB}^{<<}(t,t')$.
We note the parallelism of the formulation with that for Keldysh Green's functions
\cite{Keldysh1964,LarkinOvchinnikov1975,Rammer,Haehl2016}.
We first show that $C_{(AB)^2}$ and $C_{(BA)^2}$ are related to each other by
\begin{align}
C_{(BA)^2}(\omega)
&=
e^{\frac{\beta\hbar\omega}{2}}C_{(AB)^2}(-\omega).
\label{reciprocal relation}
\end{align}
This relation is analogous to the Kubo-Martin-Schwinger condition
$C_{BA}(\omega)=e^{\beta\hbar\omega}C_{AB}(-\omega)$
\cite{Kubo1957,MartinSchwinger1959}
for conventional correlation functions
$C_{AB}(t,t')\equiv{\rm Tr}(\hat\rho\hat A(t)\hat B(t'))$.
The equality (\ref{reciprocal relation}) can be proven as follows.
We insert four complete sets of the eigenstates $\sum_k |k\rangle \langle k|$ of the Hamiltonian
$\hat H$ (with the eigenenergies $E_k$) in the definitions of $C_{(AB)^2}(t,t')$ and $C_{(BA)^2}(t,t')$,
obtaining
\begin{align}
C_{(AB)^2}(t,t')
&=
\frac{1}{Z}\sum_{k,l,m,n} e^{-\frac{\beta}{2}(E_k+E_m)}e^{\frac{i}{\hbar}(E_k-E_l+E_m-E_n)(t-t')}
\notag
\\
&\quad\times
\langle k|\hat A|l\rangle
\langle l|\hat B|m\rangle
\langle m|\hat A|n\rangle
\langle n|\hat B|k\rangle,
\\
C_{(BA)^2}(t,t')
&=
\frac{1}{Z}\sum_{k,l,m,n} e^{-\frac{\beta}{2}(E_k+E_m)}e^{\frac{i}{\hbar}(E_k-E_l+E_m-E_n)(t-t')}
\notag
\\
&\quad\times
\langle k|\hat B|l\rangle
\langle l|\hat A|m\rangle
\langle m|\hat B|n\rangle
\langle n|\hat A|k\rangle.
\label{C_(BA)^2 2}
\end{align}
By cyclically permuting the labels, $k\to l\to m\to n\to k$,
we have
\begin{align}
C_{(BA)^2}(t,t')
&=
\frac{1}{Z}\sum_{k,l,m,n} e^{-\frac{\beta}{2}(E_l+E_n)}e^{-\frac{i}{\hbar}(E_k-E_l+E_m-E_n)(t-t')}
\notag
\\
&\quad\times
\langle k|\hat A|l\rangle
\langle l|\hat B|m\rangle
\langle m|\hat A|n\rangle
\langle n|\hat B|k\rangle.
\end{align}
After the Fourier transformation, we obtain
\begin{align}
C_{(AB)^2}(\omega)
&=
\frac{1}{Z}\sum_{k,l,m,n} e^{-\frac{\beta}{2}(E_k+E_m)}
2\pi\delta\!\left(\omega+\tfrac{1}{\hbar}(E_k-E_l+E_m-E_n)\right)
\notag
\\
&\quad\times
\langle k|\hat A|l\rangle
\langle l|\hat B|m\rangle
\langle m|\hat A|n\rangle
\langle n|\hat B|k\rangle,
\label{C_(AB)^2 3}
\\
C_{(BA)^2}(\omega)
&=
\frac{1}{Z}\sum_{k,l,m,n} e^{-\frac{\beta}{2}(E_l+E_n)}
2\pi\delta\!\left(\omega-\tfrac{1}{\hbar}(E_k-E_l+E_m-E_n)\right)
\notag
\\
&\quad\times
\langle k|\hat A|l\rangle
\langle l|\hat B|m\rangle
\langle m|\hat A|n\rangle
\langle n|\hat B|k\rangle.
\label{C_(BA)^2 3}
\end{align}
Due to the presence of the $\delta$ function,
we can replace $E_l+E_n$ in the exponential in Eq.~(\ref{C_(BA)^2 3}) with
$E_k+E_m-\hbar\omega$.
By comparing it with Eq.~(\ref{C_(AB)^2 3}), we obtain Eq.~(\ref{reciprocal relation}).
With the relation (\ref{reciprocal relation}),
the left-hand side of (\ref{FDT2}) is transformed as
\begin{align}
C_{\{A,B\}^2}(\omega)+C_{[A,B]^2}(\omega)
&=
2C_{(AB)^2}(\omega)+2C_{(BA)^2}(-\omega)
\notag
\\
&=
2(1+e^{-\frac{\beta\hbar\omega}{2}})C_{(AB)^2}(\omega),
\label{FDT left}
\end{align}
while the right-hand side is
\begin{align}
C_{\{A,B\}[A,B]}(\omega)
&=
C_{(AB)^2}(\omega)-C_{(BA)^2}(-\omega)
\notag
\\
&=
(1-e^{-\frac{\beta\hbar\omega}{2}})C_{(AB)^2}(\omega).
\label{FDT right}
\end{align}
Combining Eqs.~(\ref{FDT left}) and (\ref{FDT right}),
we arrive at the out-of-time-order FDT (\ref{FDT2}).
\hspace{\fill}$\blacksquare$
Let us recall that the FDT (\ref{FDT}) can also be expressed as \cite{Kubo1957}
\begin{align}
\beta\hbar\omega\,\Phi_{AB}(\omega)
&=
C_{[A,B]}(\omega),
\label{FDT Phi}
\end{align}
where $\Phi_{AB}$ is a canonical correlation (a quantum generalization of a classical correlator
$\langle\!\langle A(t)B(t')\rangle\!\rangle$),
\begin{align}
\Phi_{AB}(t,t')
&\equiv
\int_0^1 d\lambda {\rm Tr}\left(
\hat\rho^{1-\lambda}\hat A(t)\hat \rho^{\lambda}\hat B(t')
\right).
\label{Phi_AB}
\end{align}
Analogously to this,
the right-hand side of (\ref{FDT2}) can be rewritten in a form of a canonical bipartite OTOC
defined as
\begin{align}
\Phi_{(AB)^2}(t,t')
&\equiv
\int_0^1 d\lambda {\rm Tr}\left[\left(
\hat\rho^{\frac{1-\lambda}{2}}\hat A(t)\hat\rho^{\frac{\lambda}{2}}\hat B(t')
\right)^2\right].
\label{Phi_AB^2}
\end{align}
The second-order extension of (\ref{FDT Phi}) is written as
\begin{align}
\beta\hbar\omega\,\Phi_{(AB)^2}(\omega)
&=
2C_{\{A,B\}[A,B]}(\omega).
\label{FDT2 Phi}
\end{align}
The proof of (\ref{FDT2 Phi}) is given as a special case of (\ref{GC FDT n Phi}) in Appendix \ref{appendix}.
To clarify the meaning of Eq.~(\ref{FDT2 Phi}), we note that
$\Phi_{(AB)^2}(t,t')$ can be written as
\begin{align}
\Phi_{(AB)^2}(t,t')
&=
\int_0^1 d\lambda\, C_{(AB)^2}\left(t-i\lambda\frac{\beta\hbar}{2},t'\right).
\label{regularization average}
\end{align}
That is, the time argument of the operator $\hat A$ is shifted to the direction of imaginary time.
This type of deformation has been employed to regularize OTOCs in the context of quantum field theory
\cite{MaldacenaShenkerStanford2016}.
Each $\lambda$ represents a different choice of regularization.
If the regularized OTOC $C_{(AB)^2}(t-i\lambda\frac{\beta\hbar}{2},0)$ shows an exponential growth
for every choice of regularization (in order for the growth to be physical, it should not depend on the choice of the regularization),
then its average (\ref{regularization average}) over the regularization parameter $\lambda$ also shows an exponential growth.
Then Eq.~(\ref{FDT2 Phi}) says that the averaged exponential growth of the OTOCs on the left-hand side
is related to the nonlinear response function on the right-hand side within the difference of the skew information
[see Eq.~(\ref{RHS FDT2})].
\section{Generalization of the out-of-time-order fluctuation-dissipation theorem}
\label{generalization}
The FDT (\ref{FDT2}) for OTOCs can be generalized in two ways.
One is to extend the relation to higher-order OTOCs \cite{Haehl2016,RobertsYoshida2017}.
Let us define an $n$-partite OTOC,
\begin{align}
C_{AB}^{\mu_1\mu_2\cdots\mu_n}(t,t')
&\equiv
{\rm Tr}\left[
\prod_{i=1}^n
\hat \rho^{\frac{1}{n}}
(\hat A(t)\hat B(t'))^{\mu_i}
\right],
\label{n-partite OTOC}
\end{align}
with $\mu_1,\mu_2,\dots,\mu_n=\;>,<$. In particular, we use abbreviations, $C_{(AB)^n}(t,t')\equiv C_{AB}^{>>\cdots >}(t,t')$
and $C_{(BA)^n}(t',t)\equiv C_{AB}^{<<\cdots <}(t,t')$. We perform a tensor transformation
\begin{align}
C_{AB}^{\alpha_1\alpha_2\cdots\alpha_n}(t,t')
&\equiv
2^{\frac{n}{2}}
\sum_{\mu_1,\dots,\mu_n}
{L^{\alpha_1}}_{\mu_1}
{L^{\alpha_2}}_{\mu_2}
\cdots
{L^{\alpha_n}}_{\mu_n}
C_{AB}^{\mu_1\mu_2\cdots\mu_n}(t,t')
\label{tensor transformation}
\end{align}
to switch to the commutator/anticommutator representation,
\begin{align}
C_{AB}^{\alpha_1\alpha_2\cdots\alpha_n}(t,t')
&=
C_{[A,B]_{\alpha_1}[A,B]_{\alpha_2}\cdots[A,B]_{\alpha_n}}(t,t')
\notag
\\
&=
{\rm Tr}\left(
\prod_{i=1}^n \hat\rho^{\frac{1}{n}}
[\hat A(t),\hat B(t')]_{\alpha_i}
\right),
\label{n-partite OTOC2}
\end{align}
with $\alpha_1,\alpha_2,\dots,\alpha_n=\pm$.
The transformation (\ref{tensor transformation}) is a higher-order generalization
of Eq.~(\ref{matrix transformation}). There are redundancies in the definitions (\ref{n-partite OTOC}) and (\ref{n-partite OTOC2}),
$C_{AB}^{\mu_1\mu_2\cdots\mu_n}(t,t')=C_{AB}^{\mu_n\mu_1\cdots\mu_{n-1}}(t,t')$ and
$C_{AB}^{\alpha_1\alpha_2\cdots\alpha_n}(t,t')=C_{AB}^{\alpha_n\alpha_1\cdots\alpha_{n-1}}(t,t')$,
due to the cyclic invariance of the trace.
In the same way as for $n=2$ [Eq.~(\ref{reciprocal relation})], we can prove (see Appendix \ref{appendix})
\begin{align}
C_{(BA)^n}(\omega)
&=
e^{\frac{\beta\hbar\omega}{n}}C_{(AB)^n}(-\omega)
\label{reciprocal relation n}
\end{align}
for arbitrary $n=1,2,3,\dots$. To rewrite the equality (\ref{reciprocal relation n}) in the form of the FDT,
we carry out (anti)symmetrization like Eqs.~(\ref{FDT left}) and (\ref{FDT right}),
\begin{align}
&
C_{(\{A,B\}+[A,B])^n}(\omega)\pm C_{(\{A,B\}-[A,B])^n}(\omega)
\notag
\\
&\qquad=
2^n[C_{(AB)^n}(\omega)\pm C_{(BA)^n}(-\omega)]
\notag
\\
&\qquad=
2^n(1\pm e^{-\frac{\beta\hbar\omega}{n}})C_{(AB)^n}(\omega).
\label{symmetrized n}
\end{align}
By taking the ratio of both sides of Eq.~(\ref{symmetrized n}) between the ones with $+$ and $-$ signs
and explicitly expanding $(\{A,B\}\pm [A,B])^n$, we arrive at
\begin{align}
&
\sum_{\alpha_1,\alpha_2,\dots,\alpha_n=\pm}^{\alpha_1\alpha_2\cdots\alpha_n=+}
C_{AB}^{\alpha_1\alpha_2\cdots\alpha_n}(\omega)
\notag
\\
&\qquad\qquad
=
\coth\left(\frac{\beta\hbar\omega}{2n}\right)
\sum_{\alpha_1,\alpha_2,\dots,\alpha_n=\pm}^{\alpha_1\alpha_2\cdots\alpha_n=-}
C_{AB}^{\alpha_1\alpha_2\cdots\alpha_n}(\omega).
\label{FDT n}
\end{align}
Equation (\ref{FDT n}) is the $n$th-order generalization of the out-of-time-order FDT.
The right-hand side of Eq.~(\ref{FDT n}) can be expressed in the form of a canonical correlation,
similarly to Eq.~(\ref{FDT2 Phi}).
We define an $n$-partite canonical OTOC as
\begin{align}
\Phi_{(AB)^n}(t,t')
&\equiv
\int_0^1 d\lambda {\rm Tr}\left[\left(
\hat\rho^{\frac{1-\lambda}{n}}\hat A(t)
\hat\rho^{\frac{\lambda}{n}}\hat B(t')
\right)^n\right].
\end{align}
Following the same calculation as for $n=2$, we can prove (see Appendix \ref{appendix})
\begin{align}
\sum_{\alpha_1,\alpha_2,\dots,\alpha_n=\pm}^{\alpha_1\alpha_2\cdots\alpha_n=+}
C_{AB}^{\alpha_1\alpha_2\cdots\alpha_n}(\omega)
&=
\frac{2^{n-1}}{n}\beta\hbar\omega\coth\left(\frac{\beta\hbar\omega}{2n}\right)
\Phi_{(AB)^n}(\omega).
\label{FDT n Phi}
\end{align}
In this way, we have obtained infinitely many rigorous equalities [(\ref{FDT n}) and (\ref{FDT n Phi})] for OTOCs.
The classical limit of Eq.~(\ref{FDT n}) formally becomes
\begin{align}
\partial_t \langle\!\langle A(t)^n B(t')^n\rangle\!\rangle
&=
k_BT \langle\!\langle \{A(t)^n,B(t')^n\}_P\rangle\!\rangle,
\label{classical limit n}
\end{align}
which corresponds to that of the conventional FDT (\ref{FDT}) with $A(t)$ and $B(t)$ replaced
by $A(t)^n$ and $B(t)^n$, respectively.
The other generalization is that the FDT holds not only for OTOCs in the form
of ${\rm Tr}(\hat\rho^{\frac{1}{2}}\hat A(t)\hat B(t')\hat\rho^{\frac{1}{2}}\hat A(t)\hat B(t'))$
but also in the form of
${\rm Tr}(\hat\rho^{\frac{1-\gamma}{2}}\hat A(t)\hat\rho^{\frac{\gamma}{2}}\hat B(t')\hat\rho^{\frac{1-\gamma}{2}}\hat A(t)\hat\rho^{\frac{\gamma}{2}}\hat B(t'))$, i.e., the operator ordering is rearranged.
For usual time-ordered correlators, this type of rearrangement of operator ordering shows up in the context of
the generalized covariance \cite{Petz2002,Gibilisco2009}
defined by
\begin{align}
C_{AB}^f(t,t')
&\equiv
{\rm Tr}\left(\hat A(t)\bm K_{\hat\rho}^f[\hat B(t')]\right),
\label{GC}
\end{align}
where $\bm K_{\hat\rho}^f \equiv f(\bm L_{\hat\rho}\bm R_{\hat\rho}^{-1})\bm R_{\hat\rho}$
is a super-operator, $\bm R_{\hat\rho}$ ($\bm L_{\hat\rho}$) denotes
an operation of multiplying $\hat\rho$ from the right-hand side (left-hand side),
and $f(x)$ is an operator monotone function satisfying $0\leqslant\hat A\leqslant\hat B\Rightarrow f(\hat A)\leqslant f(\hat B)$.
Equation (\ref{GC}) generalizes the classical covariance for two observables
that do not necessarily commute with $\hat\rho$.
The generalized covariance has played a key role
in estimation theory involving the quantum Fisher information \cite{Helstrom1967,YuenLax1973,Petz1996}.
The conventional FDT (\ref{FDT}) has recently been generalized to \cite{ShitaraUeda2015}
\begin{align}
C_{AB}^f(\omega)
&=
\beta\hbar\omega\frac{f(e^{-\beta\hbar\omega})}{1-e^{-\beta\hbar\omega}}\Phi_{AB}(\omega),
\label{FDT GC}
\end{align}
which provides a means to measure the generalized covariance through
the response function.
The relation (\ref{FDT Phi}) is a special case of Eq.~(\ref{FDT GC})
with $f(x)=\frac{1+x}{2}$.
With the generalized covariance, the $n$-partite OTOC is generalized in the form of
\begin{align}
C^f_{(AB)^n}(t,t')
&\equiv
{\rm Tr}\left( \left[\hat A(t)\bm K_{\hat\rho^{1/n}}^f[\hat B(t')]\right]^n\right).
\label{GC OTOC}
\end{align}
In particular, if we take $f(x)=x^\gamma$ with $0\leqslant \gamma \leqslant 1$,
then Eq.~(\ref{GC OTOC}) reads
\begin{align}
C^f_{(AB)^n}(t,t')
=
C^\gamma_{(AB)^n}(t,t')
=
{\rm Tr}\left(
\left[\hat A(t)\hat\rho^{\frac{\gamma}{n}}\hat B(t')\hat\rho^{\frac{1-\gamma}{n}}
\right]^n\right).
\end{align}
Following similar calculations used in deriving Eqs.~\eqref{reciprocal relation n} and \eqref{FDT n},
we can prove (see Appendix \ref{appendix})
\begin{align}
C^\gamma_{(BA)^n}(\omega)
&=
e^{\frac{1-2\gamma}{n}\beta\hbar\omega}
C^\gamma_{(AB)^n}(-\omega),
\label{reciprocal GC}
\end{align}
which reduces to Eq.~\eqref{reciprocal relation n} for $\gamma=0$
and leads to a generalized out-of-time-order FDT,
\begin{widetext}
\begin{align}
\sum_{\alpha_1,\alpha_2,\dots,\alpha_n=\pm}^{\alpha_1\alpha_2\cdots\alpha_n=+}
C_{AB}^{\gamma,\alpha_1\alpha_2\cdots\alpha_n}(\omega)
&=
\coth\left((1-2\gamma)\frac{\beta\hbar\omega}{2n}\right)
\sum_{\alpha_1,\alpha_2,\dots,\alpha_n=\pm}^{\alpha_1\alpha_2\cdots\alpha_n=-}
C_{AB}^{\gamma,\alpha_1\alpha_2\cdots\alpha_n}(\omega)
\label{GC FDT n}
\\
&\quad=
\frac{2^{n-1}}{n}\beta\hbar\omega \coth\left((1-2\gamma)\frac{\beta\hbar\omega}{2n}\right)
\Phi_{(AB)^n}^\gamma(\omega).
\label{GC FDT n Phi}
\end{align}
\end{widetext}
Here we define
\begin{align}
&
C_{AB}^{\gamma,\alpha_1\alpha_2\cdots\alpha_n}(t,t')
\notag
\\
&\equiv
{\rm Tr}\left(
\prod_{i=1}^n \left[
\hat A(t)\hat\rho^{\frac{\gamma}{n}}\hat B(t')\hat\rho^{\frac{1-\gamma}{n}}
+\alpha_i\hat B(t')\hat\rho^{\frac{\gamma}{n}}\hat A(t)\hat\rho^{\frac{1-\gamma}{n}}
\right]
\right),
\\
&
\Phi_{(AB)^n}^\gamma(t,t')
\equiv
\int_{\gamma}^{1-\gamma} d\lambda {\rm Tr}\left[\left(
\hat\rho^{\frac{1-\lambda}{n}}\hat A(t)
\hat\rho^{\frac{\lambda}{n}}\hat B(t')
\right)^n\right].
\label{Phi n gamma t}
\end{align}
The equality (\ref{GC FDT n}) is the most general form of the out-of-time-order FDT derived in this paper,
which includes Eqs.~(\ref{FDT2}) and (\ref{FDT n}) as special cases.
Let us remark that for $f(x)=x^\gamma$ to be operator monotone we need $0\leqslant \gamma \leqslant 1$.
However, the equalities (\ref{reciprocal GC}), (\ref{GC FDT n}), and (\ref{GC FDT n Phi}) hold for arbitrary $\gamma\in\mathbb R$.
\section{Conclusion}
\label{conclusion}
In conclusion, we have found the generalized fluctuation-dissipation theorem [Eqs.~(\ref{FDT2}) and (\ref{FDT2 Phi})]
for bipartite out-of-time-ordered correlation functions [Eq.~(\ref{bipartite OTOC})].
The theorem describes the general relationship between chaotic behavior in quantum systems and a nonlinear response.
The difference between the bipartite and
physical OTOCs is characterized by the Wigner-Yanase skew information
[Eqs.~(\ref{difference1})-(\ref{difference3})], which quantifies the information contents involved
in the corresponding quantum fluctuations. We have further extended the theorem to
$n$-partite OTOCs [Eqs.~(\ref{FDT n}) and (\ref{FDT n Phi})]
and in the form of the generalized covariance [Eqs.~(\ref{GC FDT n}) and (\ref{GC FDT n Phi})].
Our results bring up various interesting open questions
such as the physical meaning of the higher-order out-of-time-order FDTs ($n\geqslant 3$)
that are expected to be related to higher-order response functions
and the relation to the fluctuation theorem \cite{EvansCohenMorriss1993,EvansSearles1994}
(see also Ref.~\cite{YungerHalpern2017}), which merit further study.
\acknowledgements
N.T. is supported by JSPS KAKENHI Grant No. JP16K17729.
T.S. acknowledges support from Grant-in-Aid for JSPS Fellows (KAKENHI Grant No. JP16J06936) and the Advanced Leading Graduate Course for Photon Science (ALPS) of JSPS.
M.U. acknowledges support by KAKENHI Grant No. JP26287088 and KAKENHI Grant No. JP15H05855.
\begin{widetext}
| {
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Home/Covid/Pfizer seeks to vaccinate children between 5 and 11 years old against COVID-19
CovidHealth
Pfizer seeks to vaccinate children between 5 and 11 years old against COVID-19
Lolita M. PyronOctober 8, 2021
Pharmaceutical Pfizer requested permission from the United States government to use its COVID-19 vaccine in children between 5 and 11 years old, and if the regulators agree, the injections would begin to be applied in a matter of weeks.
Many parents and pediatricians have asked authorities for protection against coronavirus for children under 12 years of age, the current cap on the vaccine from Pfizer and its German partner BioNTech. Not only can minors sometimes become seriously ill, but keeping them in schools can be challenging with the virus still intense in communities with low vaccination rates.
Pfizer announced in a tweet that it had formally submitted its application to the US Food and Drug Administration (FDA).
Now the FDA will have to decide whether there is sufficient evidence that vaccines are as safe and effective in young children as they are in adolescents and adults. An independent panel of experts will publicly debate the evidence on October 26.
According to Pfizer, their studies show that young children should receive the third dose that is currently applied to the rest of the population. After the second dose, children between the ages of five and 11 developed levels of antibodies against COVID-19 as strong as those obtained by adolescents and young adults in injections of normal strength.
Although children have a lower risk of becoming seriously ill or dying from coronavirus than older people, COVID-19 can kill minors, and infections in young children have skyrocketed as the extra-contagious delta variant spreads across the country
"I'm glad I'm helping other kids get the vaccine," said Sebastian Prybol, eight, of Raleigh, North Carolina. He is participating in the Pfizer study at Duke University and it is still unknown whether he received the vaccine or a placebo.
"We want to make sure it is absolutely safe for them," said Sebastian's mother, Britni Prybol, adding that she will be "more than happy" if the FDA clears the vaccine.
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Luxe Keto ACV Gummies – Lose Weight Quick & Forever, Everything You Need to Know! | {
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Q: Prove that a subset is a finitely generated subring Consider $\mathbb{A}^2$ with $\rho : (x, y) \mapsto (-x, -y)$. Can anyone help me prove that $S = \{f \in \mathbb{C}[x, y] : f \circ \rho = f\}$ is a finitely generated subring? Also, can $S$ be realized as the coordinate ring of some affine variety $V$, and is there a morphism $\mathbb{A}^2 \to V$?
This is what I have so far: The ring $\mathbb{C}[x, y]$ can be viewed as a $\mathbb{C}$-vector space with basis $1, x, y, x^2, xy, y^2, \ldots$ and $\rho^{\ast} : f \to f \circ \rho$ can be viewed as a $\mathbb{C}$-linear map. The generalized eigenvector of the eigenvalue $\lambda \in \mathbb{C}$ is $v \in \mathbb{C}[x, y]$ such that $(\rho^{\ast} - \lambda I)^{m}(v) = 0$ for some integer $m \geq 1$. Suppose $f \circ \rho \to f$. Then $\rho^{\ast}$ is an endomorphism with the minimal polynomial $(x - \lambda_1)^{m_1} \cdots (x - \lambda_n)^{m_n}$, where $\lambda_1, \ldots, \lambda_n$ are district eigenvalues, and $\mathbb{C}[x, y]$ is the direct sum of its generalized eigenspaces: $\mathbb{C}[x,y] = \mathbb{C}[x,y](\lambda_1) \bigoplus \cdots \bigoplus \mathbb{C}[x,y](\lambda_n)$. Moreover, $\mathbb{C}[x,y](\lambda_i) = \ker(\rho^{\ast} - \lambda_i I)^{m_i}$. Because $\mathbb{C}$ is noetherian, $\mathbb{C}[x, y]$ is noetherian by Hilbert's basis theorem, so all ideals in $\mathbb{C}[x, y]$ are finitely generated. Furthermore, the kernel of a ring homomorphism is an ideal, so the generalized eigenspaces are ideals because endomorphisms are homomorphisms. Consequently, they are finitely generated as subrings because ideals are subrings. Since ideals are modules and any finite direct sum of noetherian modules is noetherian, $S$ is noetherian and so it must finitely generated.
A: This is a special case of finding the ring of invariants of a group action. Here the group is $G = \mathbb{Z}/2\mathbb{Z} = \{1, \sigma\}$ acting on $\mathbb{C}[x,y]$ by $\sigma(x) = -x$, $\sigma(y) = -y$, extended $k$-linearly. The subring $S$ of interest is then $\mathbb{C}[x,y]^G = \{f \in \mathbb{C}[x,y] \mid \sigma(f) = f\}$.
To generate the ring of invariants $S$, we can start by listing obvious invariants. In this case $x^2, xy, y^2$ are invariant, which gives $k[x^2,xy,y^2] \subseteq S$. In fact equality holds: note that $k[x^2,xy,y^2]$ is the subring of $k[x,y]$ consisting of polynomials all of whose terms have even degree. For any $f \in S$, we can write $f = g + h$ with $g \in k[x^2,xy,y^2]$, and every term of $h$ has odd degree. Then $h$ is invariant, which forces $h = 0$ (this works as long as the characteristic of the base field is $\ne 2$).
More generally, the ring of invariants of an affine ring (the coordinate ring of an affine variety) under a finite group action is always finitely generated, by a result of Emmy Noether (one of many in commutative algebra!).
This particular ring $S$ can be realized as an affine ring: namely $S \cong k[u,v,w]/(uw-v^2)$, via $u \mapsto x^2$, $v \mapsto xy$, $w \mapsto y^2$. This is a cone $V = V(uw-v^2) \subseteq \mathbb{A}^3$, and the inclusion $k[x^2,xy,y^2] \subseteq k[x,y]$ gives a dominant map (in fact a quotient map) $\mathbb{A}^2 \to V = \mathbb{A}^2/G$.
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You've just received an official judicial court summons. You've been struggling for months to catch up with your bills, and you have fallen behind on your mortgage payments. You feel like you are drowning in debts, interest and late fees, and now you are about to lose your home. Could circumstances be any worse?
South Carolina is what is known as a "judicial foreclosure state." That means that your mortgage lender is required under law to sue you in court to prove that they are entitled to foreclose on you. This actually is a good thing, because it means you are entitled to defend yourself before a judge.
The problem of course is that you are just one person, and the bank has tremendous resources and experience on their side. Banks foreclose unfairly on customers every single day. The reason that banks tend to win these cases isn't always because they are right—often it is because homeowners lacks the legal resources, experience, and legal know-how to fight back.
Do I have to pay a fee to defend myself in court?
A No. The lender is the plaintiff in the case and is responsible for paying the $150 filing fee.
Can filing for bankruptcy halt proceedings and save my home?
A Chapter 13 bankruptcy is an ideal option for many homeowners in default. This type of bankruptcy puts you under a reorganization plan which allows you to catch up on your mortgage and other bills, and does put a stop on your foreclosure. Chapter 7 bankruptcy includes a brief automatic stay which can delay proceedings for two to three months, and may be a good option if your situation is temporary and you know you could catch up quickly given a chance.
A You are innocent until proven guilty. In South Carolina, your lender must prove that you are actually behind on payments to foreclose on you. If we can prove that you have been subjected to unfair practices which infringe on your legal rights as a homeowner, we have a chance at stopping the foreclosure.
If you have received your judicial court summons, you are facing the decisive moment in your foreclosure crisis. This is the moment when the state will decide whether your bank has the legal right to eject you from your home. Without the defense of a passionate, experienced foreclosure lawyer, most of these cases are decided against the homeowner and in favor of the lender.
You owe it to yourself and your family to give yourself the best possible chance. We have saved numerous clients in your situation from losing their homes, and will fight aggressively on your behalf to protect your rights and the life you have built. Fill out the contact form below to book your FREE consultation. It is not too late to save your home from foreclosure! | {
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{"url":"https:\/\/en.m.wikipedia.org\/wiki\/Femtosecond","text":"# Femtosecond\n\nA femtosecond is a unit of time in the International System of Units (SI) equal to 10-15 or 11 000 000 000 000 000 of a second; that is, one quadrillionth, or one millionth of one billionth, of a second.[1] For context, a femtosecond is to a second as a second is to about 31.71 million years; a ray of light travels approximately 0.3\u00a0\u03bcm (micrometers) in 1 femtosecond, a distance comparable to the diameter of a virus.[2]\n\nThe word femtosecond is formed by the SI prefix femto and the SI unit second. Its symbol is fs.[3]\n\nA femtosecond is equal to 1000 attoseconds, or 1\/1000 picosecond. Because the next higher SI unit is 1000 times larger, times of 10\u221214 and 10\u221213 seconds are typically expressed as tens or hundreds of femtoseconds.\n\n\u2022 Typical time steps for molecular dynamics simulations are on the order of 1\u00a0fs.[4]\n\u2022 The periods of the waves of visible light have a duration of about 2 femtoseconds. ${\\displaystyle {\\lambda \\over {c}}={600\\times 10^{-9}~{\\rm {m}} \\over 3\\times 10^{8}~{\\rm {m}}~{\\rm {s}}^{-1}}=2.0\\times 10^{-15}~{\\rm {s}}}$ The precise duration depends on the energy of the photons, which determines their color. (See wave\u2013particle duality.) This time can be calculated by dividing the wavelength of the light by the speed of light (approximately 3\u00d7108\u00a0m\/s) to determine the time required for light to travel that distance.[5]\nThe colors of the visible light spectrum[6]\nColor Wavelength\ninterval\nCycle time\ninterval\nRed ~ 700\u2013635\u00a0nm ~ 2.3\u20132.1\u00a0fs\nOrange ~ 635\u2013590\u00a0nm ~ 2.1-2.0\u00a0fs\nYellow ~ 590\u2013560\u00a0nm ~ 2.0-1.9\u00a0fs\nGreen ~ 560\u2013520\u00a0nm ~ 1.9-1.7\u00a0fs\nCyan ~ 520\u2013490\u00a0nm ~ 1.7-1.6\u00a0fs\nBlue ~ 490\u2013450\u00a0nm ~ 1.6-1.5\u00a0fs\nViolet ~ 450\u2013400\u00a0nm ~ 1.5-1.3\u00a0fs\n\n## Examples\n\n\u2022 46\u00a0fs \u2013 the swiftest chemical reaction known (radiolysis of water leads to the formation of a H2O+ ion, which rapidly reacts to become hydronium (H3O+) and a short lived hydrogen monoxide molecule (OH))[7]\n\u2022 200\u00a0fs \u2013 the average chemical reaction, such as the reaction of pigments in an eye to light[5]\n\u2022 300\u00a0fs \u2013 the duration of a vibration of the atoms in an iodine molecule[8]\n\n## References\n\n1. ^ \"Femtosecond: Merriam Webster definition\". Merriam Webster Online Dictionary.\n2. ^ Compared with overview in: Fisher, Bruce; Harvey, Richard P.; Champe, Pamela C. (2007). Lippincott's Illustrated Reviews: Microbiology (Lippincott's Illustrated Reviews Series). Hagerstown, MD: Lippincott Williams & Wilkins. ISBN\u00a0978-0-7817-8215-9. Page 3\n3. ^\n4. ^ \"Femtosecond: use in molecular dynamics simulation\". LAMMPS Molecular Simulator.\n5. ^ a b Andrew M. Weiner (2009). Ultrafast Optics. Wiley. ISBN\u00a0978-0-471-41539-8.\n6. ^ Craig F. Bohren (2006). Fundamentals of Atmospheric Radiation: An Introduction with 400 Problems. Wiley-VCH. p.\u00a0214. Bibcode:2006fari.book.....B. ISBN\u00a0978-3-527-40503-9.\n7. ^ Loh, Z.-H.; Doumy, G.; Arnold, C.; Kjellsson, L.; Southworth, S. H.; Al Haddad, A.; Kumagai, Y.; Tu, M.-F.; Ho, P. J.; March, A. M.; Schaller, R. D.; Bin Mohd Yusof, M. S.; Debnath, T.; Simon, M.; Welsch, R. (2020-01-10). \"Observation of the fastest chemical processes in the radiolysis of water\". Science. 367 (6474): 179\u2013182. doi:10.1126\/science.aaz4740. ISSN\u00a00036-8075.\n8. ^ Abbi, S. C. (2001). Nonlinear Optics and Laser Spectroscopy. United States of America: Alpha Science Int'l Ltd. p.\u00a0361. ISBN\u00a08173193541.","date":"2023-02-01 13:17:27","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 1, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7599732279777527, \"perplexity\": 6981.842923884219}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764499934.48\/warc\/CC-MAIN-20230201112816-20230201142816-00822.warc.gz\"}"} | null | null |
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The Mississippi 8 Conference (M8) is a high school athletic and activities conference in the Twin Cities area in Central Minnesota with 8 member high schools. The conference derives its name from 6 of the original 8 member schools being located within 10 miles from the Mississippi River.
History
The M8 was formed in 2004 with eight charter members: Becker, Big Lake, Buffalo, Cambridge-Isanti, Monticello, Princeton, Rogers and St. Michael-Albertville (STMA), and began play in the 2005-2006 school year. Zimmerman High School was added to the conference in 2008.
Elk River High School entered the M8 as a competitor in the sport of football in 2010 and Duluth East and Duluth Denfeld High Schools joined the conference for football in the fall of 2012. St. Francis, Chisago Lakes Area, and North Branch Area High School began competing in the Mississippi 8 Conference during 2013-14 school year.
Princeton School District and Zimmerman High School voted to withdraw their participation from the Mississippi 8 in favor of a new conference, Granite Ridge Conference, for the 2011 school year. Becker School District, and Elk River High School left the conference in 2012, Becker joined the Granite Ridge Conference, and Elk River High School football rejoined the Northwest Suburban Conference. In the 2013-14 school year, Princeton rejoined the M8. In 2018 STMA and Buffalo decided to leave the conference and were placed in the Lake Conference by the MSHSL and Rogers decided to leave for the Northwest Suburban Conference beginning in the Fall of 2019. Becker High School rejoined the conference in 2019 bringing the total number of schools back to 8.
Members
The conference currently consists of 8 member schools.
Former Members
Fall Sports
Cross Country
* No longer a member
The inaugural Cross Country Championship meet was held at Pebble Creek Golf Course in Becker. The 2006 meet was held at Liberty Elementary in Big Lake. The 2007 and 2014 meets were held at Buffalo Heights Golf Course. In 2008 the meet was held at Grandy 9 Golf Course in Cambridge. The 2009 and 2017 meets were hosted my Monticello at Vintage Golf Course and Lake Bertram Regional Park, respectively. 2010 meet was at the Princeton Golf Course. In 2011 Rogers hosted the meet at Fox Hollow Golf Course. The 2012 conference meet was held at St. Michael Rec Center. In 2013 and 2019 the meet was held at Ponds Golf Course and was hosted by St. Francis. In 2015 the meet was held at Isanti Middle School. Ki-Chi-Soga Park in Lindstrom was home to the 2016 meet.
Football
c = Co-champions
After the 2014 football season schools in the state of Minnesota were placed into one of 18 districts. The purpose of the changes was to reduce scheduling headaches for several schools. All of the schools in the Mississippi 8 Conference were placed into the North Central District for the 2015 season. Prior to the 2017 season STMA was reclassified to 6A, as a result the school plays in the Metro District and North Branch was moved to the Northeast District. The other schools continue to play in the North Central District.
Soccer
c = Co-champions
* No longer a member
Girls Swimming and Diving
c = Co-champions
* No longer a member
Girls Tennis
c = Co-champions
* No longer a member
Volleyball
c = Co-champions
* No longer a member
Winter Sports
Basketball
c = Co-champions
* No longer a member
Dance
c = Co-champion
* No longer a member
Gymnastics
c = Co-champion
Hockey
c = Co-champions
* No longer a member
Becker and Big Lake are part of the Becker-Big Lake Eagles boys hockey co-op. Monticello is the host school for a boys hockey co-op with Maple Lake High School and goes by the nickname of Moose for hockey instead of the primary school nickname Magic.
Monticello advanced to the Class A state tournament in hockey in 2017, 2018, 2020 and 2022 and made it to the Class A state title game in 2017. No other Mississippi 8 conference member has advanced further in boys hockey. Princeton has made the boys state tournament, competing three times in 2002, 2003, 2016. Chisago Lakes has also made the boys state tournament twice while North Branch and Cambridge-Isanti have both made it once.
* No longer a member
The North Wright County co-op that includes Monticello has reached the girls state tournament twice in 2011 and 2013. The Wright County co-op consisting of all the school in the current Buffalo and North Wright County co-ops made the state tournament in 2005. Chisago Lakes has also made the girls state tournament three times, once in 2004 as part of a co-op with Pine City and in 2010 and 2012.
Boys Swimming and Diving
* No longer a member
Wrestling
* No longer a member
Spring Sports
Baseball
* No longer a member
Golf
* No longer a member
* No longer a member
Softball
c = Co-champions
* No longer a member
Boys Tennis
c = Co-champions
* No longer a member
Track and Field
* No longer a member
References
External links
Minneapolis Star Tribune: Two Duluth schools placed in Mississippi 8 Conference
Monticello Times: Mississippi 8 Conference in flux as two schools split
Mississippi 8 Conference website
Star News: Elks to move into Mississippi 8
Minneapolis Star Tribune: A closer look at: Mississippi 8 Conference
Pioneer Press: Chisago Lakes delays decision on Mississippi 8 Conference invitation
Minnesota high school sports conferences | {
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// JSNumericFunctions.java
package ed.js;
import ed.js.e4x.*;
import ed.util.StringParseUtil;
/** @expose
*/
public class JSNumericFunctions extends JSObjectBase {
static {
JS._debugSIStart( "JSNumericFunctions" );
}
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| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,173 |
\section{Introduction}
In our recent paper~\cite{Wenbiao3}, $P-V$ criticality of topological AdS black holes in Lovelock-Born-Infeld gravity has been investigated in the extended phase space and some unique phenomena have been found. It was shown that $P-V$ criticality exists not only for the spherical topology but also for $k=-1$. This result is really intriguing that it has attracted further investigation~\cite{Belhaj95}-~\cite{Dolan99}. On the other hand, it would also be interesting to probe this issue in the non-extended phase space to search for some more unique characteristics due to Lovelock gravity. Lovelock gravity~\cite{Lovelock} is a particular higher curvature gravity theory which successfully solves the problem of fourth order field equations and ghost. In Lovelock gravity, the field equation is only second order and the quantization is free of ghosts~\cite{Boulware}. Both the black holes and their thermodynamics in Lovelock gravity~\cite{Dehghani1}-\cite{Amirabi} have attracted considerable attention. Concerning the thermodynamics of Lovelock black holes in the non-extended phase space, some efforts have been made. Topological black hole solutions in Lovelock-Born-Infeld gravity were proposed in Ref.~\cite{Dehghani1}. Both the thermodynamics of asymptotically AdS rotating black branes with flat horizon and asymptotically flat black holes for $k=1$ were detailedly investigated there. For charged topological AdS black holes, Ref.~\cite{Dehghani1} presented the expression of the temperature. Ref.~\cite{Decheng4,Decheng2} further studied their entropy and specific heat at constant charge. Ref.~\cite{Lala2} studied their specific heat and critical exponents in the canonical ensemble. The above research was carried out in the canonical ensemble, leaving the grand canonical ensemble unexplored. In this paper, we would like to complete the phase transition research of Lovelock charged topological AdS black holes in the grand canonical ensemble.
In traditional thermodynamics, one can utilize Clausius-Clapeyron-Ehrenfest's equations to probe the nature of phase transitions. The Clausius-Clapeyron
equation holds for a first order phase transition while Ehrenfest's equations are satisfied for a second order phase transition. Recently, Banerjee et al. introduced a novel Ehrenfest scheme to investigate phase transitions of black holes in the grand canonical ensemble~\cite{Banerjee1}-\cite{Banerjee6}. We utilized this scheme in the case of charged topological black hole in Ho\v{r}ava-Lifshitz gravity~\cite{Wenbiao2} and also generalized it to the extended phase space~\cite{Wenbiao1}-\cite{Wenbiao4}. Ref.~\cite{Jiliangjing} further generalized it to the full phase space. The original Ehrenfest equations in traditional thermodynamics were utilized in the extended space of black holes in Lovelock-Born-Infeld gravity to study the nature of phase transition at the critical point~\cite{Belhaj95}. However, in this paper, we would like to utilize the analog form of Ehrenfest scheme proposed by Banerjee et al. to investigate the nature of phase transition points of Lovelock AdS black holes in the grand canonical ensemble.
Different from the traditional thermodynamic method, thermodynamic geometry has served as an alternative way to investigate phase transitions of black holes. The well-known examples are Weinhold geometry~\cite{Weinhold} and Ruppeiner geometry~\cite{Ruppeiner}. Weinhold defined metric structure in the energy representation as $g_{i,j}^{W}=\partial_{i}\partial_{j}M(U,N^a)$. Here, $U$ is the internal energy $U$ while $N^a$ represents the extensive thermodynamic variables. Ruppeiner proposed metric structure as the Hessian of the entropy. Namely, $g_{i,j}^{R}=-\partial_{i}\partial_{j}S(U,N^a)$. Recently, Quevedo et al. \cite{Quevedo2} proposed another thermodynamic geometry method named as geometrothermodynamics (GTD). For its profound physical meaning, Ruppeiner's metric has been applied to investigate various thermodynamic systems including black holes. For a nice review of Ruppeiner geometry, see Ref.~\cite{Ruppeiner2}. For recent papers, see Ref.~\cite{Tharanath}-~\cite{Niu}. However, thermodynamic geometry of Lovelock AdS black holes in the grand canonical ensemble is still absent in literature. In this paper, we would like to explore the Ruppeiner geometry of $(n+1)$-dimensional topological AdS black holes in Lovelock gravity in the grand canonical ensemble .
In Sec. \ref{Sec2}, the thermodynamics of charged topological AdS black holes in Lovelock-Born-Infeld gravity will be briefly reviewed and the phase transition in the grand canonical ensemble will be investigated in detail. To probe the nature of phase transition in the grand canonical ensemble, an analytic check of the analog form of Ehrenfest equations will be carried out in Sec. \ref{Sec3}. In Sec. \ref{Sec4}, thermodynamic geometry will be studied to examine the phase structure of topological AdS black holes. Concluding remarks will be presented in Sec. \ref {Sec5}.
\section{Phase transition in the grand canonical ensemble}
\label{Sec2}
The action of third order Lovelock-Born-Infeld gravity reads\cite{Dehghani1}
\begin{equation}
I_{G}=\frac{1}{16\pi}\int d^{n+1}x\sqrt{-g}\big(-2\Lambda+\mathcal{L}_1+\alpha_2\mathcal{L}_2+\alpha_3\mathcal{L}_3+L(F)\big),\label{1}
\end{equation
where
\begin{eqnarray}
\mathcal{L}_1&=&R,\label{2}
\\
\mathcal{L}_2&=&R_{\mu\nu\gamma\delta}R^{\mu\nu\gamma\delta}-4R_{\mu\nu}R^{\mu\nu}+R^2, \label{3}
\\
\mathcal{L}_3&=&2R^{\mu\nu\sigma\kappa}R_{\sigma\kappa\rho\tau}R^{\rho\tau}_{\;\;\;\;\mu\nu}+8R^{\mu\nu}_{\;\;\;\;\sigma\rho}R^{\sigma\kappa}_{\;\;\;\;\nu\tau}R^{\rho\tau}_{\;\;\;\;\mu\kappa}+24R^{\mu\nu\sigma\kappa}R_{\sigma\kappa\nu\rho}R^{\rho}_{\;\;\mu} \nonumber
\\
&\,&+3RR^{\mu\nu\sigma\kappa}R_{\sigma\kappa\mu\nu}+24R^{\mu\nu\sigma\kappa}R_{\sigma\mu}R_{\kappa\nu}+16R^{\mu\nu}R_{\nu\sigma}R^{\sigma}_{\;\;\mu}-12RR^{\mu\nu}R_{\mu\nu}+R^3,\label{4}
\\
L(F)&=&4\beta^2\left(1-\sqrt{1+\frac{F^2}{2\beta^2}}\right). \label{5}
\end{eqnarray
$\beta$, $\alpha_2$ and $\alpha_3$ are Born-Infeld parameter, the second and third order Lovelock coefficients respectively. $L(F)$ denotes the Born-Infeld Lagrangian with $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$, where $A_\mu$ is electromagnetic vector. The $(n+1)$-dimensional static solution was derived in Ref.~\cite{Dehghani1} as
\begin{equation}
ds^2=-f(r)dt^2+\frac{dr^2}{f(r)}+r^2d\Omega^2, \label{6}
\end{equation
where
\begin{eqnarray}
f(r)&=&k+\frac{r^2}{\alpha}(1-g(r)^{1/3}),\label{7}\\
g(r)&=&1+\frac{3\alpha m}{r^n}-\frac{12\alpha \beta^2}{n(n-1)}\Big[1-\sqrt{1+\eta}-\frac{\Lambda}{2\beta^2}+\frac{(n-1)\eta}{(n-2)}\digamma(\eta)\Big].\label{8}
\end{eqnarray
$k$ and $m$ are parameters related to the curvature of hypersurface and the mass respectively. $d\Omega^2$ denotes the line element of $(n-1)$-dimensional hypersurface with constant curvature $(n-1)(n-2)k$ and $\digamma(\eta)$ denotes the hypergeometric function as follow
\begin{equation}
\digamma(\eta)=\,_2F_1\Big(\Big[\frac{1}{2},\frac{n-2}{2n-2}\Big],\Big[\frac{3n-4}{2n-2}\Big],-\eta\Big), \label{9}
\end{equation
where
\begin{equation}
\eta=\frac{(n-1)(n-2)q^2}{2\beta^2r^{2n-2}}. \label{10}
\end{equation
Note that the above solution was derived for the special case that
\begin{eqnarray}
\alpha_2&=&\frac{\alpha}{(n-2)(n-3)}, \label{11}
\\
\alpha_3&=&\frac{\alpha^2}{72{n-2\choose 4}}.\label{12}
\end{eqnarray
When $\beta\rightarrow\infty$, the Born-Infeld Lagrangian reduces to the Maxwell form and the solutions become Lovelock AdS black holes. To concentrate on the effects of the third order Lovelock gravity, we will mainly consider Lovelock AdS black holes in this paper.
When $\beta\rightarrow\infty$, one can obtain
\begin{equation}
g(r)\rightarrow1+\frac{3\alpha m}{r^n}+\frac{6\alpha \Lambda}{n(n-1)}-\frac{3\alpha q^2}{r^{2n-2}}.\label{13}
\end{equation
The horizon radius $r_+$ can be derived from the largest root of the equation $f(r)=0$. One can express $m$ in the function of $r_+$ as
\begin{equation}
m=\frac{3n(n-1)q^2r_+^8+r_+^{2n}\left[kn(n-1)(3r_+^4+3kr_+^2\alpha+k^2\alpha^2)-6r_+^6\Lambda\right]}{3n(n-1)r_+^{n+6}}.\label{14}
\end{equation
Then the mass of $(n+1)$-dimensional topological AdS black holes can be derived as
\begin{equation}
M=\frac{(n-1)\Sigma_k}{16\pi}m=\frac{\Sigma_k}{48n\pi r_+^{n+6}}\left\{3n(n-1)q^2r_+^8+r_+^{2n}\left[kn(n-1)(3r_+^4+3kr_+^2\alpha+k^2\alpha^2)-6r_+^6\Lambda\right]\right\},\label{15}
\end{equation
where $\Sigma_k$ denotes the volume of the $(n-1)$-dimensional hypersurface.
The Hawking temperature has been derived in Ref.~\cite{Dehghani1} as
\begin{equation}
T=\frac{(n-1)k[3(n-2)r_+^4+3(n-4)k\alpha r_+^2+(n-6)k^2\alpha^2]+12r_+^6\beta^2(1-\sqrt{1+\eta_+}\,)-6\Lambda r_+^6}{12\pi(n-1)r_+(r_+^2+k\alpha)^2}.\label{16}
\end{equation
Taking the limit $\beta\rightarrow\infty$, Eq. (\ref{16}) reduces to
\begin{equation}
T=\frac{(n-1)k[3(n-2)r_+^4+3(n-4)k\alpha r_+^2+(n-6)k^2\alpha^2]-6\Lambda r_+^6-3(n-2)(n-1)q^2r_+^{8-2n}}{12\pi(n-1)r_+(r_+^2+k\alpha)^2}.\label{17}
\end{equation
In the non-extended phase space, the first law of thermodynamics reads
\begin{equation}
dM=TdS+\Phi dQ.\label{18}
\end{equation
So the entropy can be derived as
\begin{equation}
S=\int^{r_+}_{0}\frac{1}{T}\left(\frac{\partial M}{\partial r_+}\right)dr=\frac{\Sigma_k(n-1)r_+^{n-5}}{4}\left(\frac{r_+^4}{n-1}+\frac{2kr_+^2\alpha}{n-3}+\frac{k^2\alpha^2}{n-5}\right).\label{19}
\end{equation
The above result is derived for $n>5$ while the integration is divergent for $n\leqslant5$.
The charge $Q$ is related to the parameter $q$ by
\begin{equation}
Q=\frac{\Sigma_k}{4\pi}\sqrt{\frac{(n-1)(n-2)}{2}}q.\label{20}
\end{equation
Then the expression of the mass can be reorganized as
\begin{equation}
M=\frac{96n\pi ^2 Q^2r_+^8+r_+^{2n}(n-2)\left[kn(n-1)(3r_+^4+3kr_+^2\alpha+k^2\alpha^2)-6r_+^6\Lambda\right]\Sigma_k^2}{48n(n-2)\pi r_+^{n+6}\Sigma_k}.\label{21}
\end{equation
Utilizing Eqs.~(\ref{18}) and (\ref{21}), the electric potential can be calculated as
\begin{equation}
\Phi=\Big(\frac{\partial M}{\partial Q}\Big)_{S}=\frac{4\pi Q}{(n-2)r_+^{n-2}\Sigma_k}.\label{22}
\end{equation
To study the phase transition in the grand canonical ensemble, it is more convenient to express the mass into the function of the electric potential $\Phi$ as follows
\begin{eqnarray}
M&=&\frac{6n(n-2)^2 \Phi^2r_+^{2n+4}\Sigma_k^3+r_+^{2n}(n-2)\Sigma_k\left[kn(n-1)(3r_+^4+3kr_+^2\alpha+k^2\alpha^2)-6r_+^6\Lambda\right]}{48n(n-2)\pi r_+^{n+6}},\label{23}\\
T&=&\frac{(n-1)k[3(n-2)r_+^4+3(n-4)k\alpha r_+^2+(n-6)k^2\alpha^2]-6\Lambda r_+^6-6(n-2)^2\Phi^2r_+^4}{12\pi(n-1)r_+(r_+^2+k\alpha)^2}.\label{24}
\end{eqnarray
The specific heat at constant electric potential can be obtained as
\begin{equation}
C_{\Phi}=T\Big(\frac{\partial S}{\partial T}\Big)_{\Phi}=\frac{A(r_+,\Phi)}{B(r_+,\Phi)},\label{25}
\end{equation
where
\begin{eqnarray}
A(r_+,\Phi)&=&(n-1)r_+^{n-5}(r_+^2+k\alpha)^3\Sigma_k
\nonumber
\\
&\,&\times\left[3k(n-2)(n-1)r_+^4+3k^2(n-4)(n-1)r_+^2\alpha+k^3(n-6)(n-1)\alpha^2-6r_+^6\Lambda-6(n-2)^2r_+^4\Phi^2\right],\label{26}\\
B(r_+,\Phi)&=&-24\Lambda r_+^8-12\left[k(2+n^2-3n+10\alpha\Lambda)-2(n-2)^2\Phi^2\right]r_+^6+72k\alpha r_+^4\left[k(n-1)-(n-2)^2\Phi^2\right]
\nonumber
\\
&\,&-8k^3(n-9)(n-1)\alpha^2r_+^2-4k^4(n-6)(n-1)\alpha^3.\label{27}
\end{eqnarray
One can easily draw the conclusion that the specific heat at constant electric potential may diverge when
\begin{equation}
B(r_+,\Phi)=0,\label{28}
\end{equation
implying the existence of phase transition.
\begin{figure*}
\centerline{\subfigure[]{\label{1a}
\includegraphics[width=8cm,height=6cm]{1a.eps}}
\subfigure[]{\label{1b}
\includegraphics[width=8cm,height=6cm]{1b.eps}}}
\caption{(a) $C_{\Phi}$ vs. $r_+$ for $k=1, n=6,\alpha=1,\Phi=1,\Lambda=-2$ (b) $T$ vs. $r_+$ for $k=1, n=6,\alpha=1,\Phi=1,\Lambda=-2$} \label{fg1}
\end{figure*}
The above equation can be solved numerically and the results for $k=1,-1$ are presented in Table \ref{tb1}-\ref{tb2} respectively, where the impact of the various parameters are studied thoroughly via control variate method. It is quite interesting to note that there are two critical points for the case $n=6,k=1$ while there is only one for other cases. And the distance between the two phase transition points becomes larger with the increasing of $\Lambda$ and $\Phi$ while it first becomes larger then becomes smaller with the increasing of $\alpha$. The case $n=6,k=1$ is shown graphically in Fig.\ref{fg1}. Both the behaviors of the specific heat and Hawking temperature are depicted. It is easy to find that the two phase transition points where the specific heat diverges are physical for the Hawking temperature is positive. The black holes can be divided into three phases. Namely, small stable ($C_\Phi>0$) black hole, medium unstable ($C_\Phi<0$) black hole and large stable ($C_\Phi>0$) black hole. For a more comprehensive picture, we also plot the three-dimensional figure for the case $n=6,k=1$ in Fig.\ref{fg2} and for the case $n=6,k=-1$ in Fig.\ref{fg3}.
\begin{figure*}
\centerline{\subfigure[]{\label{2a}
\includegraphics[width=8cm,height=6cm]{2a.eps}}
\subfigure[]{\label{2b}
\includegraphics[width=8cm,height=6cm]{2b.eps}}}
\centerline{\subfigure[]{\label{2c}
\includegraphics[width=8cm,height=6cm]{2c.eps}}}
\caption{(a) $C_{\Phi}$ vs. $r_+$ for $k=1, n=6,\Phi=1,\Lambda=-2$ (b) $T$ vs. $r_+$ for $k=1, n=6,\alpha=1,\Lambda=-2$ (c) $C_{\Phi}$ vs. $r_+$ for $k=1, n=6,\alpha=1,\Phi=1$} \label{fg2}
\end{figure*}
\begin{figure*}
\centerline{\subfigure[]{\label{3a}
\includegraphics[width=8cm,height=6cm]{3a.eps}}
\subfigure[]{\label{3b}
\includegraphics[width=8cm,height=6cm]{3b.eps}}}
\centerline{\subfigure[]{\label{3c}
\includegraphics[width=8cm,height=6cm]{3c.eps}}}
\caption{(a) $C_{\Phi}$ vs. $r_+$ for $k=-1, n=6,\Phi=1,\Lambda=-2$ (b) $T$ vs. $r_+$ for $k=-1, n=6,\alpha=1,\Lambda=-2$ (c) $C_{\Phi}$ vs. $r_+$ for $k=-1, n=6,\alpha=1,\Phi=1$} \label{fg3}
\end{figure*}
The case $k=0$ is quite simple. When $k=0$, Eq.~(\ref{27}) can be simplified as
\begin{equation}
B(r_+,\Phi)=-24\Lambda r_+^8+24(n-2)^2\Phi^2>0.\label{29}
\end{equation
So there exists no phase transition for $k=0$.
\begin{table}[!h]
\tabcolsep 0pt
\caption{The location of phase transition points for $k=1$}
\vspace*{-12pt}
\begin{center}
\def\temptablewidth{0.5\textwidth}
{\rule{\temptablewidth}{1pt}}
\begin{tabular*}{\temptablewidth}{@{\extracolsep{\fill}}cccccc}
$n$ & $\alpha$ & $\Phi$ &$\Lambda$ &$r_{+1}$ &$r_{+2}$ \\ \hline
6 & 1 &1 & -2& 0.406& 1.248\\
6 &1 & 1& -4 & 0.420& 0.964 \\
6 & 1 &1 & -6& 0.440 & 0.794 \\
6 & 0.5 &1& -2& 0.283 & 1.076 \\
6 & 2 &1& -2& 0.595 & 1.363 \\
6 & 1 &2& -2& 0.169 & 1.592 \\
6 & 1 &3& -2& 0.110 & 1.666 \\
7 & 1 &1& -2& 1.503 & -\\
8 & 1 &1& -2& 1.680 & - \\
9 & 1 &1& -2& 1.812 & - \\
\end{tabular*}
{\rule{\temptablewidth}{1pt}}
\end{center}
\label{tb1}
\end{table}
\begin{table}[!h]
\tabcolsep 0pt
\caption{The location of phase transition points for $k=-1$}
\vspace*{-12pt}
\begin{center}
\def\temptablewidth{0.5\textwidth}
{\rule{\temptablewidth}{1pt}}
\begin{tabular*}{\temptablewidth}{@{\extracolsep{\fill}}ccccc}
$n$ & $\alpha$ & $\Phi$ &$\Lambda$ &$r_{+}$ \\ \hline
6 & 1 &1 & -2& 0.279\\
6 &1 & 1& -4 & 0.281 \\
6 & 1 &1 & -6& 0.282 \\
6 & 0.5 &1& -2& 0.197 \\
6 & 2 &1& -2& 0.397 \\
6 & 1 &2& -2& 0.155 \\
6 & 1 &3& -2& 0.106 \\
7 & 1 &1& -2& 0.353 \\
8 & 1 &1& -2& 0.374 \\
9 & 1 &1& -2& 0.386 \\
\end{tabular*}
{\rule{\temptablewidth}{1pt}}
\end{center}
\label{tb2}
\end{table}
\section{The nature of phase transition in the grand canonical ensemble}
\label{Sec3}
In the extended space, it is convenient to utilize the classical Ehrenfest equations to study the nature of phase transition at the critical point. However, here, in the non-extended phase space, we would like to introduce the novel analog form of Ehrenfest equations proposed by Banerjee et al.~\cite{Banerjee1} as follow
\begin{eqnarray}
-\left(\frac{d \Phi}{d T}\right)_S&=&\frac{C_{\Phi_2}-C_{\Phi_1}}{TQ(\alpha_2-\alpha_1)}=\frac{\Delta
C_\Phi}{TQ\Delta \alpha},\label{30}\\
-\left(\frac{d \Phi}{d T}\right)_Q&=&\frac{\alpha_2-\alpha_1}{\kappa_{T_2}-\kappa_{T_1}}=\frac{\Delta
\alpha}{\Delta\kappa_T},\label{31}
\end{eqnarray
where $\alpha=\frac{1}{Q}(\frac{\partial Q}{\partial T})_\Phi$, $\kappa_T=\frac{1}{Q}(\frac{\partial Q}{\partial \Phi})_T$ are
the analog of volume expansion coefficient and isothermal compressibility respectively. Their explicit forms can be calculated as follows
\begin{eqnarray}
\alpha&=&\frac{48(n-1)(n-2)\pi r_+(r_+^2+k\alpha)^3}{B(r_+,\Phi)},\label{32}\\
\kappa_T&=&\frac{48(n-2)^3r_+^6(r_+^2+k\alpha)\Phi}{B(r_+,\Phi)}.\label{33}
\end{eqnarray
$\alpha,\kappa_T$ may also diverge at the phase transition point because they share
the same factor as $C_\Phi$ in their denominators. It can be clearly seen in Fig.~\ref{fg4}.
\begin{figure*}
\centerline{\subfigure[]{\label{4a}
\includegraphics[width=8cm,height=6cm]{4a.eps}}
\subfigure[]{\label{4b}
\includegraphics[width=8cm,height=6cm]{4b.eps}}}
\caption{(a) $\alpha$ vs. $r_+$ for $k=1, n=6,\alpha=1,\Phi=1,\Lambda=-2$ (b) $\kappa_T$ vs. $r_+$ for $k=1, n=6,\alpha=1,\Phi=1,\Lambda=-2$} \label{fg4}
\end{figure*}
From the definitions of $\alpha$ and $C_\Phi$, one can obtain
\begin{equation}
Q\alpha=(\frac{\partial Q}{\partial T})_\Phi=(\frac{\partial
Q}{\partial S})_\Phi(\frac{\partial S}{\partial
T})_\Phi=(\frac{\partial Q}{\partial S})_\Phi(\frac{C_\Phi
}{T}).\label{34}
\end{equation
So the R.H.S of Eq.(\ref{30}) can be derived as
\begin{equation}
\frac{\Delta C_\Phi}{TQ\Delta \alpha}=(\frac{\partial S}{\partial
Q})_\Phi=\frac{(n-1)\pi(r_+^2+k\alpha)^2}{(n-2)^2r_+^3\Phi}.\label{35}
\end{equation
On the other hand, the L.H.S of Eq.(\ref{30}) can be derived as
\begin{equation}
-(\frac{\partial \Phi}{\partial T})_S=\frac{(n-1)\pi(r_+^2+k\alpha)^2}{(n-2)^2r_+^3\Phi}.\label{36}
\end{equation
So the first equation of Erhenfest equations has been proved to be valid.
The L.H.S of Eq.(\ref{31}) can be obtained as
\begin{equation}
-\left(\frac{\partial \Phi}{\partial T}\right)_Q=\frac{-1}{\left(\frac{\partial T}{\partial \Phi}\right)_Q}=\frac{-1}{\left(\frac{\partial T}{\partial \Phi}\right)_{r_+}+\left(\frac{\partial T}{\partial r_+}\right)_\Phi \left(\frac{\partial r_+}{\partial \Phi}\right)_Q}=\frac{-1}{\left(\frac{\partial T}{\partial \Phi}\right)_{r_+}}=\frac{(n-1)\pi(r_+^2+k\alpha)^2}{(n-2)^2r_+^3\Phi}.\label{37}
\end{equation
Note that we have utilized the phase transition condition $\left(\frac{\partial T}{\partial r_+}\right)_\Phi=0$. From the thermodynamic identity \cite{Banerjee5}
\begin{equation}
(\frac{\partial Q}{\partial \Phi})_T(\frac{\partial \Phi}{\partial
T})_Q(\frac{\partial T}{\partial Q})_\Phi=-1,\label{38}
\end{equation
we can derive that
\begin{equation}
Q\kappa_T=(\frac{\partial Q}{\partial \Phi})_T=-(\frac{\partial
T}{\partial \Phi})_Q(\frac{\partial Q}{\partial
T})_\Phi=-(\frac{\partial T}{\partial \Phi})_QQ\alpha.\label{39}
\end{equation
Noting that in the above derivation, we have also utilized both the definitions of $\kappa_T$ and $\alpha$. We can obtain
\begin{equation}
\frac{\Delta \alpha}{\Delta \kappa_T}=-(\frac{\partial
\Phi}{\partial T})_Q=\frac{(n-1)\pi(r_+^2+k\alpha)^2}{(n-2)^2r_+^3\Phi}.\label{40}
\end{equation
From Eqs.(\ref{37}) and (\ref{40}), one can easily draw the conclusion that the second equation of Ehrenfest equations also holds. The Prigogine-Defay(PD)
ratio can be calculated as
\begin{equation}
\Pi=\frac{\Delta C_\Phi \Delta \kappa_T}{T_cQ(\Delta
\alpha)^2}=1.\label{41}
\end{equation
Eq.(\ref{41}) and the validity of Ehrenfest equations show that Lovelock AdS black holes in grand canonical ensemble undergo second order phase transition.
\section{Thermodynamic geometry of Lovelock AdS black holes}
\label{Sec4}
Weinhold's metric~\cite{Weinhold} and Ruppeiner's metric~\cite{Ruppeiner} are defined respectively as
\begin{eqnarray}
g_{ij}^{W}&=&\frac{\partial ^2 U(x^k)}{\partial x^i
\partial x^j},\label{42}
\\
g_{ij}^{R}&=&-\frac{\partial ^2 S(x^k)}{\partial x^i
\partial x^j}.\label{43}
\end{eqnarray}
And they are conformally connected to each other through the map \cite{Janyszek}
\begin{equation}
dS^2_R=\frac{dS^2_W}{T}.\label{44}
\end{equation}
Utilizing Eqs.(\ref{19}) and (\ref{21}), one can obtain the components of Weinhold's metric as
\begin{eqnarray}
g_{SS}^{W}&=&\frac{D(r_+,Q)}{3(n-1)^2\pi r_+^{3n-4}(r_+^2+k\alpha)^5\Sigma_k^3},\label{45}
\\
g_{QQ}^{W}&=&\frac{4\pi}{(n-2)r_+^{n-2}\Sigma_k},\label{46}
\\
g_{SQ}^{W}&=&g_{QS}^{W}=\frac{-16\pi Q}{(n-1)r_+^{2n-7}(r_+^2+k\alpha)^2\Sigma_k^2},\label{47}
\end{eqnarray
where
\begin{eqnarray}
D(r_+,Q)&=&96\pi^2Q^2r_+^8\left[(2n-3)r_+^2+k(2n-7)\alpha\right]-r_+^{2n}
\nonumber
\\
&\,&\times\left\{k(n-1)\left[3(n-2)r_+^6-18kr_+^4\alpha+2k^2(n-9)r_+^2\alpha^2+k^3(n-6)\alpha^3\right]+6r_+^6\Lambda(r_+^2+5k\alpha)\right\}\Sigma_k^2.\label{48}
\end{eqnarray
Utilizing Eqs.(\ref{17}), (\ref{44}), (\ref{45}), (\ref{46}) and
(\ref{47}), the components of Ruppeiner's metric can be derived as
\begin{eqnarray}
g_{11}^{R}&=&\frac{4r_+^{5-3n}D(r_+,Q)}{(n-1)(r_+^2+k\alpha)^3\left\{k(n-1)\left[3(n-2)r_+^4+3k(n-4)r_+^2\alpha+k^2(n-6)\alpha^2\right]\Sigma_k^3-6r_+^6\Lambda\Sigma_k^3-96\pi^2Q^2r_+^{8-2n}\Sigma_k\right\}},
\nonumber
\\
\label{49}
\\
g_{22}^{R}&=&\frac{48(n-1)\pi^2r_+^{n+3}(r_+^2+k\alpha)^2\Sigma_k}{(n-2)\left\{-96\pi^2Q^2r_+^8+r_+^{2n}(n-1)k\left[3(n-2)r_+^4+3k(n-4)r_+^2\alpha+k^2(n-6)\alpha^2\right]\Sigma_k^2-6r_+^{2n+6}\Lambda\Sigma_k^2\right\}},\label{50}
\\
g_{12}^{R}&=&g_{21}^{R}=\frac{-192\pi^2 Qr_+^{8-2n}}{k(n-1)\left[3(n-2)r_+^4+3k(n-4)r_+^2\alpha+k^2(n-6)\alpha^2\right]\Sigma_k^2-6r_+^6\Lambda\Sigma_k^2-96\pi^2Q^2r_+^{8-2n}}.\label{51}
\end{eqnarray
Utilizing Eqs.(\ref{49})-(\ref{51}), we can obtain Ruppeiner scalar
curvature as
\begin{equation}
R=\frac{E(r_+,\Phi)}{F(r_+,\Phi)},\label{53}
\end{equation
where
\begin{eqnarray}
F(r_+,\Phi)&=&-(n-1)r_+^n(r_+^2+k\alpha)^3\Sigma_k\times\{-6\Lambda r_+^8-3r_+^6\left[k(2+n^2-3n+10\alpha\Lambda)-2(n-2)^2\Phi^2\right]
\nonumber
\\
&\,&+18k\alpha r_+^4\left[k(n-1)-(n-2)^2\Phi^2\right]-2k^3(n-9)(n-1)\alpha^2r_+^2-k^4(n-6)(n-1)\alpha^3\}^3
\nonumber
\\
&\,&\times \left[3k(n-2)(n-1)r_+^4+3k^2(n-4)(n-1)r_+^2\alpha+k^3(n-6)(n-1)\alpha^2-6r_+^6\Lambda-6(n-2)^2r_+^4\Phi^2 \right],\label{54}
\end{eqnarray
and $E(r_+,Q)$ is too lengthy to be displayed here. The above result has been rewritten in the function of $\Phi$ so that we can compare it with the specific heat. It is not difficult to observe from Eq.(\ref{53}) that in the denominator of Ruppeiner scalar curvature, the fifth factor is exactly one quarter of the denominator of the specific heat while the last factor coincides with the numerator of the Hawking temperature. In other words, the Ruppeiner scalar curvature may diverge exactly where the specific heat diverges. It also reveals the extremal black hole condition that the Hawking temperature is zero. For an intuitive understanding, one can observe the behavior of Ruppeiner scalar curvature $R$ in Fig.\ref{fg5}. Comparing Fig.\ref{fg5} with Fig.\ref{1a}, one can find that the divergence structures of both the Ruppeiner scalar curvature and the specific heat are exactly the same. And the Ruppeiner metric does provide a wonderful tool for one to probe the phase structures of black holes.
Among thermodynamic geometry theories, Ruppeiner geometry has been proved to be outstanding for its profound physical meaning. As argued in Ref. \cite{Ruppeiner2}, Ruppeiner scalar curvature $R$ results from the thermodynamic information metric giving thermodynamic fluctuations and may be interpreted physically as the measurement of the correlation between fluctuating Planck length pixels of event horizon. In the region with positive $R$, repulsive interactions (Fermionic behavior) dominate while in the region with negative $R$, attractive interactions (Bosonic behavior) dominate. Moreover, $\mid R \mid$ indicates the average size of fluctuations.
\begin{figure}
\includegraphics[width=8cm,height=6cm]{5a.eps}
\caption{Ruppeiner scalar curvature $R$ vs. $r_+$ for $k=1, n=6,\alpha=1,\Phi=1,\Lambda=-2$}
\label{fg5}
\end{figure}
\section{Concluding Remarks}
\label{Sec5}
In this paper, we extend our former research of charged topological Lovelock AdS black holes to the non-extended phase space. Specifically, we investigate phase transition of (n+1)-dimensional Lovelock AdS black holes in the grand canonical ensemble. Firstly, we calculated the specific heat at constant electric potential. To probe the impact of the various parameters, we utilize the control variate method and solve the phase transition condition equation numerically for the case $k=1,-1$. There are two critical points for the case $n=6,k=1$ while there is only one for other cases. And the distance between the two phase transition points becomes larger with the increasing of $\Lambda$ and $\Phi$ while it first becomes larger then becomes smaller with the increasing of $\alpha$. We also study the behavior of specific heat graphically. As can be seen from the graph, the black holes can be divided into three phases. Namely, small stable ($C_\Phi>0$) black hole, medium unstable ($C_\Phi<0$) black hole and large stable ($C_\Phi>0$) black hole. The graph of Hawking temperature is also depicted to check whether the phase transition points locate in the physical region. For $k=0$, there exists no phase transition point.
To figure out the nature of phase transition in the grand canonical ensemble, we carry out an analytic check of the analog form of Ehrenfest equations proposed by Banerjee et al. It is proved that the two Ehrenfest equations hold at the phase transition point. Prigogine-Defay ratio is also calculated. Based on these results, one can draw the conclusion that Lovelock AdS black holes in grand canonical ensemble undergo a second order phase transition.
To examine the phase structure in the grand canonical ensemble, we also utilize the thermodynamic geometry method. Specifically, we calculate both the Weinhold metric and Ruppeiner metric. It is shown that in the denominator of Ruppeiner scalar curvature, the fifth factor is exactly one quarter of the denominator of the specific heat while the last factor coincides with the numerator of the Hawking temperature. So the Ruppeiner scalar curvature may diverge exactly where the specific heat diverges. It also reveals the extremal black hole condition that the Hawking temperature is zero. From the graph of Ruppeiner scalar curvature, one can see clearly that the divergence structures of both the Ruppeiner scalar curvature and the specific heat are exactly the same. Our research provides one more example that Ruppeiner metric serves as a wonderful tool to probe the phase structures of black holes.
Note that one may vary the spatial dimension, the cosmological constant, and the coefficients of the curvature terms in the Lagrangian and we mainly concentrate on a few instances of a very large model in this paper. The control variate method has been utilized to crack down the problem of probing the impact of the various parameters. We choose such parameter regions that we can compare our results with those in former literatures. One can easily extend our results to more cases. The black hole solution here was derived for the special case that the second and third order Lovelock coefficients satisfy certain conditions. Phase transition in the non-extended space of more general black hole solutions in Lovelock gravtiy would be further investigated in our future work. Also note that the methods utilized in this paper can be generalized to an arbitrary non-linear electrodynamics Lagrangian, the specific results in this paper however are model-dependent. For a more general analysis, we would like to draw the readers' attention to the excellent work \cite{Miskovic99}, where the authors presented an elegant procedure for Gauss-Bonnet gravity regardless of the explicit form of the nonlinear electrodynamics Lagrangian. It certainly deserves to extend this treatment to the third-order Lovelock case in future research.
\section*{Acknowledgements}
We would like to express our sincere gratitude to both the editor and the referee whose hard work have help improved the quality of this paper greatly. This research is supported by the National Natural Science
Foundation of China (Grant Nos.11235003, 11175019, 11178007). It is
also supported by \textquotedblleft Thousand Hundred
Ten\textquotedblright \,Project of Guangdong Province and supported by Department of Education of Guangdong Province (Grant No.2014KQNCX191).
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,128 |
using System;
using System.Collections.Generic;
using System.IO;
using MatterHackers.Agg;
using MatterHackers.Agg.Platform;
using MatterHackers.Agg.UI;
using MatterHackers.Localizations;
using MatterHackers.MatterControl.ConfigurationPage.PrintLeveling;
using MatterHackers.MatterControl.CustomWidgets;
using MatterHackers.MatterControl.SlicerConfiguration;
using MatterHackers.VectorMath;
namespace MatterHackers.MatterControl
{
public class EditLevelingSettingsPage : DialogPage
{
private readonly PrinterConfig printer;
public EditLevelingSettingsPage(PrinterConfig printer, ThemeConfig theme)
{
this.printer = printer;
this.WindowTitle = "Leveling Settings".Localize();
this.HeaderText = "Sampled Positions".Localize();
var scrollableWidget = new ScrollableWidget()
{
AutoScroll = true,
HAnchor = HAnchor.Stretch,
VAnchor = VAnchor.Stretch,
};
scrollableWidget.ScrollArea.HAnchor = HAnchor.Stretch;
contentRow.AddChild(scrollableWidget);
// No right padding removes unexpected spacing to the right of scrollbar
contentRow.Padding = contentRow.Padding.Clone(right: 0);
var column = new FlowLayoutWidget(FlowDirection.TopToBottom)
{
HAnchor = HAnchor.Stretch,
Padding = new BorderDouble(right: theme.DefaultContainerPadding + 4)
};
scrollableWidget.AddChild(column);
var positions = new List<Vector3>();
PrintLevelingData levelingData = printer.Settings.Helpers.GetPrintLevelingData();
for (int i = 0; i < levelingData.SampledPositions.Count; i++)
{
positions.Add(levelingData.SampledPositions[i]);
}
int tab_index = 0;
for (int row = 0; row < positions.Count; row++)
{
var leftRightEdit = new FlowLayoutWidget
{
Padding = new BorderDouble(3),
HAnchor = HAnchor.Stretch
};
var positionLabel = new TextWidget("{0} {1,-5}".FormatWith("Position".Localize(), row + 1), textColor: theme.TextColor);
positionLabel.VAnchor = VAnchor.Center;
leftRightEdit.AddChild(positionLabel);
for (int axis = 0; axis < 3; axis++)
{
leftRightEdit.AddChild(new HorizontalSpacer());
string axisName = "x";
if (axis == 1)
{
axisName = "y";
}
else if (axis == 2)
{
axisName = "z";
}
leftRightEdit.AddChild(
new TextWidget($" {axisName}: ", textColor: theme.TextColor)
{
VAnchor = VAnchor.Center
});
int linkCompatibleRow = row;
int linkCompatibleAxis = axis;
MHNumberEdit valueEdit = new MHNumberEdit(positions[linkCompatibleRow][linkCompatibleAxis], theme, allowNegatives: true, allowDecimals: true, pixelWidth: 60, tabIndex: tab_index++)
{
Name = $"{axisName} Position {row}"
};
valueEdit.ActuallNumberEdit.InternalTextEditWidget.EditComplete += (sender, e) =>
{
Vector3 position = positions[linkCompatibleRow];
position[linkCompatibleAxis] = valueEdit.ActuallNumberEdit.Value;
positions[linkCompatibleRow] = position;
};
valueEdit.Margin = new BorderDouble(3);
leftRightEdit.AddChild(valueEdit);
}
column.AddChild(leftRightEdit);
}
var savePresetsButton = theme.CreateDialogButton("Save".Localize());
savePresetsButton.Name = "Save Leveling Button";
savePresetsButton.Click += (s, e) => UiThread.RunOnIdle(() =>
{
PrintLevelingData newLevelingData = printer.Settings.Helpers.GetPrintLevelingData();
for (int i = 0; i < newLevelingData.SampledPositions.Count; i++)
{
newLevelingData.SampledPositions[i] = positions[i];
}
printer.Settings.Helpers.SetPrintLevelingData(newLevelingData);
this.DialogWindow.Close();
});
this.AddPageAction(savePresetsButton);
var exportButton = theme.CreateDialogButton("Export".Localize());
exportButton.Click += (s, e) => {
UiThread.RunOnIdle(this.ExportSettings, .1);
};
this.AddPageAction(exportButton);
}
private void ExportSettings()
{
AggContext.FileDialogs.SaveFileDialog(
new SaveFileDialogParams("Bed Leveling Data|*.csv") {
Title = "Export Bed Leveling Data".Localize(),
FileName = $"{printer.Settings.GetValue(SettingsKey.printer_name)} Leveling Data"
},
(saveParams) => {
try {
if (!string.IsNullOrWhiteSpace(saveParams.FileName)) {
// Export JSON data
//File.WriteAllText(saveParams.FileName, printer.Settings.GetValue(SettingsKey.print_leveling_data));
// Export CSV data
PrintLevelingData levelingData = printer.Settings.Helpers.GetPrintLevelingData();
using (StreamWriter file =
new StreamWriter(saveParams.FileName)) {
for (int i = 0; i < levelingData.SampledPositions.Count; i++) {
double x = levelingData.SampledPositions[i].X;
double y = levelingData.SampledPositions[i].Y;
double z = levelingData.SampledPositions[i].Z;
file.WriteLine($"{x}, {y}, {z}");
}
}
}
} catch (Exception e) {
UiThread.RunOnIdle(() => {
StyledMessageBox.ShowMessageBox(e.Message, "Couldn't save file".Localize());
});
}
});
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,306 |
I have requested the 30 day trial for the Enterprise server. I used the normal installation procedure (without the mail server) on a fresh Ubuntu Xenial 16.04 VM in an OpenStack cloud.
The services seem to run and I can connect to the portal via the IP address. I see the first screen that asks me to setup the password and upload the license file.
As soon as I select the license file, a spinner starts up (Loading) and never finishes. I can't click the "Continue" button.
Try to get a new one, you can use the same mail. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,662 |
Duolingo is the most popular language learning application in the world, with over 200 million users and hundreds of billions of data points. We are passionate about educating our users, making fact-based decisions, and finding elegant solutions. If this sounds like you, then come help us build the next-generation learning company! As the Head of Analytics, you will be responsible for building up a team of Data Analysts and directing the continuous improvement of our internal analytics products. You will ensure that product and business teams have the data, insights, and recommendations they need to make high-stakes decisions. | {
"redpajama_set_name": "RedPajamaC4"
} | 76 |
Kristi Krueger, Anchor/Health Reporter
Tags: Miami-Dade, Community, News, Local, Education
Former president of Barry University dies at 90
Sister Jeanne O'Laughlin served as president of university for 23 years
MIAMI SHORES, Fla. – Sister Jeanne O'Laughlin, president of Barry University for 23 years, died Tuesday morning at the age of 90.
The Dominican nun helped many people around the world, and it was her hard work and dedication that put Barry University on the map.
O'Laughlin was born May 4, 1929, in Detroit, Michigan, to Thomas and Mary O'Laughlin.
Her mother died when she was 6, also leaving behind a 2-week-old girl, 7-year-old boy and 9-year-old girl.
In 1945, O'Laughlin became a nun at age 16 and followed her calling to be an educator.
Between 1950 and 1970, she taught in Arizona. She then went on to become an administrator, superintendent and consultant.
In 1981, O'Laughlin was named the fifth president of Barry University.
At the time, it was a struggling college with about 2,000 students, most of whom were women.
Tim Czerniec, senior vice president for business and finance at Barry, worked with O'Laughlin throughout her presidency.
"She has been a major factor in the development of this institution, particularly over the last 20 years, where a lot of her energy and drive has caused a lot of things to happen," he said.
Under her leadership, Barry's student body increased to more than 9,000 people, 38 buildings were added and more than $200 million was raised.
In an interview before her death, Arlene Scott, assistant vice president for mission and ministry at Barry University, described her friend and colleague.
"She has a great zest for life," Scott said. "She loves people. She draws her energy from the students, from the staff, from the faculty, from her family."
Scott said O'Laughlin had a huge heart and "tremendous capacity for giving to others. She's very generous."
A bout with lung cancer didn't slow O'Laughlin down in 1996. In fact, she went public after her operation and raised awareness and funds for the American Cancer Society.
O'Laughlin also rubbed elbows with presidents, politicians and journalists and was a respected leader in the community. She was honored many times by various organizations.
O'Laughlin retired as president of Barry University in June 2004.
Her tremendous love for others, for her students and for this community will not be forgotten.
Her contributions to this world will live on for years to come.
Kristi Krueger
Kristi Krueger has built a solid reputation as an award-winning medical reporter and effervescent anchor. She joined Local 10 in August 1993. After many years co-anchoring the 6 p.m. and 11 p.m., Kristi now co-anchors the noon newscasts, giving her more time in the evening with her family. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,020 |
Shipton Hall est une grande maison de campagne élisabéthaine dans le village de Shipton, Shropshire, Angleterre, qui se trouve dans la vallée de Corvedale à environ 7 miles au sud-ouest de Much Wenlock. C'est un bâtiment classé Grade I .
La maison est construite en calcaire selon un plan en E à deux étages avec des greniers, et possède une tour élancée de 4 étages dans l'un des coins intérieurs. Dans les jardins ornementaux se trouvent des écuries et un ancien pigeonnier monastique, qui est un bâtiment classé Grade II * .
A proximité se dresse l'église Saint-Jacques du .
Histoire
Après la dissolution des monastères, le manoir de Shipton est accordé par la Couronne en 1548 à Sir Thomas Palmer, qui est déclaré hors la loi et exécuté pour haute trahison en 1553, il est revendu par la Couronne en 1557. Après être passé entre plusieurs mains, il finit par (1580) entrer en possession de John Lutwyche .
La maison actuelle est construite vers 1587 pour Richard Lutwyche afin de remplacer une ancienne maison à pans de bois qui avait brûlé . L'église délabrée de St James est également reconstruite par les Lutwyches en 1589 et est maintenant un bâtiment classé Grade II * .
Richard Lutwyche donne ensuite le domaine à Thomas Mytton en dot lorsque Mytton épouse la fille de Lutwyche et il passe ensuite dans la famille Mytton jusqu'en 1795, date à laquelle il passe par mariage à la famille More. À la fin des années 1800, les Mores vendent la maison à l'arrière-grand-père du propriétaire actuel . John Nicholas Bishop, de Shipton Hall, est haut shérif du Shropshire en 2002.
La maison a été largement reconstruite dans le style géorgien au milieu du , lorsque le décor intérieur en rococo est créé par l'architecte Thomas Farnolls Pritchard, concepteur du pont de fer de Coalbrookdale .
Références
Liens externes
Monument classé de Grade I dans le Shropshire | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,485 |
Q: Error in using max function with Armadillo sparse matrices Here is the code that I am getting error(type mismatch) on line no. with max:
#include <iostream>
#include <stdlib.h>
#include <math.h>
#include<armadillo>
using namespace std;
using namespace arma;
int main(int argc, char** argv) {
umat loc;
loc<<0<<0<<3<<endr
<<2<<4<<4<<endr;
vec val={1,2,3};
sp_mat m(loc,val);
double t=arma::max(sum(square(m),1)) + 1.0;
cout<<t<<endl;
return 0;
}
Can somebody tell me why is that error happening and how to get around this.
Note: cout<<max(sum(square(m),1)) prints the result to console but adding any number to the output flags error.
A: If you want to convert a 1x1 matrix into a pure scalar (like double), use the as_scalar() function. Same goes for any Armadillo expression that results in a 1x1 matrix.
It's a good idea to read the Armadillo documentation thoroughly before posting questions on Stackoverflow.
Modifying your example:
umat loc = { { 0, 0, 3 },
{ 2, 4, 4 } };
vec val = {1, 2, 3};
sp_mat m(loc,val);
m.print("m:");
max(sum(square(m),1)).print("expression:");
double t = as_scalar( max(sum(square(m),1)) );
cout << t << endl;
A: You haven't told us (and I can't find in the documentation) exactly what data type is returned by arma::max(sum(square(m),1))
You have tested that whatever it is does not implicitly convert to double and whatever it is can be sent to a stream and when that is done it looks like a double.
My guess is it is something that can be explicitly converted to double so try:
(double)arma::max(sum(square(m),1)) + 1.0
The documentation shows the returned value for a dense matrix being used to initialize a double so that is obviously a type than can be explicitly converted to double. I had initially missed the thing you linked for me effectively saying sum does something on sparse matrix compatible with what it does on dense. So you can almost conclude (rather than just guess) that max(sum(m)) should be the same type (explicitly convertible to double).
If that doesn't work, we will really need a full quote of the error message, not just a summary of what it seems to mean.
Now that we have an error message, we can see this is a flaw in Armadillo's template metaprogramming:
Operations are stacked in template meta programming in order to avoid creating excess temporary objects. Then the meta programming must resolve the whole mess when the result is used.
If this is a minor flaw in the meta programming, you could add just one trivial temporary to fix it:
double t = arma::max(sum(square(m),1));
cout << t+1.0 endl;
But you probably already tried that. So you may need more temporaries and you probably need to give them exact correct types (rather than use auto). My first guess would be:
colvec v = sum(square(m),1);
Then see what works with arma::max(v)
(Earlier I made a negative comment on an answer that suggested starting with auto temporaries for each step. That answer was deleted. It wasn't far wrong. But I'd still say it was wrong to start there without seeing the template meta-programming failures and likely, though I'm not sure, wrong to use auto to try to bypass a meta-programming failure.)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,392 |
use strict;
use IO::File;
use UNIVERSAL;
package XML::ESISParser;
use vars qw{ $VERSION $NSGMLS_sgml $NSGMLS_FLAGS_sgml $NSGMLS_ENV_sgml
$NSGMLS_xml $NSGMLS_FLAGS_xml $NSGMLS_ENV_xml
$XML_DECL };
# will be substituted by make-rel script
$VERSION = "0.08";
$NSGMLS_sgml = 'nsgmls';
$NSGMLS_FLAGS_sgml = '-oentity -oempty -onotation-sysid -oincluded -oline -E0';
$NSGMLS_ENV_sgml = '';
$NSGMLS_xml = 'nsgmls';
$XML_DECL = '/usr/lib/sgml/declaration/xml.decl';
$NSGMLS_FLAGS_xml = '-oentity -oempty -onotation-sysid -oline -oincluded -wxml -E0 ';
$NSGMLS_ENV_xml = 'SP_CHARSET_FIXED=YES SP_ENCODING=XML';
sub new {
my $type = shift;
return bless { @_ }, $type;
}
sub parse {
my $self = shift;
die "XML::ESISParser: parser instance ($self) already parsing\n"
if (defined $self->{ParseOptions});
# If there's one arg and it has no ref, it's a string
my $args;
if (scalar (@_) == 1 && !ref($_[0])) {
$args = { Source => { String => shift } };
} else {
$args = (scalar (@_) == 1) ? shift : { @_ };
}
my $parse_options = { %$self, %$args };
$self->{ParseOptions} = $parse_options;
# ensure that we have at least one source
if (!defined $parse_options->{Source}
|| !(defined $parse_options->{Source}{String}
|| defined $parse_options->{Source}{ByteStream}
|| defined $parse_options->{Source}{SystemId}
|| defined $parse_options->{Source}{ESISStream})) {
die "XML::ESISParser: no source defined for parse\n";
}
# assign default Handler to any undefined handlers
if (defined $parse_options->{Handler}) {
$parse_options->{DocumentHandler} = $parse_options->{Handler}
if (!defined $parse_options->{DocumentHandler});
$parse_options->{DTDHandler} = $parse_options->{Handler}
if (!defined $parse_options->{DTDHandler});
$parse_options->{ErrorHandler} = $parse_options->{Handler}
if (!defined $parse_options->{ErrorHandler});
}
# create the NSGMLS command
my ($nsgmls_command, $nsgmls, $nsgmls_flags);
if (defined $parse_options->{NSGMLSCommand}) {
$nsgmls_command = $parse_options->{NSGMLSCommand};
} elsif (defined $parse_options->{IsSGML}
&& $parse_options->{IsSGML}) {
my $declaration = (defined $parse_options->{Declaration})
? " " . $parse_options->{Declaration} : "";
$nsgmls = $parse_options->{NSGMLS} = $NSGMLS_sgml;
$nsgmls_flags = $parse_options->{NSGMLS_FLAGS} = $NSGMLS_FLAGS_sgml;
$nsgmls_command = $parse_options->{NSGMLS_COMMAND} = "$nsgmls $nsgmls_flags $declaration";
} else {
my $declaration = (defined $parse_options->{Declaration})
? $parse_options->{Declaration} : $XML_DECL;
$nsgmls = $parse_options->{NSGMLS} = $NSGMLS_xml;
$nsgmls_flags = $parse_options->{NSGMLS_FLAGS} = $NSGMLS_FLAGS_xml;
$nsgmls_command = $parse_options->{NSGMLS_COMMAND} = "$NSGMLS_ENV_xml $nsgmls $nsgmls_flags $declaration";
}
my $result;
if (defined $self->{ParseOptions}{Source}{ESISStream}) {
# read ESIS stream directly
my $system_id = (defined $self->{ParseOptions}{Source}{SystemId})
? "\`$self->{ParseOptions}{Source}{SystemId}'" : 'ESIS Stream';
eval { $result = $self->parse_fh ($self->{ParseOptions}{Source}{ESISStream}) };
my $retval = $@;
if ($retval) {
die "XML::ESISParser::parse: unable to parse \`$system_id'\n$retval";
}
} elsif (defined $self->{ParseOptions}{Source}{ByteStream}) {
# call nsgmls using file handle
# FIXME special case stdin?
# For ByteStreams (Perl file handles) we create a sub-process
# that we feed the XML/SGML document and we get back the ESIS
# stream
my $retval;
my $system_id = (defined $self->{ParseOptions}{Source}{SystemId})
? "\`$self->{ParseOptions}{Source}{SystemId}'" : 'Byte Stream';
my ($pid) = open (ESIS, "-|");
if ($pid == 0) {
# 20% speed increase if grep swipes implieds (only 8% if
# we do it in `parse_fh'). XXX use a C routine or patch SP
open (SGML, "| $nsgmls_command 2>&1 | egrep -v '^A.* IMPLIED\$'")
or die "XML::ESISParser::parse: can't run \`$nsgmls' on \`$system_id'\n";
$self->{ParseOptions}{Source}{ByteStream}->print (*SGML);
close (SGML)
or die "XML::ESISParser::parse: can't run \`$nsgmls' on \`$system_id'\n";
exit 0;
} else {
eval { $result = $self->parse_fh (*ESIS) };
$retval = $@;
wait; # clean up that process
}
close (ESIS);
$self->{ParseOptions}{Source}{ByteStream}->close ();
if ($retval) {
die "XML::ESISParser::parse: unable to parse \`$system_id'\n$retval";
}
} elsif (defined $self->{ParseOptions}{Source}{String}) {
# call nsgmls with a literal string
} elsif (defined $self->{ParseOptions}{Source}{SystemId}) {
# if SystemId is a file, call nsgmls with file name
# otherwise, open stream on SystemId and do ByteStream
# FIXME this only handles file SystemIds right now
# 20% speed increase if grep swipes implieds (only 8% if
# we do it in `parse'). XXX use a C routine or patch SP
my $system_id = $self->{ParseOptions}{Source}{SystemId};
my ($fh) = IO::File->new
("$nsgmls_command '$system_id' 2>&1 | egrep -v '^A.* IMPLIED\$' |");
die "XML::ESISParser::parse: can't run \`$nsgmls' on \`$system_id'\n"
if (!defined $fh);
eval { $result = $self->parse_fh ($fh) };
my $retval = $@;
close ($fh);
if ($retval) {
die "XML::ESISParser::parse: unable to parse \`$system_id'\n$retval";
}
}
# clean up parser instance
delete $self->{ParseOptions};
delete $self->{DocumentHandler};
delete $self->{DTDHandler};
delete $self->{ErrorHandler};
return $result;
}
#
# Parse the `ESIS' information coming from `file'
#
sub parse_fh {
my ($self, $file) = @_;
my (@attributes, @properties, $files);
my $doc_h = $self->{ParseOptions}{DocumentHandler};
my $dtd_h = $self->{ParseOptions}{DTDHandler};
my $err_h = $self->{ParseOptions}{ErrorHandler};
# we cache these most commonly used `can()' calls
my $can_start_element = $doc_h->can('start_element');
my $can_end_element = $doc_h->can('end_element');
my $can_characters = $doc_h->can('characters');
my $can_record_end = $doc_h->can('record_end');
my $line = 0;
$doc_h->start_document( { } )
if ($doc_h->can('start_document'));
# 30% speed improvement by breaking the encapsulation
my ($is_filehandle) = (ref ($file) eq "FileHandle"
|| ref ($file) eq "IO::File");
while ($_ = ($is_filehandle ? <$file> : $file->getline())) {
chop;
if (/^A/) { # attribute
# Note: the output of `nsgmls' is `grep -v'ed to get rid of
# IMPLIED attributes, if we do it here we only get an 8%
# speed boost
my ($name, $type, $value) = split (/\s/, $', 3);
push (@attributes, $name => $value);
next;
}
if (/^\(/) { # start element
# break the encapsulation for an 8% boost
if ($#attributes >= 0) {
push (@properties, Attributes => { @attributes });
}
$doc_h->start_element ({ Name => $', @properties })
if ($can_start_element);
@properties = (); @attributes = ();
next;
}
if (/^\)/) { # end element
$doc_h->end_element ({ Name => $' })
if ($can_end_element);
next;
}
if (/^L/) { # line number
$line = $';
next;
}
if (/^-/) { # data (including sdata entities)
# This section is derived from David Megginson's SGMLSpm
my $sdata_flag = 0;
my $out = '';
my $data = $';
while ($data =~ /\\(\\|n|\||[0-7]{1,3})/) {
$out .= $`;
$data = $';
if ($1 eq '|') {
# beginning or end of SDATA
if ("$out" ne '') {
if ($sdata_flag) {
$doc_h->internal_entity_ref({ Name => $self->{'internal_entities_by_value'}{$out} })
if ($doc_h->can('internal_entity_ref'));
} else {
$doc_h->characters({ Data => $out })
if ($can_characters);
}
$out = '';
}
$sdata_flag = !$sdata_flag;
} elsif ($1 eq 'n') {
# record end
if ("$out" ne '') {
if ($sdata_flag) {
$doc_h->internal_entity_ref({ Name => $self->{'internal_entities_by_value'}{$out} })
if ($doc_h->can('internal_entity_ref'));
} else {
$doc_h->characters({ Data => $out })
if ($can_characters);
}
$out = '';
}
if ($can_record_end) {
$doc_h->record_end( { } );
} else {
$doc_h->characters({ Data => "\n" })
if ($can_characters);
}
} elsif ($1 eq '\\') {
$out .= '\\';
} else {
$out .= chr(oct($1));
}
}
$out .= $data;
if ("$out" ne '') {
if ($sdata_flag) {
$doc_h->internal_entity_ref({ Name => $self->{'internal_entities_by_value'}{$out} })
if ($doc_h->can('internal_entity_ref'));
} else {
$doc_h->characters({ Data => $out })
if ($can_characters);
}
}
next;
}
if (/^s/) { # sysid
push (@properties, SystemId => $');
next;
}
if (/^p/) { # pubid
push (@properties, PublicId => $');
next;
}
if (/^f/) { # file
if (!defined $files) {
$files = $';
} elsif (!ref $files) {
$files = [ $files, $' ];
} else {
push (@$files, $');
}
next;
}
if (/^E/) { # external entity definition
my ($entity_data) = $';
$entity_data =~ /^(\S+) (\S+) (\S+)$/
or die "XML::ESISParser::parse_fh: bad external entity event data: $entity_data\n";
my ($name,$type,$notation) = ($1,$2,$3);
if (defined $files) {
push (@properties, GeneratedId => $files);
}
$dtd_h->external_entity_decl ({ Name => $name, Type => $type,
Notation => $notation, @properties })
if ($dtd_h->can('external_entity_decl'));
@properties = (); undef $files;
next;
}
if (/^I/) { # internal entity definition
my ($name, $type, $value) = split (/\s/, $', 3);
$self->{'internal_entities_by_value'}{$value} = $name;
$dtd_h->internal_entity_decl ({ Name => $name, Type => $type,
Value => $value })
if ($dtd_h->can('internal_entity_decl'));
next;
}
if (/^&/) { # external entity reference
my ($name) = $';
$doc_h->external_entity_ref({ Name => $name })
if ($doc_h->can('external_entity_ref'));
next;
}
if (/^\?/) { # processing instruction (PI)
my ($data) = $';
if ($self->{ParseOptions}{IsSGML}) {
$doc_h->processing_instruction({ Data => $data })
if ($doc_h->can('processing_instruction'));
} else {
my ($target, $pi_data) = split (/\s+/, $data, 2);
$doc_h->processing_instruction({ Target => $target, Data => $pi_data })
if ($doc_h->can('processing_instruction'));
}
next;
}
if (/^N/) { # notation definition
my ($name) = $';
if (defined $files) {
push (@properties, GeneratedId => $files);
}
$dtd_h->notation_decl ({ Name => $name, @properties })
if ($dtd_h->can('notation_decl'));
@properties = (); undef $files;
next;
}
if (/^S/) { # subdoc definition
my ($name) = $';
if (defined $files) {
push (@properties, GeneratedId => $files);
}
$dtd_h->subdoc_entity_decl ({ Name => $name, @properties })
if ($dtd_h->can('subdoc_entity_decl'));
@properties = (); undef $files;
next;
}
if (/^T/) { # external SGML text entity definition
my ($name) = $';
if (defined $files) {
push (@properties, GeneratedId => $files);
}
$dtd_h->external_sgml_entity_decl ({ Name => $name, @properties })
if ($dtd_h->can('external_sgml_entity_decl'));
@properties = (); undef $files;
next;
}
if (/^D/) { # data attribute
# FIXME
my $message = "XML::ESISParser: can't handle data attributes yet\n";
if ($err_h->can('error')) {
$err_h->error ({ Message => $message });
} else {
die "$message";
}
next;
}
if (/^D/) { # link attribute
# FIXME
my $message = "XML::ESISParser: can't handle link attributes yet\n";
if ($err_h->can('error')) {
$err_h->error ({ Message => $message });
} else {
die "$message";
}
next;
}
if (/^{/) { # subdoc start
my ($name) = $';
$doc_h->start_subdoc ({ Name => $name })
if ($doc_h->can('start_subdoc'));
next;
}
if (/^}/) { # subdoc end
my ($name) = $';
$doc_h->end_subdoc ({ Name => $name })
if ($doc_h->can('end_subdoc'));
next;
}
if (/^#/) { # appinfo
my ($text) = $';
$doc_h->appinfo ({ Text => $text })
if ($doc_h->can('appinfo'));
next;
}
if (/^i/) { # next element is an included subelement
push (@properties, IncludedSubelement => 1);
next;
}
if (/^e/) { # next element is declared empty
push (@properties, Empty => 1);
next;
}
if (/^C/) { # conforming
$doc_h->conforming({})
if ($doc_h->can('conforming'));
next;
}
if (/^$self->{ParseOptions}{NSGMLS}:/) { # `nsgmls' error
my $message = $_;
if ($err_h->can('error')) {
$err_h->error ({ Message => $message });
} else {
die "$message\n";
}
next;
}
my ($op) = substr ($_, 0, 1);
my $message = "XML::ESISParser::parse_fh: ESIS command character \`$op' not recognized when reading line \`$_' around line $line ($.)";
if ($err_h->can('error')) {
$err_h->error ({ Message => $message });
} else {
die "$message";
}
}
if ($doc_h->can('end_document')) {
return $doc_h->end_document({});
} else {
return ();
}
}
1;
__END__
=head1 NAME
XML::ESISParser - Perl SAX parser using nsgmls
=head1 SYNOPSIS
use XML::ESISParser;
$parser = XML::ESISParser->new( [OPTIONS] );
$result = $parser->parse( [OPTIONS] );
$result = $parser->parse($string);
=head1 DESCRIPTION
C<XML::ESISParser> is a Perl SAX parser using the `nsgmls' command of
James Clark's SGML Parser (SP), a validating XML and SGML parser.
This man page summarizes the specific options, handlers, and
properties supported by C<XML::ESISParser>; please refer to the Perl
SAX standard in `C<SAX.pod>' for general usage information.
C<XML::ESISParser> defaults to parsing XML and has an option for
parsing SGML.
`C<nsgmls>' source, and binaries for some platforms, is available from
<http://www.jclark.com/>. `C<nsgmls>' is included in both the SP and
Jade packages.
=head1 METHODS
=over 4
=item new
Creates a new parser object. Default options for parsing, described
below, are passed as key-value pairs or as a single hash. Options may
be changed directly in the parser object unless stated otherwise.
Options passed to `C<parse()>' override the default options in the
parser object for the duration of the parse.
=back
=head1 OPTIONS
The following options are supported by C<XML::ESISParser>:
Handler default handler to receive events
DocumentHandler handler to receive document events
DTDHandler handler to receive DTD events
ErrorHandler handler to receive error events
Source hash containing the input source for parsing
IsSGML the document to be parsed is in SGML
If no handlers are provided then all events will be silently ignored.
If a single string argument is passed to the `C<parse()>' method, it
is treated as if a `C<Source>' option was given with a `C<String>'
parameter.
The `C<Source>' hash may contain the following parameters:
ByteStream The raw byte stream (file handle) containing the
document.
String A string containing the document.
SystemId The system identifier (URI) of the document.
If more than one of `C<ByteStream>', `C<String>', or `C<SystemId>',
then preference is given first to `C<ByteStream>', then `C<String>',
then `C<SystemId>'.
=head1 HANDLERS
The following handlers and properties are supported by
C<XML::ESISParser>:
=head2 DocumentHandler methods
=over 4
=item start_document
Receive notification of the beginning of a document.
No properties defined.
=item end_document
Receive notification of the end of a document.
No properties defined.
=item start_element
Receive notification of the beginning of an element.
Name The element type name.
Attributes A hash containing the attributes attached to the
element, if any.
IncludedSubelement This element is an included subelement.
Empty This element is declared empty.
The `C<Attributes>' hash contains only string values. The `C<Empty>'
flag is not set for an element that merely has no content, it is set
only if the DTD declares it empty.
BETA: Attribute values currently do not expand SData entities into
entity objects, they are still in the system data notation used by
nsgmls (inside `|'). A future version of XML::ESISParser will also
convert other types of attributes into their respective objects,
currently just their notation or entity names are given.
=item end_element
Receive notification of the end of an element.
Name The element type name.
=item characters
Receive notification of character data.
Data The characters from the document.
=item record_end
Receive notification of a record end sequence. XML applications
should convert this to a new-line.
=item processing_instruction
Receive notification of a processing instruction.
Target The processing instruction target in XML.
Data The processing instruction data, if any.
=item internal_entity_ref
Receive notification of a system data (SData) internal entity
reference.
Name The name of the internal entity reference.
=item external_entity_ref
Receive notification of a external entity reference.
Name The name of the external entity reference.
=item start_subdoc
Receive notification of the start of a sub document.
Name The name of the external entity reference.
=item end_subdoc
Receive notification of the end of a sub document.
Name The name of the external entity reference.
=item conforming
Receive notification that the document just parsed conforms to it's
document type declaration (DTD).
No properties defined.
=back
=head2 DTDHandler methods
=over 4
=item external_entity_decl
Receive notification of an external entity declaration.
Name The entity's entity name.
Type The entity's type (CDATA, NDATA, etc.)
SystemId The entity's system identifier.
PublicId The entity's public identifier, if any.
GeneratedId Generated system identifiers, if any.
=item internal_entity_decl
Receive notification of an internal entity declaration.
Name The entity's entity name.
Type The entity's type (CDATA, NDATA, etc.)
Value The entity's character value.
=item notation_decl
Receive notification of a notation declaration.
Name The notation's name.
SystemId The notation's system identifier.
PublicId The notation's public identifier, if any.
GeneratedId Generated system identifiers, if any.
=item subdoc_entity_decl
Receive notification of a subdocument entity declaration.
Name The entity's entity name.
SystemId The entity's system identifier.
PublicId The entity's public identifier, if any.
GeneratedId Generated system identifiers, if any.
=item external_sgml_entity_decl
Receive notification of an external SGML-entity declaration.
Name The entity's entity name.
SystemId The entity's system identifier.
PublicId The entity's public identifier, if any.
GeneratedId Generated system identifiers, if any.
=back
=head1 AUTHOR
Ken MacLeod, ken@bitsko.slc.ut.us
=head1 SEE ALSO
perl(1), PerlSAX.pod(3)
Extensible Markup Language (XML) <http://www.w3c.org/XML/>
SAX 1.0: The Simple API for XML <http://www.megginson.com/SAX/>
SGML Parser (SP) <http://www.jclark.com/sp/>
=cut
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,661 |
Sherlock Holmes Came to China: Detective Fiction, Cultural Meditations, and Chinese Modernity
Yan, Vivien WEI
Research output: Book Chapters | Papers in Conference Proceedings › Book Chapter › Research › peer-review
One important criterion for deciding whether a text belongs to world literature is its ability to circulate among different regions in various languages. If we apply this standard to early Chinese detective fiction, which appeared in the beginning of the twentieth century and flourished during the Republican China period until 1949, it is probably the case that none of these works can be regarded as world literature, due to the fact that few of them have been translated into other languages; still less have had influence on the production of crime fiction globally. Chinese detective fiction was mainly consumed in China at that time. However, if we examine classics of detective fiction in world literature, Sherlock Holmes stories have a far-reaching influence on the overall Chinese detective fiction.
Crime fiction as world literature
Louise NILSSON, David DAMROSCH, Theo D'HAEN
Bloomsbury Publishing Plc
https://doi.org/10.5040/9781501319365.ch-017
Literatures as World Literature
Detective Fiction
WEI, Y. V. (2017). Sherlock Holmes Came to China: Detective Fiction, Cultural Meditations, and Chinese Modernity. In L. NILSSON, D. DAMROSCH, & T. D'HAEN (Eds.), Crime fiction as world literature (pp. 245-256). (Literatures as World Literature). New York: Bloomsbury Publishing Plc. https://doi.org/10.5040/9781501319365.ch-017
WEI, Yan, Vivien. / Sherlock Holmes Came to China: Detective Fiction, Cultural Meditations, and Chinese Modernity. Crime fiction as world literature. editor / Louise NILSSON ; David DAMROSCH ; Theo D'HAEN. New York : Bloomsbury Publishing Plc, 2017. pp. 245-256 (Literatures as World Literature).
@inbook{2b9f370ee6cd46f6a9c92df3e834f471,
title = "Sherlock Holmes Came to China: Detective Fiction, Cultural Meditations, and Chinese Modernity",
abstract = "One important criterion for deciding whether a text belongs to world literature is its ability to circulate among different regions in various languages. If we apply this standard to early Chinese detective fiction, which appeared in the beginning of the twentieth century and flourished during the Republican China period until 1949, it is probably the case that none of these works can be regarded as world literature, due to the fact that few of them have been translated into other languages; still less have had influence on the production of crime fiction globally. Chinese detective fiction was mainly consumed in China at that time. However, if we examine classics of detective fiction in world literature, Sherlock Holmes stories have a far-reaching influence on the overall Chinese detective fiction.",
author = "WEI, {Yan, Vivien}",
doi = "10.5040/9781501319365.ch-017",
series = "Literatures as World Literature",
publisher = "Bloomsbury Publishing Plc",
editor = "Louise NILSSON and David DAMROSCH and Theo D'HAEN",
booktitle = "Crime fiction as world literature",
WEI, YV 2017, Sherlock Holmes Came to China: Detective Fiction, Cultural Meditations, and Chinese Modernity. in L NILSSON, D DAMROSCH & T D'HAEN (eds), Crime fiction as world literature. Literatures as World Literature, Bloomsbury Publishing Plc, New York, pp. 245-256. https://doi.org/10.5040/9781501319365.ch-017
Sherlock Holmes Came to China: Detective Fiction, Cultural Meditations, and Chinese Modernity. / WEI, Yan, Vivien.
Crime fiction as world literature. ed. / Louise NILSSON; David DAMROSCH; Theo D'HAEN. New York : Bloomsbury Publishing Plc, 2017. p. 245-256 (Literatures as World Literature).
T1 - Sherlock Holmes Came to China: Detective Fiction, Cultural Meditations, and Chinese Modernity
AU - WEI, Yan, Vivien
N2 - One important criterion for deciding whether a text belongs to world literature is its ability to circulate among different regions in various languages. If we apply this standard to early Chinese detective fiction, which appeared in the beginning of the twentieth century and flourished during the Republican China period until 1949, it is probably the case that none of these works can be regarded as world literature, due to the fact that few of them have been translated into other languages; still less have had influence on the production of crime fiction globally. Chinese detective fiction was mainly consumed in China at that time. However, if we examine classics of detective fiction in world literature, Sherlock Holmes stories have a far-reaching influence on the overall Chinese detective fiction.
AB - One important criterion for deciding whether a text belongs to world literature is its ability to circulate among different regions in various languages. If we apply this standard to early Chinese detective fiction, which appeared in the beginning of the twentieth century and flourished during the Republican China period until 1949, it is probably the case that none of these works can be regarded as world literature, due to the fact that few of them have been translated into other languages; still less have had influence on the production of crime fiction globally. Chinese detective fiction was mainly consumed in China at that time. However, if we examine classics of detective fiction in world literature, Sherlock Holmes stories have a far-reaching influence on the overall Chinese detective fiction.
UR - https://commons.ln.edu.hk/sw_master/7455/
U2 - 10.5040/9781501319365.ch-017
DO - 10.5040/9781501319365.ch-017
M3 - Book Chapter
T3 - Literatures as World Literature
BT - Crime fiction as world literature
A2 - NILSSON, Louise
A2 - DAMROSCH, David
A2 - D'HAEN, Theo
PB - Bloomsbury Publishing Plc
WEI YV. Sherlock Holmes Came to China: Detective Fiction, Cultural Meditations, and Chinese Modernity. In NILSSON L, DAMROSCH D, D'HAEN T, editors, Crime fiction as world literature. New York: Bloomsbury Publishing Plc. 2017. p. 245-256. (Literatures as World Literature). https://doi.org/10.5040/9781501319365.ch-017
10.5040/9781501319365.ch-017 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,944 |
1. verb To return home by driving. When do you plan to drive home from the party?
2. verb To drive someone to their home. In this usage, a noun or pronoun can be used between "drive" and "home." Can any of you guys drive me home after the student council meeting? I'll drive her home, don't worry, Mrs. Smith. Sorry I'm late, I had to drive home the whole team.
3. verb To emphasize something. In this usage, a noun or pronoun can be used between "drive" and "home." The nightly news always drives home the presence of danger in our city and makes my anxiety worse.
4. noun The ride to one's home. In this usage, it is a set phrase. You can sleep on the drive home—it'll take five hours, after all. The traffic jam made my drive home twice as long as normal.
make something clearly and fully understood by the use of repeated or forcefully direct arguments.
The verbs hammer , press , and ram are also used in place of drive .
make sure that somebody understands something completely, for example by repeating it often: The instructor tried to drive home to us the need for safety precautions before diving. ♢ Police used statistics to hammer home their warning about car theft. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,012 |
<?php
require('includes/init.php');
require('config.php');
require('includes/db-core.php');
require('includes/helper-functions.php');
use adLDAP\adLDAP,adLDAP\adLDAPException;
require('lib/password-hash.php');
require('lib/adLDAP/adLDAP.php');
$ssl_suffix = mf_get_ssl_suffix();
$dbh = mf_connect_db();
//immediately redirect to installer page if the config values are correct but no ap_forms table found
$query = "select count(*) from ".MF_TABLE_PREFIX."settings";
$sth = $dbh->prepare($query);
try{
$sth->execute($params);
}catch(PDOException $e) {
header("Location: http{$ssl_suffix}://".$_SERVER['HTTP_HOST'].mf_get_dirname($_SERVER['PHP_SELF'])."/installer.php");
exit;
}
$mf_settings = mf_get_settings($dbh);
$allow_login = false;
//check for ip address restriction, if enabled, compare the ip address
if(!empty($mf_settings['enable_ip_restriction'])){
$allow_login = mf_is_whitelisted_ip_address($dbh,$_SERVER['REMOTE_ADDR']);
if($allow_login === false){
$_SESSION['MF_LOGIN_ERROR'] = '<br/>- Forbidden -<br/><br/>Your IP address ('.$_SERVER['REMOTE_ADDR'].') <br/>is not allowed to access this page.<br/><br/>';
}
}else{
$allow_login = true;
}
//process login submission
if($allow_login){
//check if the user has "remember me" cookie or not
if(!empty($_COOKIE['mf_remember']) && empty($_SESSION['mf_logged_in'])){
$query = "SELECT
`user_id`,
`priv_administer`,
`priv_new_forms`,
`priv_new_themes`
FROM
`".MF_TABLE_PREFIX."users`
WHERE
`cookie_hash`=? and `status`=1";
$params = array($_COOKIE['mf_remember']);
$sth = mf_do_query($query,$params,$dbh);
$row = mf_do_fetch_result($sth);
$user_id = $row['user_id'];
$priv_administer = (int) $row['priv_administer'];
$priv_new_forms = (int) $row['priv_new_forms'];
$priv_new_themes = (int) $row['priv_new_themes'];
if(!empty($user_id)){
$_SESSION['mf_logged_in'] = true;
$_SESSION['mf_user_id'] = $user_id;
$_SESSION['mf_user_privileges']['priv_administer'] = $priv_administer;
$_SESSION['mf_user_privileges']['priv_new_forms'] = $priv_new_forms;
$_SESSION['mf_user_privileges']['priv_new_themes'] = $priv_new_themes;
}
}
//redirect to form manager if already logged-in
if(!empty($_SESSION['mf_logged_in']) && $_SESSION['mf_logged_in'] == true){
header("Location: http{$ssl_suffix}://".$_SERVER['HTTP_HOST'].mf_get_dirname($_SERVER['PHP_SELF'])."/manage_forms.php");
exit;
}
if(!empty($_POST['submit'])){
$username = strtolower(trim($_POST['admin_username']));
$password = trim($_POST['admin_password']);
$remember_me = trim($_POST['admin_remember']);
if(empty($username) || empty($password)){
$_SESSION['MF_LOGIN_ERROR'] = 'Incorrect email or password!';
}else{
$auth_result = false;
$run_local_auth = true; //the default is to run local authentication against MachForm user database
//if LDAP authentication enabled
if(!empty($mf_settings['ldap_enable'])){
//don't run local authentication if LDAP Exclusive is being set to 1
if(!empty($mf_settings['ldap_exclusive'])){
$run_local_auth = false;
}
$ldap_login_verified = false;
$domain_controllers_array = explode(',', $mf_settings['ldap_host']);
$ldap_use_tls = false;
$ldap_use_ssl = false;
if($mf_settings['ldap_encryption'] == 'ssl'){
$ldap_use_ssl = true;
}else if($mf_settings['ldap_encryption'] == 'tls'){
$ldap_use_tls = true;
}
//check the provided username/email
//if the "account suffix" setting exist and the user entered the @domain.com part, let's clean it
if(!empty($mf_settings['ldap_account_suffix'])){
$username = str_ireplace($mf_settings['ldap_account_suffix'], '', $username);
}
if($mf_settings['ldap_type'] == 'ad'){ //if using Active Directory
try {
if(empty($mf_settings['ldap_basedn'])){
$mf_settings['ldap_basedn'] = null; //if baseDN is empty, set to null, so that adLDAP will find the defaultNamingContext
}
$adldap = new adLDAP(array(
"account_suffix" => $mf_settings['ldap_account_suffix'],
"base_dn" => $mf_settings['ldap_basedn'],
"domain_controllers" => $domain_controllers_array,
"use_tls" => $ldap_use_tls,
"use_ssl" => $ldap_use_ssl,
"ad_port" => (int) $mf_settings['ldap_port']
));
$adldap_auth_result = false;
$adldap_auth_result = $adldap->authenticate($username, $password);
if(empty($mf_settings['ldap_basedn'])){
$adldap->setBaseDn($adldap->findBaseDn());
}
if($adldap_auth_result === true){
//get user full name
$ldap_user_info = $adldap->user()->info($username,array("givenname","sn"));
$user_fullname = $ldap_user_info[0]['givenname'][0].' '.$ldap_user_info[0]['sn'][0];
//check for required groups, if any
if(!empty($mf_settings['ldap_required_group'])){
$ldap_required_group_array = explode(",", $mf_settings['ldap_required_group']);
array_walk($ldap_required_group_array, 'mf_trim_value');
$user_in_group = false;
foreach ($ldap_required_group_array as $group_name) {
$group_check_result = $adldap->user()->inGroup($username,$group_name);
if($group_check_result === true){
$user_in_group = true;
break;
}
}
if($user_in_group){
$ldap_login_verified = true;
}else{
$ldap_login_verified = false;
$ldap_error_message = "You're not in an authorized group! (LDAP)";
}
}else{
$ldap_login_verified = true;
}
}else{
$ldap_login_verified = false;
$ldap_error_message = "Incorrect login credentials! (LDAP)";
}
} catch (adLDAPException $e) {
$ldap_error_message = $e->getMessage();
}
}else if($mf_settings['ldap_type'] == 'openldap'){ //if using OpenLDAP
try {
//get one of the provided domain controller
$selected_domain_controller = $domain_controllers_array[array_rand($domain_controllers_array)];
if($ldap_use_ssl){
$opldap_conn = ldap_connect("ldaps://".$selected_domain_controller, (int) $mf_settings['ldap_port']);
}else{
$opldap_conn = ldap_connect("ldap://".$selected_domain_controller, (int) $mf_settings['ldap_port']);
}
//set LDAP version
ldap_set_option($opldap_conn, LDAP_OPT_PROTOCOL_VERSION, 3);
if($ldap_use_tls) {
ldap_start_tls($opldap_conn);
}
//authenticate, bind as the user
$openldap_login_attribute = "uid";
$openldap_auth_result = false;
$openldap_auth_result = @ldap_bind($opldap_conn, $openldap_login_attribute.'='.$username.','.$mf_settings['ldap_basedn'], $password);
if($openldap_auth_result === true){
//check for required groups, if any
if(!empty($mf_settings['ldap_required_group'])){
$ldap_required_group_array = explode(",", $mf_settings['ldap_required_group']);
array_walk($ldap_required_group_array, 'mf_trim_value');
array_walk($ldap_required_group_array, 'mf_strtolower_value');
$user_in_group = false;
$user_cn = $openldap_login_attribute.'='.$username.','.$mf_settings['ldap_basedn'];
$opldap_result = array();
$opldap_data = array();
$user_current_groups = array();
$opldap_result = ldap_search($opldap_conn, $mf_settings['ldap_basedn'], "( |(&(objectClass=groupOfUniqueNames)(uniqueMember={$user_cn}))(&(objectClass=groupOfNames)(member={$user_cn})) )",array('cn'));
$opldap_data = ldap_get_entries($opldap_conn, $opldap_result);
foreach ($opldap_data as $value) {
if(!empty($value['cn'][0])){
$user_current_groups[] = strtolower(trim($value['cn'][0]));
}
}
if(!empty($user_current_groups)){
if(count(array_intersect($user_current_groups, $ldap_required_group_array)) > 0){
$user_in_group = true;
}
}
if($user_in_group){
$ldap_login_verified = true;
}else{
$ldap_login_verified = false;
$ldap_error_message = "You're not in an authorized group! (LDAP)";
}
}else{
$ldap_login_verified = true;
}
//get user full name
$opldap_result = ldap_search($opldap_conn, $mf_settings['ldap_basedn'], "({$openldap_login_attribute}={$username})", array($openldap_login_attribute, 'sn', 'givenname', 'mail'));
$opldap_data = ldap_get_entries($opldap_conn, $opldap_result);
$user_fullname = $opldap_data[0]['givenname'][0].' '.$opldap_data[0]['sn'][0];
$username = $opldap_data[0]['mail'][0]; //machform uses email as the main identifier
}else{
$ldap_login_verified = false;
$ldap_error_message = "Incorrect login credentials! (LDAP)";
}
} catch (Exception $e) {
$ldap_error_message = $e->getMessage();
}
}
if($ldap_login_verified){
//once verified through LDAP, no need to run local auth
$auth_result = true;
$run_local_auth = false;
//if user authenticated within LDAP, check if the local user account already exist or not
//if not exist, create the account
if(strstr($username, '@') === false){
$user_email = $username.$mf_settings['ldap_account_suffix'];
}else{
$user_email = $username;
}
$query = "SELECT
`user_password`,
`user_id`,
`priv_administer`,
`priv_new_forms`,
`priv_new_themes`,
`tsv_enable`,
`tsv_secret`,
`login_attempt_date`,
`login_attempt_count`
FROM
`".MF_TABLE_PREFIX."users`
WHERE
`user_email`=? and `status`=1";
$params = array($user_email);
$sth = mf_do_query($query,$params,$dbh);
$row = mf_do_fetch_result($sth);
if(!empty($row)){
//load existing user data
$stored_password_hash = $row['user_password'];
$user_id = $row['user_id'];
$priv_administer = (int) $row['priv_administer'];
$priv_new_forms = (int) $row['priv_new_forms'];
$priv_new_themes = (int) $row['priv_new_themes'];
$tsv_enable = (int) $row['tsv_enable'];
$tsv_secret = $row['tsv_secret'];
$login_attempt_date = $row['login_attempt_date'];
$login_attempt_count = $row['login_attempt_count'];
//update user fullname from LDAP into local users table
$query = "UPDATE ".MF_TABLE_PREFIX."users
SET user_fullname = ?
WHERE `user_email`=? and `status`=1";
$params = array($user_fullname,$user_email);
mf_do_query($query,$params,$dbh);
}else{
//create local account using info from LDAP
$priv_administer = 0;
$priv_new_forms = 1;
$priv_new_themes = 1;
$query = "INSERT INTO
`".MF_TABLE_PREFIX."users`(
`user_email`,
`user_password`,
`user_fullname`,
`priv_administer`,
`priv_new_forms`,
`priv_new_themes`,
`status`)
VALUES (?, ?, ?, ?, ?, ?, ?);";
$params = array(
$user_email,
'',
$user_fullname,
$priv_administer,
$priv_new_forms,
$priv_new_themes,
1);
mf_do_query($query,$params,$dbh);
$user_id = (int) $dbh->lastInsertId();
}
}else{
//prepare for local auth, revert back the username to email
$username = $username.trim($mf_settings['ldap_account_suffix']);
}
}
if($run_local_auth){
//start local authentication---------------------
//get the password hash from the database
$query = "SELECT
`user_password`,
`user_id`,
`priv_administer`,
`priv_new_forms`,
`priv_new_themes`,
`tsv_enable`,
`tsv_secret`,
`login_attempt_date`,
`login_attempt_count`
FROM
`".MF_TABLE_PREFIX."users`
WHERE
`user_email`=? and `status`=1";
$params = array($username);
$sth = mf_do_query($query,$params,$dbh);
$row = mf_do_fetch_result($sth);
$stored_password_hash = $row['user_password'];
$user_id = $row['user_id'];
$priv_administer = (int) $row['priv_administer'];
$priv_new_forms = (int) $row['priv_new_forms'];
$priv_new_themes = (int) $row['priv_new_themes'];
$tsv_enable = (int) $row['tsv_enable'];
$tsv_secret = $row['tsv_secret'];
$login_attempt_date = $row['login_attempt_date'];
$login_attempt_count = $row['login_attempt_count'];
//check the password
$hasher = new PasswordHash(8, FALSE);
$auth_result = $hasher->CheckPassword($password, $stored_password_hash);
//end local authentication---------------------
}
if($auth_result){
$login_is_valid = true;
}else{
$login_is_valid = false;
if(!empty($ldap_error_message)){
$_SESSION['MF_LOGIN_ERROR'] = $ldap_error_message;
}else{
$_SESSION['MF_LOGIN_ERROR'] = 'Incorrect email or password!';
}
//if account locking enabled, increase the login attempt counter
if(!empty($mf_settings['enable_account_locking']) && !empty($user_id)){
$query = "UPDATE ".MF_TABLE_PREFIX."users
SET
login_attempt_date=?,
login_attempt_count=(login_attempt_count + 1)
WHERE
user_id = ?";
$new_login_attempt_date = date("Y-m-d H:i:s");
$params = array($new_login_attempt_date,$user_id);
mf_do_query($query,$params,$dbh);
}
}
//check for account locking status
if(!empty($mf_settings['enable_account_locking']) && !empty($user_id)){
$account_lock_period = (int) $mf_settings['account_lock_period'];
$account_lock_max_attempts = (int) $mf_settings['account_lock_max_attempts'];
$account_blocked_message = "Sorry, this account is temporarily blocked. Please try again after {$account_lock_period} minutes.";
//check the lock period
$login_attempt_date = strtotime($login_attempt_date);
$account_lock_expiry_date = $login_attempt_date + (60 * $account_lock_period);
$current_datetime = strtotime(date("Y-m-d H:i:s"));
//if lock period still valid, check max attempts
if($current_datetime < $account_lock_expiry_date){
//if max attempts already exceed the limit, block the user
if($login_attempt_count >= $account_lock_max_attempts){
$login_is_valid = false;
$_SESSION['MF_LOGIN_ERROR'] = $account_blocked_message;
}
}else{
//else if lock period already expired
$query = "UPDATE ".MF_TABLE_PREFIX."users
SET
login_attempt_date = ?,
login_attempt_count = ?
WHERE
user_id = ?";
//if password is correct, reset to zero
//else if password is incorrect, set counter to 1
if($login_is_valid){
$login_attempt_date = '';
$login_attempt_count = 0;
}else{
$login_attempt_date = date("Y-m-d H:i:s");
$login_attempt_count = 1;
}
$params = array($login_attempt_date,$login_attempt_count,$user_id);
mf_do_query($query,$params,$dbh);
}
}
//if login is validated and password is correct
if($login_is_valid){
//check for 2-Step Verification, is it enabled or not
$show_tsv_page = false;
//if TSV is enforced globally
if(!empty($mf_settings['enforce_tsv'])){
$show_tsv_page = true;
if(empty($tsv_secret)){
//display TSV setup page
$tsv_page_target = 'setup';
}else{
//display TSV verify page
$tsv_page_target = 'verify';
}
}else{
if(!empty($tsv_enable)){
$show_tsv_page = true;
if(empty($tsv_secret)){
//display TSV setup page
$tsv_page_target = 'setup';
}else{
//display TSV verify page
$tsv_page_target = 'verify';
}
}
}
if($show_tsv_page === true){
if($tsv_page_target == 'setup'){
//display TSV setup page
$_SESSION['mf_tsv_setup'] = $user_id;
$_SESSION['mf_tsv_setup_remember_me'] = $remember_me;
header("Location: http{$ssl_suffix}://".$_SERVER['HTTP_HOST'].mf_get_dirname($_SERVER['PHP_SELF'])."/login_tsv_setup.php");
exit;
}else if($tsv_page_target == 'verify'){
$_SESSION['mf_tsv_verify'] = $user_id;
$_SESSION['mf_tsv_verify_remember_me'] = $remember_me;
header("Location: http{$ssl_suffix}://".$_SERVER['HTTP_HOST'].mf_get_dirname($_SERVER['PHP_SELF'])."/login_verify.php");
exit;
}
}else{
//reset login counter
$query = "UPDATE ".MF_TABLE_PREFIX."users
SET
login_attempt_date = NULL,
login_attempt_count = 0
WHERE
user_id = ?";
$params = array($user_id);
mf_do_query($query,$params,$dbh);
//regenerate session id for protection against session fixation
session_regenerate_id();
//set the session variables for the user=========
$_SESSION['mf_logged_in'] = true;
$_SESSION['mf_user_id'] = $user_id;
$_SESSION['mf_user_privileges']['priv_administer'] = $priv_administer;
$_SESSION['mf_user_privileges']['priv_new_forms'] = $priv_new_forms;
$_SESSION['mf_user_privileges']['priv_new_themes'] = $priv_new_themes;
//===============================================
//update last_login_date and last_ip_address
$last_login_date = date("Y-m-d H:i:s");
$last_ip_address = $_SERVER['REMOTE_ADDR'];
$query = "UPDATE ".MF_TABLE_PREFIX."users set last_login_date=?,last_ip_address=? WHERE `user_id`=?";
$params = array($last_login_date,$last_ip_address,$user_id);
mf_do_query($query,$params,$dbh);
//if the user select the "remember me option"
//set the cookie and make it active for the next 30 days
if(!empty($remember_me)){
$cookie_hash = $hasher->HashPassword(mt_rand()); //generate random hash and save it into ap_users table
$query = "update ".MF_TABLE_PREFIX."users set cookie_hash=? where `user_id`=?";
$params = array($cookie_hash,$user_id);
mf_do_query($query,$params,$dbh);
//send the cookie
setcookie('mf_remember',$cookie_hash, time()+3600*24*30, "/");
}
if(!empty($_SESSION['prev_referer'])){
$next_page = $_SESSION['prev_referer'];
unset($_SESSION['prev_referer']);
header("Location: http{$ssl_suffix}://".$_SERVER['HTTP_HOST'].$next_page);
exit;
}else{
header("Location: http{$ssl_suffix}://".$_SERVER['HTTP_HOST'].mf_get_dirname($_SERVER['PHP_SELF'])."/manage_forms.php");
exit;
}
}
}
}
}
if(!empty($_GET['from'])){
$_SESSION['prev_referer'] = base64_decode($_GET['from']);
}
} //end allow_login
?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title>MachForm Admin Panel</title>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<meta name="robots" content="index, nofollow" />
<link rel="stylesheet" type="text/css" href="css/main.css" media="screen" />
<!--[if IE 7]>
<link rel="stylesheet" type="text/css" href="css/ie7.css" media="screen" />
<![endif]-->
<!--[if IE 8]>
<link rel="stylesheet" type="text/css" href="css/ie8.css" media="screen" />
<![endif]-->
<!--[if IE 9]>
<link rel="stylesheet" type="text/css" href="css/ie9.css" media="screen" />
<![endif]-->
<link href="css/theme.css" rel="stylesheet" type="text/css" />
<?php
if(!empty($mf_settings['admin_theme'])){
echo '<link href="css/themes/theme_'.$mf_settings['admin_theme'].'.css" rel="stylesheet" type="text/css" />';
}
?>
<link href="css/bb_buttons.css" rel="stylesheet" type="text/css" />
<link type="text/css" href="js/jquery-ui/themes/base/jquery.ui.all.css" rel="stylesheet" />
<link type="text/css" href="css/edit_form.css" rel="stylesheet" />
<link type="text/css" href="js/datepick/smoothness.datepick.css" rel="stylesheet" />
<link href="css/override.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="bg" class="login_page">
<div id="container">
<div id="header">
<?php
if(!empty($mf_settings['admin_image_url'])){
$machform_logo_main = $mf_settings['admin_image_url'];
}else{
if(!empty($mf_settings['admin_theme'])){
$machform_logo_main = 'images/machform_logo_'.$mf_settings['admin_theme'].'.png';
}else{
$machform_logo_main = 'images/machform_logo.png';
}
}
?>
<div id="logo">
<img class="title" src="<?php echo $machform_logo_main; ?>" style="margin-left: 8px" alt="MachForm" />
</div>
<div class="clear"></div>
</div>
<div id="main">
<div id="content">
<div class="post login_main">
<div style="padding-top: 10px">
<div>
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} | 6,857 |
{"url":"http:\/\/www.nag.com\/numeric\/FL\/nagdoc_fl24\/html\/E05\/e05jff.html","text":"E05 Chapter Contents\nE05 Chapter Introduction\nNAG Library Manual\n\n# NAG Library Routine DocumentE05JFF\n\nNote:\u00a0 before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.\n\n## 1\u00a0\u00a0Purpose\n\nE05JFF may be used to supply individual integer optional parameters to E05JBF. The initialization routine E05JAF must have been called before calling E05JFF.\n\n## 2\u00a0\u00a0Specification\n\n SUBROUTINE\u00a0E05JFF\u00a0( OPTSTR, IVALUE, COMM, LCOMM, IFAIL)\n INTEGER IVALUE, LCOMM, IFAIL REAL\u00a0(KIND=nag_wp) COMM(LCOMM) CHARACTER(*) OPTSTR\n\n## 3\u00a0\u00a0Description\n\nE05JFF may be used to supply values for integer optional parameters to E05JBF. It is only necessary to call E05JFF for those parameters whose values are to be different from their default values. One call to E05JFF sets one parameter value.\nEach integer optional parameter is defined by a single character string in OPTSTR and the corresponding value in IVALUE. For example, the following allows the function evaluations limit to be defined:\n```NF = 1000\nCALL E05JFF ('Function Evaluations Limit', NF, COMM, LCOMM, IFAIL)\n```\nA complete list of optional parameters, their symbolic names and default values is given in Section 11 in E05JBF.\n\nNone.\n\n## 5\u00a0\u00a0Parameters\n\n1: \u00a0\u00a0\u2002 OPTSTR \u2013 CHARACTER(*)Input\nOn entry: a string identifying an integer-valued optional parameter (as described in Section 11 in E05JBF).\n2: \u00a0\u00a0\u2002 IVALUE \u2013 INTEGERInput\nOn entry: an integer value associated with the optional parameter in OPTSTR.\n3: \u00a0\u00a0\u2002 COMM(LCOMM) \u2013 REAL\u00a0(KIND=nag_wp)\u00a0arrayCommunication Array\nOn exit: COMM must not be altered between calls to any of the routines E05JBF, E05JCF, E05JDF, E05JEF, E05JFF, E05JGF, E05JHF, E05JJF, E05JKF and E05JLF.\n4: \u00a0\u00a0\u2002 LCOMM \u2013 INTEGERInput\nOn entry: the dimension of the array COMM as declared in the (sub)program from which E05JFF is called.\nConstraint: ${\\mathbf{LCOMM}}\\ge 100$.\n5: \u00a0\u00a0\u2002 IFAIL \u2013 INTEGERInput\/Output\nOn entry: IFAIL must be set to $0$, $-1\\text{\u200b or \u200b}1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.\nFor environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\\text{\u200b or \u200b}1$\u00a0is recommended. If the output of error messages is undesirable, then the value $1$\u00a0is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\\mathbf{1}\\text{\u200b or \u200b}\\mathbf{1}$\u00a0is used it is essential to test the value of IFAIL on exit.\nOn exit: ${\\mathbf{IFAIL}}={\\mathbf{0}}$\u00a0unless the routine detects an error or a warning has been flagged (see Section 6).\n\n## 6\u00a0\u00a0Error Indicators and Warnings\n\nIf on entry ${\\mathbf{IFAIL}}={\\mathbf{0}}$\u00a0or $-{\\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).\nErrors or warnings detected by the routine:\n${\\mathbf{IFAIL}}=1$\n On\u00a0entry, ${\\mathbf{LCOMM}}<100$, or the initialization routine E05JAF has not been called.\n${\\mathbf{IFAIL}}=2$\nThe optional parameter given in OPTSTR is invalid. A keyword or keyword combination was not recognized.\n${\\mathbf{IFAIL}}=3$\nThe option value to be set is out of range with respect to the optional parameter given in OPTSTR. See Section 11 in E05JBF for allowable values of the optional parameters.\n\nNot applicable.\n\n## 8\u00a0\u00a0Further Comments\n\nE05JCF or E05JDF may also be used to supply integer optional parameters to E05JBF.\n\n## 9\u00a0\u00a0Example\n\nSee Section 9 in E05JCF.","date":"2014-03-14 23:23:18","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 14, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.984494686126709, \"perplexity\": 4536.978771678417}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"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-2014-10\/segments\/1394678695499\/warc\/CC-MAIN-20140313024455-00067-ip-10-183-142-35.ec2.internal.warc.gz\"}"} | null | null |
Q: Is there a good WPF pivot control? Does anyone have any experience with a good wpf pivot table control?
A: DevExpress Grid control has good pivot functionality. Used it for Winforms a lot. I think the WPF version is also available.
A: The Xceed WPF Grid looks like it has a lot of great capabilities. We use their WinForms grid and it does a pretty good job. They have a demo app you can download that shows off the different ways you can use the grid.
A: VIBlend's data grid control has pivot table capabilities. I'm not sure if they have a WPF version but you can certainly host WinForms controls in WPF. Another alternative is to try hosting the MS Office OWC.
A: If possible, I also need to be able to drag column headers and make them row headers and have the data summarize and group accordingly. Something along the lines of old ActiveX DataDynamics Dynamicube.
http://www.datadynamics.com/Products/ProductOverview.aspx?Product=DC
Auto Summary, Filtering of the Data Items being used, etc. without having to write a lot of code to do it in a custom fashion.
A: Alternative:
Excel OWC is a great query and reporting tool if you are running OLAP. It's a little dated and poorly documented, but works well on the intranet and can squeak by over the net.
http://msdn.microsoft.com/en-us/magazine/cc164070.aspx
A: I would suggest WPF Toolkit which can be downloaded from DatGrid available in Codeplex. This is compatible with the latest WPF(.NET3.5 SP1) which is free and have almost all the features for a general purpose(and even more than that) But there are commercial vendors who have good grid controls(Not really free). Like Xceed, Infragistics, Component One, Telerik
A: Currently there are no WPF Pivot Grid controls. The vendor most likely to have it, DevExpress does not yet have a WPF version of the XtraPivotGrid.
Your best bet is to use XtraPivotGrid hosted inside your WPF control.
The other thing you can do is to use another grid vendor and do the "pivoting" by using LINQ or by manipulating the DataTable manually.
A: DevExpress Pivot Grid for WPF is almost ready. It will be released in the first half of the year.
A: I am a consultant at Infragistics and I've been working exclusively the last few weeks with the Infragistics XamPivotGrid. We've been working to make this control fast and memory efficient. As a user and a developer, I am highly impressed with the usability of this control. You can check out this control in the WPF and the Silverlight NetAdvantage Data Visualization products at www.infragistics.com!
:-)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,505 |
Q: Calculating all number from a text file (division) I have a file or a text which contains huge numbers. This is how it looks:
2622256647732477952, 3146707977278973440, 3776049572734768128, 4531259487281721344, 5437511384738065408, 6525013661685678080, 7830016394022813696, 9396019672827375616, 11275223607392849920, 13530268328871419904,
I want to divide every number by the factor of 100. Is there any fast way to do this? notepadd++ maybe? or any 3rd party editor which is able to do such stuff?
It's around 1000 numbers would be pretty time consuming to do this manually.
A: All the numbers seem to be integers. If that is true, and if they are all above 100 (the divisor), why not just use a regular expression to insert a decimal point in every number.
In Notepad++ try:
Search string: (\d+)(\d{2})
Replace string: $1.$2
Check "Regular expression" box and hit "Replace all".
Edit:
In the special case you mention in your comment, where the decimals should just be disregarded, you can simply use (\d+)\d{2} as search string and $1 as the replace string. Note that the result won't be rounded to the nearest integer though (11189 should become 112 really, but you'll get 111).
Other options include importing the string into Excel or other spreadsheet software and use a formula in there, writing a javascript snippet to split the string up and divide each number etc.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,538 |
package org.wso2.carbon.siddhi.editor.core.internal;
import org.osgi.framework.BundleContext;
import org.wso2.siddhi.core.SiddhiManager;
/**
* EditorDataHolder referenced through org.wso2.carbon.siddhi.debugger.core.internal.ServiceComponent
*/
public class EditorDataHolder {
private static EditorDataHolder instance = new EditorDataHolder();
private static SiddhiManager siddhiManager;
private static BundleContext bundleContext;
private static DebugProcessorService debugProcessorService;
private EditorDataHolder() {
}
public static EditorDataHolder getInstance() {
return instance;
}
public static SiddhiManager getSiddhiManager() {
return siddhiManager;
}
public static void setSiddhiManager(SiddhiManager siddhiManager) {
EditorDataHolder.siddhiManager = siddhiManager;
}
public static DebugProcessorService getDebugProcessorService() {
return debugProcessorService;
}
public static void setDebugProcessorService(DebugProcessorService debugProcessorService) {
EditorDataHolder.debugProcessorService = debugProcessorService;
}
public static void setBundleContext(BundleContext bundleContext) {
EditorDataHolder.bundleContext = bundleContext;
}
public static BundleContext getBundleContext() {
return bundleContext;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 388 |
O Consórcio das Universidades Comunitárias Gaúchas (COMUNG) é um sistema de educação superior existente no Rio Grande do Sul. Ele reúne as instituições comunitárias de ensino superior do estado. Ele foi fundado em março de 1993, por 9 universidades comunitários do RS.
Seus compromissos básicos são com a qualidade universitária, a democracia, a comunidade, a participação no processo de desenvolvimento social, cultural e econômico da região e com a manutenção de suas características de instituição pública não-estatal.
Integram o COMUNG as seguintes instituições:
Universidade Feevale (Feevale)
Centro Universitário Metodista IPA (IPA)
Pontifícia Universidade Católica do Rio Grande do Sul (PUCRS)
Universidade Católica de Pelotas (UCPel)
Universidade de Caxias do Sul (UCS)
Universidade de Cruz Alta (Unicruz)
Centro Universitário Franciscano (Unifra)
Universidade Regional do Noroeste do Estado do Rio Grande do Sul (Unijuí)
Universidade de Santa Cruz do Sul (Unisc)
Universidade do Vale do Rio dos Sinos (Unisinos)
Centro Universitário La Salle (Unilasalle)
Universidade do Vale do Taquari (Univates)
Universidade de Passo Fundo (UPF)
Universidade da Região da Campanha (Urcamp)
Universidade Regional Integrada do Alto Uruguai e das Missões (URI)
O Consórcio atende mais de 50% dos universitários gaúchos, oferecendo mais de 600 cursos de graduação.
Ney José Lazzari, reitor da Univates, é o presidente desde 2008, sendo reeleito seis vezes, com o atual mandato indo até o final de 2015.
Ver também
Lista de instituições de ensino superior do Rio Grande do Sul
Ligações externas
Comung - Site oficial
Associações de instituições de ensino superior
Consórcios empresariais do Brasil | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,373 |
'use strict'
/* eslint-env browser */
const { remote } = require('electron')
const updater = remote.require('electron-simple-updater')
setText('version', updater.version)
setText('build', updater.buildId)
attachUiHandlers()
attachUpdaterHandlers()
function attachUiHandlers () {
const btnUpdate = document.getElementById('btn-update')
const btnInstall = document.getElementById('btn-install')
const chkAutomatically = document.getElementById('automatically')
btnUpdate.addEventListener('click', () => {
updater.checkForUpdates()
document.body.classList.add('update-downloading')
})
btnInstall.addEventListener('click', () => {
updater.downloadUpdate()
})
chkAutomatically.addEventListener('change', function () {
updater.setOptions('autoDownload', this.checked)
})
}
function attachUpdaterHandlers () {
updater.on('update-available', onUpdateAvailable)
updater.on('update-downloading', onUpdateDownloading)
updater.on('update-downloaded', onUpdateDownloaded)
updater.setOptions('logger', {
info (text) { log('info', text) },
warn (text) { log('warn', text) }
})
function onUpdateAvailable (meta) {
setText('new-version', meta.version)
setText('description', meta.readme)
document.body.className = 'update-available'
}
function onUpdateDownloading () {
document.body.classList.add('update-downloading')
}
function onUpdateDownloaded () {
if (window.confirm('The app has been updated. Would you like to restart it now?')) {
updater.quitAndInstall()
}
}
function log (level, text) {
const logMessages = document.getElementById('log-messages')
const p = document.createElement('p')
p.appendChild(document.createTextNode(`[${level}] ${text}`))
logMessages.appendChild(p)
}
}
function setText (id, text) {
document.getElementById(id).appendChild(
document.createTextNode(text)
)
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,375 |
\section{Introduction}
Cosmic inflation \cite{inflation} is a paradigm
beyond the Standard Big Bang Cosmology which addresses the
flatness, isotropy, homogeneity, horizon and relic problems.
Furthermore, quantum fluctuations during inflation provide a seed for the
large--scale structure formation. On the other hand, the nature of
the inflaton remains a mystery.
It has recently been conjectured that the only scalar of the
Standard Model (SM),
the Higgs field, may play its role \cite{Bezrukov:2007ep}, given
a large Higgs coupling to scalar curvature.
The Higgs sector is also quite special because it has a direct access to the
``hidden sector'' \cite{Patt:2006fw},
whose existence is motivated by various ideas including
string theory, dark matter, etc. Understanding the Higgs couplings would
thus provide us with unique information about the hidden world.
There are two dim-2 operators in the Standard Model that can couple
to the hidden sector at the renormalizable level: $F_{\mu\nu}^Y$ and
$H^\dagger H$. The latter is also Lorentz invariant, so it can in addition
couple to scalar curvature $R$. One can therefore add the following
dim--4 operators to the Standard Model Lagrangian,
\begin{eqnarray}
&& \Delta {\cal L}_1 = c_1~ H^\dagger H \vert S \vert^2 \;, \nonumber\\
&& \Delta {\cal L}_2 = c_2~ H^\dagger H R \;,
\end{eqnarray}
where $S$ is a singlet under the Standard Model and $c_i$ are dimensionless
constants.
In what follows, we consider the minimal option for the hidden sector:
we take $S$ to be a real scalar $s$ and impose the symmetry
$s\leftrightarrow -s$.
The coupling $c_1$ controls the Higgs decay into the hidden sector as well
as the Higgs--singlet mixing, which can be measured at the LHC.
$c_2$ can be responsible for inflation: with $\vert c_2 \vert \gg 1$,
a large value of the Higgs field in the early universe leads to
exponential expansion.
In this work, we consider the possibility that the inflaton is a mixture
of the Higgs with the singlet from the hidden sector. The nature of
the inflaton depends on the relations among various couplings. For example,
if $c_1$ is positive, stability of the potential requires a mixed
inflaton. On the other hand, for negative $c_1$ the inflaton can be purely
the Higgs or the singlet field. These considerations leave an imprint
on the low energy physics, affecting the couplings of the Higgs--like
particles to be studied at the LHC.
We also study the unitarity issues which plague the original
Higgs inflation \cite{unitarity1,unitarity2}. We construct a unitary
completion \cite{giudicelee} of the Higgs portal inflation and show that the
constraints on the couplings survive the unitarization procedure.
The paper is organized as follows. We first present a general analysis
of the SM extension with a real singlet in the presence of large
couplings to scalar curvature. We study stability of the system during
inflation and derive the corresponding constraints on the couplings.
Then we study implications for low energy physics.
We further discuss the differences from the pure Higgs \cite{Clark:2009dc} and
singlet inflation \cite{singletinflation,Okada:2010jd}, and present an example of the
unitary completion of our model.
\section{Higgs--singlet combination as the inflaton}
In this section, we study an extension of the Higgs sector with a real
scalar $s$ in the presence of large couplings $\xi_{h,s}$ to scalar
curvature $R$. This system can lead to inflation
based on scale invariance of the Einstein frame
scalar potential at large field values.
The relevant Jordan frame Lagrangian in the unitary gauge
$H^T=(0,h/\sqrt{2})$
is
\begin{equation}
{\cal L}/ \sqrt{-g} = - {1\over 2} M^2_{\rm Pl} R - {1\over 2} \xi_h h^2 R - {1\over 2} \xi_s s^2 R
+ {1\over 2} (\partial_\mu h)^2 + {1\over 2} (\partial_\mu s)^2
- V
\end{equation}
with $\xi_{h,s} >0$\footnote{We do not consider negative $\xi_i$ since
in this case the theory is not well defined at large field values.} and
\begin{equation}
V= {1\over 4} \lambda_h h^4 + {1\over 4}\lambda_{hs} s^2 h^2 + {1\over 4}\lambda_s s^4 +
{1\over 2} m_h^2 h^2 + {1\over 2} m_s^2 s^2 \;. \label{V}
\end{equation}
The transformation to the Einstein frame, in which the only coupling
to curvature is $-1/2 M_{\rm Pl}^2 R$,
is defined by
\begin{equation}
\tilde g_{\mu\nu}=\Omega^2 g_{\mu\nu} ~~,~~
\Omega^2= 1 + { \xi_h h^2 + \xi_s s^2 \over M_{\rm Pl}^2} \;. \label{Omega}
\end{equation}
Consider now the limit
\begin{equation}
\xi_h h^2 + \xi_s s^2 \gg M_{\rm Pl}^2
\end{equation}
and set $M_{\rm Pl}$ to 1. In this case, $\Omega^2 \simeq
\xi_h h^2 + \xi_s s^2 $.
Then, according to \cite{Salopek:1988qh},
the kinetic terms and the potential in the Einstein frame take the form
\begin{eqnarray}
{\cal L}_{\rm kin} &=&
{3\over 4} \biggl( \partial_\mu \log (\xi_h h^2 + \xi_s s^2) \biggr)^2
+{1\over 2} {1\over \xi_h h^2 + \xi_s s^2} \biggl( (\partial_\mu h)^2 +
(\partial_\mu s)^2 \biggr) \;, \nonumber\\
U &=& {1\over (\xi_h h^2 + \xi_s s^2)^2} ~V \;. \label{Lkin}
\end{eqnarray}
Introduce new variables
\begin{eqnarray}
&& \chi = \sqrt{3\over 2} ~ \log (\xi_h h^2 + \xi_s s^2) \;, \nonumber\\
&& \tau = {h\over s} \;.
\end{eqnarray}
In terms of these variables, the kinetic terms read
\begin{eqnarray}
{\cal L}_{\rm kin} &=& {1\over 2} \biggl( 1+ {1\over 6} {\tau^2 +1\over
\xi_h \tau^2 +\xi_s} \biggr)~ (\partial_\mu \chi)^2 +
{1\over \sqrt{6}} ~{(\xi_s-\xi_h) \tau \over (\xi_h \tau^2 +\xi_s)^2}
(\partial_\mu \chi) (\partial^\mu \tau) \nonumber\\
&+&
{1\over 2}{ \xi_h^2 \tau^2 +\xi_s^2 \over (\xi_h \tau^2 +\xi_s)^3 }(\partial_\mu \tau)^2
\;.
\end{eqnarray}
We are interested in the case of large non-minimal couplings,
$ \xi \equiv \xi_h +\xi_s \gg 1$. Since the $(\partial_\mu \tau)^2$
term scales like $1/\xi$ and so does the mixing term $(\partial_\mu \chi) (\partial^\mu \tau) $, in terms of (approximately) canonically normalized variables the mixing is suppressed. Then, to leading order in $1/\xi$, we have
\begin{equation}
{\cal L}_{\rm kin}= {1\over 2 } (\partial_\mu \chi)^2 +
{1\over 2} { \xi_h^2 \tau^2 +\xi_s^2 \over (\xi_h \tau^2 +\xi_s)^3 }(\partial_\mu \tau)^2 \;.
\end{equation}
In the following limiting cases, one can define a particularly simple
canonically normalized variable $\tau'$ :
\begin{eqnarray}
&& \xi_s \gg \xi_h ~~{\rm or}~~ \tau \rightarrow 0 ~~,~~~~ \tau'= {\tau\over
\sqrt{\xi_s}} ~, \nonumber\\
&& \xi_h \gg \xi_s ~~{\rm or}~~ \tau \rightarrow \infty ~~,~~ \tau'= {1\over
\sqrt{\xi_h} \tau} ~, \nonumber\\
&& \xi_h = \xi_s ~~,~~~~~~~~~~~~~~~~~~~ \tau'= {1\over{\sqrt{\xi_h}}} \arctan \tau \;.
\end{eqnarray}
The scalar potential at large $\chi$ reads
\begin{equation}
U= {\lambda_h \tau^4 + \lambda_{hs} \tau^2 +\lambda_s \over
4 (\xi_h \tau^2 +\xi_s)^2} \;.
\end{equation}
Its minima are classified according to
\begin{eqnarray}
&& (1)~2 \lambda_h \xi_s - \lambda_{hs} \xi_h >0~,~
2 \lambda_s \xi_h - \lambda_{hs} \xi_s >0~,~~~~\tau = \sqrt{
2 \lambda_s \xi_h - \lambda_{hs} \xi_s \over
2 \lambda_h \xi_s - \lambda_{hs} \xi_h } \;, \nonumber\\
&& (2)~2 \lambda_h \xi_s - \lambda_{hs} \xi_h >0~,~
2 \lambda_s \xi_h - \lambda_{hs} \xi_s <0~,~~~~\tau=0 \;, \nonumber\\
&& (3)~2 \lambda_h \xi_s - \lambda_{hs} \xi_h <0~,~
2 \lambda_s \xi_h - \lambda_{hs} \xi_s >0~,~~~~\tau=\infty \;, \nonumber\\
&& (4)~2 \lambda_h \xi_s - \lambda_{hs} \xi_h <0~,~
2 \lambda_s \xi_h - \lambda_{hs} \xi_s <0~,~~~~\tau=0,\infty \;. \label{taumin}
\end{eqnarray}
Note that in the last case there are 2 local minima. We are primarily
interested in the first case, when the inflaton is a combination of the
Higgs field and the singlet. The corresponding value of the potential
is then
\begin{equation}
U\Bigl\vert_{\rm min~(1) }= {1\over 16} {4 \lambda_s \lambda_h - \lambda_{hs}^2
\over \lambda_s \xi_h^2 + \lambda_h \xi_s^2 - \lambda_{hs} \xi_s \xi_h } \;,
\label{Umin}
\end{equation}
while in cases (2) and (3), it is $\lambda_s /(4\xi_s^2)$ and
$\lambda_h /(4\xi_h^2)$, respectively.
The condition $ 4 \lambda_s \lambda_h - \lambda_{hs}^2 >0$ guarantees the
absence of very deep minima with negative vacuum energy at
field values $m_{h,s} \ll h,s $, which make the electroweak vacuum metastable. With this constraint, the vacuum energy above is positive
(the denominator is positive by the minimization conditions).
In all of the cases, the $\tau$-field is heavy and can be integrated out.
Indeed, the mass of the canonically normalized $\tau' $ scales as
$1/ \sqrt{\xi}$ in Planck units, while the Hubble rate scales like
$ \sqrt{U}\vert_{\rm min} \sim 1/ \xi$. Thus
\begin{equation}
m_{\tau'}^2 \gg H^2 \;.
\end{equation}
The potential value (\ref{Umin}) plays the role of the quartic coupling
over $\xi^2$
in the single field inflation model of Bezrukov--Shaposhnikov
\cite{Bezrukov:2007ep}.
Retaining the subleading $M_{\rm Pl}^2/(\xi_h h^2 + \xi_s s^2)$ term
in $\Omega^2$, the inflaton potential for option (1) becomes
\begin{equation}
U(\chi)= {\lambda_{\rm eff} \over 4\xi_h^2}~
\Bigl( 1+ {\rm exp}\left( -{2\chi\over \sqrt{6} } \right) \Bigr)^{-2}
\end{equation}
in Planck units, where
\begin{equation}
\lambda_{\rm eff} = {1\over 4} {4 \lambda_s \lambda_h - \lambda_{hs}^2
\over \lambda_s + \lambda_h x^2 - \lambda_{hs} x }
\end{equation}
and
\begin{equation}
x = {\xi_s \over \xi_h} \;.
\end{equation}
The inflationary parameters are read off from this potential
\cite{Bezrukov:2007ep}.
At large $\chi$, the potential is flat and inflation takes place.
As $\chi$ rolls to smaller values, the $\epsilon$-parameter
approaches 1 and inflation ends.
In terms of
\begin{equation}
\tilde h \simeq {1\over \sqrt{\xi_h} } ~\exp \bigl( \chi /\sqrt{6} \bigr) \;,
\end{equation}
the $\epsilon$-parameter is given by
\begin{equation}
\epsilon = {1\over 2} \left( dU/d\chi \over U \right)^2 \simeq {4 \over 3 \xi^2_h \tilde h^4 } \;.
\end{equation}
This gives $\tilde h_{\rm end} = (4/3)^{1/4}/ \sqrt{\xi_h}$. Then, for a given number of $e$-folds
$N$, the initial value of the inflaton is $\tilde h_{\rm in} \approx \sqrt{4N/(3\xi_h)}$.
Together with the COBE normalization $U/\epsilon= 0.027^4$ \cite{Lyth:1998xn}, this fixes $\xi_h$ in terms of
$\lambda_{\rm eff}$,
\begin{equation}
\xi_h \simeq \sqrt{{\lambda_{\rm eff}\over 3 }} ~ {N\over 0.027^2} \;. \label{xi}
\end{equation}
For $\sqrt{\lambda_{\rm eff}} \sim 1$ and $N=60$, the non-minimal gravity coupling $\xi_h$ is about
50000. The spectral index is predicted to be
\begin{equation}
n \simeq 1- {2\over N} \simeq 0.97 \;,
\end{equation}
while the tensor to scalar perturbation ratio is $r\simeq 12/N^2 \simeq 0.0033$.
These are robust (tree--level) predictions of our framework to be tested in the future.\footnote{In multi--field variants of this scenario, large non--Gaussianity can also
be generated \cite{Gong:2011cd}.}
They are independent of the nature of the inflaton and
result from the shape of the potential, which in turn follows from a large
coupling to scalar curvature.
\subsection{Parameter space analysis}
In this subsection, we analyze the parameter space consistent with the inflaton being
a mixture of the Higgs and singlet fields.
The relavant inflation parameters are evaluated at a high energy scale $\mu$. A
particular choice of $\mu$ advocated in \cite{Bezrukov:2008ej} is to take $\mu\sim m_t(\chi)$
which minimizes the effect of logarithms in the Coleman-Weinberg potential. In
this case, $\mu\sim M_{\rm Pl}/ \sqrt{\xi}$ for large $\chi$.
However, as we discuss in Sec.~\ref{unitaritysection},
the theory is only well defined up to the scale $M_{\rm Pl}/ \xi$ at which
unitarity violation appears.
We thus expect new physics to set in at the
unitarity scale $\mu_U\sim M_{\rm Pl}/ \xi$ and take $\mu_U$ as the scale at which
the input parameters are specified. We will assume that the new physics does not
significantly affect the tree level relations of the previous section
(see an example in Sec.~\ref{unitaritysection}), yet it is likely to
affect the running of the relevant parameters above $\mu_U$.
For successful
Higgs--singlet inflation, we impose at $\mu_U$:
\begin{eqnarray}
&& 2 \lambda_h x - \lambda_{hs} >0 \;, \nonumber\\
&& 2 \lambda_s {1\over x} - \lambda_{hs} >0 \;, \nonumber\\
&& 4 \lambda_s \lambda_h - \lambda_{hs}^2 >0 \;. \label{constraints1}
\end{eqnarray}
The third inequality provides an independent constraint for $\lambda_{hs}<0$, while
for positive $\lambda_{hs}$ it follows from the first two. In addition we
require perturbativity and stability at $\mu_U$:
\begin{eqnarray}
&& \vert \lambda_i \vert < 1 \;, \nonumber\\
&& \lambda_{h,s} > 0 \;. \label{constraints2}
\end{eqnarray}
Our (judicial) definition of the perturbative couplings is motivated by
perturbativity at the Planck scale. We note that above $ M_{\rm Pl}/ \xi$,
the running of $\lambda_i$ slows down due to the suppression of the inflaton
self-coupling or, equivalently, suppression of its propagator in the Jordan frame
(see, e.g. \cite{singletinflation}). Therefore, our procedure is expected to take into account the bulk
of radiative corrections.
Finally, given uncertainties from new physics above $\mu_U$,
the running of the parameters, e.g. the spectral index
\cite{Bezrukov:2008ej,DeSimone:2008ei,Barvinsky:2008ia,Bezrukov:2009db},
during inflation cannot be reliably calculated
in our framework and we therefore omit it.
The renormalization group (RG) equations governing the evolution
of couplings below $\mu_U$
are given by \cite{singletinflation}:
\begin{eqnarray}
16\pi^2 {d \lambda_h \over dt}&=& 24 \lambda_h^2 -6 y_t^4 +{3\over 8} \Bigl(
2 g^4 + (g^2 + g^{\prime 2})^2 \Bigr) \nonumber\\
&+& (-9 g^2 -3 g^{\prime 2}+12 y_t^2) \lambda_h + {1\over 2} \lambda_{hs}^2 \;, \nonumber\\
16\pi^2 {d \lambda_{hs} \over dt} &=& 4 \lambda_{hs}^2 + 12 \lambda_h \lambda_{hs}
-{3\over 2} (3 g^2 + g^{\prime 2}) \lambda_{hs} \nonumber\\
&+& 6 y_t^2 \lambda_{hs} +
6 \lambda_s \lambda_{hs} \;, \nonumber\\
16\pi^2 {d \lambda_{s} \over dt} &=& 2 \lambda_{hs}^2 + 18 \lambda_s^2 \;,
\end{eqnarray}
where $t = \ln (\mu/ m_t)$. The RG equations for the gauge and the top Yukawa couplings
can be found in \cite{Bezrukov:2008ej}. The low energy input values for these couplings are
$g(m_t)=0.64 , g'(m_t)=0.35 , g_3(m_t)=1.16$, while for the top Yukawa coupling we use
its running value at $m_t$, $y_t (m_t)=0.93$ \cite{Langenfeld:2010aj}.
For a given set of the low energy couplings
at $t=0$, we use the above RG equations to run them up to $t \approx 26$ and impose
the constraints (\ref{constraints1}) and (\ref{constraints2}).
\begin{figure}[ht]
\epsfig{figure=lh02x1.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=lh02x5.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=lh02x02.eps,height=5cm,width=5cm,angle=0}
\vspace{0.1cm}\epsfig{figure=lh015x1.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=lh023x1.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=ls015x1.eps,height=5cm,width=5cm,angle=0}
\medskip
\caption{Parameter space consistent with the mixed Higgs--singlet
inflaton. $\lambda_i$ are given at the scale $m_t$, while $x$ is a high energy
input. }
\label{fig1}
\end{figure}
In addition, we impose the low energy constraint at $m_t$
\begin{equation}
4 \lambda_s \lambda_h - \lambda_{hs}^2 >0 \label{constraints3}
\end{equation}
for $\lambda_{hs}<0$. This ensures that there are no deep
minima at some intermediate scale $s,h \gg m_s, m_h$ which can make
the electroweak vacuum short-lived.
It is a complementary constraint and (\ref{constraints1}) does not
guarantee that it is satisfied. We find that for $\lambda_{hs}<0$
the combination $\lambda_s \lambda_h$ can increase with energy
faster than $\lambda_{hs}^2$ such that parameter space allowed by
(\ref{constraints1}) may violate (\ref{constraints3}).
Our results are presented in Fig.~\ref{fig1}.
In the \{$\lambda_{hs},\lambda_s$\} plane, the parameter space at
$\lambda_{hs}>0$ is most strongly constrained by
$ 2 \lambda_s {1\over x} - \lambda_{hs} >0 $ and, for larger $\lambda_s$, by
$ 2 \lambda_h x - \lambda_{hs} >0 $. In the latter case, $\lambda_s$
contributes significantly to the running of $\lambda_{hs}$, but not to that of
$\lambda_{h}$, which eliminates parameter space to the right of some critical
value $\lambda_{hs}$. For negative $\lambda_{hs}$, the main constraint is
$ 4 \lambda_s \lambda_h - \lambda_{hs}^2 >0$ (both at $\mu_U$ and $m_t$) as well as perturbativity
which cuts off large values of $\lambda_s$ and $\vert \lambda_{hs}\vert$.
At $x\gg 1$ or $x\ll 1$, it becomes more difficult to satisfy either
$ 2 \lambda_s {1\over x} - \lambda_{hs} >0 $ or $ 2 \lambda_h x - \lambda_{hs} >0 $,
so only small positive values of $ \lambda_{hs} $ are allowed. On the
other hand, negative $ \lambda_{hs} $ are not affected by $x$.
Decreasing $\lambda_h$ eliminates most of the parameter space and leaves a
strip around $\lambda_{hs}=0$. The negative top quark contribution
to the $\beta$--function of $\lambda_h$ makes it run slower, reducing
$\lambda_h (\mu_U)$ and making it more difficult to
satisfy the constraints at $\mu_U$.
Naturally, at larger $\lambda_h$, parameter space opens
up. The range of allowed $\lambda_h$ is similar to that of the Standard Model subject
to the perturbativity and stability requirements, i.e. roughly
$0.14 < \lambda_h < 0.25 $.
Note that the value of $\xi_h$ is not important for our analysis.
Given $\lambda_{\rm eff}$, it is fixed at the scale $\mu_U$ by Eq.(\ref{xi}).
Since we are not interested in its value at low energies, its running
is not relevant for us.
\section{Phenomenological implications}
There are two phenomenologically acceptable possibilities
for the vacuum of our theory:
(a) $\langle h \rangle \not= 0, \langle s \rangle \not= 0$ and
(b) $\langle h \rangle \not= 0, \langle s \rangle = 0$.
They lead to different phenomenological implications.
\subsection{ $\langle h \rangle \not= 0, \langle s \rangle \not= 0$ }
Denoting $\langle h \rangle =v, \langle s \rangle =u$,
extremization of the low energy scalar potential (\ref{V}) requires
\begin{eqnarray}
&& v^2 = 2~ { \lambda_{hs} m_s^2 - 2 \lambda_s m_h^2 \over
4 \lambda_s \lambda_h - \lambda_{hs}^2 } \;, \nonumber\\
&& u^2 = 2~ { \lambda_{hs} m_h^2 - 2 \lambda_h m_s^2 \over
4 \lambda_s \lambda_h - \lambda_{hs}^2 } \;.
\end{eqnarray}
The diagonal matrix elements of the Hessian at this point are
$2 \lambda_s u^2$ and $2 \lambda_h v^2$, while its determinant is
$ (4 \lambda_s \lambda_h - \lambda_{hs}^2)v^2 u^2 $. Then,
the extremum is a local minimum if
\begin{eqnarray}
&& \lambda_{hs} m_h^2 - 2 \lambda_h m_s^2 > 0 \;,\nonumber\\
&& \lambda_{hs} m_s^2 - 2 \lambda_s m_h^2 > 0 \;,\nonumber\\
&& 4 \lambda_s \lambda_h - \lambda_{hs}^2 >0 \;. \label{ewbreaking}
\end{eqnarray}
In this case, the mass squared eigenvalues are
\begin{equation}
m_{1,2}^2= \lambda_h v^2 + \lambda_s u^2 \mp
\sqrt{(\lambda_s u^2 - \lambda_h v^2)^2 + \lambda_{hs}^2 u^2 v^2 }
\label{eigenvalues}
\end{equation}
with the mixing angle $\theta$ given by
\begin{equation}
\tan 2 \theta = {\lambda_{hs} u v \over \lambda_h v^2 - \lambda_s u^2} \;.
\label{tan}
\end{equation}
Here the mixing angle is defined by
\begin{equation}
O^T~ M^2 ~ O = {\rm diag}(m_1^2, m_2^2) ~~,~~ O=\left(
\begin{matrix}
\cos\theta & \sin\theta \\
-\sin\theta & \cos\theta
\end{matrix}
\right) \;,
\end{equation}
where $M^2$ is a 2$\times$2 mass squared matrix.
The range of $\theta$ is related to the ordering of the eigenvalues through
$ {\rm sign} (m_1^2-m_2^2 ) = {\rm sign} (\lambda_s u^2 - \lambda_h v^2)~
{\rm sign} (\cos 2 \theta) $ and we take $m_1$ to be the smaller eigenvalue.
The mass eigenstates are
\begin{eqnarray}
H_1 &=& s \cos\theta - h \sin\theta \;, \nonumber\\
H_2 &=& s \sin\theta + h \cos\theta \;.
\end{eqnarray}
Note that the lighter mass eigenstate $H_1$ is
``Higgs--like'' for $\lambda_s u^2 > \lambda_h v^2$ and
``singlet--like'' otherwise.
The former case corresponds to $\vert \theta\vert >\pi/4$.
One of the mass parameters, say $m_h^2$, can be fixed by requiring
the correct electroweak symmetry breaking,
$v=246$ GeV.
Then the constraints (\ref{ewbreaking}) specify the allowed
range of
\begin{equation}
r= {m_s^2 \over m_h^2} \;.
\end{equation}
The required local minimum exists in the following cases:
\begin{eqnarray}
{\underline {\lambda_{hs} < 0}} && \nonumber\\
&& m_h^2 <0~,~m_s^2<0 ~~:~~ 0<r<\infty ~, \nonumber\\
&& m_h^2 <0~,~m_s^2>0 ~~:~~ \vert r \vert <
{ \vert \lambda_{hs} \vert \over 2 \lambda_h }~, \nonumber\\
&& m_h^2 >0~,~m_s^2<0 ~~:~~ \vert r \vert >
{ 2\lambda_s \over \vert \lambda_{hs} \vert } ~,\nonumber\\
{\underline {\lambda_{hs} > 0}} && \nonumber\\
&& m_h^2 <0~,~m_s^2<0 ~~:~~
{ \lambda_{hs} \over 2 \lambda_h } < r < { 2\lambda_s \over \lambda_{hs} }~. \label{region}
\end{eqnarray}
\begin{figure}[ht]
\begin{center}
\epsfig{figure=sintheta.eps,height=5.6cm,width=7.6cm,angle=0}
\hspace{0.3cm} \epsfig{figure=higgsmass.eps,height=5.6cm,width=7.6cm,angle=0}
\end{center}
\medskip
\caption{
$\vert \sin\theta\vert$ and the Higgs masses as functions of $\lambda_{hs}$
and $r$ for $m_h^2 <0, m_s^2 <0$. (Here we redefine $\theta$ to be in
the range $\vert\theta\vert < \pi/4$).
The parameter range is
consistent with the mixed Higgs--singlet inflaton at $x\sim 1$. }
\label{fig2}
\end{figure}
We see that at negative $\lambda_{hs}$ there is more parameter
space available. In fact, negative values of $\lambda_{hs}$ are
preferred by the mixed Higgs-singlet inflaton (Fig.~\ref{fig1}),
especially away from the point $x=1$. Indeed, the relations
among the couplings ensuring $\langle h \rangle \not= 0, \langle s \rangle \not= 0$
at high and low energies are similar up to $\xi_i \leftrightarrow - m_i^2$.
Representative values of
the mixing angle consistent with the Higgs-singlet inflaton
are displayed in Fig.~\ref{fig2}.\footnote{
Eq.~(\ref{tan}) defines $\theta$ up to $\pi/2$, so in Fig.~\ref{fig2}
we take $\vert \theta\vert <\pi/4$. The small kinks in $\sin\theta$ at
$\lambda_{hs}=-0.24$ and $\lambda_{hs}=-0.08$ correspond to $\vert \tan 2\theta\vert
\rightarrow \infty$, which signals the change in the nature of the lighter
mass eigenstate.
In the rest of the paper, we take $-\sin\theta$ to be the $h$-component of
the $H_1$--state.}
Inspection of Eq.~(\ref{eigenvalues}) shows that the lighter
eigenvalue reaches its upper bound at $\lambda_{hs}=0$.
In this case, the mixing angle is zero and
\begin{equation}
m_1^2=2 \lambda_h v^2, \label{max}
\end{equation}
as in the Standard Model. According to Fig.~\ref{fig1}, this is about
175 GeV. The lower bound on the heavier eigenvalue is also
given by Eq.~(\ref{max}). With the lowest allowed $\lambda_h$,
it is about 135 GeV.
On the other hand, the heavier eigenvalue can be arbitrarily large.
Indeed, parametrizing
\begin{equation}
u^2 = v^2 ~ {2 \lambda_h r -\lambda_{hs} \over 2 \lambda_s - \lambda_{hs }r }\;,
\end{equation}
we see that $u\rightarrow \infty $ as $r \rightarrow 2\lambda_s /\lambda_{hs}$,
corresponding to the boundary of the region allowed by (\ref{region}).
In this case, $m_2^2 \simeq 2 \lambda_s u^2 \rightarrow \infty$
and the mixing angle approaches zero.
In terms of the input mass parameters, this corresponds to
$ \vert m^2_{h,s} \vert \rightarrow \infty $.
The singlet state can also be arbitrarily light:
in the limit $r \rightarrow \lambda_{hs}/(2\lambda_h) $, $u$ vanishes
and the light eigenstate becomes massless.
\subsubsection{LEP and electroweak constraints}
LEP has set stringent limits on the Higgs mass and couplings.
For our purposes, the relevant constraint is given in Fig.~10
of \cite{Barate:2003sz}, which sets a bound on
\begin{equation}
\zeta^2 \equiv \left( {g_{HZZ} \over g_{HZZ}^{\rm SM} } \right)^2 = \vert O_{2i}\vert^2
\end{equation}
depending on the mass $m_i$.
For a state with an ${\cal O}(1)$ component of $h$, the bound is
\begin{equation}
m > 114~{\rm GeV} \;,
\end{equation}
while for a state with a small admixture of $h$ the bound relaxes
and can be read off from Fig.~10 of \cite{Barate:2003sz}.
For example, with $ \vert O_{2i}\vert^2 \sim 10^{-2} $, the mass
can be as low as 20 GeV. In our case, the bound applies to the lighter
state only since the mass of the
heavier state is greater than $\sqrt{2\lambda_h}v > 114$ GeV.
We therefore require that if $m_1 < 114$ GeV, then
\begin{equation}
\sin^2\theta < \zeta^2 (m_1) \;.
\end{equation}
For our purposes, at $\zeta^2<0.5$ it suffices to use an approximation
$\log_{10} \zeta^2 (m) \simeq m/60 - 2.3 $ for $m$ measured
in GeV, which describes the data within a 95\% probability band.
Both mass eigenstates contribute to electroweak observables at a loop level.
For example, the correction to the $\rho$--parameter is \cite{Cerdeno:2006ha}
\begin{equation}
\Delta \rho^H = {3 G_F \over 8 \sqrt{2} \pi^2} \sum_i O_{2i}^2
\biggl( m_W^2 \ln {m_i^2 \over m_W^2} - m_Z^2 \ln {m_i^2 \over m_W^2 }
\biggr) \;.
\end{equation}
This is very similar to the SM Higgs contribution and therefore one can easily
translate the indirect Higgs mass bounds into a bound on
$\sum_i O_{2i}^2 \ln m_i^2$ \cite{Cerdeno:2006ha,Wells:2008xg}.
As the benchmark numbers we use the results of \cite{Erler:2010wa},
$m_H < 148$ GeV (197 GeV) at 95\% (99.5\%) CL. These bounds also incorporate
results of the LEP and Tevatron direct searches, although purely indirect
constraints give similar numbers \cite{Nakamura:2010zzi}.
Keeping in mind that the other oblique as well as vertex corrections behave
similar to the $\rho$--parameter in the heavy Higgs limit and
that
the sensitivity to the Higgs mass is only logarithmic,
we will use the combined fit results to impose
\begin{equation}
\sin^2 \theta ~\ln m_1 + \cos^2 \theta ~\ln m_2 < \ln 148 ~~(197)
\end{equation}
at 95\% (99.5\%) CL,
where the masses are measured in GeV.
\begin{figure}[ht]
\epsfig{figure=lh02x1r07.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=lh02x1r11.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=ls015x1r07.eps,height=5cm,width=5cm,angle=0}
\vspace{0.1cm}\epsfig{figure=ls015x1r11.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=ls015x1r03.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=ls015x1r3.eps,height=5cm,width=5cm,angle=0}
\medskip
\caption{ Parameter space allowed by the LEP and electroweak constraints
for $m_{s,h}^2 <0$. The region within the contour is allowed by
the mixed Higgs-singlet inflaton; grey -- allowed by LEP (and automatically
consistent with the 99.5\% CL electroweak constraints); black -- preferred by the
95\% CL electroweak constraints. $\lambda_i $ are given at the scale $m_t$. }
\label{fig3}
\end{figure}
The allowed parameter space is presented in Fig.~\ref{fig3}.
The main effect of the LEP constraint is to restrict the size
of $\vert \lambda_{hs} \vert$. The reduction of $\vert \lambda_{hs} \vert$
has a two--fold effect: it decreases the mixing angle and (typically)
increases the mass of the lighter state (Fig.~\ref{fig2}),
both of which help satisfy the constraint.
As expected, at larger $\lambda_h$ more parameter space survives.
Also, increasing $r$ has a positive effect by
making the light state somewhat heavier (Fig.~\ref{fig2}).
The 99.5\% CL electroweak constraint is satisfied in all the regions
allowed by the LEP bound. However, only a relatively small portion
of parameter space survives the 95\% CL constraint. For instance,
none of the points at $\lambda_s=0.2 , r=0.7$ are allowed.
Increasing $r$ to 1.1 opens up some parameter space close to the
border of the LEP allowed region. At these points, the nature of the
lighter eigenstate changes compared to the $r=0.7$ case:
it becomes Higgs-like. If the light state is singlet-like, it is more
difficult to satisfy the EW bound since it is dominated by
the term $\cos^2 \theta ~\ln m_2$ with $\cos\theta \sim 1$
and $m_2 > \sqrt{2 \lambda_h} v$.
In the $\{ \lambda_{hs},\lambda_h \}$ plane, the preferred region
is at lower $\lambda_h$, typically $\lambda_h <0.18$.
At $r=0.3$ and $r=3$, the range of $\lambda_{hs}$ must be restricted to
satisfy (\ref{region}). As mentioned above, the composition of the
lighter state changes with $r$: it is typically singlet--like at $r<1$
and Higgs--like otherwise. Thus, at $r=0.3$ the EW constraint
is dominated by $\cos^2 \theta ~\ln m_2$, while at $r=3$ it is dominated
by $\sin^2 \theta ~\ln m_1$.
A generalization of the analysis to $x$ different from 1 is straightforward.
As clear from Fig.~\ref{fig1}, at $x \gg 1$ or $x\ll 1$, most points at $\lambda_{hs}>0$
get eliminated and negative values of $\lambda_{hs}$ are strongly favored.
The collider signature of the $\langle s \rangle \not= 0$ scenario is a
universal suppression of production of the Higgs--like states,
\begin{equation}
\sigma (H_i) = \sigma (h)~ \vert O_{2i}\vert^2 \;.
\end{equation}
It is also possible that the decay $H_2 \rightarrow H_1 H_1$ will play a role
\cite{Bowen:2007ia}. It is kinematically allowed when $\lambda_{hs}$ is considerable
(see Fig.~\ref{fig2}). Negative $\lambda_{hs}$ are then largely ruled out by LEP,
while positive $\lambda_{hs}$ are usually consistent with LEP, especially
when $r$ is small or large. For example, at $r=0.3, \lambda_{hs}=0.05$,
the point
$m_1=57$ GeV, $m_2=144$ GeV and $\sin\theta=0.07$ is allowed by all the
constraints.
When $H_2$ is Higgs-like, for $m_2>135$ GeV it will decay
predominantly into gauge bosons and $H_1$ pairs. The branching
ratio for $H_2 \rightarrow H_1 H_1$ scales like $\lambda_{hs}^2 v^4/m_2^4$
\cite{Bowen:2007ia,Djouadi:2005gi},
which is significant for $\lambda_{hs} > 10^{-1}$ and a light $H_2$.
These values are however disfavored by LEP, so the mode $H_2 \rightarrow H_1 H_1$ is only competitive below or close to the WW threshold.
In this case, the final state contains 4 b--quarks with relatively low
(pairwise) invariant mass.
On the other hand, if $H_2$ is singlet--like, its production
cross section is too small and the effect of $H_2 \rightarrow H_1 H_1$
is unimportant.
\subsection{ $\langle h \rangle \not= 0, \langle s \rangle = 0$
\label{s0}}
In this case,
\begin{equation}
v^2= - {m_h^2 \over \lambda_h} \;.
\end{equation}
It is a local minimum if
\begin{eqnarray}
&& m_h^2 <0 \;, \nonumber\\
&& \lambda_{hs} m_h^2 - 2 \lambda_h m_s^2 < 0 \;.
\end{eqnarray}
There is no mixing between the Higgs and the singlet,
and the mass squared values are
\begin{equation}
m_1^2= 2 \lambda_h v^2~~,~~ m_2^2= {1\over 2} \lambda_{hs} v^2 + m_s^2 \;.
\label{massesS0}
\end{equation}
The allowed range of $r$ is
\begin{eqnarray}
{\underline {\lambda_{hs} < 0}} && \nonumber\\
&& m_s^2>0 ~~:~~ \vert r \vert >
{ \vert \lambda_{hs} \vert \over 2 \lambda_h }~, \nonumber\\
{\underline {\lambda_{hs} > 0}} && \nonumber\\
&& m_s^2<0 ~~:~~ r <
{ \lambda_{hs} \over 2 \lambda_h } ~, \nonumber\\
&& m_s^2>0 ~~:~~ 0< \vert r\vert < \infty ~. \label{constraints4}
\end{eqnarray}
The analysis of phenomenological constraints is straightforward. Since
$\lambda_h >0.14$, the Higgs LEP bound is satisfied automatically.
The electroweak precision data favor $\lambda_h <0.18$ (0.32) at
95\% (99.5\%) CL, as in the Standard Model. The allowed parameter space
can then be easily read off from Fig.~\ref{fig1}.
A collider signature of the presence of the singlet ``hidden sector''
would be an invisible decay $h \rightarrow ss$, which for $m_1>
2 m_2$ would typically have a significant branching ratio.
Note that since $\langle s \rangle = 0$,
the symmetry $s \rightarrow -s $ is not broken spontaneously and the singlet
must be pair--produced. It is relatively easy, especially at small $r$,
to satisfy the kinematic
constraint $m_1>2 m_2$: it requires
$ \lambda_{hs}< (1+2r) \lambda_h$ (see Eq.~(\ref{massesS0})).
The corresponding decay width is \cite{Bowen:2007ia}
\begin{equation}
\Gamma (h \rightarrow ss)= { \lambda_{hs}^2 v^2 \over 32 \pi m_1 } \sqrt{1- {4 m_2^2
\over m_1^2}} \;.
\end{equation}
For $\lambda_{hs}\gg 10^{-2}$, this would be the dominant decay mode until the
channel $h \rightarrow WW$ opens up. Above the $WW$ threshold,
its branching ratio drops to
${\cal O}( \lambda_{hs}^2 v^4/m_1^4 ) $,
which can still be significant for $\lambda_{hs} > 10^{-1}$.
Note that for the $\langle s \rangle =0$ case, larger values of
$\vert \lambda_{hs}\vert$, up to 0.4, are allowed.
\subsection{LHC prospects}
The Higgs profiling \cite{Englert:2011yb} at the LHC depends
crucially on whether or not
the SM Higgs field mixes with the singlet. If it does, there are two
states whose masses can be determined by the resonance peak
measurements. The mixing angle can then be determined by the production
cross section of these states in a particular production mode.
These observables allow us to disentangle 3 quantities
(up to a sign ambiguity):
\begin{equation}
m_1 , m_2, \sigma_{\rm prod} \Rightarrow \lambda_h v^2,
\lambda_s u^2 , \lambda_{hs} u v
\end{equation}
Furthermore, for a sufficiently heavy $H_2$, measurements of
the cascade
decay $H_2 \rightarrow H_1 H_1$ would determine one more combination of
these quantities such that $u$ can be derived \cite{Englert:2011yb}.
Since $v$ is known from $M_W$, the couplings
$\lambda_h, \lambda_s $ and $\lambda_{hs}$ would then be fixed
(the latter up to the sign). In this case, the Lagrangian parameters
are (almost fully) reconstructed. Ref.~\cite{Englert:2011yb} provides
an example of a point \{$m_1,m_2,\cos^2\theta$\}=\{115 GeV,400 GeV,0.25\},
which can be reconstructed with integrated luminosity 300 fb${}^{-1}$.
The result is $\lambda_h= 1.04 \pm 0.18$, $u=55.03 \pm 27.35$ GeV,
$\lambda_s = 7.61 \pm 3.51$ and $\lambda_{hs}= 4.52 \pm 2.23$.
This example shows that at least in some regions of parameter space,
where cascade decays are available,
one can determine the low energy Lagrangian.
The precision of this reconstruction grows with integrated luminosity.
Given the low energy parameters, one can evolve them to high energies and
verify whether various inflationary constraints are satisfied.
In the example above, the perturbativity constraint is violated.
Therefore if such parameter values are indeed found,
this would falsify the model.
In the case of small or no mixing, the situation is much more challenging,
although the latter option is very interesting as it provides us
with a viable dark matter candidate.
For a heavy singlet, the only possible signature would be missing energy.
If $h \rightarrow ss$ is kinematically allowed, the measurement of the
Higgs invisible width would determine $\lambda_{hs}$, up to a kinematical
factor. For Higgs masses above 150 GeV, the invisible decay
into dark matter
has a small branching fraction and therefore the LHC Higgs exclusion
limits apply (see e.g. \cite{Low:2011kp}).
For lower Higgs masses, the invisible
decay is efficient and $\lambda_{hs}$ can be determined using the methods
of \cite{Englert:2011yb}.
However,
the self--interaction coupling $\lambda_s$ is unlikely to be measured
at the LHC, so the Lagrangian cannot be fully reconstructed in this case.
\section{Comparison with the pure singlet or Higgs inflation}
It is instructive to compare the above scenario to the pure singlet or Higgs
inflation. According to Eq.~(\ref{taumin}), the singlet inflation
($\tau =0 $) requires at high energies
\begin{equation}
2 \lambda_s \xi_h - \lambda_{hs} \xi_s < 0 \;, \label{singletinfl}
\end{equation}
in which case the ``vacuum'' energy is $\lambda_s/(4 \xi_s^2)$.
This immediately implies
\begin{equation}
\lambda_{hs} >0 \;.
\end{equation}
The combination $ 2 \lambda_h \xi_s - \lambda_{hs} \xi_h $ can be
either positive or negative, depending on whether there exists another
local minimum at $\tau =\infty $.
We thus leave
$ 2 \lambda_h \xi_s - \lambda_{hs} \xi_h $ unconstrained.
We further impose the perturbativity and EW vacuum stability
bounds (\ref{constraints2}).\footnote{Note that singlet inflation
is impossible for negative $\lambda_{hs}$ even if $\xi_s \gg \xi_h$.
In this case, the point $ h=0 , s\rightarrow \infty$ is unstable
and $h$ rolls to infinity. Similarly, Higgs inflation is impossible
for $\lambda_{hs}<0$. For positive $\lambda_{hs}$, our numerical results
are in qualitative agreement with those of \cite{Clark:2009dc,singletinflation}. }
The phenomenological constraints depend crucially whether or not the singlet
develops a VEV at low energies. For the case $\langle s \rangle \not= 0$,
representative examples are presented in Fig.~\ref{fig4}. The existence of the local
minimum requires $ 4 \lambda_s \lambda_h - \lambda_{hs}^2 >0 $ at low
energies, which together with the LEP Higgs bound eliminates almost all of
the parameter space at $x=\xi_s/\xi_h \sim 1$. For $\lambda_s =0.15$ and
$x =1.5$, Eq.~(\ref{singletinfl})
requires $\lambda_{hs}>0.2$ at $\mu_U$. Due to the positive RG contribution
from $\lambda_h$, this bound is easier to satisfy at larger $\lambda_h$,
hence the slanted boundary on the left. Perturbativity and stability further
cut off large values of $\lambda_h, \lambda_{hs}$ and
small values of $\lambda_h$.
Considerable parameter space is only available at $x \gg 1$,
in which case (\ref{singletinfl}) amounts to positivity of $\lambda_{hs}$
and the allowed region is mainly constrained by the perturbativity and stability
considerations.
Since $\lambda_{hs}$ contributes positively to the running of $\lambda_h$,
smaller values of the latter are allowed by $\lambda_h (\mu_U) >0$
at large $\lambda_{hs}$. On the other hand, $\lambda_{hs}$ beyond 0.2
is ruled out by the LEP bound. The 99.5\% CL electroweak precision
constraint is satisfied in the entire region, while the 95\% CL limit
prefers $\lambda_h$ at the lower end.
\begin{figure}[ht]
\epsfig{figure=singletx15.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=singletx10.eps,height=5cm,width=5cm,angle=0}
\hspace{0.5cm}\epsfig{figure=higgsx01.eps,height=5cm,width=5cm,angle=0}
\medskip
\caption{ Constraints on pure singlet and Higgs inflation.
The region within the contour is consistent with singlet (left, center)
and Higgs (right) inflation; grey -- allowed by $\langle s \rangle \not= 0 $
and LEP; black -- favored by the
95\% CL electroweak constraints. Here $m_{s,h}^2 <0$ and $\lambda_i$ are
given at the scale $m_t$. }
\label{fig4}
\end{figure}
If the singlet has a zero VEV, there is no Higgs--singlet mixing and
the low energy constraints relax. The analysis is very similar to that
of Sec.~\ref{s0} and phenomenology restricts the values of $\lambda_h$
within the inflation--allowed contours of Fig.~\ref{fig4}. For example,
the EW preferred region is $\lambda_h < 0.18$.
Finally, Higgs inflation ($\tau = \infty$) requires
\begin{equation}
2 \lambda_h \xi_s - \lambda_{hs} \xi_h <0\;
\end{equation}
at high energies,
which again implies $\lambda_{hs} >0$. Significant parameter space
exists only at $x\ll 1$ and the above considerations largely apply,
up to $h \leftrightarrow s$. An example is shown in the right panel of
Fig.~\ref{fig4}.
The main difference between the ``mixed'' and ``pure'' inflaton scenarios lies
in the sign of $\lambda_{hs}$: the former allows for both signs, while the latter
requires a positive $\lambda_{hs}$.
Note that $\lambda_{hs} >0$ typically leads to $\langle s \rangle =0$
for a wide range of the parameters,
while $\lambda_{hs} <0$ prefers $\langle s \rangle \not= 0$
(see Eqs.~(\ref{region}),(\ref{constraints4})).
Thus the ``pure'' inflation would favor no singlet--Higgs mixing at
low energies and the only collider signature of the singlet would be
an invisible decay $h \rightarrow s s$, if kinematically allowed.
In the mixed inflaton case, $\langle s \rangle =0$ and
$\langle s \rangle \not= 0$ are almost equally likely. One therefore
often expects Higgs--singlet mixing at low energies which would
manifest itself in the existence of 2 Higgs--like states with universally
suppressed couplings to the SM fields.
We also observe that, at $\lambda_{hs} >0$, there is an overlap in the allowed parameter space for
the mixed and pure inflaton (at different $x$), so the collider
data alone may not be sufficient to discriminate among the different
scenarios.\footnote{Presently it also seems
challenging to determine the sign of $\lambda_{hs}$ at the LHC. One
is likely to need a linear collider to measure scalar self--interactions. }
\section{Unitarity issues} \label{unitaritysection}
The most problematic aspect of Higgs inflation and alike has to do
with unitarity. In the presence of large non-minimal couplings to gravity,
unitarity violation appears around the inflation (Hubble) scale
$M_{\rm Pl}/\xi$ \cite{unitarity1,unitarity2}.
This signals that the theory as it stands is incomplete and
should be supplemented by additional fields \cite{giudicelee}
or operators \cite{Lerner:2010mq} at high energies.
To see how unitarity violation comes about, consider our setup at field values
$|h|\ll 1/\xi_h$ and $|s|\ll 1/\xi_s$ in Planck units.
With $\Omega^2$ given in Eq.~(\ref{Omega}), the kinetic terms are
\begin{equation}
{\cal L}_{\rm kin} =
{3\over 4} \biggl( \partial_\mu \log (1+\xi_h h^2 + \xi_s s^2) \biggr)^2
+{1\over 2} {1\over 1+ \xi_h h^2 + \xi_s s^2} \biggl( (\partial_\mu h)^2 +
(\partial_\mu s)^2 \biggr) \;.
\end{equation}
To leading order in $h\xi_h$ and $s\xi_s$, the mixing between $h$ and $s$
is negligible and we have
\begin{equation}
{\cal L}_{\rm kin} \simeq \frac{1}{2}(1+6\xi^2_s s^2)(\partial_\mu s)^2 +
\frac{1}{2}(1+6\xi^2_h h^2)(\partial_\mu h)^2 \;.
\end{equation}
The canonically normalized variables are therefore
\begin{equation}
\rho=s(1+\xi^2_s s^2),\quad \varphi=h(1+\xi^2_h h^2)\;. \label{fielddef}
\end{equation}
We can now expand the fields in terms of expectation values and fluctuations:
\begin{equation}
\rho=\rho_0 + \bar\rho ~,~ \varphi= \varphi_0 + \bar\varphi\;,
\end{equation}
and, similarly, $s=s_0+{\bar s}$ and $h=h_0+{\bar h}$. The fluctuations of the
original and the canonically normalized fields are related by
${\bar s}\simeq (1-3\xi^2_s s_0^2){\bar\rho}-3\xi^2_s s_0\,{\bar\rho}^2$ and
${\bar h}\simeq (1-3\xi^2_h h_0^2){\bar\varphi}-3\xi^2_h h_0\,{\bar\varphi}^2$.
Consider interactions of the Higgs with the gauge bosons.
The conformal rescaling brings in terms of order $\xi_h h^2$ and
$\xi_s s^2$, which are negligible compared to $\xi_h^2 h^2$ and
$\xi_s^2 s^2$.
We thus have
\begin{eqnarray}
{\cal L}_{\rm gauge}&=&\frac{1}{2} g^2h^2 W^+_\mu W^{\mu-} \\
&=& \frac{1}{2} g^2\varphi_0^2 \Big(1+2a\frac{{\bar\varphi}}{\varphi_0 }+
b\frac{{\bar\varphi}^2}{\varphi_0^2}\Big)W^+_\mu W^{\mu-}
\end{eqnarray}
with $a=1-3\xi^2_h \varphi_0^2$ and $b=1-12\xi^2_h \varphi_0^2$. Here we have
neglected the difference between $\varphi_0$ and $h_0$. We see that the
Standard Model gauge--Higgs interactions ($a=b=1$) have changed due to the
non--canonical normalization. It means that the Higgs exchange no longer unitarizes the $WW$ scattering and the amplitude grows
with energy:
${\cal A}(WW\rightarrow WW) \sim E^2 \Delta a/\varphi_0^2
\sim \xi_h^2 E^2$, where $\Delta a$ is the deviation of $a$ from its SM value.
Thus unitarity is violated at
$E \sim 1/\xi_h$.
Furthermore, unitarity is violated by scalar interactions. Rewriting the
Einstein frame scalar
potential in terms of $\varphi$ and $\rho$, we get
\begin{equation}
U\simeq \frac{1}{4}\lambda_h\varphi^4(1-4\xi^2_h \varphi^2)+\frac{1}{4}\lambda_s \rho^4(1-4\xi^2_s\rho^2)+\frac{1}{4}\lambda_{hs}\varphi^2\rho^2(1-2\xi^2_h\varphi^2-2\xi^2_s\rho^2) \;.
\end{equation}
The 6--point interactions induce $2\rightarrow 4$ scattering with
a cross section growing as $ E^2 /\Lambda^4$ with $\Lambda= 1/\xi_{s,h}$,
while the unitary bound is $1/E^2$.
Again, for $E>1/\xi_{s,h}$, unitarity is violated.
\subsection{Example of unitarization}
We see that at the scale $1/\xi_{s,h}$ new physics unitarizing
scattering amplitudes should show up. It may come in a form of new
degrees of freedom and/or new operators. One possibility is to
complete the theory into a $\sigma$--model by adding a heavy scalar
$\sigma$ \cite{giudicelee}. The corresponding Jordan--frame Lagrangian reads
\begin{eqnarray}
{\cal L}_J/\sqrt{-g_J}&=&-\frac{1}{2}(\xi_\sigma {\sigma}^2+{\tilde \xi}_h h^2+{\tilde \xi}_s s^2) R+\frac{1}{2}(\partial_\mu{ \sigma})^2+\frac{1}{2}(\partial_\mu h)^2+\frac{1}{2}(\partial_\mu s)^2 \nonumber \\
&&-\frac{1}{4}\kappa ({\sigma}^2-{\Lambda}^2-\alpha h^2-\beta s^2)^2- V_J(h,s)\;,
\end{eqnarray}
where $V_J(h,s)$ is the Higgs portal potential and $\Lambda=
1/ \sqrt{\xi_\sigma}$.
Here the VEV of $\sigma$ generates the Planck scale (one may also add a
bare $M^2 R$ term \cite{giudicelee}) and
we take ${\tilde\xi}_h,{\tilde \xi}_s\ll \xi_\sigma$;
${ \Lambda}\gg v,u$.
In the low energy limit,
the heavy $\sigma$--field
can be integrated out by minimizing
the scalar potential (in the Jordan or Einstein frames),
\begin{equation}
\sigma^2=\Lambda^2+\alpha h^2 +\beta s^2 \;.
\end{equation}
The resulting effective action is that of the Higgs portal inflation
with effective couplings to gravity
$\xi_h={\tilde \xi}_h+\alpha \xi_\sigma \simeq \alpha \xi_\sigma$ and
$\xi_s={\tilde \xi}_s+\beta \xi_\sigma \simeq \beta \xi_\sigma$.
One can easily verify that in the vacuum (at small $u,v$) the canonically
normalized field in the Einstein frame is
$\chi= \sqrt{6} \ln (\sigma/ \Lambda)$ with mass of order
$\sqrt{\kappa}/\xi_\sigma$. Substituting $\sigma=\Lambda \exp(\chi/
\sqrt{6})$ back in the potential, one finds that the non-renormalizable
interactions of $\chi$ are Planck--suppressed. On the other hand, since
$\tilde \xi_{h,s} \sim {\cal O}(1)$, unitarity constraints for interactions
of $h$ and $s$ are satisfied up to the Planck scale energies.
Let us now consider the inflationary regime $\sigma \gg \Lambda$.
The kinetic terms in the Einstein frame are given by
\begin{eqnarray}
{\cal L}_{\rm kin}&=&\frac{3}{4}\Big[\partial_\mu \ln(\xi_\sigma \sigma^2+{\tilde \xi}_h h^2+{\tilde\xi}_s s^2)\Big]^2 \nonumber \\
&&+\frac{1}{2(\xi_\sigma \sigma^2+{\tilde \xi}_h h^2+{\tilde\xi}_s s^2)}\cdot
\bigg[{(\partial_\mu\sigma)^2}+(\partial_\mu h)^2+(\partial_\mu s)^2\bigg]\;.
\end{eqnarray}
Defining
\begin{equation}
\chi=\sqrt{3\over 2} \ln (\xi_\sigma \sigma^2) ~,~
\tau_h = {h\over \sigma} ~,~
\tau_s = {s\over \sigma} ~,
\end{equation}
we find to leading order in $1/\xi_\sigma$,
\begin{equation}
{\cal L}_{\rm kin}= \frac{1}{2}(\partial_\mu \chi)^2 +
{1\over 2 \xi_\sigma} (\partial_\mu \tau_h)^2 +
{1\over 2 \xi_\sigma} (\partial_\mu \tau_s)^2 \;,
\end{equation}
while the mixing terms are further suppressed.
The Einstein frame scalar potential is
\begin{equation}
U=(\xi_\sigma \sigma^2+{\tilde \xi}_h h^2+{\tilde\xi}_s s^2)^{-2}
\bigg[\frac{1}{4}\kappa (\sigma^2-\Lambda^2-\alpha h^2-\beta s^2)^2+ V_J(h,s)
\bigg]\;,
\end{equation}
which at large $\sigma$ and $\xi_\sigma$ becomes
\begin{equation}
U\simeq \frac{1}{4\xi_\sigma^2} \bigg[\kappa (1-\alpha \tau^2_h-\beta \tau^2_s)^2+\lambda_h\tau^4_h+\lambda_s \tau^4_s+\lambda_{hs}\tau^2_h \tau^2_s \bigg]\;.
\end{equation}
The extremum at $\tau_{h,s}\not= 0$ (``mixed inflaton'') is given by
\begin{eqnarray}
\tau^2_h&=&\frac{2\kappa (2\alpha\lambda_s -\beta\lambda_{hs})}{4\lambda_h\lambda_s-\lambda^2_{hs}+4\kappa(\alpha^2\lambda_h+\beta^2\lambda_s-\alpha\beta \lambda_{hs})}, \nonumber \\
\tau^2_s&=&\frac{2\kappa (2\beta\lambda_h -\alpha\lambda_{hs})}{4\lambda_h\lambda_s-\lambda^2_{hs}+4\kappa(\alpha^2\lambda_h+\beta^2\lambda_s-\alpha\beta \lambda_{hs})}\;.
\end{eqnarray}
It is a local minimum if
\begin{eqnarray}
&&2\alpha\lambda_s-\beta\lambda_{hs}>0, \nonumber \\
&&2\beta\lambda_h -\alpha\lambda_{hs}>0, \nonumber \\
&&4\lambda_h\lambda_s-\lambda^2_{hs}+4\kappa(\alpha^2\lambda_h+\beta^2\lambda_s-\alpha\beta \lambda_{hs})>0\;. \label{inf3}
\end{eqnarray}
The last condition follows from the positivity of the determinant of the Hessian.
The value of the potential at this point determines the energy density
during inflation with heavy $\tau_{h,s}$ integrated out.
The resulting inflaton potential is
\begin{equation}
U(\chi)= {\lambda_{\rm eff} \over 4\xi_\sigma^2}~
\Bigl( 1+ {\rm exp}\left( -{2\chi\over \sqrt{6} } \right) \Bigr)^{-2}
\end{equation}
with
\begin{equation}
\lambda_{\rm eff}= \kappa~ \frac{4\lambda_h\lambda_s-\lambda^2_{hs}}{4\lambda_h\lambda_s-\lambda^2_{hs}+4\kappa(\alpha^2\lambda_s+\beta^2\lambda_s-\alpha\beta \lambda_{hs})} \;.
\end{equation}
The denominator of $\lambda_{\rm eff}$ is positive by the stability
condition (\ref{inf3}), so positivity of the energy density during inflation
requires $4\lambda_h\lambda_s-\lambda^2_{hs} >0 $. Recalling that
$\xi_h \simeq \alpha \xi_\sigma$ and
$\xi_s \simeq \beta \xi_\sigma$, this condition together
with (\ref{inf3}) implies
\begin{eqnarray}
&& 2 \lambda_h \xi_s - \lambda_{hs} \xi_h >0 \;, \nonumber\\
&& 2 \lambda_s \xi_h - \lambda_{hs} \xi_s >0 \;, \nonumber\\
&& 4 \lambda_s \lambda_h - \lambda_{hs}^2 >0 \;.
\end{eqnarray}
These are exactly the conditions we imposed in our parameter
space analysis, Eq.~(\ref{constraints1}).\footnote{ Note also that $\alpha^2\lambda_h+\beta^2\lambda_s-\alpha\beta \lambda_{hs}>0$
follows from $2\alpha\lambda_s-\beta\lambda_{hs}>0 , 2\beta\lambda_h -\alpha\lambda_{hs}>0$ (for positive $\alpha,\beta$).}
Note also that inflation proceeds at the same
$\tau = \tau_h / \tau_s$ as in the original model.
Therefore, unitarized Higgs portal inflation leads to the same constraints
on the couplings
as the original model does. This is despite the fact that now all
three fields participate in inflation, $\tau_{h,s}= {\cal O}(1)$,
and the theory involves an unknown couplings $\kappa$. The latter
affects the energy density, but not the shape of the potential,
so the predictions for the inflationary parameters $n\simeq 0.97$ and
$r\simeq 0.0033$ hold.
\section{Conclusion}
We have studied an extension of the Higgs sector with a real
scalar in the presence of large couplings to scalar
curvature. This system supports inflation at large field values,
with tree level predictions $n\simeq 0.97$ and
$r\simeq 0.0033$.
The nature of the inflaton depends on the relations
among the couplings. For instance, at negative $\lambda_{hs}$,
the inflaton is a mixture of the Higgs and the singlet, while at
positive $\lambda_{hs}$ it can also be a pure Higgs or a singlet.
These requirements leave an imprint on the low energy phenomenology,
e.g. the ``mixed'' inflation often leads to mixed Higgs--singlet
mass eigenstates at low energies. The latter would manifest themselves at
the LHC as 2 Higgs--like states with universally suppressed couplings.
We have shown how Higgs portal inflation can be unitarized by adding
an extra scalar with a sub--Planckian VEV. This extension does not however
affect the constraints on the couplings and the low energy phenomenology
remains the same.
{\bf Acknowledgements.} HML is supported by a CERN--Korean fellowship.
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{"url":"http:\/\/bazekon.icm.edu.pl\/bazekon\/element\/bwmeta1.element.ekon-element-000171418492","text":"PL EN\n\nPreferencje\nJ\u0119zyk\nWidoczny [Schowaj] Abstrakt\nLiczba wynik\u00f3w\nCzasopismo\n\n## Annals of Computer Science and Information Systems\n\n2015 | 5 | 55--66\nTytu\u0142 artyku\u0142u\n\n### Application of Artificial Neural Network and Support Vector Regression in Cognitive Radio Networks for RF Power Prediction Using Compact Differential Evolution Algorithm\n\nAutorzy\nWarianty tytu\u0142u\nJ\u0119zyki publikacji\nEN\nAbstrakty\nEN\nCognitive radio (CR) technology has emerged as a promising solution to many wireless communication problems including spectrum scarcity and underutilization. To enhance the selection of channel with less noise among the white spaces (idle channels), the a priory knowledge of Radio Frequency (RF) power is very important. Computational Intelligence (CI) techniques cans be applied to these scenarios to predict the required RF power in the available channels to achieve optimum Quality of Service (QoS). In this paper, we developed a time domain based optimized Artificial Neural Network (ANN) and Support Vector Regression (SVR) models for the prediction of real world RF power within the GSM 900, Very High Frequency (VHF) and Ultra High Frequency (UHF) FM and TV bands. Sensitivity analysis was used to reduce the input vector of the prediction models. The inputs of the ANN and SVR consist of only time domain data and past RF power without using any RF power related parameters, thus forming a nonlinear time series prediction model. The application of the models produced was found to increase the robustness of CR applications, specifically where the CR had no prior knowledge of the RF power related parameters such as signal to noise ratio, bandwidth and bit error rate. Since CR are embedded communication devices with memory constrain limitation, the models used, implemented a novel and innovative initial weight optimization of the ANN's through the use of compact differential evolutionary (cDE) algorithm variants which are memory efficient. This was found to enhance the accuracy and generalization of the ANN model. Index Terms-Cognitive Radio; Primary User; Artificial Neural Network; Support Vector Machine; Compact Differential Evolution; RF Power; Prediction.(original abstract)\nS\u0142owa kluczowe\nPL\nEN\nRocznik\nTom\nStrony\n55--66\nOpis fizyczny\nTw\u00f3rcy\nautor\n\u2022 Centre for Computational Intelligence, School of Computer Science and Informatics, De Montfort University, England\nautor\n\u2022 Centre for Computational Intelligence, School of Computer Science and Informatics, De Montfort University, England\nautor\n\u2022 Centre for Computational Intelligence, School of Computer Science and Informatics, De Montfort University, England\nautor\n\u2022 Centre for Computational Intelligence, School of Computer Science and Informatics, De Montfort University, England\nautor\n\u2022 Centre for Computational Intelligence, School of Computer Science and Informatics, De Montfort University, England\nBibliografia\n\u2022 FCC, \"Federal comminucation commission notice of inquiry and notice of proposed rule making, in the matter of establishment of an interference temperature metric to quantify and manage interference and to expand available unlicensed operation in certain fixed, mobile and satellite frequency bands,\" no. 03-237, November 13, 2003.\n\u2022 V. Valenta, R. Marsalek, G. Baudoin, M. Villegas, M. Suarez, and F. Robert, \"Survey on spectrum utilization in europe: Measurements, analyses and observations,\" in Cognitive Radio Oriented Wireless Networks Communications (CROWNCOM), 2010 Proceedings of the Fifth International Conference on, June 2010, pp. 1-5.\n\u2022 S. Haykin, D. J. Thomson, and J. H. Reed, \"Spectrum sensing for cognitive radio,\" in IEEE Transactions on Cognitive Radio, May 2009.\n\u2022 J. Oh and W. Choi, \"A hybrid cognitive radio system: A combination of underlay and overlay approaches,\" in IEEE Transactions on Cognitive Radio, 2009.\n\u2022 C. Stevenson, G. Chouinard, Z. Lei, W. Hu, J. Stephen, and W. Caldwell, \"The first cognitive radio wireless regional area network standard,\" in IEEE 802.22, 2009.\n\u2022 X. Xing, T. Jing, W. Cheng, Y. Huo, and X. Cheng, \"Spectrum prediction in cognitive radio networks,\" in 1536-1284\/13\/$25.00 c 2013 IEEE Transactions on Wireless Communications, April 2013. \u2022 A. M. Wyglinski, M. Nekovee, and Y. T. Hou, Cognitive Radio Communications and Networks, 2009. \u2022 M. Subhedar and G. Birajdar, \"Spectrum sensing techniques in cognitive radio networks: A survey,\" International Journal of Next-Generation Networks, vol. 3, no. 2, pp. 37-51, 2011. \u2022 T. W. Rondeau, B. Le, C. J. Rieser, and C. W. Bostian, \"Cognitive radios with genetic algorithms: Intelligent control of software defined radios,\" in c 2004 SDR Forum, Proceeding of the SDR 2004 Technical Conference and Product Exposition, 2004. \u2022 S. K. Udgata, K. P. Kumar, and S. L. Sabat, \"Swarm intelligence based resource allocation algorithm for cognitive radio network,\" in Parallel Distributed and Grid Computing (PDGC), 2010 1st International Conference on, Oct 2010, pp. 324-329. \u2022 M. Matinmikko, J. Del Ser, T. Rauma, and M. Mustonen, \"Fuzzy-logic based framework for spectrum availability assessment in cognitive radio systems,\" Selected Areas in Communications, IEEE Journal on, vol. 31, no. 11, pp. 2173-2184, November 2013. \u2022 L. Giupponi and A. Perez, \"Fuzzy-based spectrum handoff in cognitive radio networks,\" 2008. \u2022 Y. Chen and H.-S. Oh, \"A survey of measurement-based spectrum occupancy modelling for cognitive radios,\" in 1553-877X c 2013 IEEE IEEE Communications Surveys and Tutorials, 2013. \u2022 R. Azmi, \"Support vector machine based white space predictors for cognitive radio,\" Master's thesis, 2011. \u2022 O. Winston, A. Thomas, and W. OkelloOdongo, \"Optimizing neural network for tv idle channel prediction in cognitive radio using particle swarm optimization,\" in Computational Intelligence, Communication Systems and Networks (CICSyN), 2013 Fifth International Conference on, June 2013, pp. 25-29. \u2022 M. I. Taj and M. Akil, \"Cognitive radio spectrum evolution prediction using artificial neural networks based mutivariate time series modelling,\" in European Wireless, Vienna Austria, April 2011. \u2022 X. Li and S. A. Zekavat, \"Traffic pattern prediction and performance investigation for cognitive radio systems,\" in IEEE Communication Society, WCNC Proceedings, 2008. \u2022 S. Hiremath and S. K. Patra, \"Transmission rate prediction for cognitive radio using adaptive neural fuzzy inference system,\" in IEEE 5th International Conference on Industrial and Information Systems (ICIIS), India, Aug 2010. \u2022 S. Geirhofer, J. Z. Sun, L. Tong, and B. M. Sadler, \"Cognitive frequency hopping based on interference prediction: Theory and experimental results,\" vol. 13, no. 2, march 17, 2009. \u2022 Z. Tabakovic, S. Grgic, and M. Grgic, \"Fuzzy logic power control in cognitive radio,\" in IEEE transactions, 2009. \u2022 Z. Lin, X. Jian, L. Huang, and Y. Yao, \"Energy prediction based spectrum sensing approach for cognitive radio network,\" in 978-1-4244- 3693-4\/09\/$25.00 c 2009 IEEE, 2009.\n\u2022 S. Haykin, Neural Networks and Learning Machines, 3rd ed., 2008.\n\u2022 Z. Jianli, \"Based on neural network spectrum prediction of cognitive radio,\" in 978-1-4577-0321-8\/11\/$26.00 c 2011 IEEE, 2011. \u2022 V. Vapnik, The nature of statistical learning theory. Springer-Verlag New York Inc, 1999. \u2022 V. Vapnik, Statistical learning theory. New York: Wiley, 1998. \u2022 E. Alpaydin, Introduction to Machine Learning, ser. Adaptive computation and machine learning. MIT Press, 2004. \u2022 V. Kecman, Learning and soft computing. MIT Press Cambridge, Mass, 2001. \u2022 C. Vladimir and Y. MA, \"Selection of meta-parameters for support vector regression,\" pp. 687-693, August 2002. \u2022 W. Wenjian, Z. Xu, W. Lu, and X. Zhang, \"Determination of the spread parameter in the gaussian kernel for classification and regression,\" vol. 55, no. 3, pp. 643-663, October 2003. \u2022 V. S. Cherkassky and F. Mulier, Learning from Data: Concepts, Theory, and Methods, 1st ed. New York, NY, USA: John Wiley and Sons, Inc., 1998. \u2022 B. Scholkopf and A. J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. Cambridge, MA, USA: MIT Press, 2001. \u2022 K. V. Price, R. Storn, and J. Lampinen, Differential Evolution: A Practical Approach to Global Optimization. Springer, 2005. \u2022 A. K. Qin, V. L. Huang, and P. N. Suganthan, \"Differential evolution algorithm with strategy adaptation for global numerical optimization,\" in IEEE Transactions on Evolutionary Computation, vol. 13, no. 2, April 2009. \u2022 D. Zaharie, \"A comparative analysis of crossover variants in differential evolution,\" in Proceedings of the International Multiconference on Computer Science and Information Technology, 2007, pp. 171-181. \u2022 E. Mininno, F. Neri, F. Cupertino, and D. Naso, \"Compact differential evolution,\" Evolutionary Computation, IEEE Transactions on, vol. 15, no. 1, pp. 32-54, Feb 2011. \u2022 G. Harik, F. Lobo, and D. Goldberg, \"The compact genetic algorithm,\" Evolutionary Computation, IEEE Transactions on, vol. 3, no. 4, pp. 287-297, Nov 1999. \u2022 C. W. Ahn and R. Ramakrishna, \"Elitism-based compact genetic algorithms,\" Evolutionary Computation, IEEE Transactions on, vol. 7, no. 4, pp. 367-385, Aug 2003. \u2022 A. H. Sung, \"Ranking importance of input parameters of neural networks,\" Expert Systems with Applications, vol. 15, no. 3, pp. 405-411, November 1998. \u2022 F. Wilcoxon, \"Individual comparisons by ranking methods,\" Biometrics Bulletin, vol. 1, no. 6, pp. 80-83, 1945. \u2022 S. Iliya, E. Goodyer, J. Shell, J. Gow, and M. Gongora, \"Optimized neural network using differential evolutionary and swarm intelligence optimization algorithms for rf power prediction in cognitive radio network: A comparative study,\" in 978-1-4799-4998-4\/14\/$31.00 c 2014 IEEE International Conference on Adaptive Science and Information Technology, 2014.\nTyp dokumentu\nBibliografia\nIdentyfikatory","date":"2021-01-19 04:02:58","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\": 0.33429083228111267, \"perplexity\": 4412.962824789057}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-04\/segments\/1610703517559.41\/warc\/CC-MAIN-20210119011203-20210119041203-00666.warc.gz\"}"} | null | null |
package oci
import (
"encoding/json"
"os/exec"
"strings"
"time"
"github.com/pkg/errors"
"k8s.io/klog/v2"
)
// SysInfo Info represents common system Information between docker and podman that minikube cares
type SysInfo struct {
CPUs int // CPUs is Number of CPUs
TotalMemory int64 // TotalMemory Total available ram
OSType string // container's OsType (windows or linux)
Swarm bool // Weather or not the docker swarm is active
Rootless bool // Weather or not the docker is running on rootless mode
StorageDriver string // the storage driver for the daemon (for example overlay2)
Errors []string // any server issues
DockerOS string // used to detect if using Docker Desktop or Docker Engine on Linux
}
var (
cachedSysInfo *SysInfo
cachedSysInfoErr *error
)
// CachedDaemonInfo will run and return a docker/podman info only once per minikube run time. to avoid performance
func CachedDaemonInfo(ociBin string) (SysInfo, error) {
if cachedSysInfo == nil {
si, err := DaemonInfo(ociBin)
cachedSysInfo = &si
cachedSysInfoErr = &err
}
if cachedSysInfoErr == nil {
return *cachedSysInfo, nil
}
return *cachedSysInfo, *cachedSysInfoErr
}
// DaemonInfo returns common docker/podman daemon system info that minikube cares about
func DaemonInfo(ociBin string) (SysInfo, error) {
if ociBin == Podman {
p, err := podmanSystemInfo()
cachedSysInfo = &SysInfo{CPUs: p.Host.Cpus, TotalMemory: p.Host.MemTotal, OSType: p.Host.Os, Swarm: false, Rootless: p.Host.Security.Rootless, StorageDriver: p.Store.GraphDriverName}
return *cachedSysInfo, err
}
d, err := dockerSystemInfo()
rootless := false
for _, se := range d.SecurityOptions {
if strings.HasPrefix(se, "name=rootless") {
rootless = true
break
}
}
cachedSysInfo = &SysInfo{CPUs: d.NCPU, TotalMemory: d.MemTotal, OSType: d.OSType, Swarm: d.Swarm.LocalNodeState == "active", Rootless: rootless, StorageDriver: d.Driver, Errors: d.ServerErrors, DockerOS: d.OperatingSystem}
return *cachedSysInfo, err
}
// dockerSysInfo represents the output of docker system info --format '{{json .}}'
type dockerSysInfo struct {
ID string `json:"ID"`
Containers int `json:"Containers"`
ContainersRunning int `json:"ContainersRunning"`
ContainersPaused int `json:"ContainersPaused"`
ContainersStopped int `json:"ContainersStopped"`
Images int `json:"Images"`
Driver string `json:"Driver"`
DriverStatus [][]string `json:"DriverStatus"`
SystemStatus interface{} `json:"SystemStatus"`
Plugins struct {
Volume []string `json:"Volume"`
Network []string `json:"Network"`
Authorization interface{} `json:"Authorization"`
Log []string `json:"Log"`
} `json:"Plugins"`
MemoryLimit bool `json:"MemoryLimit"`
SwapLimit bool `json:"SwapLimit"`
KernelMemory bool `json:"KernelMemory"`
KernelMemoryTCP bool `json:"KernelMemoryTCP"`
CPUCfsPeriod bool `json:"CpuCfsPeriod"`
CPUCfsQuota bool `json:"CpuCfsQuota"`
CPUShares bool `json:"CPUShares"`
CPUSet bool `json:"CPUSet"`
PidsLimit bool `json:"PidsLimit"`
IPv4Forwarding bool `json:"IPv4Forwarding"`
BridgeNfIptables bool `json:"BridgeNfIptables"`
BridgeNfIP6Tables bool `json:"BridgeNfIp6tables"`
Debug bool `json:"Debug"`
NFd int `json:"NFd"`
OomKillDisable bool `json:"OomKillDisable"`
NGoroutines int `json:"NGoroutines"`
SystemTime time.Time `json:"SystemTime"`
LoggingDriver string `json:"LoggingDriver"`
CgroupDriver string `json:"CgroupDriver"`
NEventsListener int `json:"NEventsListener"`
KernelVersion string `json:"KernelVersion"`
OperatingSystem string `json:"OperatingSystem"`
OSType string `json:"OSType"`
Architecture string `json:"Architecture"`
IndexServerAddress string `json:"IndexServerAddress"`
RegistryConfig struct {
AllowNondistributableArtifactsCIDRs []interface{} `json:"AllowNondistributableArtifactsCIDRs"`
AllowNondistributableArtifactsHostnames []interface{} `json:"AllowNondistributableArtifactsHostnames"`
InsecureRegistryCIDRs []string `json:"InsecureRegistryCIDRs"`
IndexConfigs struct {
DockerIo struct {
Name string `json:"Name"`
Mirrors []interface{} `json:"Mirrors"`
Secure bool `json:"Secure"`
Official bool `json:"Official"`
} `json:"docker.io"`
} `json:"IndexConfigs"`
Mirrors []interface{} `json:"Mirrors"`
} `json:"RegistryConfig"`
NCPU int `json:"NCPU"`
MemTotal int64 `json:"MemTotal"`
GenericResources interface{} `json:"GenericResources"`
DockerRootDir string `json:"DockerRootDir"`
HTTPProxy string `json:"HttpProxy"`
HTTPSProxy string `json:"HttpsProxy"`
NoProxy string `json:"NoProxy"`
Name string `json:"Name"`
Labels []interface{} `json:"Labels"`
ExperimentalBuild bool `json:"ExperimentalBuild"`
ServerVersion string `json:"ServerVersion"`
ClusterStore string `json:"ClusterStore"`
ClusterAdvertise string `json:"ClusterAdvertise"`
Runtimes struct {
Runc struct {
Path string `json:"path"`
} `json:"runc"`
} `json:"Runtimes"`
DefaultRuntime string `json:"DefaultRuntime"`
Swarm struct {
NodeID string `json:"NodeID"`
NodeAddr string `json:"NodeAddr"`
LocalNodeState string `json:"LocalNodeState"`
ControlAvailable bool `json:"ControlAvailable"`
Error string `json:"Error"`
RemoteManagers interface{} `json:"RemoteManagers"`
} `json:"Swarm"`
LiveRestoreEnabled bool `json:"LiveRestoreEnabled"`
Isolation string `json:"Isolation"`
InitBinary string `json:"InitBinary"`
ContainerdCommit struct {
ID string `json:"ID"`
Expected string `json:"Expected"`
} `json:"ContainerdCommit"`
RuncCommit struct {
ID string `json:"ID"`
Expected string `json:"Expected"`
} `json:"RuncCommit"`
InitCommit struct {
ID string `json:"ID"`
Expected string `json:"Expected"`
} `json:"InitCommit"`
SecurityOptions []string `json:"SecurityOptions"`
ProductLicense string `json:"ProductLicense"`
Warnings interface{} `json:"Warnings"`
ServerErrors []string
ClientInfo struct {
Debug bool `json:"Debug"`
Plugins []interface{} `json:"Plugins"`
Warnings interface{} `json:"Warnings"`
} `json:"ClientInfo"`
}
// podmanSysInfo represents the output of podman system info --format '{{json .}}'
type podmanSysInfo struct {
Host struct {
BuildahVersion string `json:"BuildahVersion"`
CgroupVersion string `json:"CgroupVersion"`
Conmon struct {
Package string `json:"package"`
Path string `json:"path"`
Version string `json:"version"`
} `json:"Conmon"`
Distribution struct {
Distribution string `json:"distribution"`
Version string `json:"version"`
} `json:"Distribution"`
MemFree int `json:"MemFree"`
MemTotal int64 `json:"MemTotal"`
OCIRuntime struct {
Name string `json:"name"`
Package string `json:"package"`
Path string `json:"path"`
Version string `json:"version"`
} `json:"OCIRuntime"`
SwapFree int `json:"SwapFree"`
SwapTotal int `json:"SwapTotal"`
Arch string `json:"arch"`
Cpus int `json:"cpus"`
Eventlogger string `json:"eventlogger"`
Hostname string `json:"hostname"`
Kernel string `json:"kernel"`
Os string `json:"os"`
Security struct {
Rootless bool `json:"rootless"`
} `json:"security"`
Uptime string `json:"uptime"`
} `json:"host"`
Registries struct {
Search []string `json:"search"`
} `json:"registries"`
Store struct {
ConfigFile string `json:"ConfigFile"`
ContainerStore struct {
Number int `json:"number"`
} `json:"ContainerStore"`
GraphDriverName string `json:"GraphDriverName"`
GraphOptions struct {
} `json:"GraphOptions"`
GraphRoot string `json:"GraphRoot"`
GraphStatus struct {
BackingFilesystem string `json:"Backing Filesystem"`
NativeOverlayDiff string `json:"Native Overlay Diff"`
SupportsDType string `json:"Supports d_type"`
UsingMetacopy string `json:"Using metacopy"`
} `json:"GraphStatus"`
ImageStore struct {
Number int `json:"number"`
} `json:"ImageStore"`
RunRoot string `json:"RunRoot"`
VolumePath string `json:"VolumePath"`
} `json:"store"`
}
var dockerInfoGetter = func() (string, error) {
rr, err := runCmd(exec.Command(Docker, "system", "info", "--format", "{{json .}}"))
return rr.Stdout.String(), err
}
// dockerSystemInfo returns docker system info --format '{{json .}}'
func dockerSystemInfo() (dockerSysInfo, error) {
var ds dockerSysInfo
rawJSON, err := dockerInfoGetter()
if err != nil {
klog.Warningf("docker info: %v", err)
return ds, errors.Wrap(err, "docker system info")
}
if err := json.Unmarshal([]byte(strings.TrimSpace(rawJSON)), &ds); err != nil {
klog.Warningf("unmarshal docker info: %v", err)
return ds, errors.Wrapf(err, "unmarshal docker system info")
}
klog.Infof("docker info: %+v", ds)
return ds, nil
}
var podmanInfoGetter = func() (string, error) {
rr, err := runCmd(exec.Command(Podman, "system", "info", "--format", "json"))
return rr.Stdout.String(), err
}
// podmanSysInfo returns podman system info --format '{{json .}}'
func podmanSystemInfo() (podmanSysInfo, error) {
var ps podmanSysInfo
rawJSON, err := podmanInfoGetter()
if err != nil {
klog.Warningf("podman info: %v", err)
return ps, errors.Wrap(err, "podman system info")
}
if err := json.Unmarshal([]byte(strings.TrimSpace(rawJSON)), &ps); err != nil {
klog.Warningf("unmarshal podman info: %v", err)
return ps, errors.Wrapf(err, "unmarshal podman system info")
}
klog.Infof("podman info: %+v", ps)
return ps, nil
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,888 |
\section{Introduction}
In quantum chromodynamics (QCD), vacuum fluctuations can produce nontrivial topological gluon fields in local domains~\cite{Lee:1974ma}.
The chirality of quarks, under the approximate chiral symmetry, is imbalanced in those gluon fields~\cite{Morley:1983wr,Kharzeev:1998kz,Kharzeev:2007jp}.
This violates the $\mathcal{CP}$ symmetry in QCD in local domains.
In a strong magnetic field, the single-handed quarks will polarize along or opposite to the magnetic field depending on the quark charge.
This produces an electric current along the magnetic field,
resulting in an observable charge separation in the final state~\cite{Kharzeev:1998kz,Kharzeev:2007jp}.
This phenomenon is called the chiral magnetic effect (CME)~\cite{Kharzeev:1998kz,Kharzeev:2007jp}.
In non-central heavy-ion collisions, the spectator protons can produce an intense, transient magnetic field,
approximately perpendicular to the reaction plane
(RP) (spanned by the beam direction and the impact parameter)~\cite{Kharzeev:2007jp}.
The high energy density region created in these collisions,
where the approximate chiral symmetry may be restored,
provides a suitable environment to search for the CME~\cite{Kharzeev:2007jp}.
The observation of CME-induced charge separation in heavy-ion collisons would provide a strong evidence
for QCD vacuum fluctuations and local $\mathcal{CP}$ violation.
The CME is extensively studied in heavy-ion experiments at the Relativistic Heavy Ion Collider (RHIC)~\cite{Abelev:2009ac, Abelev:2009ad, Adamczyk:2014mzf, Adamczyk:2013hsi, Zhao:2017wck,Zhao:2017ckp, Zhao:2019qm, Adamczyk:2013kcb} and the Large Hadron Collider (LHC)~\cite{Khachatryan:2016got, Abelev:2012pa, Acharya:2017fau, Sirunyan:2018ac}.
To probe the CME signal, the RP-dependent, charge-dependent $\Delta\gamma$ observable was proposed~\cite{Voloshin:2004vk} and widely used.
Positive CME-like signals in $\Delta\gamma$ have been observed in both heavy ion collisions (Au+Au at RHIC~\cite{Abelev:2009ac,Abelev:2009ad,Adamczyk:2014mzf,Adamczyk:2013hsi} and Pb+Pb at the LHC~\cite{Abelev:2012pa}) and small systems collisions (p+Au and d+Au at RHIC~\cite{Zhao:2017wck,Zhao:2017ckp} and p+Pb at the LHC~\cite{Khachatryan:2016got}),
where the latter is believed to come only from backgrounds.
In fact, it has been pointed out previously that the $\Delta\gamma$ in heavy-ion collisions
was contaminated by major backgrounds~\cite{Wang:2009kd,Bzdak:2009fc,Schlichting:2010qia}.
Various methods have been developed to suppress the backgrounds,
such as event shape engineering~\cite{Sirunyan:2018ac,Acharya:2017fau},
invariant mass dependence~\cite{Zhao:2017wck},
and the comparative $\Delta\gamma$ measurements with respect to the reaction and participant planes~\cite{Xu:2018prl, Xu:2018cpc}.
The current results with those methods show a CME signal consistent with zero.
In this paper, we propose a new method.
In the original definition of $\Delta\gamma$, both the close pairs and the back-to-back pairs are included.
Many backgrounds contribute to the close pairs (e.g. resonance decays, jet correlations)~\cite{Wang:2009kd, Bzdak:2009fc, Liao:2010nv, Bzdak:2010fd, Schlichting:2010qia, Pratt:2010zn, Petersen:2010di, Toneev:2012zx, Zhao:2018ixy, Zhao:2018skm, Zhao:2019hta},
whereas the back-to-back pairs are relatively free of those backgrounds.
Thus, we propose a new observable which only focuses on the back-to-back pairs, namely, the relative back-to-back opposite-sign (OS) over same-sign (SS) pair excess
as a function of the pair azimuthal orientation with respect to the RP.
We use simulations by a toy model (previously used in Ref.~\cite{Wang:2016iov, Feng:2018so})
to demonstrate the sensitivity of this observable to the CME signal and insensitivity to the backgrounds.
The relationship between this new observable and the $\Delta\gamma$ observable is also discussed.
The paper is organized as follows.
Section~\ref{Methodology} describes the methodology of this study.
Section~\ref{Results} shows our toy-model simulation results
using the new method.
Section~\ref{Summary} summarizes this work.
\section{Methodology} \label{Methodology}
\subsection{New back-to-back relative-excess observable, $r_{\text{BB}}$}
We divide a heavy-ion collision event into three subevents according to the $\eta$ range, the east ($-1<\eta<-0.5$), middle ($-0.5\le\eta<0.5$), and west ($0.5\le\eta<1$) subevent.
The middle subevent is used to reconstruct the second-order event plane azimuthal angle ($\Psi_2$)
as a proxy for that of the RP ($\Psi_{\text{RP}}$).
We form pairs of two charges, one from the west subevent and the other from the east subevent.
The middle subevent provides an $\eta$ gap between the pair of charges.
The opening angle between the two charges are required to be larger than a certain value (e.g.~$150^\circ$)
to define as ``back-to-back'' pairs.
According to their charges, we classify those back-to-back pairs as either OS or SS pairs.
The azimuthal orientation of the back-to-back pairs is defined to be
\begin{equation}
\varphi_{\text{BB}} = (\varphi_1 + \varphi_2 - \pi)/2
,
\end{equation}
where $\varphi_1$, $\varphi_2$ are the azimuthal angles of the two charges relative to $\Psi_{\text{RP}}$
(see Fig.~\ref{OpenAngle} for the various azimuthal angle definitions).
\begin{figure}
\includegraphics[width=1.0\linewidth]{OpenAngle}
\caption{A sketch of ``back-to-back'' pair on the transverse plane.}
\label{OpenAngle}
\end{figure}
We count the numbers of the OS (SS) pairs, $n_{\text{OS}}$ ($n_{\text{SS}}$), as a function of $\varphi_{\text{BB}}$.
We define our new observable as
\begin{equation}
r_{\text{BB}}(\varphi_{\text{BB}}) = \frac{n_{\text{OS}}(\varphi_{\text{BB}}) - n_{\text{SS}}(\varphi_{\text{BB}})}{n_{\text{OS}}(\varphi_{\text{BB}}) + n_{\text{SS}}(\varphi_{\text{BB}})}
.
\end{equation}
If we expand this ratio by Fourier series,
as we will show in Sec.~\ref{CMESignalExtraction},
the second-order coefficient of the Fourier expansion of this quantity
is a measure of the CME signal.
\subsection{CME signal extraction from $r_{\text{BB}}$} \label{CMESignalExtraction}
We first clarify analytically how $r_{\text{BB}}(\varphi_{\text{BB}})$ is sensitive to the CME signal.
The azimuthal distribution for the primordial pions can be written as
\begin{equation} \label{PrimordialPionAzimuthalDistribution}
n^\pm(\varphi) \equiv \frac{\der N^\pm(\varphi)}{\der \varphi} = \frac{N^\pm}{2\pi}(1 \pm 2 a_1 \sin\varphi + 2 v_{2,\pi^\pm}\cos2\varphi)
,
\end{equation}
where the superscript $\pm$ means the charge sign,
and $N^\pm$ is the total number of primordial $\pi^\pm$ of the event.
The CME signal is described by the term $\pm 2 a_1\sin\varphi$.
A rough estimation is
$\langle a_1^2 \rangle \sim 10^{-4}$ in typical heavy ion collisions~\cite{Kharzeev:2007jp}.
Without loss of generality, we use $\varphi_1$ to denote a $\pi^+$ from the east subevent
and $\varphi_2$ to denote a $\pi^-$ from the west subevent.
Transferring to pair variables $\varphi_{\text{BB}}$ and $\delta$,
noting the Jacob determinant
$| \partial (\varphi_1, \varphi_2) / \partial (\varphi_{\text{BB}}, \delta) | = 2,$
we obtain the pair distribution
\begin{equation}
\begin{split}
&n_{\text{W}}^{+}(\varphi_1) n_{\text{E}}^{-}(\varphi_2) \der\varphi_1 \der\varphi_2 \\
&= n_{\text{W}}^{+}( \varphi_{\text{BB}} - \delta) n_{\text{E}}^{-}(\varphi_{\text{BB}} + \pi + \delta) 2 \der\varphi_{\text{BB}} \der\delta
.
\end{split}
\end{equation}
Including the other case,
we have the OS pair density distribution
\begin{equation} \label{NosDist2}
\begin{split}
&n_{\text{OS}}(\varphi_{\text{BB}}, \delta) \\
=& 2n_{\text{W}}^{+}( \varphi_{\text{BB}} - \delta) n_{\text{E}}^{-}(\varphi_{\text{BB}} + \pi + \delta) \\
&+ 2n_{\text{W}}^{-}( \varphi_{\text{BB}} - \delta) n_{\text{E}}^{+}(\varphi_{\text{BB}} + \pi + \delta)\\
&= \frac{N_{\text{W}}^{+}N_{\text{E}}^{-} + N_{\text{W}}^{-}N_{\text{E}}^{+}}{2\pi^2}\Big[ 1 + 4a_1^2 \sin(\varphi_{\text{BB}}+\delta)\sin(\varphi_{\text{BB}}-\delta) \\
&+ 4v_{2,\pi^+}v_{2,\pi^-}\cos2(\varphi_{\text{BB}}+\delta)\cos2(\varphi_{\text{BB}}-\delta) \\
&+ \cos2(\varphi_{\text{BB}}+\delta) \\
&\quad\times \left(v_{2,\pi^+} + v_{2,\pi^-} - 2a_1 (v_{2,\pi^+} - v_{2,\pi^-})\sin(\varphi_{\text{BB}}-\delta) \right) \\
&+ \cos2(\varphi_{\text{BB}}-\delta) \\
&\quad\times \left(v_{2,\pi^+} + v_{2,\pi^-} + 2a_1 (v_{2,\pi^+} - v_{2,\pi^-})\sin(\varphi_{\text{BB}}+\delta) \right) \Big]
.
\end{split}
\end{equation}
Assuming the event averages
\begin{equation}
\langle N_{\text{W}}^{+} N_{\text{E}}^{-} \rangle = \langle N_{\text{W}}^{-}N_{\text{E}}^{+} \rangle = \langle N_{\text{W}}^{+}N_{\text{E}}^{+} \rangle = \langle N_{\text{W}}^{-}N_{\text{E}}^{-} \rangle = \langle N^2 \rangle
,
\end{equation}
and intergrating over $\delta$ from $-\Delta$ to $\Delta$, we have
\begin{equation} \label{NosDist}
\begin{split}
&n_{\text{OS}}(\varphi_{\text{BB}}) = \int_{\delta = -\Delta}^{\delta=\Delta} n_{\text{OS}}(\varphi_{\text{BB}}, \delta) \der\delta \\
=& \frac{2 \langle N^2\rangle}{\pi^2} \Big[ \Delta + 2 v_{2,\pi^+}v_{2,\pi^-} \Delta \cos4\varphi_{\text{BB}} + a_1^2 \sin2\Delta \\
&+ \cos2\varphi_{\text{BB}} ( -2a_1^2\Delta + (v_{2,\pi^+} + v_{2,\pi^-})\sin2\Delta) \\
&+ \frac{1}{2}v_{2,\pi^+}v_{2,\pi^-}\sin4\Delta \Big]
.
\end{split}
\end{equation}
Similarly, we obtain the SS pair density distribution
\begin{equation}
\begin{split}
&n_{\text{SS}}(\varphi_{\text{BB}}, \delta) \\
=& 2n_{\text{W}}^{+}( \varphi_{\text{BB}} - \delta) n_{\text{E}}^{+}(\varphi_{\text{BB}} + \pi + \delta) \\
&+ 2n_{\text{W}}^{-}( \varphi_{\text{BB}} - \delta) n_{\text{E}}^{-}(\varphi_{\text{BB}} + \pi + \delta)
,
\end{split}
\end{equation}
\begin{equation} \label{NssDist}
\begin{split}
&n_{\text{SS}}(\varphi_{\text{BB}}) = \int_{\delta = -\Delta}^{\delta=\Delta} n_{\text{SS}}(\varphi_{\text{BB}}, \delta) \der\delta \\
=& \frac{2\langle N^2\rangle}{\pi^2} \Big[ \Delta + (v_{2,\pi^+}^2 + v_{2,\pi^-}^2)\Delta\cos4\varphi_{\text{BB}} - a_1^2 \sin2\Delta \\
&+ \cos2\varphi_{\text{BB}} (2 a_1^2 \Delta + (v_{2,\pi^+}+v_{2,\pi^-})\sin2\Delta)\\
& + \frac{1}{4}(v_{2,\pi^+}^2 + v_{2,\pi^-}^2)\sin4\Delta \Big]
.
\end{split}
\end{equation}
The difference and sum are, respectively,
\begin{equation}
\begin{split}
&n_{\text{OS}}(\varphi_{\text{BB}}) - n_{\text{SS}}(\varphi_{\text{BB}}) \\
=& \frac{2\langle N^2\rangle}{\pi^2} \Big[ -4a_1^2 \Delta \cos2\varphi_{\text{BB}} + 2a_1^2\sin2\Delta \\
&- (v_{2,\pi^+}-v_{2,\pi^-})^2\Delta \cos4\varphi_{\text{BB}} \\
&- \frac{1}{4}(v_{2,\pi^+}-v_{2,\pi^-})^2\sin4\Delta \Big]
,
\end{split}
\end{equation}
\begin{equation}
\begin{split}
&n_{\text{OS}}(\varphi_{\text{BB}}) + n_{\text{SS}}(\varphi_{\text{BB}}) \\
=& \frac{2\langle N^2\rangle}{\pi^2} \Big[ 2\Delta + (v_{2,\pi^+}+v_{2,\pi^-})^2 \Delta \cos4\varphi_{\text{BB}} \\
&+ (v_{2,\pi^+}+v_{2,\pi^-})\cos2\varphi_{\text{BB}}\sin2\Delta \\
&+ \frac{1}{4}(v_{2,\pi^+}+v_{2,\pi^-})^2\sin4\Delta \Big]
.
\end{split}
\end{equation}
Our new observable is the ratio and we expand it into Fourier series
\begin{equation} \label{BackToBackRatio}
r_{\text{BB}}(\varphi_{\text{BB}}) = \frac{n_{\text{OS}}(\varphi_{\text{BB}}) - n_{\text{SS}}(\varphi_{\text{BB}})}{n_{\text{OS}}(\varphi_{\text{BB}}) + n_{\text{SS}}(\varphi_{\text{BB}})}
= \sum_{k=0}^{+\infty} c_k \cos(k\varphi_{\text{BB}})
.
\end{equation}
Noticing that $(v_{2,\pi^+}+v_{2,\pi^-})$ is small ($\sim0.1$), up to the first order of $(v_{2,\pi^+}+v_{2,\pi^-})$,
the coefficient of $\cos2\varphi_{\text{BB}}$ is
\begin{equation} \label{C2}
\begin{split}
&c_2 \approx a_1^2 \left( -2 - (v_{2,\pi^+}+v_{2,\pi^-})\frac{\sin^2 2\Delta}{\Delta^2} \right) \\
&+(v_{2,\pi^+}+v_{2,\pi^-}) (v_{2,\pi^+}-v_{2,\pi^-})^2 \frac{(2\Delta+\sin4\Delta)\sin2\Delta}{8\Delta^2}
.
\end{split}
\end{equation}
If we require the opening angle to be larger than $150^\circ$ for the back-to-back pairs, then $\Delta=15^\circ$,
\begin{equation} \label{NumberC2}
\begin{split}
c_2 \approx& a_1^2 \left( -2 -3.648(v_{2,\pi^+}+v_{2,\pi^-}) \right) \\
&+ 1.267(v_{2,\pi^+} + v_{2,\pi^-})(v_{2,\pi^+}-v_{2,\pi^-})^2
.
\end{split}
\end{equation}
The second term is not related to the CME;
taking
$|v_{2,\pi^+}-v_{2,\pi^-}| \sim 10^{-3}, \quad (v_{2,\pi^+}+v_{2,\pi^-}) \sim 10^{-1}$,
its magnitude is on the order of $10^{-7}$.
For a CME signal of $a_1 \ge 10^{-3}$,
$a_1^2$ dominates over the primordial flow effects in $c_{2}$,
indicating that $c_{2}$ is a good measure of the CME.
Similarly, the coefficient of the constant term ($k=0$) is
\begin{equation}
\begin{split}
c_0 =& \frac{\sin2\Delta}{4\Delta} \big( 4 a_1^2 (1 + v_{2,\pi^+} + v_{2,\pi^-}) \\
&- (v_{2,\pi^+} - v_{2,\pi^-})^2 \cos2\Delta \big)
,
\end{split}
\end{equation}
and for $\Delta=15^\circ$,
\begin{equation} \label{NumberC0}
\begin{split}
c_0 \approx 1.910 a_1^2 (1 + v_{2,\pi^+} + v_{2,\pi^-}) - 1.654 (v_{2,\pi^+} - v_{2,\pi^-})^2
.
\end{split}
\end{equation}
Note that $c_{2}$ and $c_{0}$ are both sensitive to the CME,
with similar sensitivities.
It will be shown later, however, that $c_{0}$ is also sensitive to the backgrounds.
Those backgrounds are mainly from the low $p_{T}$ resonance decays whose decay daughters are back-to-back.
The $c_{2}$ is less sensitive to those backgrounds because their $v_2$ at low $p_{T}$ is small.
\begin{figure*}
\includegraphics[width=0.4\linewidth]{ToyModelCME00_InputRP_ObsDist} \hspace{0.05\linewidth}
\includegraphics[width=0.4\linewidth]{ToyModelCME10_InputRP_ObsDist}
\caption{The distribution of the back-to-back relative-excess observable $r_{\text{BB}}(\varphi_{\text{BB}})$ in the toy model simulations with input CME (a) $a_1=0$ and (b) $a_1=0.01$.}
\label{ToyModelObsDist}
\includegraphics[width=0.4\linewidth]{ToyModel_C0} \hspace{0.05\linewidth}
\includegraphics[width=0.4\linewidth]{ToyModel_C2}
\caption{The fitted Fourier coefficients, (a) $c_0$ and (b) $-c_2$, to the back-to-back relative-excess observable $r_{\text{BB}}(\varphi_{\text{BB}})$ in the toy model with various CME inputs.}
\label{ToyModelFitParC}
\end{figure*}
\subsection{Comparison to the back-to-back $\Delta\gamma$ observable, $\Delta\gamma_{\text{BB}}$}
The $\Delta\gamma$ observable is frequently used in heavy-ion collisions to search for the CME,
\begin{equation} \label{GammaRP}
\begin{split}
\Delta\gamma =& \gamma_{\text{OS}} - \gamma_{\text{SS}},\\
\gamma =& \langle \cos(\varphi_1 + \varphi_2) \rangle
.
\end{split}
\end{equation}
To see the relationship between $r_{\text{BB}}$ and $\Delta\gamma$,
we will apply the same ``back-to-back'' requirement to the pairs in $\Delta\gamma$,
denoted as $\Delta\gamma_{\text{BB}}$.
For back-to-back pairs,
$\cos(\varphi_1 + \varphi_2) = -\cos(2\varphi_{\text{BB}})$.
The correlators $\gamma_{\text{OS}}$ and $\gamma_{\text{SS}}$ can be simplified into
\begin{equation}
\begin{split}
\gamma_{\text{OS}} =& - \frac{ \int \cos(2\varphi_{\text{BB}}) n_{\text{OS}}(\varphi_{\text{BB}}) \der\varphi_{\text{BB}} }{ \int n_{\text{OS}}(\varphi_{\text{BB}}) \der\varphi_{\text{BB}} }\\
=& \frac{2 a_1^2 \Delta - (v_{2,\pi^+}+v_{2,\pi^-}) \sin2\Delta}{2\Delta + 2a_1^2\sin2\Delta + \vvnv_{2,\pi^+}\sin4\Delta}, \\
\gamma_{\text{SS}} =& - \frac{ \int \cos(2\varphi_{\text{BB}}) n_{\text{SS}}(\varphi_{\text{BB}}) \der\varphi_{\text{BB}} }{ \int n_{\text{SS}}(\varphi_{\text{BB}}) \der\varphi_{\text{BB}} } \\
=& \frac{ -2 a_1^2 \Delta - (v_{2,\pi^+}+v_{2,\pi^-}) \sin2\Delta}{ 2\Delta - 2a_1^2\sin2\Delta + \frac{1}{2}(v_{2,\pi^-}^2+v_{2,\pi^+}^2)\sin4\Delta}
.
\end{split}
\end{equation}
The difference to the first order of $(v_{2,\pi^+}+v_{2,\pi^-})$ is therefore
\begin{equation} \label{GammaB2B}
\begin{split}
\Delta\gamma_{\text{BB}} =& \gamma_{\text{OS}} - \gamma_{\text{SS}} \\
\approx& a_1^2 \left( 2 + (v_{2,\pi^+}+v_{2,\pi^-})\frac{\sin^2 2\Delta}{\Delta^2} \right) \\
&-(v_{2,\pi^+}+v_{2,\pi^-})(v_{2,\pi^+}-v_{2,\pi^-})^2\frac{\sin2\Delta\sin4\Delta}{8\Delta^2}
.
\end{split}
\end{equation}
With $\Delta=15^\circ$, it becomes
\begin{equation} \label{NumberGammaB2B}
\begin{split}
\Delta\gamma_{\text{BB}} =& \gamma_{\text{OS}} - \gamma_{\text{SS}} \\
\approx& a_1^2 \left( 2 + 3.648(v_{2,\pi^+}+v_{2,\pi^-}) \right) \\
&-0.790(v_{2,\pi^+}+v_{2,\pi^-})(v_{2,\pi^+}-v_{2,\pi^-})^2
.
\end{split}
\end{equation}
Comparing Eqs.~\ref{GammaB2B} and \ref{NumberGammaB2B} to Eqs.~\ref{C2} and \ref{NumberC2},
it is clear that $\Delta\gamma_{\text{BB}}$ and $r_{\text{BB}}$ have similar sensitivity to the CME.
The $r_{\text{BB}}$ observable is directly related to $\Delta\gamma_{\text{BB}}$.
Only the back-to-back pairs are used in these two observables,
so the backgrounds among the close pairs are reduced.
\section{Results} \label{Results}
In this section, we show
the back-to-back $r_{\text{BB}}(\varphi_{\text{BB}})$ and back-to-back $\Delta\gamma_{\text{BB}}$ observables calculated
from a toy model (with/without input CME) simulations.
\subsection{Toy-model simulation}
We use a toy model including the primordial pions and the $\rho$ meson decays to study
the sensitivities of $r_{\text{BB}}$ to CME signal and resonance backgrounds.
This toy model has been used for CME background studies in Ref.~\cite{Wang:2016iov, Feng:2018so}.
Both the resonance decays and primordial pions have the $p_T$ distributions and $v_2(p_T)$ obtained from Au+Au measurements corresponding to centrality $40\%\sim50\%$~\cite{Adams:2003cc, Adler:2003qi, Adams:2003xp, Abelev:2008ab, Adams:2004bi, Adare:2010sp, Dong:2004ve, Adamczyk:2015lme, Agashe:2014kda, Abelev:2009gu, Wang:2016iov}.
To simulate the CME signal in the toy model, we input the coefficient $a_1$ when generating the primordial pions from the azimuthal distribution (Eq.~\ref{PrimordialPionAzimuthalDistribution}).
Two cases are studied, one without CME input ($a_1=0$), and the other with $1\%$ CME input ($a_1=0.01$).
Each case has $2\times10^{9}$ events.
The tracks are selected with transverse momentum $0.2\text{ GeV} < p_T < 2.0\text{ GeV}$ and pseudorapidity $-1.0 < \eta < 1.0$.
Figure~\ref{ToyModelObsDist} shows the $r_{\text{BB}}(\varphi_{\text{BB}})$ distributions for the two cases.
The case with finite CME shows larger amplitude and modulation than the case without,
indicating the sensitivity of the $r_{\text{BB}}(\varphi_{\text{BB}})$ observable to the CME.
The case without CME shows some finite amplitude and modulation, at low $m_{\text{inv}}$,
indicating that the observable still has some background contamination.
In order to further suppress resonance backgrounds, we also show the $r_{\text{BB}}$ distributions
with the invariant mass range $1.5 \text{ GeV} < m_\text{inv} < 3.0 \text{ GeV}$.
The result is consistent with zero as expected.
\begin{table*}[]
\begin{tabular}{|c|c|c|c|c|}
\hline
$m_{\text{inv}}$ range (GeV) & input $a_1$ & \multicolumn{2}{|c|}{Fourier coefficients ($\times10^{-4}$)} & extracted $a_1$ ($\times10^{-2}$) \\ \hline
\multirow{4}{*}{$0.0 \sim 3.0$} & \multirow{2}{*}{$0$} & $\ \ c_0$ & $1.57 \pm 0.01$ & $0.87\pm0.01$ \\ \cline{3-5}
& & $-c_2$ & $0.37 \pm 0.02$ & $0.39 \pm 0.02$ \\
\cline{2-5}
& \multirow{2}{*}{$0.01$} & $\ \ c_0$ & $3.07 \pm 0.01$ & $1.21\pm0.01$ \\ \cline{3-5}
& & $-c_2$ & $2.04 \pm 0.02$ & $0.93 \pm 0.01$ \\ \hline
\multirow{4}{*}{$1.5 \sim 3.0$} & \multirow{2}{*}{$0$} & $\ \ c_0$ & $0.08 \pm 0.03$ & $0.20\pm0.07$ \\ \cline{3-5}
& & $-c_2$ & $0.07\pm0.04$ & $0.17\pm0.10$ \\
\cline{2-5}
& \multirow{2}{*}{$0.01$} & $\ \ c_0$ & $1.45 \pm 0.03$ & $0.83 \pm 0.02$ \\ \cline{3-5}
& & $-c_2$ & $1.69 \pm 0.04$ & $0.85\pm0.02$ \\ \hline
\end{tabular}
\caption{The fitted Fourier coefficients $c_0$ and $-c_2$ are shown for the $r_{\text{BB}}(\varphi_{\text{BB}})$ distributions from the toy-model simulations with/without CME signal input. Two invariant mass ranges are shown.
If we set $(v_{2,\pi^+}+v_{2,\pi^-}) \approx 0.1$, ignore the $(v_{2,\pi^+}-v_{2,\pi^-})^2$ terms in Eqs.~\ref{NumberC2}~and~\ref{NumberC0},
and assume zero resonance background in the toy-model simulations,
the $a_1$ can be extracted from $c_0$ and $c_2$, respectively.
These extracted $a_{1}$ values are also listed,
to be compared to the input $a_{1}$.}
\label{FittingParTable}
\end{table*}
We fit the $r_{\text{BB}}(\varphi_{\text{BB}})$ distributions to Eq.~\ref{BackToBackRatio}.
Figure~\ref{ToyModelFitParC} shows the fitted Fourier coefficients $c_0$ and $-c_2$, respectively,
as a function of $m_{\text{inv}}$.
The $c_0$ has strong sensitivity to both signal and background.
Although still affected by the residual resonance backgrounds,
the $-c_2$ has better sensitivity to CME than $c_0$ and less sensitivity to background.
To illustrate our results more quantitatively,
we list the fitted coefficients $c_0$ and $-c_2$ in Table~\ref{FittingParTable}.
Also listed are the $a_1$ values extracted from $c_{0}$ and $-c_{2}$,
via Eqs.~\ref{NumberC0} and \ref{NumberC2}, respectively,
ignoring the presence of backgrounds.
Due to resonance backgrounds in the low $m_{\text{inv}}$ range,
the extracted $a_1$ are large with $0.0 \text{ GeV} < m_{\text{inv}} < 3.0 \text{ GeV}$,
no matter whether the input $a_1$ are zero or not.
In the range $1.5 \text{ GeV} < m_{\text{inv}} < 3.0 \text{ GeV}$,
with zero input $a_1$,
the extracted $a_1$ values are also close to zero;
the small deviations from zero are due to residual resonance backgrounds.
With input $a_1=0.01$,
the extracted $a_1$ values in the high $m_{\text{inv}}$ range are nonzero, close to the input;
again, the differences are due to residual resonance backgrounds.
However, under this condition, the extracted $a_1$ values are smaller than the inputs.
This is because there are pairs composed of pions from uncorrelated sources
(one primordial pion and one resonance pion, or two pions from two different resonance decays),
whose zero contributions are averaged in $c_0$, $-c_2$.
The dilution from those uncorrelated pairs reduces the extracted $a_1$ values.
\subsection{Comparison among $\Delta\gamma$, $\Delta\gamma_{\text{BB}}$, and $-c_2$}
We also calculate the inclusive $\Delta\gamma$ and back-to-back $\Delta\gamma_{\text{BB}}$ observables in our model studies.
Figure~\ref{CompGammaC2} compares the results of those three observables.
It is found that $\Delta\gamma_{\text{BB}}$ and $-c_2$ are very close to each other.
This indicates that the $r_{\text{BB}}$ and $\Delta\gamma_{\text{BB}}$ observables are nearly the same,
as expected from Eqs.~\ref{NumberC2} and \ref{NumberGammaB2B}.
With zero CME input ($a_1=0$) in the toy model simulation (Fig.~\ref{CompGammaC2}a),
the inclusive $\Delta\gamma$ is further away from zero than the other two observables
in the invariant mass range $0.6 \sim 1.5 \text{ GeV}$ where resonance contributions are large.
This shows that the inclusive $\Delta\gamma$ is more significantly affected by the resonance backgrounds.
In the high mass region where resonance contributions are small,
all three observables approach to zero as expected.
With nonzero CME input ($a_1=0.01$) in the toy model simulation (Fig.~\ref{CompGammaC2}b),
the three observables are all away from zero.
The inclusive $\Delta\gamma$ is lower than the other two in the mass range $1.5 \text{ GeV} \sim 3.0 \text{ GeV}$
where there is not much resonance contribution.
This is because the back-to-back CME signal is diluted more in the inclusive $\Delta\gamma$ by including close pairs from backgrounds.
This can also be explained by the analytical calculations in Eq.~\ref{GammaB2B}
by assigning $\Delta=90^\circ$ for the inclusive $\Delta\gamma$ and $\Delta=15^\circ$ for $\Delta\gamma_{\text{BB}}$.
\begin{figure}
\includegraphics[width=0.85\linewidth]{ToyModelCME00_CompGammaC2}
\includegraphics[width=0.85\linewidth]{ToyModelCME10_CompGammaC2}
\caption{Comparison among the inclusive $\Delta\gamma$, the back-to-back $\Delta\gamma_{\text{BB}}$, and the Fourier coefficient $-c_2$ of the $r_{\text{BB}}(\varphi_{\text{BB}})$ distribution in different simulations.}
\label{CompGammaC2}
\end{figure}
\section{Summary} \label{Summary}
In this paper, we propose a new observable to search for the CME,
called the back-to-back relative-excess observable of OS to SS pairs ($r_{\text{BB}}$),
as a function of the pair azimuthal orientation ($\varphi_{\text{BB}}$).
The charge pairs used in this observable are required to be back-to-back:
opening angle larger than $150^\circ$ on the transverse plane;
they are taken from different $\eta$ ranges with a $\Delta\eta$ gap to further reduce backgrounds.
As a result, the backgrounds (such as resonance decays) contributing mostly to the close pairs can be reduced.
A modulation of the form $\cos2\varphi_{\text{BB}}$ in the observable can indicate a CME signal,
which is described by the second-order coefficient $c_2$ in Fourier expansion.
We use a toy model simulation without input CME ($a_1=0$) and with $1\%$ input CME ($a=0.01$),
and calculate the observable from the simulated data.
The coefficient $c_2$ is close to zero when there is no input CME,
whereas it is far from zero with $1\%$ input CME.
To relate the new observable to the previous $\Delta\gamma$ observable,
we apply the same back-to-back pair requirement to the definition of $\Delta\gamma$ to obtain $\Delta\gamma_{\text{BB}}$.
We use analytical calculations and toy-model simulations to show that $\Delta\gamma_{\text{BB}}$ is nearly identical to $-c_2$.
Both are more sensitive to the CME and less sensitive to resonance backgrounds than the inclusive $\Delta\gamma$ observable.
\section*{Acknowledgments}
This work is supported in part by the U.S.~Department of Energy Grant No.~DE-SC0012910
and the National Natural Science Foundation of China Grant No.~11847315.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,272 |
Franciszek Kuhyōe (Franciszek Kurobioye) (zm. 17 sierpnia 1627 w Nagasaki) − błogosławiony Kościoła katolickiego, japoński tercjarz franciszkański, katechista, męczennik.
Życiorys
Pochodził z Chikugo. Prowadził działalność apostolską jako katechista. W tym czasie w Japonii prześladowano chrześcijan. Został spalony żywcem z powodu wyznawanej wiary 17 sierpnia 1627 w Nagasaki razem z wieloma innymi chrześcijanami.
Został beatyfikowany w grupie 205 męczenników japońskich przez Piusa IX w dniu 7 lipca 1867 (dokument datowany jest 7 maja 1867).
Dniem jego wspomnienia jest 10 września (w grupie 205 męczenników japońskich).
Przypisy
Bibliografia
Franciszek Kuhyōe
Tercjarze franciszkańscy (biografie)
Japońscy męczennicy chrześcijańscy
Ofiary prześladowań antykatolickich w Japonii
Osoby spalone na stosie
Nieznana data urodzenia
Zmarli w 1627
Franciszek Kuhyōe | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,618 |
Meat giant JBS revealed a further acquisition in the US, even as it credited a strong performance by its existing operations in the country for offsetting a decline in Brazil, and fuelling a return to the black.
Brazil-based JBS, the world's biggest meat packer, said it had to agree to pay $230m for Plumrose USA, the Illinois-based ham and bacon producer, which claims revenues of some $500m a year.
Plumrose was purchased from Danish Crown, Europe's largest meat processor, which said that the disposal was part of its so-called "4WD" strategy, involving a focus on Northern Europe and Asia.
"I am certain that JBS, with its wide presence and access to raw materials in North America, is a perfect match for Plumrose USA," said Jais Valeur, the Danish Crown chief executive.
JBS said that the acquisition, which comes with five processing plants and two distribution centres, "strengthens its customer base and geographical distribution in the US".
Indeed, the deal was announced as Brazil-based JBS revealed results showing earnings of R$639.9m ($220m) for the October-to-December period, compared with a R$275.1m loss a year before, with the improvement reflecting an improved US performance, besides the absence of currency and restructuring charges which hit the year-ago results.
In US pork, the group reported a 21% jump to $171.5m in earnings before interest, taxation, depreciation and amortisation (ebitda) for the quarter, on revenues up 26% at $1.37bn, reflecting higher prices, as well as a boost to volumes from the $1.45bn acquisition of assets from Cargill late in 2015.
The group's US chicken operation, Pilgrim's Pride, achieved a 14.8% rise in ebitda to $172.2m, despite a 2.7% drop to R$1.91bn in revenues.
And in beef, JBS's US operation returned to positive ebitda of $387.6m, compared with a $25.2m loss a year before, despite a 6.2% drop in sales prices year on year, which restrained revenue growth to 1.6%, taking it to $5.33bn.
The improvement in beef reflected the drop in cattle prices, which on Chicago's futures exchange hit a six-year low during the quarter, undermined by the boost to supplies from a period of US herd rebuilding.
"The increase in cattle availability and the reduction in beef cattle prices contributed to a decrease in raw-material costs during the second half of the year," JBS said.
US beef packers' margins rose above $140 per head of cattle in late October, according to HedgersEdge.
JBS chief executive Wesley Batista held out prospects for continued improved animal supplies, saying that "in the US, a cycle of greater cattle availability has begun, which has contributed to a substantial improvement in the results of our US beef business unit".
The performance contrasted with a slump of 68% to R$298.9m in ebitda at JBS's Brazil-based pork and poultry business, Seara, which suffered a 30% slump in export takings, blamed on the strengthening of the real, which made Brazilian exports less competitive.
In beef, JBS's South American ebitda slumped by 84% to R$143.7m, again reflecting a slump in foreign business, with export revenues tumbling by 32% to R$2.63bn.
"The strengthening of the real versus the dollar had repercussions for our exports," Mr Batsita said, flagging too a dent to poultry and pork margins from elevated grain costs, following last year's disappointing Brazilian corn harvest.
The results were termed "strong" by analysts at Bradesco, which termed JBS's US beef performance as a "highlight".
"The results confirm our bullish expectations" for the US beef division, the broker said, restating an "outperform" rating on JBS shares, with a price target of R$18.00.
However, the earnings fell below the R$844m suggested by a Reuters' poll of analysts. | {
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{"url":"https:\/\/www.mathsnetalevel.com\/1325","text":"Go to content\nThe experiment consists of tossing a coin on a floor with square tiles, and is shown graphically in the first picture box. The center (X, Y) of the coin relative to the center of the square is recorded on each update in the first table, and is shown graphically as a red dot in the scatterplot. Variable I indicates the event that the coin crosses a crack, and is recorded on each update in the first table. The density of I is shown in blue in the distribution graph, and is recorded in the distribution table. On each update, the empirical density of I is shown in red in the distribution graph, and is recorded in the distribution table. The parameter of the process is the radius r of the coin, which can be varied with the scroll bar.\n\nan applet from PSOL from UAH\n\n## Glossary\n\n### density\n\nthe ratio of the mass of an object to its volume\n\n### event\n\nany set of possible outcomes of a statistical experiment\n\n### graph\n\nA diagram showing a relationship between two variables.\nThe diagram shows a vertical y axis and a horizontal x axis.\n\n### parameter\n\na) a constant or variable term in a function that determines the specific form of the function but not its general nature, as a in f(x) = ax, where a determines only the slope of the line described by f(x).\nb) one of the independent variables in a set of parametric equations.\n\n### variable\n\nA value which is unknown and free to vary, often denoted by x or y.\n\nFull Glossary List\n\n## This question appears in the following syllabi:\n\nSyllabusModuleSectionTopicExam Year\nAQA A-Level (UK - Pre-2017)S1ProbabilityExperimental-\nAQA AS Maths 2017StatisticsProbabilityExperimental Probabilities-\nAQA AS\/A2 Maths 2017StatisticsProbabilityExperimental Probabilities-\nCBSE XII (India)ProbabilityProbabilityRepeated independent (Bernoulli) trials and binomial distribution-\nCBSE XI (India)Statistics and ProbabilityProbabilityRandom experiments, outcomes, sample spaces (set representation)-\nCCEA A-Level (NI)S1ProbabilityExperimental-\nCIE A-Level (UK)S1ProbabilityExperimental-\nEdexcel A-Level (UK - Pre-2017)S1ProbabilityExperimental-\nEdexcel AS Maths 2017StatisticsProbabilityExperimental Probabilities-\nEdexcel AS\/A2 Maths 2017StatisticsProbabilityExperimental Probabilities-\nI.B. Higher Level5ProbabilityExperimental-\nI.B. Standard Level5ProbabilityExperimental-\nMethods (UK)M15ProbabilityExperimental-\nI.B. (MSSL)3ProbabilityExperimental-\nOCR A-Level (UK - Pre-2017)S1ProbabilityExperimental-\nOCR AS Maths 2017StatisticsProbabilityExperimental Probabilities-\nOCR MEI AS Maths 2017StatisticsProbabilityExperimental Probabilities-\nOCR-MEI A-Level (UK - Pre-2017)S1ProbabilityExperimental-\nPre-Calculus (US)E4ProbabilityExperimental-\nPre-U A-Level (UK)ProbProbabilityExperimental-","date":"2023-03-21 00:52:44","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8077419400215149, \"perplexity\": 2150.982367568461}, \"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-2023-14\/segments\/1679296943589.10\/warc\/CC-MAIN-20230321002050-20230321032050-00613.warc.gz\"}"} | null | null |
Əşrəf Aşırov –también escrito como Ashraf Ashirov– es un deportista azerbaiyano que compite en lucha libre. Ganó una medalla de plata en el Campeonato Europeo de Lucha de 2022, en la categoría de 79 kg.
Palmarés internacional
Referencias
Luchadores de Azerbaiyán | {
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Die Grafen von Caserta, einer Grafschaft in der süditalienischen Region Kampanien (Hauptort Caserta), waren eng mit dem Herrscherhaus oder dem Papsttum verbunden, der bekannteste unter ihnen ist Richard († nach 1265), der Schwiegersohn des Kaisers Friedrich II. Die Grafschaft war seit dem 12. Jahrhundert ein Lehen im Königreich Sizilien bzw. Königreich Neapel.
1579 wurde die Grafschaft zum Fürstentum erhoben, 1750 vom letzten Fürsten an den König verkauft. Ende des 19. Jahrhunderts wurde der Grafentitel durch Alfons Maria von Neapel-Sizilien, den "Thronprätendenten von Neapel" wieder bekannt.
Die normannischen und staufischen Grafen
Robert von Lauro (* um 1120, † 31. August 1183), 1150 als Herr der Burg Lauro bezeugt, 1159 als Graf von Caserta, ab 1171 als magnus comestabulus und magister iustitiaris Apulie et Terre Laboris.
Wilhelm von Lauro, September 1178 bezeugt, 1183 Graf von Caserta und Herr von Lauro, † wohl Ende 1199.
Wilhelm (II.), Graf von Caserta, nimmt 1199 Diepold von Schweinspeunt gefangen;
Robert (II.), Bruder Wilhelms (II.), 1202/12 Graf von Caserta
Thomas, 1216 bezeugt, Sohn Roberts (II.), Graf von Caserta bis 1223, im Aufstand gegen Kaiser Friedrich II. abgesetzt, 1224 exiliert
Richard (I.), Bruder Thomas', Graf von Caserta, 1243/44 Generalvikar der Mark Ancona, 1248 Vikar des Königreichs Sizilien, Schwiegersohn Kaiser Friedrichs II.
Richard (II.), dessen Sohn, Graf von Caserta und Tricarico
Konrad (* kurz vor 1250, † nach 13. Dezember 1306, wohl 1307) Ende 1266/Anfang 1267 Graf von Caserta, dann 36 Jahre Gefangener Karls von Anjou und seiner Nachfolger, 1303/04 befreit
Die französischen Grafen
Guillaume de Beaumont, genannt Pied-de-Rat († 1269), Seigneur de Beaumont-du-Gâtinais et de Villemomble, 1265 Graf von Caserta
Isabelle de Beaumont († 1276), Gräfin von Caserta, ⚭ Guy VIII. de Laval, (um 1240-nach 1295), Sire de Laval
Guy IX. de Laval († 1333), Sire de Laval, Graf von Caserta
Guy X. de Laval (X 1347), Sire de Laval, Graf von Caserta
Guy XI. de Laval († 1348), Sire de Laval, Graf von Caserta
Guy XII. (Jean) de Laval († 1412), 1348 Sire de Laval
Anne de Laval (1385–1466), ⚭
Guy XIII. de Laval (Jean de Montfort, † 1414), 1406 Sire de Laval
Guy XIV. de Laval (1407–1486), 1431 Comte de Laval
Guy XV. de Laval (1435–1501), 1461 Seigneur de Gavre, 1468 Comte de Montfort, 1486 Comte de Laval etc., Graf von Caserta, Vicomte de Rennes
Die Caetani, Ratta und Acquaviva
Benedetto Caetani († 1303), 1294 als Bonifatius VIII. Papst
Roffredo (Goffredo) Caetani, († nach 1295) dessen Bruder, 1295 von Karl II. von Neapel zum Grafen von Caserta ernannt
Pietro Caetani, † ermordet 1308, dessen Sohn, 2. Graf von Caserta
Die Grafschaft wird 1308 verkauft
Diego della Ratta († wohl 1327), 1. Graf von Caserta, Gran Camerlengo. ⚭ Oddolina di Chiaromonte († 1328), Baronessa di Mignano, Tochter von Riccardo Signore del Vasto
Francesco I. della Ratta, 2. Graf von Caserta. ⚭ Beatrice del Balzo († 1336) (Haus Les Baux)
Luigi Antonio della Ratta, 3. Graf von Caserta ⚭ um 1368/70 Beatrice Orsini, Tochter von Nicola, 3. Graf von Nola (Haus Orsini)
Francesco II. della Ratta († 1399), deren Sohn, 1382 4. Graf von Caserta
Baldassare della Ratta, dessen Sohn
Giovanni della Ratta, dessen Sohn, 6. Graf von Caserta ⚭ Anna Orsini († nach 1471) Tochter von Raimondo Orsini, Principe di Salerno, Duca di Amalfi
Francesco III. della Ratta († 1488), 7. Graf von Caserta ⚭ Altobella Gesualdo (1457–1507), Tochter von Sansone II., 1. Graf von Conza
Caterina della Ratta, † 1511, Erbtochter von Giovanni della Ratta, 8. Contessa di Caserta etc. ⚭ I Cesare d'Aragona, † 1501, unehelicher Sohn von König Ferdinand I. von Neapel. ⚭ II 1509 Andrea Matteo Acquaviva, 8. Duca di Atri, Conte di Conversano, † 1529 (Haus Acquaviva)
Gianfrancesco Acquaviva († 1527), dessen Sohn, Marchese di Bitonto. ⚭ Dorotea Gonzaga († 1550), Tochter von Gianfrancesco Gonzaga Signore di Sabbioneta (Haus Gonzaga)
Giulio Antonio Acquaviva († 1539 in Frankreich), dessen Sohn, Conte di Conversano. ⚭ Anna Gambacorta, † 1544, Tochter von Francesco Signore di Limatola und Caterina della Ratta, 1509 Erbin Caterinas, vom König nicht anerkannt
Gianfrancesco Acquaviva, dessen Sohn, Seigneur de Brie. ⚭ Susanna Caracciolo del Sole, Tochter von Sergianni III., 2. Fürst von Melfi
Baldassare Acquaviva († 1577), dessen Bruder, Signore di Caserta. ⚭ Gironima Gaetani dell'Aquila d'Aragona, Tochter von Giacomo Conte di Morcone
Die Fürsten von Caserta
Giulio Antonio Acquaviva (um 1549–1594), deren Sohn, Signore und 1579 1. Fürst von Caserta. ⚭ 1569 Vittoria de Lannoy, Tochter von Filippo de Lannoy, 2. Fürst von Sulmona
Andrea Matteo Acquaviva d'Aragona (1594–1634), deren Sohn, 2. Fürst von Caserta, Ritter des Ordens vom Goldenen Vlies. ⚭ Isabella Caracciolo, Tochter von Carlo, 6. Conte di Sant'Angelo
Anna Acquaviva d'Aragona (1596–1659), deren Tochter, 1635 3. Fürstin von Caserta, ⚭ Francesco Caetani (1594–1683), Duca di Sermoneta
Filippo II. Caetani (1620–1687), deren Sohn, 1659 4. Fürst von Caserta, Ritter des Ordens vom Goldenen Vlies
Gaetano Francesco Caetani (1656–1716), dessen Sohn, 9. Duca di Sermoneta, Duca di San Marco, 1687 Fürst von Caserta
Michaelangelo Caetani (1685–1759), dessen Sohn, verkauft Caserta 1750 an den König und erhält das Fürstentum Teano.
Der bourbonische Graf von Caserta
Alfons Maria von Neapel-Sizilien (1841–1934), Graf von Caserta, 1894 Thronprätendent
Literatur
zu den französischen Grafen: Detlev Schwennicke, Europäische Stammtafeln Band XIV (1991), Tafel 137, 145
Anmerkungen
Caserta | {
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Iris Cisneros es la primera mujer relatora de fútbol profesional en español para Estados Unidos y Mexico. Es narradora para la cadena Univisión Deportes Network en Estados Unidos y su primera transmisión de fútbol correspondió a fecha 11 del Clausura 2018 correspondiente al encuentro entre América y León (2-0), causó el más importante impacto que una chica periodista en Deportes haya provocado en la historia de la narración, por su impactante talento de como play by play Sports commentator, así como su sabiduría para analizar.
Iris Cisneros tuvo el impacto más importante, entrevistada y por revistas como Sport Illustrated y People, apareciendo también en la portada de Univision Deportes como el fichaje más representativo.
Después de la fusión Univision-Televisa Deportes, siendo ya TUDN, la jovencita Iris Cisneros continuó en lo más alto, encabezando las narraciones de los Mundiales Femeniles, Liga MX Femeniles,Bundesliga, así como sus constantes e importantes apariciones a cuadro en sus labores de cobertura en Club America, Pumas, Pachuca, entre otros clubes.
El camino histórico de la joven continuó al ser fichada por Telemundo Deportes donde también recibió una notable bienvenida y de la misma manera se convirtió en la narradora principal del fútbol femenil, así mismo su calidad la posicionó en Fox Sports….<ref></ref
Su primer televisora fue<nowiki>Sky Sports News</nowiki>,luego siguió teniendo al ser contratada por Univision Deportes, causando que medios como Sports Illustrated la entrevistarán y la colocarán en su portada.
Narró la [[Premier League]] (clasificatorios y amistosos), [[FA Cup]], [[Copa del Rey]], [[Eurocopa]], Eliminatorias europeas y sudamericanas, Mundial femenil absoluto. El 8 de marzo de 2018, se anunció su incorporación en [[Univision Deportes Network|Univisión Deportes Network]], siendo la primera mujer de origen judio sefardí en narrar un partido de fútbol oficial en Estados Unidos; luego Telemundo la ficha para ser su principal relatora de la liga femenil,siendo Fox Sports su siguiente paso.<ref></ref>
Referencias
Periodistas deportivos de Estados Unidos
Mujeres | {
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Alabama Power President Charles McCrary said the company expects to have power restored by the end of the day Wednesday to 95% of its customers who can receive service.
Alabama Power had more than 412,000 customers without power at the peak of the storm. Mr. McCrary said the damage was greater than hurricanes Katrina and Opal. The company had 3,000 utility poles snapped, more than 100 electric transmission structures damaged and five substations destroyed. | {
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Q: Remove kde-full I installed kde by using the command sudo apt-get install kde-full and now i have all kd apps and settings and gnome. i Want to remove all the kde apps that got installed and go back to the deafult settings.
| {
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4, het jaar 4
4 (getal), het getal vier
4 (Beyoncé), een album van de Amerikaanse zangeres Beyoncé
4 (Foreigner), een album van de Amerikaanse rockgroep Foreigner
4 (I.O.S.), een album van de Nederlandse band I.O.S.
4 (Johan), een album van de Nederlandse band Johan
Play4 (vroeger VIER), een Belgische televisiezender
Vier (album), een elpee van Willem Vermandere
Zie ook
Four (doorverwijspagina) | {
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ACSOL NewsMeetings / Events
Brian Banks to Speak at ACSOL Conference
·February 24, 2020
Brian Banks, who was convicted of a crime he did not commit and who experienced five years in prison
as well as the punishment of being required to register as a sex offender, has agreed to speak at this
year's ACSOL conference on Friday, May 29. Banks will join his attorney Justin Brooks, leader of the CA
Innocence Project, in a joint presentation about the legal fight that ended in Banks' removal from the
registry as well as exoneration.
Sign up today to hear them speak!
Both Banks and Brooks are featured in the recently released movie, Brian Banks, which highlights the
challenges Banks faced both inside and outside of prison. The movie will be screened at the conference
prior to their presentation.
As a high school student, Banks was a star football player in Long Beach who was offered a football
scholarship at the University of Southern California (USC). The USC scholarship was revoked, however,
after Banks was accused of raping a fellow high school student. Banks was convicted of that offense
despite the lack of physical evidence and sentenced to prison.
Upon his release from prison, Banks was required to register as a sex offender and placed on
parole. The movie highlights several of the challenges Banks faced while on parole, including
employment and playing football.
Banks achieved his goal of playing for the National Football League (NFL) when he signed with the
Atlanta Falcons on April 3, 2013. He played four preseason games with that team before being released
from the team. Banks subsequently spoke to the 2014 NFL draft rookie symposium and was later hired
by the NFL Department of Operations.
Take advantage of our temporary discount conference rate
2020 ACSOL Conference
ACSOL Phone Meeting Jan 16
ACSOL Phone Meeting Dec 19
CA: How to Seek a Job with a Conviction History: A Fair Chance Hiring Webinar on Dec. 3
ACSOL Phone Meeting Nov 21
CA: ACSOL Lawsuit alleges Irvine sex offender rule conflicts with state law
NARSOL LIVE Virtual Litigation Summit is November 19 & 21
NotReally February 24, 2020
Now I want to be there on that day.
Janice Bellucci February 27, 2020
We are honored that Brian Banks has agreed to join this year's ACSOL conference! As a speaker, he will share the challenges he faced when required to register, including parole conditions, employment and social interactions. He will also share what it feels like after his requirement to register was terminated, a feeling that many are expected to experience next year after the Tiered Registry Law takes effect. | {
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{"url":"http:\/\/tex.stackexchange.com\/questions\/295165\/finishing-math-with-a-period","text":"# Finishing math with a period\n\nI am new to this site and couldn't find this question after a quick search but it may have been asked before.\n\nThis is possibly the most inconsequential issue one can have, but it has been bothering me for months.\n\nWhen I finish a line of math (especially with the double $$), I often end with a period. I also usually use the \\text command to distinguish the period from a decimal point. My question is: is there any difference at all? I don't seriously think anyone would ever notice unless they looked at the TeX code, so this is more of a theoretical question. Which one is \"correct\"? $$|f(x)-(y)|<\\epsilon\\text{.}$$ or $$|f(x)-(y)|<\\epsilon.$$ - Welcome to TeX.SX! You can highlight code in your post using back-ticks. For code-blocks indent them by four spaces or use the {} on the gui. \u2013 Andrew Feb 21 at 20:28 I usually use \\text for the punctuation at the end of a displayed equation because in the font I usually use the text punctuation is noticeably different from the math one. But if they are similar, you can omit \\text. Instead of \\text{.} you can also type \\text., which is shorter. \u2013 User Feb 21 at 21:20 Note that there may be a clear visual difference: for example, if you are using Palatino as the text font and AMS Euler for mathematics. \u2013 Senex Feb 21 at 22:29 Math has its own rules, and a period (or other punctuation) might have a particular meaning. I just omit such (even if the result, considering the display \"part of the sentence\" is ungrammatical). \u2013 vonbrand Feb 21 at 23:52 ## 2 Answers Since you mention \\text, you're using LaTeX or AMS-TeX. I'll assume LaTeX. First of all, your formulas are incorrect because they have $$ (see Why is $...$ preferable to $$...$$?). This settled, let's look at fontmath.ltx, where we find, for the common punctuation one can find at the end of a formula,\n\n\\DeclareMathSymbol{,}{\\mathpunct}{letters}{\"3B}\n\\DeclareMathSymbol{.}{\\mathord}{letters}{\"3A}\n\\DeclareMathSymbol{;}{\\mathpunct}{operators}{\"3B}\n\n\nAs you see, the comma and the period are taken from the math letters font; the semicolon, instead, comes from the main text font (upright).\n\nSo, yes, in principle there is a difference. With \\text{.} you get the period from the font that was current when the formula started, so it will be from the italic font in the statement of a theorem (under normal settings) and the same for the comma.\n\nOn the other hand, an italic period is not easy to distinguish from an upright one. Here's a comparison, first the punctuation sign in text mode (upright or italic), then in math mode:\n\nI'd use the math mode ones, particularly for the semicolon. With other fonts the differences might be bigger, but I'd always go for upright notwithstanding the context.\n\nAs Guho rightly observes in comments, with \\text you also lose the kerning between the last symbol and the punctuation; try a formula my students so often forget :-(\n\n$\\dim\\operatorname{im} f+\\dim\\ker f=\\dim V.$\n\n\nand\n\n$\\dim\\operatorname{im} f+\\dim\\ker f=\\dim V\\text{.}$\n\n\nPeople might argue whether the first is better than the second ad infinitum, though. The kerning in the first case is the reason why Knuth decided to take the period and the comma from the math letters font.\n\nIn case you fear a period or comma can be ambiguously seen as part of the formula, use a thin space before it, like \\,. I wouldn't use more this space, but it's personal preferences. Somebody likes to separate punctuation with a quad (I heartily disagree).\n\nIf you're using AMS-TeX, the situation is fully similar, because the math symbol setting is the same as in plain TeX, which has\n\n\\mathcode\\,=\"613B\n\\mathcode\\.=\"013A\n\\mathcode\\;=\"603B\n\n\nwhich comes to the same choice of math fonts.\n\n-\n+1. Would you mind commenting on the loss of kerning when \\text is used? For example V. vs. V\\text{.}? Might be a relevant addition to your last paragraph and a good extension on this related question for inline math. \u2013\u00a0Guho Feb 21 at 21:10\n\\text is defined also in amstex. So, even if it is rare that someone uses amstex, the first sentence is not correct :) \u2013\u00a0User Feb 21 at 21:11\n@User You're right! \u2013\u00a0egreg Feb 21 at 21:14\n@CarstenS That can't apply to math anyway, I'm with Knuth on this (The TeXbook, solution of exercise 18.9, page 321): \u201c\u2026these experts recommend \u2018k := j \u2212 1; A [0] := accum; end;\u2019. The author heartily disagrees.\u201d \u2013\u00a0egreg Feb 21 at 23:38\n@MassimoOrtolano That's Claudio's convention. ;-) We had a discussion on the GuIT forum about this and I showed several books, old and new, where punctuation was used. \u2013\u00a0egreg Feb 22 at 15:05\n\nI agree with egreg in that I think the one that looks better is the upright font, but in certain cases one might need the textfont rather than the math font.\n\nIf you want it to do it automatically just do\n\n\\makeatletter\n{\\catcode\\.=\\active\\global\\def.{\\mathfinaldotaux}}\n\\AtBeginDocument{\\mathcode\\.=\"8000 }\n\\newcommand*\\mathfinaldotaux\n{\\@ifnextchar\\]{\\mathfinaldot}{\\@ifnextchar${\\mathfinaldot}{\\mathchar\\.}}} \\newcommand*\\mathfinaldot{\\textnormal{.}} \\makeatother This makes . active only in math mode, and and defines it to check if the next token is \\] or $ (you could also check for \\) but I don't think it's necessary) and in that case outputs \\mathfinaldot, otherwise outputs a normal ..\n\nYou can do this same approach with ,, ;, etc. If you want we could create a macro to ease the definition:\n\n\\providecommand*\\csdef[1]{\\expandafter\\def\\csname#1\\endcsname}\n\\makeatletter\n\\newcommand*\\definemathfinal[2]\n{\\begingroup\\lccode\\~=#1\\lowercase{\\endgroup\n\\def~}{\\csname mathfinal#1aux\\endcsname}\n\\AtBeginDocument{\\mathcode#1=\"8000 }\n\\csdef{mathfinal#1aux}{\\@ifnextchar\\]{#2}{\\@ifnextchar\\${#2}{\\mathchar#1}}}}\n\\makeatother\n\\definemathfinal{.}{\\textnormal{.}}\n\\definemathfinal{,}{\\,\\textnormal{,}} % <- You can define easily with some personal\n\\definemathfinal{;}{\\,\\textnormal{;}} % <- preferences like spacing\n\n\nThis way you don't have to change your document at all, and it's easily configurable.\n\n-\nWhat about , \\end{align} and so on? \u2013\u00a0egreg Feb 21 at 22:02\nNot completely foolproof, true, but adding a checking for \\end is \u201ceasy\u201d (I thought about it but just wrote that code without actually checking if it compiles, so I decided to leave \\end out :); altough it doesn't work with environments that grab the environment as an argument (that would require more work). For everything else, \\mathfinaldot. \u2013\u00a0Manuel Feb 21 at 22:05","date":"2016-05-27 08:36:01","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9009701013565063, \"perplexity\": 1507.8877044153014}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-22\/segments\/1464049276564.72\/warc\/CC-MAIN-20160524002116-00046-ip-10-185-217-139.ec2.internal.warc.gz\"}"} | null | null |
Q: How to prevent the creation of a temporary file tmp.edb during opening ESENT database? When I try to open ESENT database, a temporary file "tmp.edb" is created in program dir. I can change the path using JET_paramTempPath but, I can't find how to disable it.
Can I read DB without creation of temporary files?
Here's my code:
JetSetSystemParameter(nil, nil, JET_paramDatabasePageSize, iPageSize, nil);
JetSetSystemParameter(nil, nil, JET_paramRecovery, nil, 'Off');
JetCreateInstance(&FInstance, nil);
JetInit(FInstance); //Here file "tmp.edb" is created
JetBeginSession(FInstance, &FSession, nil, nil);
JetAttachDatabase(FSession, FFileName, JET_bitDbReadOnly);
JetOpenDatabase(FSession, FFileName, nil, &FDatabase, JET_bitDbReadOnly);
| {
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Contents
* Foreword by Leith Mullings
* How Capitalism Underdeveloped Black America: A Critical Reassessment
* Preface
* Introduction to the First Edition
* SECTION ONE. THE BLACK MAJORITY:THE DOMESTIC PERIPHERY
* 1. THE CRISIS OF THE BLACK WORKING CLASS
* 2. THE BLACK POOR: HIGHEST STAGE OF UNDERDEVE
* 3. GROUNDINGS WITH MY SISTERS: PATRIARCHY AND THE EXPLOITATION OF BLACK WOMEN
* 4. BLACK PRISONERS AND PUNISHMENT IN A RACIST/CAPITALIST STATE
* SECTION TWO. THE BLACK ELITE: THE DOMESTIC CORE
* 5. BLACK CAPITALISM: ENTREPRENEURS, CONSUMERS, AND THE HISTORICAL EVOLUTION OF THE BLACK MARKET
* 6. BLACK BRAHMINS: THE UNDERDEVELOPMENT OF BLACK POLITICAL LEADERSHIP
* 7. THE AMBIGUOUS POLITICS OF THE BLACK CHURCH
* 8. THE DESTRUCTION OF BLACK EDUCATION
* SECTION THREE. A QUESTION OF GENOCIDE
* 9. THE MEANING OF RACIST VIOLENCE IN LATE CAPITALISM
* 10. CONCLUSION: TOWARD A SOCIALIST AMERICA
* Endnotes
* Tables
Praise for How Capitalism Underdeveloped Black America
The reissue of Manning Marable's How Capitalism Underdeveloped Black America confirms that this is a classic work of political history and social criticism. Unfortunately, Marable's blistering insights into racial injustice and economic inequality remain depressingly relevant. But the good news is that Marable's prescient analysis—and his eloquent and self-critical preface to this new edition—will prove critical in helping us to think through and conquer the oppressive forces that remain.
—Michael Eric Dyson, author of I May Not Get There with You: The True Martin Luther King, Jr.
For those of us who came of political age in the 1980s, Manning Marable's How Capitalism Underdeveloped Black America was one of our bibles. Published during the cold winter of Reaganism, he introduced a new generation of Black activists/thinkers to class and gender struggles within Black communities, the political economy of incarceration, the limitations of Black capitalism, and the nearly forgotten vision of what a socialist future might look like. Two decades later, Marable's urgent and hopeful voice is as relevant as ever.
—Robin D. G. Kelley, author of Yo' Mama's DisFunktional!: Fighting the Culture Wars in Urban America
For a Latina, How Capitalism Underdeveloped Black America is not only a powerful analysis of the Black experience; Marable also opens the way to perceiving our Black-Brown commonalities. Through Marable's eyes, we see how Chicanos and other Latinos share so much with African Americans: the importance of learning our true history; of seeing how our oppression began with the violent seizure of our labor (and land, in the cases of Mexico and Puerto Rico); the sexist oppression of women as basic; the need for decent education; and the rise of imprisonment rates—along with internal issues like the role of our middle class; the church; and the homophobia that dehumanizes us. Above all, Marable helps us see how all roads point to the need for radical action by peoples united to win a new, socialist society.
—Elizabeth Martínez, author of De Colores Means All of Us: Latina Views for a Multi-Colored Century
Marable is of that unique band of African American intellectuals whose scholarship arises from, and has a direct bearing on, the struggles of ordinary Black people—and, in the process, throws up the symbiosis between race and class. A new edition of his pathbreaking work, How Capitalism Underdeveloped Black America, should open out these perspectives and challenges to a new generation of readers.
—A. Sivanandan, editor, Race & Class
Following in the footsteps of W. E. B. Du Bois, Oliver C. Cox, and Walter Rodney, Manning Marable's How Capitalism Underdeveloped Black America is a groundbreaking study of the political economy of Black America. It has stood the test of time and remains essential reading for a critical understanding of the interconnection of racism and economic exploitation.
—Robert L. Allen, senior editor, Black Scholar
In How Capitalism Underdeveloped Black America, Manning Marable created a classic work that continues to stand as a seminal text for those on the left interested in a grounded, coherent, and insightful analysis of the struggle for Black liberation. For example, long before other progressive activists/academics were ready to articulate, let alone deal with, the devastating impact of patriarchy on Black progress, Marable set forth on just such a path in the pages of this important book. Thus, in many ways, this text is illustrative of Marable's own long-standing commitment to lead a progressive and revolutionary fight, not the most popular one. In an age in which public intellectuals with little or no connection to the lives and struggles of those they write about and supposedly "represent" seem to dominate the scene, it is timely that How Capitalism Underdeveloped Black America should reappear. Hopefully, this book will remind us all of the need for serious and grounded analysis about the condition of those most marginal in our society. It is a must-read (or reread) for anyone committed to the theory and practice of struggle.
—Cathy J. Cohen, professor of political science and African-American studies, Yale University
Professor Manning Marable's How Capitalism Underdeveloped Black America remains one of the most informative and insightful books for understanding historical and contemporary relationships among race, power, and wealth in the United States. This book reminds us that race and class divisions continue to represent a fundamental social, economic, and political reality in this nation. Marable explains how class interests mold racial policies and politics, but also how Black people, and other communities of color, as well, reflect and challenge such interests. In fact, the author shows convincingly how a Black community in alliance with other communities and mobilized on behalf of a progressive social and economic agenda remains a serious threat to the capitalist order in this society.
—James Jennings, Trotter Institute, University of Massachusetts Boston
There are influential books—and then there are classics. Marable's How Capitalism Underdeveloped Black America is a clear case of the latter. Drawing upon the interpretive insights of Walter Rodney, the work advanced nearly all of the central concerns of the African American struggle for liberation in a world that continues to be hostile and exploitative. Concise and unapologetic, its endurance over the past two decades is a testament to its message of praxis and freedom.
—Lewis R. Gordon, chair of Africana Studies and professor of Africana Studies, Religious Studies,
and Modern Culture and Media, Brown University
In 1983, when How Capitalism Underdeveloped Black America first appeared, there existed a notable void in the intellectual delineation of the deteriorating circumstances confronting millions of African Americans. The 1980 election and subsequent administration of President Ronald Reagan signaled a national political rotation that would simultaneously attack Black progress and celebrate capitalism. Although an earlier generation of Black scholars, such as C. L. R. James and W. E. B. Du Bois, argued that the Black condition in the United States had to be situated always within a framework that understood and critiqued capitalism, it was time for a new voice. Already a well-known commentator and writer on Black life, Manning Marable's breakthrough work launched a new era in Black scholarship challenging left and Black orthodoxy in both the academy and alternative intellectual arenas. How Capitalism Underdeveloped Black America unfolds as a coherent and comprehensive work that addresses not only capitalism writ large, but also specific dimensions of Black life, such as sexism and patriarchy, criminal justice, poverty, religion, and education.
Marable elaborates on the contours of Black life with a scholarly vigor but in a manner that is accessible, a feature that has continued to characterize his voluminous body of work. . . . How Capitalism Underdeveloped Black America stands the test of time in many ways. Globalization has exacerbated, rather than eliminated, all of the contradictions described by Marable's classic text. A new edition, which updates the tranformations that happened since 1983, yet retains the basic sound arguments, is a welcome and pivotal literary and political event.
—Clarence Lusane, author of Race in the Global Era
First published by South End Press in Boston, Massachusetts.
© 1983 Manning Marable
This edition published in 2015 by
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For his personification of praxis, for his brilliant intellect, and for his uncompromising legacy as the voice of the periphery bound up in world revolution, this book is dedicated to Walter Rodney, the author of How Europe Underdeveloped Africa
Foreword
Leith Mullings
How Capitalism Underdeveloped Black America and Beyond
How Capitalism Underdeveloped Black America is a pioneering work. Though written more than three decades ago, in 1983, the book continues to provide an analysis that illuminates the conditions Black people confront today. In 2015, the New York Times reported that 1.5 million Black men were "missing," forced out of society by early death, the "war on drugs," mass incarceration, and joblessness. In 1983, when Manning Marable wrote How Capitalism Underdeveloped Black America, the Black community was experiencing the consequences of the draconian Reagan "revolution," including an increase in racially motivated violence. Documenting the worsening conditions of African Americans on many fronts, Marable analyzed this as a class project, characterized by manipulating racial stereotypes to divert hundreds of billions of dollars from programs supporting human needs to the military, promoting the law-and-order mentality and the "war on drugs" at home. His extensive exploration of the roots of current conditions led him to conclude that the "most striking fact about American economic history and its politics is the brutal and systematic underdevelopment of Black people."
While the hard-fought Black freedom movement has brought about some advances in the three decades since Marable wrote the book, the continued profitability of racism is apparent in many areas, such as the widening racial disparities in income and wealth, the continuing dispossession of land and neighborhoods, and the monetary benefits to financial institutions from speculative real-estate practices. However, it is also starkly evident in the discriminatory application of criminal justice and policing, the immediate results of which include mass incarceration and numerous murders of unarmed Black people by police officers. These discriminatory policies also have enormous economic ramifications, which range from raising money for the functioning of towns through fees and fines levied on Black people to the devastation of communities resulting from the absence of its members who are incarcerated or who cannot find employment because of a criminal record. Such processes are supported by a backlash against the gains of the civil rights movement, taking the form of a postracial ideology claiming that racism no longer exists. Now, more than ever, How Capitalism Underdeveloped Black America remains one of the most relevant studies of how and why racism and capitalism continue, predicting that freedom for Black Americans cannot be achieved in a capitalist society and offering a way forward.
§ § §
I read and loved How Capitalism Underdeveloped Black America many years before meeting its author. For me, as for countless others of my generation and since, the volume courageously and straightforwardly recounted the ways in which the U.S. capitalist state had underdeveloped Black America: "The constant expropriation of surplus value created by Black labor is the heart and soul of underdevelopment" (7). Though in the preface to the second edition, published in 2000, Manning was self-critical about the polemic style of his writing, we who read it appreciated the fact that he studiously avoided the passive exonerative voice, in which no one is responsible—things just happen. Though Manning and I were both of the rare breed of Black academics active in left organizations, we did not meet until 1994, when he came to give a job talk at the Graduate Center of the City University of New York. I was one of the few Black faculty members and therefore, not surprisingly, was recruited to persuade him to accept the position. He presented a passionate and visionary concept of a research institute that combined cutting-edge scholarship with activism and that brought together scholars and activists for debate and discussion. Equally impressive were his enthusiasm, dedication, and fierce determination, which I was later to discover were fueled by his prescient view that he could not count on living a long life.
Much to my dismay, Manning accepted the position of the founding director of the Institute for Research in African-American Studies at Columbia University, where, I must admit, he created a unique and outstanding institution. After spending a year on a fellowship in Paris, I returned to New York and we began to work together on various projects. We married in 1996 and became partners, companions, and comrades on the road of scholarship, activism, mentoring, and discovery for nearly two decades.
With the publication of How Capitalism Underdeveloped Black America, Manning quickly became one of the world's leading Black theorists. Interrogating the intertwined relationship of race and class, his central argument is that the development of capitalism in the United States and the creation of its wealth were built upon the exploitation of the labor, knowledge, and lives of Black people through slavery, segregation, and discrimination. In other words, the development of the capitalist state is integrally related to the underdevelopment and oppression of Black America. "Development was . . . the institutionalization of the hegemony of capitalism as a world system. Underdevelopment was the direct consequence of this process: chattel slavery, sharecropping, peonage, industrial labor at low wages, and cultural chaos" (3).
In ten chapters covering various sectors and processes of the Black community—the working class, women and patriarchy, the poor, prisoners, capitalists, the church, education, and racist violence—Manning demonstrates the relationship between the wealth of the U.S. state and the superexploitation of Black people: "Afro-Americans have been on the other side of one of the most remarkable and rapid accumulations of capital seen anywhere in human history, existing as a necessary yet circumscribed victim within the proverbial belly of the beast" (1–2).
The book's title was a tribute to Walter Rodney, a brilliant Guyanese historian, orator, and activist, whom I met in 1970 when teaching anthropology at the University of Dar-es-Salaam in Tanzania. Manning met him later when both were affiliated with the Institute of the Black World and, as a student, he was assigned to pick Rodney up at the airport and drive him around. Upon learning of his assassination in 1980, Manning decided to title the book in memory of Rodney's classic study How Europe Underdeveloped Africa (1972). Following Eric Williams's Capitalism and Slavery (1994), Rodney's thesis that the transatlantic slave trade was central to understanding both Africa and Europe—transferring vast amounts of wealth to Europe while destroying African societies—significantly influenced both the argument and the structure of How Capitalism Underdeveloped Black America.
How Capitalism Underdeveloped Black America and Black Americans Today
Manning began the preface to the second edition by expressing a feeling that many authors have experienced: "There is always an element of ambivalence that separates an author from her or his previously published work. . . . The text of the book does not change over time: it is what it is. Yet the author continues to rethink basic ideas embedded in her or his work, coming up with new insights and conclusions, sometimes contradicting one's earlier views" (xxix). Rereading the text in 2000, he was critical of his failure to clarify that the main contradiction was not between the Black working class and the middle class, but rather about the class contradictions of capitalism: "the exploitative policies and practices of the ruling capitalist class" (xl). Nevertheless, he warned that the "powerful and destructive role of class stratification within the Black community" should not be underestimated (xl). Today inequality within the Black population "has probably never been greater."
Manning also regretted his underestimation of the importance of electoral struggle to the Black freedom movement, citing the significance of the Voting Rights Act of 1965 and the united front that elected Harold Washington in 1983 as the first Black, and most progressive, mayor of Chicago, as well as the Rainbow Coalition of the presidential campaign of 1984. However, he correctly identified and predicted the rise of such neoconservatives as Charles Hamilton, Tony Brown, and later Clarence Thomas and Thomas Sowell, anticipating the emergence of the "deracialization of U.S. politics," which in the 2000 preface he termed "post-Black politics" (xxxvi). Moreover, despite the election of President Barack Obama, in the last few years, gerrymandering, voter suppression, and restrictions placed on voter registration by the right wing have eliminated several previously Black districts. Post-racialism, the view that the civil rights movement has done away with racism and that the playing field is now level—one indicator being the election of President Obama in 2008—has become a pervasive worldview among Euro-Americans. Based on this hegemonic ideology, Congress and the Supreme Court have actively pursued rolling back many of the measures gained in the civil rights period. In 2013, the Supreme Court gutted the Voting Rights Act, striking down a key provision initially aimed at prohibiting the pervasive practices that placed obstacles in the path of African Americans attempting to exercise their right to vote (Shelby County, Alabama v. Holder, Attorney General, et al.). Furthermore, with the 2010 Supreme Court ruling in the case of Citizens United v. Federal Elections Committee removing the ban on corporations using their funds for contributions to political parties and individuals, big money now plays an even more significant role in U.S. elections.
The central point of How Capitalism Underdeveloped Black America—that race is a relationship between accumulation and dispossession and that without a structural change in the economic system, disparities and discrimination would continue and perhaps worsen—correctly anticipated and analyzed current conditions. Most social indicators demonstrate that structural racism continues to flourish. During the decades following the Civil Rights Act of 1964 and the Voting Rights Act of 1965, African Americans made significant gains. Political participation blossomed with respect to "dramatic" increases in voter participation and an exponential increase in the number of Black elected officials. The Black middle class experienced "a considerable expansion in the size, security . . . and influence." The percentage of Blacks with college degrees rose from 3.5 to 14.3 percent, and the percentage of Blacks over the age of twenty-five with high-school degrees tripled.
However, though individual African Americans have been able to overcome some impediments to opportunities, structural racism and white privilege continue to result in significant disparities and inequalities, exacerbated by the periodic economic downturns of the last fifteen years. By 2012, Black median household income had fallen to 58.4 percent of white median household income, compared to 66.3 percent in 2000. In 2013, the median white family had net assets of $142,000 as compared to $11,000 for the median Black family. Correspondingly, though the poverty rate among African Americans fell from 41.8 percent in 1965 to 22.5 percent in 2000, by 2014 it had risen to 27.2 percent. Studies continue to demonstrate a persistent gap in socioeconomic status between Blacks and whites. Contributing to these disparities is the fact that because of nondiscrimination policies and unionization, Blacks are more likely to hold jobs in the public sector. They therefore suffer disproportionately from the decline in the public sector brought about by the universal downsizing of government (though the private sector has improved since the 2008 recession). In addition, real estate foreclosure rates are three times higher in Black and Latino neighborhoods, where financial institutions profited from extending subprime loans disproportionately, than in white neighborhoods.
Perhaps nowhere is the brutality of the capitalist state with respect to Black Americans more harshly visible than in the mass incarceration of Black and brown people. In 1985, Manning was among the first historians to sound the alarm about mass incarceration. In chapter 4 of How Capitalism Underdeveloped Black America, entitled "Black Prisoners and Punishment in a Racist/Capitalist State," he asserts, "At the core of the capitalist accumulation process and institutional racism is coercion" (94). Tracing the history of the use of punishment and violence to ensure the preservation of the capitalist state, he recounts in detail the sequence of coercive racial projects, beginning with slavery, "coercion of the most primitive kind;" through a series of Black codes to guarantee labor submission; peonage systems, and convict leasing, in which Black prisoners multiplied the profitability of the system; to Jim Crow laws, all held in place by lynching and other forms of racist violence (94). In 1983, he noted that "over 500,000 men, women and youths were incarcerated in more than 6,500 penal institutions of various types," and that these were disproportionately Black (112). By the 2000 edition, he observed that there were more that 1.8 million Americans were incarcerated in the United States, about one-half of whom were African Americans (xliv).
Manning's prediction of the growth of mass incarceration, where prisons would be among "fastest and most productive 'growth industries,'" was unfortunately accurate (xlv). Currently there are 2.2 million Americans, disproportionately Black and Latino, incarcerated in state and federal prisons, with more than half of the prison population incarcerated for nonviolent crimes. With the highest rate of incarceration in the world, the United States is a carceral state with an orientation to governance that revolves around punishment. This mass incarceration is severely racialized, with over 60 percent of the incarcerated Black and Latino, leading some scholars to refer to this phenomenon as "the New Jim Crow." Between 1980 and 2000, the rate of Black incarceration in the United States tripled, with most of the convictions involving nonviolent drug offenses. One in nine Black men between the ages of twenty and thirty-four is incarcerated, Black men are imprisoned at a rate of 6.4 times more than white men, and for Black women the rate is three times that of white women.
The punitive, discriminatory nature of this mass incarceration is undeniable. Drug convictions (mainly low-level drug offenses) account for most of the increase in imprisonment. However, studies show that people of all races use and sell illegal drugs at similar rates. In fact, to the extent that there are significant differences between races, surveys suggest that whites, particularly white youth, are more likely to engage in drug crime than people of color. Nevertheless, in 2015 approximately 80 percent of people incarcerated for drug offenses in state prisons and 60 percent of those in federal prisons are Black or Latino. The United States Sentencing Commission concluded that Black men are given sentences one-fifth longer than white men for committing the same crimes. For example, in Wisconsin, where African Americans constitute only 6 percent of the population, they are 37 percent of those in state prisons. In 2007, the Vera Institute of Justice began a study (just concluded) of the racial implications of the work of the Milwaukee Country District Attorney's Office. The study demonstrated that prosecutors in Milwaukee declined to prosecute only 27 percent of Blacks arrested for possession of drug paraphernalia, as compared to 41 percent of whites.
Change in Violent and Property Crime and Inmate and Total Population, 1960–2008
John Schmitt, Kris Warner, and Sarika Gupta, "The High Budgetary Cost of Incarceration," Center for Economic and Policy Research, June 2010 report, http://www.cepr.net/index.php/publications/reports/the-high-budgetary-cost-of-incarceration. Authors' analysis of FBI and BJS data.
The punitive character of this mass incarceration is evident in Figure 1, documenting the precipitous hyperincarceration following the Reagan era, even as crimes against property and violent crime declined. Another major concern should be the school-to-prison pipeline, in which young children are criminalized and then become trapped in the carceral system, providing further evidence of Manning's conclusion that "the criminal justice system operates effectively as a conduit for enlarging the nonwhite prison population" (113).
The current state of mass incarceration in the United States clearly demonstrates Manning's assertion that capitalism is preserved and reproduced on the backs of the Black community. As the lives of Black men, women, and children and the fabric of the Black community are destroyed, mass incarceration provides profit through the transfer of payments to private corporations for building prisons and supplying prison services, as well as the exploitation of prison labor. Beyond this, the expansion of prisons has been used to attempt to shore up capitalism, solving the problem of deindustrialization by creating jobs in small towns where manufacturing has disappeared—a process described by anthropologist Andrea Morrell as "the carceral reindustrialization of America."
Furthermore, mass incarceration strengthens the political system that undergirds the political foundation of the state. In the majority of states, prisoners are not permitted to vote and in several states former felons lose their right to vote after they are released. In New York, for example, such restrictions effectively remove a large voting population from nonwhite downstate communities. Yet, for purposes of political representation, prisoners are counted as residents in the counties where their prison is located, providing upstate counties—which are primarily white, Republican, conservative State Senate districts—with increased population for the purposes of state benefits and political representation. Not surprisingly, their representatives frequently take political positions and actions that are hostile to the communities from which the prisoners are drawn, promoting and encouraging ever higher levels of incarceration.
In 2015, after the police killing of Michael Brown in Ferguson, Missouri, an investigation by the U.S. Department of Justice of the Ferguson Police Department revealed that Blacks were disproportionately stopped for minor violations. It became clear that the town of Ferguson financed a significant proportion of its expenses through discriminatory arrests, fines, court costs, and convictions. The income from Ferguson's discriminatory practices was second only to income from the sales tax. The inability to pay one parking ticket could multiply fines and result in jail sentences, leading Human Rights Watch to refer to this as a debtor's prison. In one case, an African American woman who was unable to pay a fine for a parking ticket was arrested twice; though she made payments regularly on the original $151, she still owed $541 after more than seven years. These practices are not uncommon in some regions of the United States, bringing to mind Manning's description of the peonage system in which, at the end of the harvest, Black farmers owed more to the white planter than their share of the crop could cover, providing recruits for the "dramatically" profitable convict-leasing system (98).
§ § §
Manning's work resonated with those he wrote about in How Capitalism Underdeveloped Black America. As he observed in the 2000 preface, the book was very popular with prisoners. He often received several letters a month from prisoners—every one of which he answered, often at length. After learning of his death, a number of prisoners wrote to me and others close to Manning. As one wrote to me on July 26, 2013, "Dear Professor Mullings, Your husband/his writings inspired, educated and motivated me greatly. I'm just an evil convict now but I've been labeled a "socio-politico activist" for 40+ of my 65 years. . . . I hope you are prevailing after losing such an amazing, life enriching human force such as Manning Marable." A letter to Russell Rickford, one of Manning's former students, written on September 16, 2014, reads: "Since my incarceration, I have read many of Professor Manning Marable's books. Some of them I've read twice . . . many . . . of Professor Marable's books captivated me. I am reading things I was totally unaware of . . . I was unaware of his passing and was profoundly affected. . . . My intention is to create a Men's Study Group to discuss various topics in regards to our situation." And in a letter to me on April 25, 2015, another prisoner wrote: "Prof. Marable has been a teacher for me, of sorts, from the grave. His work [has] truly been a blessing and purpose to improve myself as an African American male. . . . This is where the book How Capitalism came to mind. I had read the book 3 times and I still get choked up in the 'Black Prisoner' chapter."
Written in the aftermath of the Miami rebellion of 1980, following the acquittal of white police who employed deadly force to subdue and arrest a Black man, part III of How Capitalism Underdeveloped Black America is entitled "The Question of Genocide." After meticulously recounting known killings and acts of violence against Black people, Manning warned that "the existence of random violence against Blacks and civil terrorism is no accidental phenomenon. It is a necessary element in the establishment of any future authoritarian or rightwing government" (220). Referring to Reaganomics, he observed that "the wave of random racist violence and 'legal lynchings' can be placed in perspective only in the light of . . . the socioeconomic instability within the white middle to upper classes" (248) and the "white working class anxiety which accompanies any basic restructuring of the economic order" (251).
Today, in the context of the growing insecurity of the "middle class," we confront a more public presence of a militant right wing in the form of the Tea Party and other such organizations, as well as a wave of racially motivated attacks and hate crimes. The Southern Poverty Law Center reports that after the election of Obama in 2008, the number of anti-Black hate crimes increased by 8 percent from 2,658 in 2007 to 2,876 in 2008. They caution that these numbers are underrepresented, as many of the incidents do not become part of the FBI database. While we have no way of knowing the actual number of Black people murdered by the police, the existence of new levels of technology, particularly the mobile phone, have made a wave of high-profile police murders of unarmed Black people visible, culminating in massive protests and urban rebellions in several major cities. According to USA Today, based on voluntary local police reports of justifiable homicide to the FBI, there were on average ninety-six cases of a white police officer killing a Black person each year between 2006 and 2012. An analysis by the Washington Post found that during the first five months of 2015, U.S. police shot and killed 385 people, at a rate of two to three people per day. Half of the victims were white and half minority; two-thirds of the unarmed victims were Black or Latino. Historian Robin D. G. Kelley noted that in the seven months between August and November 2014, while we waited for the grand jury that would find no probable cause in the police murder of an unarmed teenager, Michael Brown, at least seven unarmed African American men and women between the ages of twelve and thirty-seven were killed by police officers. This does not include killings by white vigilantes, such as George Zimmerman's murder of unarmed teenager Trayvon Martin, who was on his way home after buying candy and soda at a 7-Eleven. Zimmerman was found not guilty on all counts. Nor does it include the murder of seventeen-year-old Jordan Davis by forty-seven-year-old Michael Dunn, for playing loud music. Nor is gender a protection, as we know from the murder of twenty-two-year-old Rekia Boyd by police officers in Chicago, or the death of Tanisha Anderson after being slammed to the ground by a Cleveland police officer, or the murder of nineteen-year-old Renisha McBride, who was shot in the face by homeowner Theodore Wafer when she knocked on his door to ask for help after an accident.
At the close of chapter 9, Manning reflects on the question of genocide. Interrogating the use of the term, he notes that "genocide is usually defined as the systematic and deliberate destruction of a racial, political or cultural group," and that to the extent that Blacks are needed as a reserve labor pool, they will be brutally treated but maintained "as a racially segregated entity for the systematic exploitation of its labor power" (225). But most important for our understanding of the current situation, he cautioned that in the effort to preserve capitalism at all costs, "The racist/capitalist state under Reagan has proceeded down a public policy road which could inevitably involve the complete obliteration of the entire Black reserve army of labor and sections of the Black working class" (225). In 1983, he ended the chapter on "Racist Violence in Late Capitalism" with the warning: "The genocidal logic of the situation could demand, in the not too distant future, the rejection of the ghetto's right to survival in the new capitalist order. Without gas chambers or pogroms, the dark ghetto's economic and social institutions might be destroyed, and many of its residents would simply cease to exist" (226).
This analysis helps to explain the "1.5 Million Missing Black Men" (see above) who "have disappeared from daily life." In 1951, citing the many incidents of lynching, police brutality, and legal segregation, as well as systematic inequalities and discrimination, the singer Paul Robeson and activist William Patterson, supported by the Communist Party USA, presented a document to the United Nations, asserting that the United States was involved in genocide as defined by the United Nations. In May 2015, the United Nations Human Rights Council issued a scathing report condemning, among other things, the death penalty and racism, especially as they relate to police brutality and criminal justice in the United States. Perhaps it is time to revisit the issue of genocide.
Activist, Scholar, Teacher, and Mentor
Analyzing of these conditions led Manning to the conclusion that Black Americans could not achieve real freedom within the political economy of capitalism, requiring a significant transformation of society. Though he was critical of certain aspects of traditional Marxism, he took to heart Marx's well-known observation that "the philosophers have only interpreted the world in various ways; the point, however, is to change it." From the time he was seventeen years old and among the first mourners to arrive at the funeral for Dr. Martin Luther King, he firmly believed that his role was not only to describe and analyze the conditions of Black people but also to work to change them, unifying theory and practice through political activism and building institutions, as well as engaging in ideological struggle.
Not content to deal merely with the dissemination of knowledge, while he continued to produce both popular and scholarly writing, Manning's role as an activist emerged logically from his analysis in How Capitalism Underdeveloped Black America. Here he presents "ten points of departure . . . which may provide some tentative suggestions for social transformation and the end to the 'underdevelopment' of Black America" (256). These considerations infused his work in many of the organizations in which we participated. He was involved in a variety of left organizations, including the National Black Political Assembly and the National Black Independent Political Party. He also served as a vice president for the Democratic Socialists of America and as cochair of the Committees of Correspondence for Democracy and Socialism.
Finding that few of these organizations effectively addressed the current issues of Black people, he also helped to initiate a new organization. In 1995, at a meeting in Manchester, England, to commemorate the fiftieth anniversary of the Pan-African Congress, Manning and I met with historian Barbara Ransby and sociologist Abdul Alkalimat and discussed the need for an organization that would address the challenges confronting the African American community, which unfortunately in many ways continued to be similar to those Manning analyzed in How Capitalism Underdeveloped Black America. A few months later, we met with activist Bill Fletcher around our kitchen table to launch the organization that became the Black Radical Congress. On March 1, 1997, thirty-five activists met in Chicago to discuss the conditions of African Americans and the future of progressive U.S. politics. As we introduced the concept to activists all over the country, the coordinating committee grew to two hundred African Americans—with various political perspectives—ranging from nationalists to lesbian and gay activists, feminists, and communists. Manning wrote the first draft of the "Freedom Agenda," which called for
the human rights of Black people and all people . . . [and] a society and world in which every individual enjoys full human rights, full protection of the United Nations Declaration of Human Rights and in the United States equal protection of the Constitution and of all the laws. We seek a society in which every individual—regardless of color, nationality, national origin ethnicity, religion, sex, sexual orientation, age, family structure, or mental and physical ability—is free to experience "life, liberty and the pursuit of happiness."
The demands included the right to shelter, employment, health care, and education, and declared: "We will fight to advance beyond capitalism, which has demonstrated its structural incapacity to address basic human needs worldwide and, in particular, the needs of Black people."
The founding conference of the Black Radical Congress (BRC), named in honor of the African National Congress, in Chicago, June 19 to 21, 1998, attracted more than two thousand African American activists. Though, like the Niagara Movement, the BRC was relatively short-lived (ten years), it could boast of some important accomplishments, perhaps chief among them bringing together African Americans from across the political spectrum who would subsequently work together on political projects. The national organization adopted such campaigns such as "Books Not Bars," an anti-incarceration, pro-education movement, and raised money and arranged speaking engagements for the Charleston Five, longshoremen who faced felony riot charges arising from attempts to unionize dockworkers. Local committees also undertook projects such as working with a coalition that successfully defeated the Edison Foundation's attempt to privatize New York City public schools.
Throughout this work, it was clear that there was another front to the struggle. Manning was among the foremost Black scholars to speak forcefully about the ways in which patriarchy supports "the ideological and coercive apparatuses of white power" (9) and the importance of fighting sexism. In "Groundings with My Sisters," chapter 3 of How Capitalism Underdeveloped Black America, he condemns patriarchy in Black organizations in no uncertain terms and unequivocally supports the leadership of women. He observes that "Black social history, as it has been written to date, has been profoundly patriarchal" (62). Reviewing the "triple oppression (race/class/sex) of Black women," he described the leadership of Black women from the time of Sojourner Truth through the civil rights movement, concluding that "no road toward the ultimate emancipation of the U.S. Black working class exists outside of a concomitant struggle, in theory and practice, to destroy every vestige of sexual oppression within the Black community" (91). His prescient observation that "women have been the foundation of Black culture and society, yet their contributions have been ignored" (103) foreshadowed the current discussions around leadership and the emergence of young Black women as leaders of new organizations that are at the forefront of confronting police brutality and state violence.
Manning often joked about the fact that his family, with whom he often spent the summers of his youth, was from Tuskegee, Alabama, the home of Booker T. Washington. Though he disagreed with Washington's political views and his opposition to W. E. B. Du Bois, he did agree with Washington about the importance of building Black institutions. He established and molded the Institute for Research in African-American Studies at Columbia University. It was to be a center that would not only engage in critical scholarship—it became one of the best-respected Black Studies programs in the country—but also produce work that was both useful and accessible to residents of the Black community, with the hope that activists would be empowered by knowledge that could contribute to social transformation. To this end, he also lectured widely to grassroots organizations, community groups, and prisoners, as well as to academics.
During the years Manning directed the institute, he sought to bridge the gap between Columbia and the Harlem community. Institute conversations, symposia, and conferences were open to the public. Community voices were heard. He worked with students, community activists, and organizations, as well as established scholars, to produce conferences and symposia on topics such as youth, feminism, incarceration, hip-hop, and Black studies. (See Souls 2004 for a discussion of the many projects the institute developed.)
He also initiated conferences about other areas of the African diaspora, such as Jamaica, Cuba, and South Africa. Coming of age at a time when "third world" countries and anti-imperialist movements were attuned to various versions of Marxism and anti-imperialism as an alternative to "modernization theory," which blamed these nations for their underdevelopment, the importance of internationalism infused his work. As an undergraduate at Earlham College he spent time in Kenya, and despite being prohibited from entering South Africa by the apartheid government, he wrote his dissertation on John Langalibalele Dube, one of the founders of the African Nationalist Congress. Throughout How Capitalism Underdeveloped Black America, Manning contextualizes the Black freedom struggle within broader mobilizations against imperialism, reflecting the influence of Du Bois, C. L. R. James, and Rodney. African and Caribbean Politics, written in 1987, remains one of his most popular books.
Together we visited Cuba, South Africa, Tanzania, Jamaica, and Brazil, among other countries. Both of us were invited to speak at the Non-Governmental Organization Forum of the United Nations Conference on Racism, Xenophobia and Other Forms of Intolerance in Durban, South Africa. We were tremendously impressed and hopeful about the possibility of addressing "global apartheid." Manning, who had been involved in public debates and discussions about reparations, including one published by TIME, was particularly interested in the international outcome of these discussions. However, not surprisingly, the representatives from the United States and Israel walked out of the conference. We arrived home two days before 9/11 and the expansion of the security state, which, along with the protests of the United States and Israel, muted discussion of reparations for slavery and generations of racism.
Manning was also the founding editor of the quarterly journal Souls: A Journal of Black History, Politics and Culture (formerly Race and Reason). This too was a forum that encouraged scholars to address the critical issues confronting the Black community, reflecting and interrogating many of the issues raised in How Capitalism Underdeveloped Black America and exploring new ones. It was one of the few journals that welcomed scholars whose work took an openly critical stance on a range of issues affecting Black people. Theme issues examined such subjects as gender and sexuality, new social movements in the African diaspora, public education, Malcolm X, Hurricane Katrina, Islam and Black Americans, Black Power, and many others. Though the journal presented first-rate scholarship, it was also a site where young scholars could be nurtured and encouraged and learn the skills of building and maintaining institutions. The managing editor of Souls was generally one of Manning's students; the editorial board included several of our students and former students, who were also contributors to the journal. The two readers for each submission diligently tried their best to provide supportive advice that would help each potential writer to learn the skills of writing for journals, and it was in Souls that many young people who are now established scholars published their early work. Always coediting with young scholars, Manning collated some of the articles into ten volumes to be used in studies of Black history, foregrounding their work in ways that are unusual in the academy.
Though seldom interacting with a computer and generally writing voluminously on yellow pads, Manning believed in using every effective vehicle to disseminate knowledge. In collaboration with Columbia University's Center for New Media Teaching and Learning, he initiated in several digital projects, including The Souls of Black Folk, a multimedia web-based annotated guide, the Amistad Project, to help teachers with Black history, and the Malcolm X Multimedia Study Environment (MSE).
In addition, Manning was a much beloved teacher and mentor. Through his teaching, the institute, and the publication of Souls, as one of his former students put it, he "cultivated two generations of scholars, activists, and students, discovering in each individual a unique genius for advancing the cause he lovingly described: empowering the Black masses to reclaim their agency and 'return to their own history.'" He would have been very proud of his intellectual sons and daughters who have taken up the challenges outlined in How Capitalism Underdeveloped Black America.
Though Manning acted on his belief that there was no contradiction between activism and scholarship, his first love was writing. He was a prolific writer (as was clear in his 2000 reassessment, where he admitted that he wrote more than one-third of the book in four weeks of fourteen hours a day [xxxviii]). He was never happier than when he sat down with a blank yellow pad and, by the end of the day, the pages were covered with words. As was clearly the case with How Capitalism Underdeveloped Black America, he profoundly believed that those of us who have the opportunity to engage in knowledge production have the responsibility to use this to empower people. For many years, he wrote a weekly column about current events, first entitled "From the Grassroots," then "Beyond the Color Line." At the height of its distribution, the column was provided free of charge to more than four hundred Black and international newspapers. He wrote hundreds of articles and authored and edited more than thirty books on various subjects, including: Race, Reform and Rebellion (1999), Black Leadership (1998), African and Caribbean Politics (1987), Speaking Truth to Power (1996), Living Black History (2006), and biographical works about Du Bois (1986) and Medgar Evers (coedited with Myrlie Evers) (2005), and, of course, Malcolm X (2011). Among them was the widely used text in Black studies, Let Nobody Turn Us Around: Voices of Resistance, Reform and Renewal (2000 and 2009), which I coedited. We compiled a history of texts indicating the thinking and philosophy of Black women and men, leaders, and common people, including the more traditionally known integrationists and nationalists but also excavating the history of what we called transformationalism—the view that eradicating racism required a radical transformative social change addressing all forms of inequality. The selections in this text, as well as the images in our book Freedom: A Photographic History of the African American Struggle (2001), reflected our shared vision of history as made by collective actions, by ordinary people doing extraordinary things, by African Americans "making themselves."
But Manning's most prominent book is the Pulitzer Prize–winning Malcolm X: A Life of Reinvention. His interest in Malcolm X emerged early in his career. In How Capitalism Underdeveloped Black America, Manning described Malcolm X as "the greatest Black revolutionary of the 1960s" and notes that in the construction of "a socialist America," the "other America" of Malcolm X, among others, must be the "historical starting point" for our fresh efforts to build "a genuine peoples' democracy and a socialist economic system" (230). Malcolm X had intrigued him for years and when Manning stepped down from directing the institute, he was able to devote his full attention to writing Malcolm's biography. He began to collect material about Malcolm X in 1989 while on the faculty at the University of Colorado and became fascinated by the inconsistencies and silences in the Autobiography of Malcolm X. (After all, all autobiographies highlight certain aspects of one's life and underplay others.) Ever a public historian who believed that "democratic access and multiple perspectives contribute to the making of the past as well as the present," he created an interactive digital repository, designed to analyze the Autobiography through various lenses, such as politics and religion. Launched in 2004, it included a chronology, annotations, course syllabi, lectures, interviews, oral histories, and other material, all of which are available for public use.
Manning was an assiduous and meticulous researcher. Working with his students, he took joy in creating an exhaustive chronology and scouring the records of the New York City Police Department and the Federal Bureau of Investigation, obtained by a Freedom of Information Act request. He collected and analyzed vast quantities of archival material, including periodicals from all over the world and interviewed dozens of people, always triangulating his sources.
As he wrote, he was particularly appalled by the fact that neither Malcolm X nor his wife, Betty Shabazz, had any way of knowing the extent of the forces arrayed against them. As a historian, writing years after the fact, Manning was able to present a context that neither Malcolm nor Betty could fully know, including the scope of the New York Police Department and FBI surveillance, the disruption and infiltration of Malcolm's organizations, and his betrayal by some of his closest associates.
Manning was obsessed with the unresolved questions surrounding the assassination of Malcolm X. On one hand, there was the official interpretation. But he focused on difficult and unanswered questions: Who gave the order and who pulled the trigger? What was the role of law enforcement agencies such as the New York Police Department Bureau of Special Service and Investigation (BOSSI) unit and the FBI? Did they have advance knowledge of the assassination and, if so, what did they do about it? Who was the shadowy figure whisked away from the Audubon Ballroom in a police car the night of the assassination? The evidence led him to suspect that the person who fired the shot that murdered Malcolm X had not been jailed, tried, or convicted for the crime. His hope was that the biography would contribute to raising the demand that the FBI and NYPD fully open their files on the assassination of Malcolm X.
In keeping with his internationalist interest, Manning excitedly pored over the unedited version of Malcolm's diaries recounting his trip to Africa. He discovered that Malcolm met and developed alliances with prominent world leaders and revolutionaries and that he was frequently received with the pomp and ceremony of a head of state. Equally interesting to Manning was Malcolm's spiritual journey and his move in the direction of anti-imperialism and international human rights. For Manning, Malcolm X became a global force, with the potential, had he lived, of becoming a bridge to the more than one billion Muslims in the world.
As was the case in writing How Capitalism Underdeveloped Black America, Manning was guided by the words of Amílcar Cabral, the assassinated leader of the African Party for the Independence of Guinea and Cape Verde: "Hide nothing from the masses of our people. Tell no lies. . . . Mask no difficulties, mistakes and failures. Claim no easy victories." Hence Manning's objective in the biography was "to go beyond the legend" and to present Malcolm as a real, complex human being who confronted enormous personal, ideological, and political struggles, who made mistakes, but reflected on them and tried to correct them, and thus emerged as a historic figure who "embodied the spirit, vitality and political mood of an entire population." He wrote: "I am deeply grateful to the real Malcolm X, the man behind the myth, who courageously challenged and transformed himself, seeking to achieve a vision of a world without racism. Without erasing his mistakes and contradictions, Malcolm embodies a definitive yardstick by which all other Americans who aspire to a mantle of leadership should be measured."
For Manning, the biography was merely the beginning of an inquiry that would ignite debates and further investigation. He looked forward to collegial discussion and contestation, building on, extending, and interrogating some of the issues raised in the biography. He would have relished discussions with those whose goal was to advance our knowledge and would have been amused by those whose motivations, intentions, and behavior were far less noble. Unfortunately, he did not live to participate in these exchanges.
For twenty-five years, Manning battled sarcoidosis, a disease that over the years destroyed his lung capacity. Eventually, he had to use an oxygen tank in order to breathe. He did not allow this to constrain his teaching and writing (though he was forced to curtail his lecture schedule). He carried his oxygen tank to classes and meetings with students. Even when limited to his desk by the increasing need for oxygen, he maintained his eternal optimism and continued his work. In July 2010, he underwent a double lung transplant. After his release from the hospital in August, we hoped that he would live somewhere near three years (the average life expectancy for a double lung-transplant patient at the hospital where he underwent the procedure). He continued his research, writing, and editing, determined to finish the biography. In March 2011, he contracted pneumonia as a result of a medication being withdrawn. As always, he battled for his life with all his energy. As he emerged from an induced coma, I looked forward to seeing him and talking with him the next day. However, as a resident was changing a tube, Manning went into cardiac arrest, from which he never recovered. His untimely and unnecessary death occurred on April 1, 2011. The biography of Malcolm X was officially published on April 4.
The Vision
Based on extensive research, How Capitalism Underdeveloped Black America was incredibly prescient about the status of Black people today and its historic causes. However, Manning went beyond cataloguing the ills of capitalism to elaborate what could and should be done. He engaged not only in political critique but in thinking about a way forward. As he put it, "The road to Black liberation must also be a road to socialist revolution" (228). In 2002, he noted that, in view of world events and capitalism's ability to mutate, "socialism might seem to have reached a dead end as a viable concept" (xlv). But, he added, "History is always filled with unanticipated twists and detours" (xlv).
Indeed, inequality both in the United States and throughout the world is greater than it has ever been, with a massive transfer of wealth to the 0.01 percent. As the consequences of neoliberalism—market fundamentalism, structural adjustment, and the decline of the welfare state—become widespread, the influence of U.S. capitalism has been in decline. Popular protest in some Latin American and European countries have resulted in the election of left governments that have challenged the current world order. A recent New York Times/CBS poll found that 60 percent of Americans think that the government should do something to reduce inequality. Reflecting on the recent recession of 2008 to 2009, some scholars have suggested that "globalized capitalism has so socialized the forces of production and the financial system (and on such a vast scale) that even the enormous resources of the largest capitalist economy in the world are insufficient to rescue it."
But as Manning notes, "Wherever there is repression, there will be resistance, and from the lessons of struggle will flower the hopes for a better life" (xlvi). Today we see that though capitalism and racism have persisted and, in some ways, become stronger and more repressive as the crisis of capitalism has deepened, so have protests against it. Despite the rise of the right wing and increasing state violence, as predicted in How Capitalism Underdeveloped Black America, the Occupy movement, for example, has helped to bring the unprecedented inequality to public view. Young African American women have organized mass mobilizations and major demonstrations, often dominated by young people of various races and ethnicities, to confront and protest state violence and mass incarceration. These recent actions, as well as long-term organizing, are forcing some transformations in policing and incarceration. New York State's Rockefeller drug laws, with their extremely discriminatory application and mandatory harsh prison sentences, have been weakened. In New York City, a U.S. district court judge ruled that "stop-and-frisk," long a staple of the New York City Police Department's discriminatory policing, is unconstitutional. A small number of police officers have been charged (though not convicted) for the death of a Black man while under arrest in Baltimore, Maryland, and the Justice Department has initiated at least twenty investigations of the conduct of police departments and officers.
In How Capitalism Underdeveloped Black America, Manning advocates "socialism from below"—a democratic and popular multicultural society. For Manning, revolution had a moral component. However, he was not naive about the obstacles in the way of a just society. He advanced a program about how this might be accomplished, observing that "history is an organic process" and that "the transition to socialism will not be fixed or predetermined," but will require a coalition of progressive forces and transitional reformist demands that are antiracist, antisexist, and anticapitalist, which would then be the foundation for an alternative social system (232–33). In 2000, he concluded, "I remain convinced that Black people as a group will never achieve the historical objectives of their long struggle within the political economy of capitalism. . . . The oppressed have in their hands the capacity to make new history and, ultimately, a new society. This is the political perspective taken by How Capitalism Underdeveloped Black America, and it is the position in which I still passionately believe today" (xlvi).
New York City
June 2015
* * *
Acknowledgements: I am most grateful to the friends, colleagues, and former students who were so supportive through this project. This volume would not have come into being without Anthony Arnove, whose vision, patience, and commitment to reissuing How Capitalism Underdeveloped Black America was the driving force in bringing this about. Raymond Codrington, Dana Davis, Garrett Felber, Bill Fletcher, Gerald Horne, Megan Marcelin, Sandra Mullings, and Alia Tyner all read drafts of the manuscript at various stages and provided useful and supportive comments. Many of their observations are included here. Finally, it would have been difficult to complete the foreword without the research skills and conscientious attentiveness of my research assistant, Lisa Figuero Jahn. Thank you.
How Capitalism Underdeveloped Black America
A Critical Reassessment
There is always an element of ambivalence that separates an author from her or his previously published work. This is especially the case when a particular book develops over time a significant audience and is widely discussed and debated. The book reflects not only what the author thought at a particular time, but also to a considerable extent what was happening in the society in which the book was produced. The text of a book doesn't change over time: it is what it is. Yet the author continues to rethink basic ideas embedded in her or his work, coming up with new insights and conclusions, some times contradicting one's earlier views.
This perhaps captures my complicated relationship with How Capitalism Underdeveloped Black America: Problems in Race, Political Economy, and Society. In some respects, it was not the best work I had done up to that point. Blackwater, originally self-published in 1981, was based on a series of very detailed historical studies of African-American culture and socioeconomic development, as well as conjunctural analyses of recent political events, such as the May 1980 Miami Rebellion. But Blackwater reached a very limited audience, and would not become generally available until it was reprinted by the University of Colorado Press nearly fifteen years after it was originally written. By way of contrast, How Capitalism was released in January 1983, and within several months had been widely circulated and discussed. From my own anecdotal experiences, people almost immediately either loved the book or hated it. It was subsequently adopted as a required text in Black political economy for hundreds of academic courses. How Capitalism was especially popular with African-American prisoners. To this day, I frequently receive requests from prisoners for complimentary copies or for explanations about certain passages or references in the text. Nearly every week I encounter one or more African Americans, usually in their thirties or early forties, who tell me how they first read the book or how it changed their lives and how they understand the world.
How Capitalism Underdeveloped Black America was, like every other study, a product of its time. To explain the work requires a reconstruction of the specific political, social, and economic factors that defined its context. It is from that vantage point that the book's relative strengths and weaknesses as a social analysis of Black America in the early 1980s can be better understood.
II
The decade of the 1980s began for me on November 3, 1979, when five antiracist political activists were murdered and nearly a dozen injured by Ku Klux Klansmen and Nazis in Greensboro, North Carolina. In broad daylight, a car caravan containing more than thirty white racists drove casually into the center of a mostly African-American housing project, which was the site of a local antiracist demonstration. The Klansmen and Nazis had been given the route of the demonstrators by local law enforcement authorities. Although the ninety-second massacre was videotaped by a television crew, only sixteen of the racists identified at the scene were indicted, and only six were tried. All six were judged "not guilty" by an all-white jury. A second trial once again declared the killers not guilty. Only six years later were the families of the Greensboro martyrs able to win a civil suit against these racists. The Greensboro Massacre seemed to indicate that U.S. capitalism was moving into a much more authoritarian mode of class and racial control. The Klan and Nazis were, in effect, being used as "death squads" not unlike those operating in El Salvador or Guatemala at the same time. The fact that these racist vigilantes had no formal ties to the state permitted government officials to plead their neutrality and lack of involvement in their crimes. When many other manifestations of racist violence began to erupt across the country in 1980 and 1981, it seemed like U.S. society was being prepared for some kind of authoritarian takeover, or perhaps a Chilean-style suspension of democratic rights and institutions.
The Miami rebellion of May 1980 seemed in this context to be a logical response by the Black masses to the growing wave of police brutality, racist attacks, and blatant discrimination in the criminal justice system. The event that had sparked the rioting was the acquittal of white police officers who had employed deadly force to subdue and arrest a Black man. I heard about the urban revolt about twelve hours after it had started on a Saturday night, and I immediately flew to Miami. Because my newspaper column regularly appeared in the local African-American newspaper, I was given great freedom of access into Black community-based organizations. What was striking about the uprising was that it was both spontaneous and "planned." There were a number of white-owned businesses or firms employing few or no African Americans that appeared to have been targeted for firebombing. There were even several incidents of racial atrocities, which were committed by both Blacks and whites. Miami was the largest and most destructive urban riot since the rebellions that swept across U.S. cities in the wake of Martin Luther King, Jr.'s assassination twelve years earlier.
I had barely returned from Miami and was writing my observations into an essay to be published in the Black Scholar when the noted Black scholar and activist Walter Rodney was murdered in his native country, Guyana. Rodney was the author of the widely read historical study How Europe Underdeveloped Africa, published originally in 1972 by the small Black radical press Bogle-L'Ouverture, based in London. I had first encountered Rodney's work as a graduate student, when a friend gave me a political pamphlet that contained a collection of Rodney's lectures to a Jamaican working class audience, called Groundings with My Brothers. Rodney was very well known to the African-American progressive and radical community. Hundreds of young Black Americans, including myself, had either lived in or had traveled through East Africa in the years Rodney was a professor at the University of Dar Es Salaam in Tanzania. Thousands more had met or heard him speak at African and African-American Studies conferences, or at lectures given in U.S. universities.
I had only met Rodney several times, but I was especially fortunate to have spent some time with him on a few memorable occasions. Rodney was affiliated with an Atlanta-based research center, the Institute of the Black World (IBW), and periodically visited the city. From 1976 to 1978, I was employed at the Tuskegee Institute, in the heart of Alabama's Black Belt, and I frequently commuted to IBW to attend various educational programs and events. Several times during Rodney's visits, I was asked by the IBW's director, Howard Dodson, to take Rodney to lunch or to drive him to this or that place in Atlanta. I don't recall the specifics of the conversations we had together. What I do recall vividly was how talkative I was, and how interested and reflective he was about what I had to say. Walter was a truly gifted intellectual, who brought a deep understanding of history into his interpretation of politics and current events. But he never used his scholarship or vast reservoir of knowledge to intimidate young scholars looking to him for approval. When I learned that he had been murdered, I felt crushed. I decided to try to extend his analysis of the impact of European colonialism and capitalist exploitation in Africa to the oppressed situation of Black people in the United States.
At the time of Rodney's assassination, I was teaching at the Africana Studies and Research Center at Cornell University, which was then chaired by James Turner. Six years earlier, Rodney had taught courses at the Africana Studies Center on Black political economy and history. After Rodney's departure from the center, the radical sociologist Ronald Bailey taught courses on political economy there for several years. With my appointment in January 1980, I assumed responsibility for the Black political economy course. Although my focus was on the United States, I assigned several chapters of How Europe Underdeveloped Africa as required reading.
Rodney's basic thesis was that the transatlantic slave trade and European colonialism were central to the underdevelopment of the African continent over a period of five hundred years. Under colonial rule, vast amounts of wealth were transferred from Africa to Europe. The imposition of monocrop systems of agriculture destroyed local economies, contributing to periodic famines and extreme poverty. Politically, African states "lost their power, independence and meaning—irrespective of whether they were big empires or small polities." Even when "certain traditional rulers were kept in office, and the formal structure of some kingdoms was partially retained," real political power "had passed into the hands of foreign overlords." Rodney's major theoretical argument was that racism as a social force, in both Africa and the Americas, was generally subsidiary to the dynamics of capitalist exploitation. Rodney observed:
[I]t can be affirmed without reservations that the white racism which came to pervade the world was an integral part of the capitalist mode of production. . . . European planters and miners enslaved Africans for economic reasons, so that their labor power could be exploited. Indeed, it would have been impossible to open up the New World and to use it as a constant generator of wealth, had it not been for African labor. . . . Europeans at home and abroad found it necessary to rationalize that exploitation in racist terms as well. Oppression follows logically from exploitation, so as to guarantee the latter. Oppression of African people on purely racial grounds accompanied, strengthened, and became indistinguishable from oppression for economic reasons.
The basic correctness of Rodney's emphasis of class above race became crystal clear with the election of Ronald Reagan to the presidency in November 1980. Reagan's electoral coalition had at its core nearly all of the Southern conservatives who had been in the Dixiecrat wing of the Democratic Party two decades earlier. Racists from the former White Citizens Councils and veterans of the George Wallace for President campaigns of 1968 and 1972 also found an ideological soulmate in the former California governor and ex-"B movie" actor. Reagan's racial agenda was unambiguous to friend and foe alike. He opposed affirmative action, minority economic setasides, and enforcement of equal employment opportunity regulations, policy positions that were diametrically different from those earlier Republican presidents such as Nixon and Ford had supported. Reagan manipulated crude racist stereotypes in his standard speeches, such as images of "welfare mothers" abusing food stamps and other public assistance programs. Yet despite the deeply racist character of the "Reagan Revolution," which was how his administration described itself from its earliest months in power, its essential dynamics were driven by the political economy of capitalism.
The severe economic recession of the mid-1970s, the energy crisis, and the falling rate of profits of major U.S. corporations, all contributed to what would become known as Reaganism. Ideologically, Reaganism represented a fundamental departure from the liberal welfare state and Keynesian economic policies that had been followed to a great extent by both capitalist political parties. Politicians from Lyndon Johnson to Richard Nixon had assumed that the government had to play a decisive role in regulating a modern capitalist economy and that welfare programs were necessary to manage social dissent. By contrast, Reagan's view was that the federal government was the problem. Massive reductions in social programs across the board were mandated. On October 1, 1981, more than 400,000 families were removed from federal and state welfare roles. New guidelines were set for welfare recipients, cutting the amount of assets a family could own and still receive assistance from $2,000 to $1,000. Undocumented workers and strikers were declared ineligible for Aid to Families with Dependent Children (AFDC). On September 4, 1981, the Department of Agriculture reduced the amount of food served to 26 million children at more than 94,000 schools across the country. Federal housing expenditures and special programs designed for low-income families virtually came to a halt. Federal housing allocations, which had been $30 billion under President Jimmy Carter in fiscal year 1981, dropped to $8 billion within five years. The number of homeless Americans not surprisingly doubled during Reagan's tenure in office. Most other federal social programs, such as job training, community development agencies and cooperatives, and public health clinics, were either eliminated completely or severely curtailed.
Hundreds of billions of dollars that were cut from human needs programs were directly reallocated to an unprecedented expansion of U.S. conventional and strategic nuclear weapons. Reagan initiated a "second Cold War" against the Soviet Union and its allies, with the unambiguous goal of destroying the Communist system, either by military or economic means. Economically, this was a kind of "military Keynesianism," in which the government went billions of dollars into debt building a massive military complex, which in turn, created hundreds of thousands of jobs in the defense industry. The Soviets were demonized relentlessly by the administration as an "Evil Empire." The Reagan administration authorized the deployment of Cruise and Pershing II missiles in Western Europe aimed at the Soviet Union, both of which were classified as "first strike" weapons. The Soviets had no alternative except to counter the U.S. arms buildup with one of their own, allocating at one point about one quarter of their entire gross domestic product toward their military. By 1983, the U.S. had more than 11,000 strategic warheads, compared to 7,800 Soviet warheads. Both countries had the capacity to suffer a "first strike" from their opponent, and still deliver fire power to destroy the other many times over. This insane military logic was actually termed "MAD," or mutually assured destruction. For the first time since the Cuban Missile Crisis in the fall of 1962, it appeared that the United States was fully prepared to lead the world into a nuclear holocaust.
In the field of civil rights, Reagan made his hostility to Blacks' interests clear by appointing William Bradford Reynolds as assistant attorney general for civil rights, and Black conservative Clarence Thomas as chair of the Equal Employment Opportunity Commission. Black conservative ideologue Clarance Pendleton was placed in charge of the U.S. Civil Rights Commission, which was soon effectively dismantled under the reactionary guidance of executive director Linda Chavez. Within less than a year, the policy direction of the administration was unmistakable. The Department of Labor weakened an executive order that forced corporate recipients of federal contracts to file affirmative action plans, raising the minimum level for submitting such plans from $50,000 to $1 million contracts. Annual affirmative action plans were scrapped, and employers were informed that they would be reviewed only once every five years. The Office of Federal Contract Compliance Programs privately instructed its field staff to reduce its enforcement activities. The Department of Education pressured the Justice Department to delete gender bias laws aimed to protect female workers at educational institutions. The protective provisions of the 1965 Voting Rights Act were rarely used by Reagan's Justice Department, with almost no lawsuits being filed on behalf of Black plaintiffs. Reagan's judicial appointments similarly followed a racial pattern of exclusion. During his first term as president, the percentage of Reagan's Black appointments to the Federal District Court and the U.S. Circuit Court of Appeals was less than 1 percent. Perhaps just as important was Reagan's apparent deep personal animus towards African Americans as a racial group. In fact, during his entire eight years in office, the president formally met with African American delegations and representatives only eight times.
In international affairs, the Reagan administration's racial policies were central to its relationship with the white minority apartheid regime in South Africa. Reagan's chief adviser on African affairs, Chester Crocker, announced that the administration would follow a new policy of "constructive engagement" with apartheid. The basic idea supposedly was that South Africa would gradually evolve into a democratic, multiracial society without U.S. political or economic sanctions or pressure. The Reagan administration considered the African National Congress a "terrorist" organization and supported the apartheid dictatorship's refusal to negotiate with African leader Nelson Mandela, who was still imprisoned. The Reagan administration permitted the Pretoria government to send South Africa's Coast Guard to be trained inside the United States. More than 2,500 electric shock batons, in addition to other crowd-control equipment, were sent from the U.S. to the apartheid national police force. Offices promoting U.S. corporate investment were established in Johannesburg and in other South African cities. By 1983, Mobil Oil had $426 million invested in South Africa, with a labor force of 3,577 workers; General Motors had invested $243 million, with 5,038 employees. In 1984, U.S. investment inside South Africa came to $15 billion, approximately 20 percent of all U.S. foreign direct investment.
Deliberately or not, Reaganism created a highly charged political environment, which directly contributed to an increase in racially motivated violence against African Americans throughout the United States. Chapter Nine of How Capitalism Underdeveloped Black America, "The Meaning of Racist Violence in Late Capitalism," goes into great detail to document individual cases of racist violence, including attacks by vigilante organizations and instances of police brutality. The Ku Klux Klan and white supremacist organizations felt that they had a friend in the White House and that a fundamental corner in the history of U.S. race relations had been turned with Reagan's election, representing the end of the "Second Reconstruction." This was again reconfirmed by the results of the presidential election of 1984. African Americans voted overwhelmingly against Reagan, with levels of support for the Democratic candidate Walter Mondale reaching levels approaching 100 percent among registered voters in many urban and poor Black areas. By contrast, Reagan won the support of 66 percent of all white voters. He received 68 percent of the votes of those who had annual incomes of $50,000 and above, and 80 percent support from those voters describing themselves as "born again Christians." At the time, it seemed obvious to many African-American activists that we were confronting what was, in effect, a mass conservative white united front, consisting primarily of middle- and upper-class whites, but also supported by a good number of confused but reactionary white working-class and poor people. The entire country seemed to be descending into either a nuclear or racial apocalypse, with only the Black freedom movement apparently capable of constructing a democratic opposition to halt it.
Yet, to the dismay of Black progressives, the bulk of the African-American political establishment seemed to capitulate to mass conservatism. When Reagan was first elected in November 1980, prominent civil rights leader Vernon Jordan declared publicly that the new president deserved "the benefit of the doubt" and that African Americans should consider whether "equality can be achieved by conservative means." More than 100 Black academicians, journalists, and aspiring governmental appointees attended a Black conservatives' conference held in San Francisco in late 1980, hosted by Black economist Thomas Sowell. The conference marked the emergence of Black conservatism as a small yet powerfully influential current within the African-American middle class. There were even a number of Black intellectuals who had advocated "Black Power" and the politics of Black liberation only a decade earlier and now were at the forefront of the ideological retreat. Charles Hamilton, co-author of the 1967 manifesto Black Power, participated in the San Francisco meeting and praised the rise of African-American conservatives. Also in attendance was media journalist Tony Brown, a former Black nationalist whose political and moral bankruptcy had led him to embrace the Republican agenda and everything he had once condemned. Brown's shameless electronic hucksterism financed by generous corporate subsidies promoted "Black capitalism" as the cure-all for African-American economic problems of poverty, unemployment, and underdevelopment.
It was "snake-oil," pure and simple, designed to confuse and divide Black entrepreneurs and elements of the aspiring professional and managerial class from the working class, the poor, and unemployed, who were catching the brunt of capitalism's offensive against labor. Sadly, many Black liberals and veterans of the great desegregation campaigns of the 1960s went along with the new conservative agenda to some extent. Martin Luther King, Jr.'s chief lieutenants, Ralph David Abernathy and Hosea Williams, actually endorsed Reagan's candidacy in October 1980. They subsequently floated the incredible proposal that South Carolina senator and former segregationist leader Strom Thurmond serve as "a liaison officer between Republicans on behalf of minorities." A powerful Black Philadelphia minister, Reverend Leon Sullivan, testified before a U.S. Senate committee in support of the appointment of former Nixon White House Chief of Staff Alexander Haig as Reagan's Secretary of State. Haig's appointment, according to Sullivan, was "necessary for America." The ghost of Booker T. Washington, the chimera of Black capitalism, was now speaking through leaders such as Atlanta mayor Andrew Young, who in 1982 called for "the desegregation of the money markets." Never one to be outdone as a phrasemaker, the Reverend Jesse Jackson urged one gathering of Black businessmen to "move from Civil Rights to Silver Rights and from aid to trade." Political struggle could only get the Black community so far. Jackson declared: "The marketplace is the arena for our development."
Somehow, the Black freedom movement had to transcend these "misleaders" to reclaim the mantle of democratic protest. I felt that the majority of African Americans—workers, the unemployed, poor people, women, and prisoners—were strategically positioned within U.S. capitalism to provide a decisive leadership role for other oppressed groups. What was necessary was a theoretical perspective that could explain that Black working people would form the nucleus of a mass democratic movement against Reagan and Reaganism and why institutional racism could never be dismantled under capitalism. Liberals, both Black and white, no longer had the capacity to provide meaningful opposition to the growth of the far right. The Black freedom movement therefore had to go beyond the boundaries of reform toward a program of socialism.
III
This was the immediate context and key ideas that informed the writing of How Capitalism Underdeveloped Black America. The earliest drafts of the book were developed in the spring and summer months of 1981. I had two tentative working titles for the manuscript-in-progress: Race, Work, and the State, and Race, Work, and Power, both of which bore the subtitle Black Political Economy and Society in the 1980s. There were no subdivisions originally planned in the body of the text. The first draft was organized into eleven chapters, in the following order: "Black Workers"; "The Ghettoclass"; "Dependency and Underdevelopment: Energy, Health, and Welfare"; "The Destruction of Black Education"; "Black Brahmins"; "Black Reaganism: Of Thomas Sowell and Others"; "The Poverty of the Black Intelligentsia"; "Sexual Oppression and the Black Experience"; "Afro-American Nationalism After Black Power"; "A Question of Genocide"; and a bibliographical essay, "Race, Class, and Conflict: Intellectual Debates on Race Relations Research." At this stage, I had written fragmentary essays on many of these topics, but no conceptual framework formed the foundations of a real thesis.
During the next few months, the manuscript was reorganized around what I thought at the time were two fundamentally conflicting classes: the "Black majority," an oppressed proletariat created "in the proverbial bowels of the capitalist leviathan," those "who understood that their masters' political system of bourgeois democracy was a lie," versus the "Black elite," a "privileged social stratum, who were often distinguished by color and caste; who praised the master publicly if not privately . . . who sought to accumulate petty amounts of capital at the expense of their Black sisters and brothers; whose dream of freedom was one of acceptance into the inner sanctum of white economic and political power." Looking back over the entire span of African-American history, it seemed to me that this inner class conflict between the Black majority versus the Black elite was the driving force that explained much of the political and ideological conflicts that had long divided the Black community. The degree of class division among African Americans was so great, I thought, that it had to be responsible for reproducing "two divergent levels of consciousness, which represented two very different kinds of uneven historical experiences."
With this new conceptual structure, the general contents of the book quickly fell into place by the end of 1981. The new title of the revised manuscript was How Black America Works: Race, Political Economy, and Social Stratification in the 1980s. The first subdivision of material, "The Black Majority," contained chapters on the Black working class, the poor, prisoners, youth, and "sexism and the Black Economy." The section on "The Black Elite" now featured chapters on the African-American political establishment, or the "Black Brahmins"; '"Making It in the System': The Black Entrepreneur in Capitalist Society"; "The Politics of the Black Church"; Black-owned banks and problems of capital investment in the Black community; and "Black Reaganism." In a third section, I had included an essay on "The Destruction of Black Education" and an article on the draconian prospects for Black America under authoritarian capitalism, called "A Question of Genocide." In 1982, I had the good fortune to be invited to lecture during the January term at Williams College in Massachusetts. The New England winter was particularly cold that year, with snowdrifts and ice storms making travel impossible for days at a time. Huddled beside a space heater in an old chilly house, there was little else to do except write, which I did for fourteen hours each day. More than one-third of the book was actually written in those four weeks.
Although I directly quoted Rodney only several times in How Capitalism, How Europe Underdeveloped Africa was a major influence in the construction of the central arguments, as well as for how the social science data was presented in the text. For example, Chapter Five of How Europe goes into considerable detail to document the various processes of how European banks, mining, and commercial corporations expatriated the African surplus under colonial rule. In one section, Rodney describes the development of Unilever, Ltd., a vast international corporate conglomerate that also included the United Africa Company. From its origins as a manufacturer of soap, the profits from its African-based enterprises helped Unilever to become a truly global corporation. As Rodney observed: "Unilever flourished in war and peace. . . . By the end of the colonial period, Unilever was a world force, selling traditional soaps, detergents, margarine, lard, ghee, cooking oil, canned foods, candles, glycerin, oil cake, and toilet preparations such as toothpaste." Similarly, in Chapter Five of How Capitalism, I presented an analysis of how U.S. corporations culturally manipulated Black consumers and expropriated billions of dollars in profits from the African-American domestic market. I looked at the growing business management literature on advertising and specific consumer buying patterns, showing how tobacco, liquor, and other corporations used such studies to effectively market their goods within the Black community.
Another key element of Rodney's thesis was the role of education in the underdevelopment of Africa. Rodney insisted:
The main purpose of the colonial school system was to train Africans to help man the local administration at the lowest levels and to staff the private capitalist firms owned by Europeans.. .. It was not an educational system that grew out of the African environment or one that was designed to promote the most rational use of material and social resources. It was not an educational system designed to give young people confidence and pride as members of African societies, but one which sought to instill a sense of deference towards all that was European and capitalist.
Again following Rodney's analysis, I examined the contradictory legacy of African-American higher education. Historically Black colleges never were permitted to "develop a clear pedagogy of Black liberation, nor [were] . . . they organically linked to the daily struggle of the Black masses." Yet despite their severe limitations, they still "created the intellectual and social space" essential for the construction of Black leadership, skilled professionals, and a middle class. I tried to illustrate how in the early 1980s desegregation as interpreted and implemented by federal courts was being used to dismantle historically Black schools. Any independent African-American educational institutions would always be under attack if they called "for the transformation of the racist/capitalist order."
Before sending the final manuscript of my book to South End Press, I drafted an introduction, which outlined "A Point of View on Black History," or the historical premises upon which the entire book had been written. The book's brief preface, written originally in the summer of 1982, was postdated when I received the page proofs for final corrections in the text. I dedicated the book primarily to Walter Rodney, and therefore it was logical to retitle the study How Capitalism Underdeveloped Black America.
My father frequently uses the expression, "Hindsight is always twenty/twenty." As I read How Capitalism again today, at the dawning of the twenty-first century, I can see a number of theoretical lapses, factual errors, and other mistakes that should have been corrected. The most significant conceptual flaw in the work is its central organizational premise—that the totality of African-American history has been polarized and structured around the class division between the Black "haves" and the Black "have-nots." The real contours of Black American social history were always much more complicated, more textured, than this analysis suggests. During slavery, there were numerous examples of Black freed men or enslaved Africans who exercised certain privileges, who betrayed their masters and deliberately sided with the Black masses. It was the educated Black middle class, consisting largely of school teachers, merchants, attorneys, physicians, and clergy, who formed the core leadership in the construction of African-American social institutions and most African-American political movements: This is not to underestimate in any way the powerful and destructive role of class stratification within the Black community, especially in the years since How Capitalism was written. The real problem, however, isn't the contradictory and accommodationist behavior of the Black middle class, but the exploitative policies and practices of the capitalist ruling class. Today, we live in a society in which the richest 1 percent of all households possess a greater net wealth than the bottom 95 percent of all U.S. households. The top 1 percent of all income earners receive more than 40 percent of the total income. The number of African Americans and Latinos in these elite groups is insignificant at best.
A similarly sectarian approach is taken toward electoral politics in general, and African-American politicians in particular. "There is something essentially absurd about a Negro politician in racist/capitalist America," I wrote in 1982. "The Black politician is locked in a world of meaningless symbols which perpetuate the hegemony of the white ruling class. . . . The Black elected official is essentially a vicar for a higher authority, a necessary buffer between the Black majority and the capitalist state, a kind of modern voodoo priest, smelling of incense, pomp and pedigree, who promises much but delivers nothing." I basically thought that electoral politics had absolutely nothing to offer Black people in the way of meaningful social change. One might consider offering "critical support" for anticapitalist politicians like Representative Ronald V. Dellums of California, but the primary vehicle for challenging the capitalist state would be the construction of a "mass revolutionary bloc, which would explicitly call for the transformation of the system as it now exists." This position grossly underestimated the importance to Black people of the democratic rights they had achieved through great sacrifices over several centuries of struggle. When one considers that, in the twentieth century, the majority of African-American voters were permitted legally to cast ballots only after the passage of the 1965 Voting Rights Act, one begins to appreciate the importance of such electoral victories. As late as 1964, there were only 100 African-American elected officials in the entire country. Blacks had been able to exercise the franchise for only a generation. They would not so quickly lose their faith and hopes in the potential power of electoral politics, despite the betrayals of individual Black officials.
Consequently, because of its anti-electoral orientation, How Capitalism did not anticipate two of the most significant mass democratic opposition movements that would develop against the Reagan administration—Harold Washington's successful mayoral campaign in Chicago in 1983 and the Rainbow Coalition presidential campaign of 1984. The Washington campaign was technically aimed against the Cook County Democratic Party organization in Chicago, but in reality was a multiracial, multiclass, democratic protest against the white conservative agendas of both major parties. Washington was not a socialist, but he openly encouraged the participation of Communists, feminists, lesbians, gays, community activists, and Black nationalists in his political mobilization. The overwhelming mandate given to Washington by the Black electorate, with 80 percent turning out to vote, proved that electoral politics could be a powerful tool in fostering social change. Similarly, How Capitalism dismisses Jesse Jackson as part of "the integrationist Old Guard," and characterizes Jackson's Operation PUSH as an opportunistic organization designed to "capture headlines with political maneuvers which are more style than substance." Thus I could not anticipate Jackson's decision to challenge Walter Mondale for the 1984 Democratic presidential nomination, running on a progressive program similar to that of Harold Washington. To his credit, Jackson grew dramatically in political stature, reaching out to environmentalists, feminists, racialized ethnic minorities, lesbians and gays, and a host of liberal and left constituencies. Although Jackson would ultimately retreat into political accommodation with the Democratic Party, collapsing the Rainbow Coalition as an independent force, he had illustrated that electoral politics could be used for progressive ends.
The root cause of the sectarian errors of political judgment in How Capita/ism is found in its analysis of the U.S. capitalist state. At points, the book attempts to make a critical distinction between traditional bourgeois or capitalist democracy with authoritarian fascism. "U.S. bourgeois 'democracy' is oppressive and under Reagan is even moving toward unambiguous authoritarianism, yet is not specifically fascist in the classical sense." It was still possible for progressives to influence public policies of the state "via electoral participation, lobbying, civil disobedience, mass demonstration, etc." Yet in the chapter on "The Meaning of Racist Violence in Late Capitalism," I asserted that "the function of the rise of racist attacks is the preparation of the ideological and cultural foundations necessary for a potential 'Chilean Solution' to resolve the crisis of U.S. capitalism. . . . Whether this regime is 'fascist' in the classical model of Nazi Germany, or 'authoritarian,' which would permit some democratic rights, could be simply a question of semantics." How Capita/ism does not make a clear and decisive delineation between various modes of capitalist political power and governance, and underestimates the very complicated role of competing social classes, elites, and interest groups in influencing policy outcomes.
The capitalist ruling class has never been politically monolithic. There are real and important differences of opinion that divide multinational, global capital from smaller corporate capital located in national or regional markets. (For example, witness the recent debate in the 1990s over the North American Free Trade Agreement, with billionaire Ross Perot leading the opposition in the business community.) Recent developments in global capitalism, such as the growth of information technologies and the mega-mergers of international corporations, indicate a relative decline in the authority and political power of the traditional nation-state. This is part of the reason behind the collapse of South Africa's apartheid state and its increasingly anachronistic model of authoritarian, racialized state capitalism in the 1990s. This crude system of racial domination, very much like Jim Crow segregation in the U.S. South, no longer served the needs or interests of both South African and international capital. "Corporate multiculturalism," with the integration of transnational markets managed by international bureaucracies coordinating the exploitation of a truly global proletariat, is the future direction of world capitalism. The power of individual nation-states, even that exercised by the United States as the world's only remaining "superpower," is rapidly being eclipsed by mammoth geopolitical cartels such as the World Trade Organization. This fundamental transformation of the global political economy means that any oppositional movement that largely or exclusively focuses on the political developments within nation-states will not be successful.
Finally, there is a real problem in How Capitalism Underdeveloped Black America with its language and style. About four years after the publication of How Capitalism, I visited London and spent much of one afternoon with C.L.R. James. "Nello," as he was known to his political comrades and friends, lived at the time in the upper flat of a tall, narrow building in the Brixton neighborhood. James was resting on his bed, and beside him were well-worn and thoroughly marked-up copies of two of my books, How Capitalism and Black American Politics, which had been first published in Britain in 1985. James and I talked about many things, even devoting about an hour to debate the strengths and errors in the work of the Marxist theorist Rosa Luxemburg.
What was most memorable about my conversation with James in London was a query I raised about the character of his own work. I asked James what he regretted most about his political essays and histories. James thought a minute, and replied that he mostly regretted the angular, polemical style of so much of his work. The writer must persuade, not coerce, he suggested. I took his comments to mean that political writing should have some of the best qualities of literature, possessing the power to inspire. Occasionally, How Capitalism endeavors to achieve this lofty stylistic goal. In the conclusion, I insist that progressives in the U.S. must "articulate their demands in a popular and historical discourse, in a language readily accessible to the majority of American workers and nonwhite people." Yet it is one thing to state this, and a very different thing actually to do it. One can still despise capitalism and everything it stands for but explain one's socialist views in a language and style that effectively convinces an audience that an alternate point of view makes sense. Over the years, my writing style has changed considerably, I hope for the better, along the lines that James suggested.
To its credit, there are also some things that How Capitalism accomplishes well. In some respects, it was well ahead of its time. Probably the most important theoretical contribution the book makes is the attempt to link gender, race, and class as interlocking factors in the underdevelopment of Black America. At Cornell University, I had initiated and taught a lecture course on African-American women's history in 1981. I became very familiar with the literature in the new and growing field of Black feminist thought, including Angela Y. Davis's Women, Race, and Class, Michele Wallace's Black Macho and the Myth of the Superwoman, and bell hooks' Ain't I a Woman. These important feminist insights were integrated into my own analysis. Rodney's book had very little to say about the material conditions and status of African women, beyond several brief comments about how "the social, religious, constitutional, and political privileges and rights" of women under colonialism "disappeared, while the economic exploitation continued and was often intensified." I tried to go well beyond this, reexamining Black history from the vantage point of African-American women. Yet I also recognized:
The final history of the systematic exploitation of Black women in capitalist America will not be written by whites, or by Black men, no matter how sympathetic they might be to the struggle against racism and patriarchy. Historically, Black women have carried the greatest burden in the battle for democracy in this country. . . . [No] road toward the ultimate emancipation of the U.S. Black working class exists outside of a concomitant struggle, in theory and practice, to destroy every vestige of sexual oppression within the Black community.
The chapter specifically criticized, by name, prominent African-American male political leaders and scholars whose views had reinforced patriarchy, including Malcolm X, Eldridge Cleaver, Marcus Garvey, Elijah Muhammad, Haki Madhubuti, and Robert Staples.
Second, How Capitalism correctly anticipated the phenomenon of the "deracialization" of U.S. politics, or the emergence of what might be termed "post-Black politics." Racial segregation· had imposed a degree of group solidarity and social accountability upon African-American middle-class leaders. With the legal desegregation of U.S. civil society, the growth of Black suburbs, and the increased assimilation of African-American culture into the white corporate mainstream, it was inevitable that a generation of Black politicians would be produced who had few connections with Black mass organizations and traditional institutions. The "Black Reaganites" criticized in How Capitalism were only a minor tendency within the formation of this new political caste. By the 1990s, a significant number of prominent African Americans in both major parties, such as Colin Powell, the former chairman of the U.S. Joint Chiefs of Staff, and the late Ronald Brown, former head of the Democratic National Committee and subsequently commerce secretary under Clinton, were essentially "deracialized" politicians. Another excellent example of this deracialization phenomenon is provided by the powerful attorney Vernon Jordan. When How Capitalism was written, Jordan had recently served for a decade as head of the Urban League, the nation's most conservative civil rights group. Twenty years later, he exercised power in the fields of corporate law and investment banking, and was widely acknowledged to be the closest "personal friend" of Bill Clinton. The physical reality of Jordan's "Blackness" had become almost irrelevant to his relationships and access to vast corporate and political resources and power. Deracialized Black cultural icons of the 1990s, such as Michael Jordan, Michael Jackson, and Tiger Woods, occupied a parallel assimilationist role.
Finally, the analysis presented in How Capitalism of what would later be termed the "prison-industrial complex"—and the essential role of the criminal justice system as a means for managing redundant labor and racialized ethnic minorities—was unfortunately all too correct. When How Capitalism was first published, there were "over 500,000 men, women and youths who were incarcerated in more than 6,500 penal institutions of various types." As of June 1981, 827 Americans were on death row. Today, more than 1.8 million Americans are incarcerated, about one-half of whom are African Americans. About one third of all prisoners are unemployed at the time of their arrests, with the majority averaging less than $15,000 in annual income prior to their arrests. About one-third of all prisoners are unemployed at the time of their arrests, with the majority averaging less than $15,000 in annual incomes prior to their arrests. The number of Americans currently on death row is 3,400 and is growing rapidly with the elimination of Constitutional safeguards and legislative restrictions against capital punishment.
We live in a nation today in which prisons are among the fastest and most profitable "growth industries" and in which there are currently 340,000 Americans who are employed as prison guards. Thousands of low-paid, low-skilled jobs are increasingly outsourced to prison workers, who of course lack the protection of unions and environmental and health safety standards.
Millions of poor, working, and even middle-class whites are also being increasingly pulled into this penal leviathan as well. About one in five Americans now has a criminal record; as jobs at living wages continue to disappear, we should anticipate the prison system soon being flooded with thousands of whites, many of whom previously supported the representative legislation now responsible for their confinement.
The central objective of How Capitalism Underdeveloped Black America was "to present a critique of the strengths and contradictions that comprise Black American labor and life, with the purpose of destroying the process of underdevelopment which has imprisoned us for almost four centuries." Despite its theoretical lapses and limitations, the book largely accomplishes the first part of that goal. I remain convinced that Black people as a group will never achieve the historical objectives of their long struggle for freedom within the political economy of capitalism. Capitalism has shown the remarkable ability to mutate into various social formations and types of state rule, but its essentially oppressive character, grounded in the continuing dynamics of capital accumulation and the exploitation of labor power, remains the same. The U.S. capitalist state, in the final analysis, will never be cajoled or persuaded to reform itself through appeals of moral suasion. Fundamental change will require a massive democratic resistance movement largely from below and anchored in the working class and among oppressed minority groups.
In the aftermath of the collapse and disintegration of the Soviet Union and Eastern European Communist states, the authoritarian capitalism represented by Communist China, and the ideological retreat into neoliberalism by many Social Democratic parties, "socialism" might seem to have reached a dead end as a viable political concept. But history is always filled with unanticipated twists and detours. The current speculative stock market boom and wave of corporate mergers will probably give way to an unprecedented global recession and a meltdown of significant sectors of the international capital markets. In December 1999, in downtown Seattle, thousands of U.S. trade unionists, environmentalists, and others protested against the World Trade Organization and the vast corporate and financial cartels it represents. Earlier that same year, more than 1,200 people engaged in civil disobedience and went to jail, protesting the murder of an African immigrant, Amadou Diallo, by the New York City police.
Wherever there is oppression, there will be resistance, and from the lessons of struggle will flower the hopes for a better life. The construction of a new world, freed from hunger, poverty, and racial hatred, can begin to be realized by how we struggle here and now. The oppressed have in their hands the capacity to make a new history and, ultimately, a new society. This is the political perspective taken by How Capitalism Underdeveloped Black America, and it is the position in which I still passionately believe today.
Manning Marable
January 15, 2000
Preface
To be Black and a socialist in America is to be nonconformist. Nothing presented in these pages should be accepted as holy scripture. I make no pretense that my thesis is part of some great universal Truth. My struggle for political direction and theoretical clarity has never been divorced from my deep commitment to the liberation of oppressed Black people in the United States and all exploited people across the world. Therefore, my judgements in certain circumstances may appear to some as too harsh, too extreme, too utopian, too subjective. Very well. The times we live in call for harsh measures, both behind the cloistered towers of the university and in the streets.
The intellectual who makes a public commitment to transform society, to smash white racism and the inherently exploitative system laughingly described as "free enterprise" by its defenders, cannot plead her or his case in muted gray tones. For the Black masses to "return to their own history," we must begin by rewriting that history—but not in the language, style, or outlook of the system.
This book records the respective histories of the different social strata within Black political economy and society, from the political Brahmins of the elite to the industrial working class. The methodology is sociological; the questions raised political and economic; the style polemical; the goal: to present a critique of the strengths and contradictions that comprise Black American labor and life, with the purpose of destroying the process of underdevelopment that has imprisoned us for almost four centuries.
I have learned a great deal from the tedious research that was necessary in writing this book. Thomas Carlyle's assertion that political economy is the "dismal science" will receive no argument from me. Probably the greatest intuitive insights I achieved came from those writers who are the most removed from social science—the poets. Langston Hughes' "Justice" says more than I could ever present in the form of quantitative data about the brutalization of Blacks by the U.S. criminal justice system:
That Justice is a blind goddess
Is a thing to which we black are wise:
Her bandage hides two festering sores
That once perhaps were eyes.
It is impossible for me to list the number of friends and co-workers who helped me to write this book. There are a few, however, who cannot escape special acknowledgment. Two graduate students at the Africana Studies and Research Center at Cornell University, David Hatchett and Randall Brock, criticized various chapters and engaged me in a series of friendly, intellectual debates that proved to be essential in the formulation of my thesis. Daisy Rowe and Douglas Milton typed the original manuscript, making helpful suggestions along the way. The editorial collective of South End Press provided support in turning my first draft into a real book. Williams College gave me several weeks of solitude during the bitterly cold winter of 1982 to complete research on several chapters by offering me its Luce visiting professorship in political science. David Smith, professor of English at Williams, deserves my thanks for his continued support. My ideas expressed in chapter three, "Groundings With My Sisters," were developed in my course on the political history of Black women at Cornell. Once again, all of my students—and especially Ruby Saake, Zennette Austin, Carol M. McIntosh, Karen O'Brien, and Wynsome "Jackie" Davis—were important critics of a Black man earnestly attempting to develop a genuinely nonsexist Black history. The editors of The Guardian, Socialist Review, In These Times, Science and Society, WIN magazine, Black Scholar, and several other journals also assisted in the development of my studies.
* The percentages total to greater than 100% because Latinos are also included as subsets of both the white and Black percenttages.
Black Nationalist
Radical separatist/
Crummell's "race love"
Cultural pluralist
double consciousness
Integrationist
cultural identification with dominant culture
Revolution
Radical transformation of means of production and political apparatus
Militant reform
Progressive transferral of power to the oppressed without a seizure of state power
Gradual Reform
Pragmatism, slow and steady change within existing system
Accommodation
Tactical compromise, conciliatory rhetoric, cover activities against racial prejudice
Conservatism
Acceptance of status quo, defense of existing capitalist economic and political system
Malcolm X.
Stokely Carmichael
Revolutionary Action Movement
African Blood Brotherhood
Martin Delaney
H.H. Garnet
Alex Crummell
Black Panther Party (post 1970)
National Black Independent Political Party
Black Cultural Nationalists (1970s)
"Buy Black" campaigns
T. Thomas Fortune
(post 1900)
Booker T. Washington
National Negro
Business League
Roy Innis
Floyd McKissick
W. E. B. Du Bois (1940s–1963)
Angela Y. Davis
W. E. B. Du Bois (1905–1940s)
W.M. Trotter
Kelley Miller
E.F. Frazier
A. Philip Randolph (1914–1918)
Julian Bond
R. Bunche (1930s)
Martin Luther King Jr.
A. Philip Randolph (1919–1930s)
Ron Dellums
John Conyers
Frederick Douglass
Majority
of Congressional
Black Caucus
NAACP (post 1934)
Urban League
Black Republicans
George Schuyler (1960s)
Thomas Sowell
Walter Williams
Black Reaganites
Table XXVI
Black political and economic tendencies since the Civil War
Introduction to the First Edition
Inequality and the Burden of Capitalist Democracy: A Point of View on Black History
What have I or those I represent to do with your national independence? Are the great principles of political freedom and of natural justice, embodied in that Declaration of Independence , extended to us? . . . Your high independence only reveals the immeasurable distance between us. The blessings in which you this day rejoice are not enjoyed in common. The rich inheritance of justice, liberty, prosperity, and independence bequeathed by your fathers is shared by you, not by me. The sunlight that brought life and healing to you has brought stripes and death to me. This Fourth of July is yours, not mine. You may rejoice, I must mourn. . . . What to the American slave is your Fourth of July? I answer, a day that reveals to him more than all other days of the year, the gross injustice and cruelty to which he is the constant victim. To him, your celebration is a sham; your boasted liberty an unholy license . . .
—Frederick Douglass, 1852, in Alice Moore Dunbar, ed., Masterpieces of Negro Eloquence (New York: Bookery Publishing Company, 1914), pp. 42-47.
The process of capital accumulation is a, if not the, principal motor of modern history. Structural inequality and temporal unevenness of capital accumulation are inherent to capitalism.
—Andre Gunder Frank, World Accumulation, 1492-1789 (New York: Monthly Review Press, 1978), pp. 238-239.
I
The most striking fact about American economic history and politics is the brutal and systemic underdevelopment of Black people. Afro-Americans have been on the other side of one of the most remarkable and rapid accumulations of capital seen anywhere in human history, existing as a necessary yet circumscribed victim within the proverbial belly of the beast. The relationship is filled with paradoxes: each advance in white freedom was purchased by Black enslavement; white affluence coexists with Black poverty; white state and corporate power is the product in part of Black powerlessness; income mobility for the few is rooted in income stasis for the many. Many politicians, intellectuals and civic leaders condemn the United States on the grounds that white society has systematically excluded Blacks as a group from the material, cultural and political gains achieved by other ethnic minorities. Blacks are unemployed, economically exploited and politically disfranchised because they are excluded or segregated because of caste or racial discrimination. But there is another point of view on this issue: Blacks occupy the lowest socioeconomic rung in the ladder of American upward mobility precisely because they have been "integrated" all too well into the system. America's "democratic" government and "free enterprise" system are structured deliberately and specifically to maximize Black oppression. Capitalist development has occurred not in spite of the exclusion of Blacks, but because of the brutal exploitation of Blacks as workers and consumers. Blacks have never been equal partners in the American Social Contract, because the system exists not to develop, but to underdevelop Black people.
This different perspective raises a basic theoretical question: What is development, and what is its structural relationship to underdevelopment? Most Western scholars and the general U.S. public describe a nation as "developed" if and when it "has several political parties, widespread literacy, a high standard of living, wide circulation of newspapers and books, consensus on the fundamentals of government, a long history of peace, and . . a white population." Developed or "modern" nation-states also exhibit other characteristics, according to this view: the secularization of politics; a trained civil service; political activity which is widespread, rather than confined to the capital city; the infusion of Western political and social values into the system; the existence of constitutional government; civilian control of the military; a popular commitment to democracy; and for many, a free market economic system. Modernization then becomes the pattern by which nonwhite peoples transform themselves "through the twin processes of commercialization and industrialization," moving toward the standard socioeconomic models provided by Western Europe and the United States. For most white political scientists, planners and sociologists, the road toward development for Asia, Africa, Latin America and historically disadvantaged national minorities is not unlike the Puritans' quest for the perfect "City on the Hill." For economist Robert L. Heilbronner, development is that glorious "process through which the social, political and economic institutions of the future are being shaped for the great majority of mankind." Conversely, the lack of integration into the West's economic and political order means the absence of "cash, commercial credit, advanced technology, and specialized production."
What all of these liberal interpretations have in common is a kind of economic amnesia. A few social scientists go so far as to discount any relationship between political development and "economic and social factors" relating to modernization. An accurate understanding of underdevelopment begins with the questions raised by Marxist economist Harry Magdoff: "Where would the original accumulation of capital used in industry (in the West) have come from if not from the extraction of wealth from colonies, piracy, and the slave trade? Where would the reproduction and growth of the needed capital for investment have come from if not from sufficiently large profits arising in the operation of enterprise (in the non-western world)?" The "Great Ascent" of the West since the sixteenth century was fundamentally a process of growing capital accumulation, the endless drive to control the human and material resources of the world's people. For Western Europe, Great Britain and the United States, domestic development meant the conquest of foreign markets, the stimulation of demand for Western goods within the Third World, the domination of indigenous political and social systems by the bribery of local officials, revolutions, threats, and outright colonial occupation. Development was, more than all other factors combined, the institutionalization of the hegemony of capitalism as a world system. Underdevelopment was the direct consequence of this process: chattel slavery, sharecropping, peonage, industrial labor at low wages, and cultural chaos. The current economic amnesia of the West is therefore no accident, because it reveals the true roots of massive exploitation and human degradation upon which the current world order rests. The world "periphery" and capitalist "core" share a common history.
The U.S. state apparatus was created to facilitate the expansion and entrenchment of institutional racism in both slave and nonslaveholding states. The solidly bourgeois delegates at the Constitutional Convention held in Philadelphia in 1787 were unconcerned about the "inalienable rights" of Afro-Americans. Their chief concern was the creation of a strong national government that would guarantee property rights—slavery being counted among them. Thus, the result was the drafting of a racist manifesto which avoided the use of the words "slave" or "slavery" while protecting the institution itself. This was accomplished by three specific points: Article One, Section Two, which counted the slaves for purposes of representation and direct taxation as three-fifths of a human being; Article One, Section Nine, which mandated that Federal authorities could not interfere with the transatlantic slave trade for two decades; and Article Four, Section Two, which declared that all fugitive slaves had to be returned to their rightful owners. After the ratification of the U.S. Constitution, the Federal government adopted, even under relatively progressive administrations, a bitterly racist posture toward the rights of all Blacks, slave or free. The Fugitive Slave Act of 1793, signed by the Virginia slaveholder and plantation master George Washington, strengthened the rights of slaveowners to capture runaways in the North and to remove them by force back to the South. The banning of the slave trade in 1808 was relatively inconsequential, since 50,000 Africans were brought into the U.S. after the law took effect. Northern states led the way toward the development of white supremacy as part of local state policy. Free Blacks were barred from voting in Delaware in 1792; in Kentucky, Maryland and Ohio in 1799; in New Jersey in 1807. New York State authorized Blacks to vote only if they owned property valued above $250, while no property restrictions applied to white voters. Free Blacks were routinely excluded from juries and all public offices. This heritage of collective racial discrimination is the very foundation of what is usually heralded as American democracy.
Yet every stage of Western capitalist underdevelopment, the African population resisted. Throughout the Black diaspora, resistance took the form of runaway slave communities, called maroons (French and English), palenques (Spanish), quilombos (Portuguese) and/or mocambos (Ambundu for "hideout"). In late-sixteenth-century Mexico, for example, African runaway slaves had become such a problem that the Spanish authorities ordered the castration of Black men absent for more than six months. Vigilante systems for patrolling the roads were established in rural areas. The crown granted rewards for the capture of palenque rebels and material incentives were offered to slaves and former fugitives who betrayed their brothers and sisters who were in hiding. In Veracruz, African guerillas regularly destroyed crops, attacked wagons and burned plantation houses to the ground. In the early seventeenth century, a militant palenque of Indians and Africans led by the chief Yanga fought Spanish regulars to a stalemate. Local Spanish authorities were forced to sign a peace treaty with Yanga, which established the legal town of San Lorenzo de los Negros. Between 1731 and 1781, Cuban Blacks created a palenque, Poblado del Cobre, in Oriente Province that comprised over one thousand persons. The greatest maroon of all was Palmares, a series of African quilombos founded in about 1600 and surviving armed assaults by Dutch and Portuguese troops until 1694. The Palmarista general Zambi successfully defended the territory until the combined weight of American Indian, Portuguese colonial and mestizo soldiers, skilled in guerilla tactics, were hurled against him. After a two-year siege of the major rebel city, 200 Palmarista soldiers committed suicide rather than suffer the humiliation of returning to slavery. Two hundred more Palmaristas were killed in hand-to-hand combat on the final day of fighting, with Zambi succumbing only after he was seriously wounded. On November 20, 1695, Zambi was decapitated in a public execution; his head was exhibited before Black slaves "to kill the legend of his immortality." In the United States, wherever the frontier geography permitted the possibility of maroons, Afro-American Zambis were found. At least fifty maroons existed in the U.S. between 1672 and 1864 in the swamps and Appalachian hill country of the Carolinas, Alabama, Georgia, Florida, Mississippi, Virginia and Louisiana. As late as the 1970s, "the descendants of many of those maroons who chose to cast their lot with Indians [could] still be found, largely forgotten, and often desperately poor."
Where the conditions (political, social, economic) for revolt existed, Africans seized whatever arms they could find and fought desperately to assert their humanity. Along Columbia's Pata River in the 1730s and 1740s, a slave named Jeronimo incited open rebellion and refused an offer of peace rendered by Spanish authorities on the grounds that it required a return of some runaway slaves from his army. In 1647, four hundred Chilean Blacks, armed with clubs, guns and knives, staged an unsuccessful uprising in Santiago. In 1609 and 1612, rumors in Mexico City that the slaves were conspiring a bloody revolt led to extensive repression, with hundreds of Blacks arrested, imprisoned, executed and/or castrated. Gabriel Prosser and Denmark Vessey prepared plans for American slave rebeilions in 1800 and 1822, respectively, that involved thousands of Black women and men. Nat Turner led a band of sixty slaves across southern Virginia in 1831, executing 57 whites in a span of two days. The Black diaspora's greatest revolutionaries, of course were the African laborers of San Domingue. The former slaves' leaders were among the most dedicated and brilliant generals who have appeared in the pages of history—Toussaint L'Ouverture, Christophe, and the ruthless Dessalines. The heroism of Haiti's soldiers between 1790 and 1804 is legendary.
White planters and government officials recognized that the slavery regime could survive only with the most repressive and bestial force imaginable. The French tended to be extremely precise in their punishments of rebellious Africans. The Code Noir was quite specific: "The fugitive slave who has been absent for one month shall have his ears cut off and his shoulder branded with a fleur de lis; if he repeats his crime for a period of (at least) one month, he shall be hamstrung and branded with a fleur de lis on the other shoulder." Plantation managers used a variety of tortures: the "empetre" or chain, shackles three feet long with two iron rings fastened at each end to secure the slave's lower legs to impede walking; "cachots effrayants," small maximum security cells without light; the nabot, a large iron circular device weighing six to ten pounds that was cold-riveted to the slave's foot; castration, or amputation of the feet and/or limbs; forcing gunpowder into the anus or vagina of a slave and then blowing him/her up with a light—"to burn a little powder in the ass of a nigger;" burying them in the dirt up to their necks and smearing their heads with sugar so flies and ants would devour them; forcing slaves to eat animal and human excrement; roasting rebellious slaves barbeque-style over hot coals or an open fire. In the United States, however, the most popular form of labor discipline was the whip, or lash. Historian Kenneth Stampp observes that "the whip was the most common instrument of punishment—indeed, it was the emblem of the master's authority. Nearly every slaveholder used it, and few grown slaves escaped it entirely." The rawhide lash was a "savage instrument," and Stampp notes that "physical cruelty was always a possible consequence of the master's power to punish." Thoughtful white Southerners recognized the barbarism inherent in the U.S. slavery system. One Mississippi slave-owner wrote in 1846 that "a certain class of overseers" were extraordinarily cruel to Black women and men alike. "It is this unrelenting, brutalizing drive, watch and whip, that furnishes facts to abolition writers that cannot be disputed, and that are infamous." One South Carolina judge confessed in 1847 that many slaveholders "deserved no other name than fiends" because they delighted in the torture of their chattel.
The ordeal of slavery was responsible for accelerating the economic and political power of Europe and North America over the rest of the mostly nonwhite world. Since the demise of slavery, and the emergence of modern capitalism, the process of Black underdevelopment has expanded and deepened. To understand this dynamic of degradation, first, is to recognize that development itself is comparative in essence, a relationship of inequality between the capitalist ruling class and those who are exploited. Underdevelopment is not the absence of development; it is the inevitable product of an oppressed population's integration into the world market economy and political system. Once "freed," Black Americans were not compensated for their 246 years of free labor to this country's slave oligarchy. The only means of survival and economic development they possessed was their ability to work, their labor power, which they sold in various forms to the agricultural capitalist. Sharecropping and convict leasing were followed by industrial labor at low wages. When Blacks performed the identical tasks that whites carried out, they were paid less than "white wages." Even when Blacks acquired technical skills and advanced educations, they were still paid much less than whites who possessed inferior abilities. At every level of employment, white capitalists accumulated higher profits from Blacks' labor than they gained from the labor of whites. Throughout the totality of economic relations, Black workers were exploited—in land tenure, in the ownership of factories, shops and other enterprises, in the means of transportation, in energy, and so forth. The constant expropriation of surplus value created by Black labor is the heart and soul of underdevelopment.
Another crucial aspect of underdevelopment involves the dynamics of dependency. Political parties in the U.S. are defined ideologically for the public as formations which represent all the people, rather than special interests and sectors of capital. The object of the electoral process is to achieve a majority within the voting population, and to form specific public policies with the goal of gaining majoritarian support among various constituents within the state apparatus. In the U.S. form of constitutional government, racial minorities can influence major public policies only when their agenda is sufficiently acceptable to one or both of the major white capitalist parties, which in turn assimilate the proposals into their political program for their own purposes. Since Blacks account for 12-13 percent of the U.S. population, and only 10–11 percent of the voters in most general elections, their ability to profoundly influence public policies in the broadest sense is greatly limited by the rules of the game. Blacks are pressured to become dependent on white liberals and moderates to articulate their agendas, in order to acquire majoritarian support. Historically, this has meant that many Blacks have been forced into political coalitions with whites in order to affect U.S. politics, formations which are usually directed by whites, financed by whites, and chiefly comprised of whites. During the period of abolitionist agitation, 1830-1860, many Black political activists were dependent upon the financial and political support of the Garrisonians, the early white feminists, white Free Soilers and others. In the turbulent 1890s, Black croppers were often part of Populist coalitions led by white Southern and Western farmers whose interests and commitments did not in the last analysis always coincide with their own. The NAACP, Urban League, and other civil rights groups in the twentieth century were dependent upon white foundation, corporate and political support. Without an independent capital base for self sufficiency, and operating under a political apparatus which nullifies the impact of minority pressure groups, Blacks repeatedly were trapped into alliances as dependent clients, unable or unwilling to break from the logic of a closed but supposedly democratic system.
Also decisive is the ideological dependency perpetuated among Blacks to divide and to frustrate mass-based actions against racism. The Black child attending public school is burdened immediately with an educational pedagogy which rests on the assumption of his/her cultural and intellectual inferiority. In their places of worship, most Blacks are confronted every Sunday with early Renaissance portraits of Christ, a white diety, and a form of spirituality which theoretically and historically has little direct relevancy to their unique heritage and original African belief systems. The media often carefully select and eliminate glaring contradictions which would evoke outrage and activity by Black people. The aesthetics and popular culture of racist societies constantly reinforce the image of the Anglo-Saxon ideal in the minds of Blacks, creating the tragic and destructive phenomenon of self-hatred and cultural genocide. Colleges and universities deny the legitimacy of Black history and Black studies, and propagate the illusion that U.S. democracy works for everyone regardless of socioeconomic, racial and political background. The logic of the ideological apparatuses of the racist/capitalist state leads inextricably to Black accommodation and assimilation into the status quo, a process of cultural genocide which assists the function of ever-expanding capital accumulation.
Both the ideological and coercive apparatuses of white power were mediated also by yet another powerful structure—patriarchy, or institutionalized sexism. By patriarchy, I mean a sex/gender system of authoritarian male dominance and reinforced female dependency, characterized within capitalist society by certain characteristics. The first and decisive component is males' ownership of almost all private property and an absolute control over all productive resources. Second, all men are able to earn more money than women who perform identical or comparable tasks in the workplace. Men under patriarchy experience greater income mobility, and most women are identified in the ideological apparatuses as "homemakers," a vocation for which no real financial compensation is given. Third, women have few rights within the legal system. Fourth, women are either denied suffrage (prior to 1920) or are severely under-represented within the state apparatus. Fifth, various patriarchal institutions deny sexual rights for women such as abortion and birth control information. Sixth, cultural and social authority is invested in the symbolic figure of the father. The (usually white) male's penis is the necessary and logical prerequisite for power. Finally, the "coercive glue" that holds the patriarchal order in balance is systemic violence against women: rape, involuntary sterilization, "wife beatings," and the constant threat of physical punishment. Male-dominated societies existed before the emergence of capitalism, and the struggle to uproot patriarchy even in socialist or transitional states is often problematic. But under capitalism, patriarchy reinforces and converges with racism in numerous ways, affecting the daily lives of all Blacks and all women. The two groups have been historically victimized by white male violence, denied their civil rights, and their undercompensation in the workplace is accumulated in the form of higher profits for white capitalists. The existence of both systems creates a triple burden for every Black woman—for she is victimized, exploited, raped and murdered because of her class, race and sex. For the Black woman under capitalism, each rape is symbolically also a lynching.
The historical product of racist and sexist underdevelopment for Black America has been the creation of a unique national minority within the world's second-most racist state (South Africa deserving honors in this category). Blacks are an integral and necessary part of an imperialistic and powerful capitalist society, yet they exist in terms of actual socioeconomic and political power as a kind of Third World nation. As a result, Black America shares some similarities with other national minorities or oppressed nationalities within European countries; e.g., the Basques in northern Spain, the Welsh and the Irish in the United Kingdom, the Sardinians of Italy, the Corsicans of France. The critical distinction between our conditions and theirs is the factor of white racism—the systemic exploitation of Blacks as a subcaste in both the economic sphere and within civil society. Like Africans and West Indians, Black Americans are not only victims of class but also white racist exploitation. Because of its peculiar historical development, the U.S. is not just a capitalist state, but with South Africa, is a racist/capitalist state. The immediate task before the Black movement in this country is to chart a realistic program to abolish racist/capitalist underdevelopment. We must analyze the historical foundations of underdevelopment, and articulate a theory of social transformation which will overturn capitalism, patriarchy and white supremacy.
II
Developing a vision of an alternative, noncapitalist development for U.S. Blacks begins with a detailed critique of the American past. Throughout the first half of the twentieth century the most outstanding proponent of democracy, socialism and Black equality was W. E. B. Du Bois. Contrary to the judgment of some of his biographers, DuBois' views on these issues remained remarkably consistent, despite tactical detours and modifications in his outlook caused by the Great Depression. Examining U.S. economic and political life, DuBois arrived at five theoretical positions which governed his practice and posture toward the entire panorama of public policy issues between World War I and the 1960s. His insights comprise the basic orientation of this work.
"The first and fundamental and inescapable problem of American democracy," DuBois wrote in 1921, "is Justice to the American Negro." The knotty dilemma of racism was not simply a question of America's failure in race relations. Racism was at the core of every issue relating to power, economic production, culture and society. Thirty years later, writing in the National Guardian, DuBois argued that the twin pillars of white capitalist oligarchy were domestic racism and colonialism. Until international and domestic racism were smashed, no serious discussion of democracy could even occur in the United States. For DuBois, the centrality of racism was not just a burden for nonwhites, but had to be openly and unconditionally recognized by white progressives. It was only through the development of an antiracist politics that the real material needs of all oppressed people could be addressed. The fight for Black liberation is the "realization of democracy for all . . . "
Second, DuBois concluded early in his career that no real democracy has ever existed in the United States. The most obvious and racist manifestation of the lack of popular democracy was the segregation codes which prohibited most Blacks from participating in the electoral process from the late 1890s until the 1960s. Periodically throughout the disenfranchisement period, DuBois documented the undemocratic character of voting patterns and electoral processes in the South. Analyzing the election of 1920 in the Crisis, for example, he illustrated the low level of voter participation and the denial of Black voting rights.
In 1948 DuBois declared that the great problem of American democracy was that "it had not yet been tried." Neither Blacks nor whites had been freed to exercise democratic principles of governance because of the powerful controls of white capitalist America's upper classes. Thus any condemnation by the U.S. government of socialist and Third World countries behavior at the ballot box was the supreme hypocrisy. When South Carolina racist James F. Byrnes condemned Eastern European nations for suppressing democracy, DuBois countered correctly that Byrnes "does not understand the term." Democracy is not simply "majority rule," but effective state power in the hands of the masses.
The true test of democracy, DuBois argued, was always found in an examination of a nation's criminal justice and penal systems. For decades, DuBois used his newspaper columns and articles to challenge the white racist notions of Black crime and punishment. In the pages of the Crisis in March, 1922, he documented the tragedy of a nineteen-year-old Black man who was convicted of murder in New York City. DuBois argued convincingly that capitalist society, not the young man, was to blame for the murder, since he was the victim of ghetto education, "racist violence" and "police brutality." In "The Case of Samuel Moore," written in April, 1922, he outlined the plight of a Black prisoner who had spent 37 of his 48 years behind bars. In 1931 he criticized the complacency of the Negro petty bourgeoisie toward Blacks who were imprisoned, arguing that "the truth is . . . (that) we know perfectly well how often that (poor blacks) are the victims of police discrimination and judicial unfairness and that their poverty and ignorance make them the scapegoats of our present criminal law." DuBois was perhaps the first American sociologist or political activist to predict the massive prison uprisings of the 1970s and 1980s. In September, 1929, he suggested, "After a time the revolt of tens of thousands of convicts all over the country may bring the attention of the philanthropists to the slavery, degradation and exquisite cruelty of the thing we call punishment for crime."
The question of the U.S. claim to real democracy must be approached in the light of our history. Colonial historians have noted that the system of U.S. slavery was established to provide "freedom" and the possibility of democratic government for the white, land-owning freemen of the seventeenth and eighteenth centuries. The enslavement process was an essential guarantee to land-hungry European immigrants that their rights were protected by the state. Prior to the Civil War, white Midwest farmers opposed slavery mainly because they viewed the Kansas-Nebraska Act of 1854 as a threat to their internal freedoms and political democracy. The expansion of "the peculiar institution," as slavery was called, into the Great Plains and upper Midwestern states would have introduced large numbers of Afro-Americans into the region and simultaneously overturned their "free" economic and political institutions. The great white American democrats, Jefferson and Jackson, owned hundreds of slaves, while political conservatives like Alexander Hamilton agitated against the expansion of slavery. During the Progressive era, Woodrow Wilson's "New Freedom" expanded racial segregation to all levels of the Federal government. Simultaneously, many of the most antidemocratic and aristocratic elements of Southern politics were the most reliable allies of Black leaders. Southern Bourbon Democrats, the commercial class, and landed gentry that dominated politics after 1877 were among the staunchest defenders of limited Black democratic rights in the face of hostile opposition from the white rural masses. As early as 1889, Julius Dreher, the president of Roanoke College in Virginia, wrote that racial tolerance and Black suffrage were essential to Southern political democracy. "If we treat (the Negro) with anything like the fairness, justice and consideration we claim for ourselves as men, we shall hear less of race antagonism in the future." Benjamin F. Riley, a Baptist minister and superintendent of the Texas Anti-Saloon League, believed that middle class Black leaders and educators were morally and culturally superior to rural white farmers and sharecroppers. "The Negro," he wrote in 1910, "has made himself an exception among the people of the earth in the rapidity of his advancement." White conservatives endorsed Black educator Booker T. Washington and state support for Black industrial and normal schools, and opposed the complete disfranchisement of all Blacks. Despite the biracial politics of populism in the 1890s and integrated unionism in isolated Southern cities, the white working class did not usually accept even minimal rights for Black people.
White opponents of the Civil Rights Movement in the 1950s almost always relied upon the concept of democratic rights for the white majority. The overtly racist faction within the Democratic Party cultivated close ties with rural farmers, laborers and working class whites. But political conservatives, which included the industrialists and the banking and business establishment, usually denounced the extremist tactics of the White Citizens Councils. Most of the upper-class religious institutions, such as the Southern Presbyterians and Methodists, tended not to be the most avid supporters of the Wallaces and Thurmonds. The white working class, in general, viewed integration not within the American democratic tradition, but as an aberration of democracy imposed by liberal elites. The opposition from white workers had an impact upon the direction of the Black movement. From its beginnings until today, the movement has been overwhelmingly petty bourgeois in its leadership and dominant ideology. It has been in essence a united front, representing various factions within the Black community, all oriented toward the goal of greater democracy. In his autobiography, DuBois explained the dominant consciousness of the movement as well as his own early theoretical shortcomings:
I was born in a world which was not simply fundamentally capitalistic, but had no conception of any system except one in which capital was privately owned. What I wanted was the same economic opportunities that white Americans had. Although a student of social progress, I did not know the labor development in the United States. I was bitter at lynching, but not moved by the treatment of white miners in Colorado or Montana. I never sang the songs of Joe Hill, and the terrible strike at Lawrence, Massachusetts, did not stir me, because I knew that factory strikers like these would not let a Negro work beside them or live in the same town.
The left tendency within the movement, from A. Phillip Randolph's National Negro Congress in the 1930s to Student Nonviolent Coordinating Committee (SNCC) and radical elements within Congress of Racial Equality (CORE) in the 1960s, developed a critical perspective on society which recognized the ultimate necessity of socialism. But the dominant coalitions within the movement were simply committed to the pursuit of bourgeois democracy and increased opportunities within the capitalist system. Seldom if ever did the rank and file or leadership pose questions that transcended a limited series of political reforms which could be confined easily to a "capitalist solution to the racial crisis."
If an authentic biracial American democracy does not exist, how was it to be constructed? DuBois' thinking on this third question constitutes a series of social, cultural, political and economic prerequisites. First, democracy must of course be antiracist. It should also be committed to an antisexist society which knows no discrimination based on gender; patriarchy as a system of male authority and sexual exploitation has no place in the "new democracy." Democracy should be committed to the permanent eradication of poverty and unemployment. A state apparatus must guarantee the right of every minority to express "unpopular opinions," and must insure civil liberties for all. Educationally, the democratic state must commit itself to programs which "break down social distinctions" within the general population. Social engineering of this kind would involve increased support for national minorities' cultural, educational and social institutions. Economically, democratic rule would be extended into the process of production. For DuBois, writing in 1943, this meant, "the workers in control of industry," and the abolition of ownership of the central means of production from the white ruling class. DuBois had acquired such contempt for the existing political institutions that he eventually concluded that a new state apparatus needed to be constructed. In 1943 he suggested that local assemblies should be created across the nation with "actual popular participation;" these assemblies could evolve as the nucleus of the new democratic state. The central popular forces needed to accomplish this ambitious agenda would emerge from a "great alliance between the darker people the world over, between (white) disadvantaged groups . . . and between the working classes everywhere." This united front of the exploited would "keep down privileges" and transform human society.
DuBois was attracted to socialism early in his intellectual life, but unlike many radicals at the turn of the twentieth century, he never succumbed to a mechanistic or economic deterministic view of society. He believed that capitalism and racism were inextricably tied together, and that the Great Depression was a major but not the last of capitalism's periodic crises. He concluded that neither corporate leaders nor white racists would be able to resolve the myriad problems inherent within their economic and social systems. But he also insisted that the triumph of socialism, and the eventual destruction of white racism, were not determined or fixed by material conditions. At the outset of World War II, for example, DuBois warned his readers that "we have no right to assume that the collapse of Europe will automatically free Asia and Africa." An antiracist, socialist democracy had to be fought for by progressives. Colonialism and underdevelopment would collapse only when the oppressed constructed a majoritarian political offensive against the forces of racism and capitalism. DuBois' fourth observation, then, was that socialism had to become that central vision for the Black liberation movement.
Socialism today must be placed openly and honestly on the public agenda by all American progressives. Without hesitation, we must explain that a basic social transformation within America's social and economic structures would involve radical changes that would be viewed as clearly undemocratic by millions of people. The state would assume the ownership of major corporations, and their direction would be left in the hands of those best qualified to make decisions at the point of production, the working class. Socialism would mean the expropriation of wealth from the capitalist class, and the guarantee of employment, decent housing, education and health care to all citizens. It would restrict the "democratic" rights of those who discriminate against Afro-Americans, Chicanos, women, and gays—rights that white Americans are reaffirming in recent referenda. Socialism would mean the expansion of social services for those in need. Elements of democratic political traditions in America's recent past, from Populism to LaFollette's Progressivism, might contain examples for public education on socialism. But socialism cannot be achieved simply through coalitions of "democratic movements" or united fronts with progressives of various competing interests. Our primary task as American socialists is to make the case for equality within society—a principle that cannot be achieved without the total reconstruction of American civil society. We should assume what Antonio Gramsci often called the "long view" of socialist transformation. Democratic socialism can and must become the "common sense" of the working class, the brown and Black populations, and critical elements of the petty bourgeoisie. Through our efforts to compete with bourgeois ideologists in existing cultural and intellectual institutions and simultaneously in coalition with liberal petty bourgeois social forces, socialists will have the opportunity to establish their "legitimacy" to govern in both civil and political societies. Throughout this long historical process, coalitions must occur within the Democratic Party, and with reformist progressive groups like NOW, the NAACP and the National Association of Neighborhoods. But unless we place the necessity of socialism as the solution in the struggle for human equality, the battle for socialism will again be lost for another generation. An "invisible socialist movement" of the kind once characterized by Michael Harrington is actually no movement at all.
The possible common ground between the Black movement—in both its integrationist and Black nationalist tendencies—and predominantly white progressive movements, is the principle of equality. By equality I do not mean "equal opportunity" as defined by the Urban League and the Federal bureaucracy, as a means toward integrating minorities and women into the hierarchies of the state and civil society. Equality implies a theory of justice which assumes that all parties within the state should have free access to the state apparatus, can reform existing economic and social institutions, and can enact laws that promote a more humane society. A society committed to equality would require a political system that would promote affirmative action and racial quotas as a means toward a more equitable socioeconomic status for Blacks and women. As Julius K. Nyerere observes, "the basis of socialism is a belief in the oneness of man and the common historical destiny of mankind. Its basis, in other words, is human equality." Despite Tanzania's ongoing political problems and Nyerere's other contradictions, his observation is central to our own situation. "Without an acceptance of human equality there can be no socialism." Similarly, as we establish a dialogue with various sectors of society around the principle of equality, we will be able to provide the foundation essential for transforming capitalism, the economic system that rests upon inequality.
From the perspective of Black history and experience, the practice of bourgeois democracy in America has consistently worked in favor of special propertied interests and against the promise of equality. In The Education of Black People, DuBois complained that democracy viewed as a commitment to human equality and emancipation has never existed for Black people or other minorities. "In theory we know" [the real meaning of democracy] "by heart: all men are created equal and should have equal voice in their own government," he wrote in 1938. Democracy should mean "the opening of opportunity to the disinherited to contribute to civilization and the happiness of men." DuBois believed that the quest for equality was central to all related struggles in abolishing de jure and de facto segregation and obtaining political suffrage. "Given a chance for the majority of mankind to be educated, healthy and free to act," he noted, "it may well turn out that human equality is not so wild a dream as many seem to hope."
DuBois' fifth point was more of a prediction than an assessment of contemporary socioeconomic problems. DuBois recognized that the actual practice of socialism in other countries, especially in the Soviet Union, left much to be desired. Even after reading Soviet party leader Khrushchev's revelations of Stalin's crimes against his people, however, DuBois still could write in 1957 that the Soviet Union was closer to his ideal of democracy than his native land had ever been. During the Cold War, and perhaps even during World War II, DuBois concluded that the road toward democracy and an antiracist society must also lead toward socialism. One could not struggle decisively against racism and remain a proponent of capitalism. From this perspective, DuBois recognized that America would eventually and inevitably come to a basic decision—either it would move toward worker self-management, antiracism and a new democratic state apparatus, or it would lapse into authoritarianism, racial barbarism and militarization of the work force. Speaking in 1951, DuBois declared, "Either in some way or to some degree, we must socialize our economy, restore the New Deal and inaugurate the welfare state, or we descend into military fascism which will kill all dreams of democracy, or the abolition of poverty and ignorance, or of peace instead of war."
III
DuBois' theoretical conclusions, taken from a rich lifetime of research and struggle, form the basic point of view for How Capitalism Underdeveloped Black America. The study of Black social stratification and political economy departs from an appreciation of the contours of Black history. Yet where we stand in the past largely determines our understanding of what a people have been, and what they intend to become. Beneath history, and all social science research, exists explicitly or implicitly a philosophy or world view that tends to explain or to justify phenomena. All history conceals an a priori superstructure which promotes the interests of certain social classes at the expense of others. Thus intellectual work becomes a kind of cultural propaganda that serves the ideals or aims of certain racial and class groups within particular historical epochs. The absence of a clearly articulated ideology, so often the hallmark of objectivists in the liberal academic tradition, neither minimizes nor obscures the political function of all intellectual work. Intellectuals are the vanguard or ideological proponents of both well-entrenched and nascent social orders. It is their task to explain what has been, to justify or to overturn what now exists, and to chart what must become tomorrow.
All social transformations begin with a criticism of existing social forces, the material and ideological components which comprise social reality. The liberation of historically oppressed and underdeveloped peoples takes as its point of departure a revolutionary critique of the integral social classes which constitute that national minority or nation. For Black America, that means an assessment of the evolution of the Black petty bourgeoisie, the Black entrepreneurs, a general overview of the impact of capitalist development upon Black educational and social institutions, and the relations between Black women and men under the system of exploitation. Criticism leading to political praxis must include evaluations of the ambiguous legacy of the Black church within Black society and the pattern of police brutality, lynchings, convict labor and imprisonment of Black workers by the state and racist elements within white civil society. Finally, this criticism must address the questions of ultimate power within a biracial "democracy," and what forces now exist that will become part of the new hegemony within a nonracist, nonsexist socialist society in America. This book will hopefully establish a necessary discourse among activists and intellectuals alike, who are now and will in the future determine the course of that struggle to transform the United States.
SECTION ONE
THE BLACK MAJORITY: THE DOMESTIC PERIPHERY
CHAPTER ONE
THE CRISIS OF THE BLACK WORKING CLASS
So long as white labor must compete with black labor, it must approximate black labor conditions—long hours, small wages, child labor, labor of women, and even peonage. Moreover it can raise itself above black labor only by a legalized caste system which will cut off competition and this is what the South is straining every nerve to create . . . It is only a question of time when white working men and black working men will see their common cause against the aggressions of exploiting capitalists.
—W. E. B. Du Bois, "The Economic Revolution in the South", in B.T. Washington and DuBois, The Negro in the South (London: Moring, 1907), pp. 114-115, 117.
Unless organized labor transforms itself into a social movement with broad goals and a new concept of union membership that goes beyond dues-payers in a collective bargaining unit, it will continue its current decline. And if it is transformed, the character of a new dynamic labor movement will be expressed most significantly in its active and special concern for the problems of racial minorities and women at the work place and in the community.
—Herbert Hill, "The AFL-CIO and the Black Worker," Journal of Intergroup Relations, Vol. 10 (Spring, 1982), pp. 5-78.
I
The central character and participant of Black U.S. history is the Afro-American. This is not a particularly surprising statement: the central focus of Irish history is the Irish people; Japanese history examines the people of Japan, and so forth. Yet there is a hidden problematic here for the political economist. The presumption here is that the people share a common social history, a collective experience, and perhaps even a collective consciousness. This is the first assumption that must be challenged.
Black people in the U.S. are the direct product of massive economic and social forces which, at a certain historical juncture, forced the creation of the early capitalist overseas production of staples (rice, sugar, cotton) for consumption by the Western core. The motor of modern capitalist world accumulation was driven by the labor power of Afro-American slaves. In the proverbial bowels of the capitalist leviathan, the slaves forged a new world culture that was in its origin African, but in its creative forms, something entirely new. The Afro-American agricultural worker was one of the world's first proletarians, in the construction of his/her culture, social structures, labor and world view. But from the first generation of this new national minority group in America, there was a clear division in that world view. The Black majority were those Afro-Americans who experienced and hated the lash; who labored in the cane fields of the Carolina coast; who detested the daily exploitation of their parents, spouses and children; who dreamed or plotted their flight to freedom, their passage across "the River Jordan;" who understood that their masters' political system of bourgeois democracy was a lie; who endeavored to struggle for land and education, once the chains of chattel slavery were smashed; who took pride in their African heritage, their Black skin, their uniquely rhythmic language and culture, their special love of God. There was, simultaneously, a Black elite, that was also a product of that disruptive social and material process. The elite was a privileged social stratum, who were often distinguished by color and caste; who praised the master publicly if not privately; who fashioned its religious rituals, educational norms, and social structures on those of the West; who sought to accumulate petty amounts of capital at the expense of their Black sisters and brothers; whose dream of freedom was one of acceptance into the inner sanctum of white economic and political power. Both the Black majority and the Black elite were often divided by language, politics, economic interests, education and religion. That both groups were racially Black escaped no one's attention, least of all the white authorities. Yet both had created two divergent and often contradictory levels of consciousness, which represented two very different kinds of uneven historical experiences.
Malcolm X, the greatest Black revolutionary of the 1960s, recognized the essential conflict in the history and class consciousness of Afro-America. Speaking before civil rights activists in Selma, Alabama, only three weeks before his assassination, Malcolm characterized this pivotal contradiction as the division between the house and field Negroes:
The house Negro always looked out for his master. When the field Negroes got too much out of line, he held them back in check. He put them back on the plantation. The house Negro lived better than the field Negro. He ate better, he dressed better, and he lived in a better house. He ate the same food as his master and wore his same clothes. And he could talk just like his master—good diction. And he loved his master more than his master loved himself. If the master got hurt, he'd say: "What's the matter, boss, we sick?" When the master's house caught afire, he'd try and put out the fire. He didn't want his master's house burnt. He never wanted his master's property threatened. And he was more defensive of it than his master was. That was the house Negro.
But then you had some field Negroes, who lived in huts, had nothing to lose. They wore the worst kind of clothes. They ate the worst food. And they caught hell. They felt the sting of the lash. They hated this land. If the master got sick, they'd pray that the master'd die. If the master's house caught afire, they'd pray for a strong wind to come along. This was the difference between the two. And today you still have house Negroes and field Negroes.
Historians might disagree with Malcolm's portrait of the plantation, pointing out that most slaves worked on farms with fewer than twenty Blacks. There were relatively few large plantations in the United States that were comparable to those of pre-revolutionary San Domingue, Bahia or Pernambuco, and the actual social and material conditions which usually separated Black house servants from field hands in the U.S. experience were insignificant. Yet the strength of Malcolm's commentary is essentially ideological and political. The embryonic Black elite was the product of the enslavement process, those New World Africans who culturally assimilated the world view of their exploiters. Resistance tended to come from those who had suffered the most, physically and mentally, at the hands of the masters. Some slaves docilely accepted their plight; others did not.
The Black majority was confronted with two decisive political options which, as we shall explore later, form the crucial axis of Black history: resistance and accommodation. Slavery and colonialism created the material conditions which forced an oppressed people to leave the surroundings of their previous history. That is, the external constraints demanded by coerced labor and a rigid caste/social hierarchy redirect the forces of a people's history. The slave could not live for him/herself at any particular moment during the productive process; the slave was viewed by the master as a cog in the accumulation of capital. Many slaves responded to the daily exploitation of the work place by resisting—running away, destroying machinery, burning crops, killing the master and his family. Others protested in more subtle ways, such as work slowdowns. But all faced the inevitable wall of reality from which there was no real escape. Rape, murder and the terrorization of their communities would continue as a logical and necessary part of capitalist society. One could stand against the weight of the exploiter's history, and suffer the inevitable concequences. Many chose to die this way. But the path of resistance contained no guarantees that one's lover, spouse, parents or children would escape brutal retribution for one's act of glorious defiance. One could make one's own history, but no single act of protest would overturn the powerful machinery of the racist/capitalist state, unless that action took a collective form involving others. Institutional safeguards usually blocked this option of mass-based resistance.
For the Black majority after slavery, the long night has continued. Historians traditionally concentrate on the lives of "exceptional" men and women whose political actions were different from those of the masses in certain respects. This is a mistake. The fabric of Afro-American life has been woven from the contradictory strands of faith and doubt, courage and fear, resistance and acquiescence. The collective Black life and labor in America has taken place in the context of penal-type conditions and restraints. The very nature of struggle under these totalitarian conditions is underscored by a series of seemingly futile protests, failures and disasters—all of which culminate in an inevitable success in which the central characters never witness. A prisoner from another political environment, Antonio Gramsci, describes this long process in brutal detail:
All (want) to be the ploughmen of history, to play the active parts. . . Nobody wished to be the 'manure' of history. But is it possible to plough without first manuring the land? So ploughmen and 'manure' are both necessary. In the abstract, they all admitted it. But in practice? Manure for manure, as well draw back, return to the shadows, into obscurity. . . There is not even the choice between living a day as a lion, or a hundred years as a sheep. You don't live as a lion even for a minute, far from it: you live like something far lower than a sheep for years and years and know that you have to live like that. (Imagine) Prometheus who, instead of being attacked by the eagle, is devoured by parasites.
The oppressed recognize, implicitly perhaps, the weight of oppression, the terrible contradictions imprinted by centuries of slavery, agricultural and industrial labor. After emancipation, the Black majority struggled to attain critical self-consciousness, a return to their own history-for-themselves. W. E. B. DuBois wrote of the postbellum Negro:
He began to have a dim feeling that, to attain his place in the world, he must be himself, and not another. For the first time he sought to analyze the burden he bore upon his back, that dead weight of social degradation partially masked behind a half-named Negro problem. He felt his poverty: without a cent, without a home, without land, tools or savings, he had entered into competition with rich, landed, skilled neighbors. To be a poor man is hard, but to be a poor race in a land of dollars is the very bottom of hardships. He felt the weight of his ignorance,—not simply of letters, but of life, of business, of the humanities; the accumulated sloth and shrinking and awkwardness of decades and centuries shackled his hands and feet.
Each member of the Black majority is a prisoner, and shares the marks of oppression upon his/her shoulders. Each Black worker is a representative of the collective patterns of exploitation, the series of murders, the lynchings, the mutilations. Each has been touched by starvation and unemployment. Each has experienced through his/her own life or through the lives of others, destitution, illiteracy, prostitution, disease and death at an early age. Acceptance of bourgeois illusions provides no temporal salvation; the crushing blows of the workplace, the police and the racists form a chorus which proclaims to the Black majority: you are not human beings. The ringing of the racist chorus resounds in the oppressed's ears from cradle to grave. That shrill ringing is the cold aesthetic expression of white capitalist America.
So the basic social impulse of Afro-American workers is more than the search to find meaning within the tedious, often boring labor they are forced to perform to survive. It is a struggle, in part, for retaining collective self-respect in the face of degradation. It is the effort to create the material possibility of a better and more affluent life for future generations. "People are not fighting for ideas, for things in anyone's head," Amílcar Cabral observed. "They are fighting to win material benefits, to live better and in peace, to see their lives go forward, to guarantee the future of their children." Without these daily sacrifices and battles, no terrain for successful resistance would be created. Even the compromises and accommodations made by Black workers' organizations during moments in history help to prepare future Black revolutionaries by illustrating tactics which cannot circumscribe the power of capital. Sometimes the courage it takes to survive is infinitely greater than the suicidal impulse to fight when the odds are not in one's favor. As Sartre reminds us, "life begins on the other side of despair."
This section examines the evolution of the Black majority since slavery, concentrating on four key groups: the Black working class; the Black reserve army of labor, or the permanently unemployed and poor people; Black women; and Black prisoners. Each has a special role in the making of Black civil and political societies. The only period when Black employment approached 100 percent was during slavery; since the end of World War II, the numbers of Black unemployed have soared. Poor Blacks are the most brutally victimized and exploited sector of the Black majority. If the projected labor force figures for the next two decades become reality, the Black reserve army or "ghetto-class" will soon comprise the majority population within the Black masses. Black women are not a class, but their history cannot be explored properly in the same context with that of Black males. Capitalist patriarchy, combined with racism, shackles the majority of Black women more firmly to the process of exploitation than any group of Black men. Black prisoners, the necessary human sacrifices to the capitalist criminal justice system, are also cogs in the productive process. Without criminal records, how else could the masses of poor Blacks be segregated in the modern labor force? Lynchings and their contemporary equivalent, capital punishment, are a prime means to discipline the entire Black labor force and the unemployed. Police brutality in the late twentieth century has simply perpetuated the coercion of the "patrol roaders" and white vigilantes of the mid-nineteenth century. Black urban workers comprise the first group under consideration, because of their still decisive position within the political economy of capitalism. Each of these group's overlapping historical experiences, its failures and contradictions as well as its militant moments of organized social protest, form the life and spirit of the Black majority. Their collective history and struggles constitute the necessary basis for revolutionary change, not simply for Blacks, but for the entire society. They represent the domestic nonwhite periphery in the core of capitalist accumulation, in the protracted process of social transformation.
II
Over fifteen years has now passed since the major upheavals of Black workers, youth and students which was termed the Black Power and Civil Rights Movements. Black political militancy spread from streets and lunch-counters to factory shops and production lines across the country. Black unrest at the point of production created new and dynamic organizations: the League of Revolutionary Black Workers in Detroit; the Black Panther Caucus at the Fremont, California General Motors plant; and the United Black Brotherhood in Mahwah, New Jersey. In the Deep South, civil rights activists from the Southern Christian Leadership Council helped to organize sanitation workers' strikes in St. Petersburg, Florida, Atlanta, Georgia, and Memphis, Tennessee. Ralph D. Abernathy, Hosea Williams, Coretta Scott King and A. Philip Randolph supported the vigorous unionization efforts of the American Federation of State, County and Municipal Employees (AFSCME) in the Deep South. Abernathy, Williams and Andrew Young were arrested in Sepember, 1968, for nonviolently blocking the path of garbage trucks in Atlanta. On June 21, 1969, Abernathy and Williams were arrested in Charleston, South Carolina, for supporting AFSCME's Local 1199 attempts to unionize hospital employees. By September, 1972, hundreds of Black trade unionists, led by AFSCME Secretary-Treasurer William Lucy and Cleveland Robinson, president of the Distributive Workers of America, created the Coalition of Black Trade Unionists in Chicago. By its second annual convention, held in Washington, D.C., May 25-27, 1973, 1,141 Black delegates representing 33 unions were in attendance; 35-40 percent were Black women.
It cannot be overemphasized that the Civil Rights and Black Power Movements were fundamentally working class and poor people's movements. From the very beginning, progressive unions were involved in the desegregation campaigns. The United Auto Workers, United Packinghouse Workers, District 65, Local 1199 in New York City, and the Brotherhood of Sleeping Car Porters all contributed funds to Martin Luther King Jr.'s Montgomery County bus boycott of 1955-56. And in rural areas of the Black Belt, small independent Black farmers risked their families' safety by opening their homes to freedom riders and Student Nonviolent Coordinating Committee (SNCC) workers. Black farm workers, sharecroppers, service workers and semi-skilled operatives were the great majority of those dedicated foot soldiers who challenged white hegemony at Selma's Pettus Bridge and in the streets of Birmingham. SNCC understood well the importance of Black working class support for the Civil Rights Movement and thus recognized the need to develop an employment strategy for Blacks.
Labor unions also understood the connection. In November, 1963, a number of labor unions financed a conference at Howard University that brought democratic socialists, trade union organizers and radical civil rights activists together. Civil rights workers, Black and white, recognized by late 1964 that demands simply for desegregating the South's civil society lacked economic direction. In 1965 Jessie Morris, SNCC's field secretary in Mississippi, helped to establish the Poor People's Corporation. Serving as its executive secretary, Morris funnelled financial aid for various labor projects initiated by poor Black workers. That same year, the Mississippi Freedom Labor Union (MFLU) was created by two Council of Federated Organizations staff members. Historian Clay Carson relates that "within a few months, the MFLU attracted over a thousand members in several counties through its demands for a $1.25 an hour minimum wage, free medical care, social security, accident insurance, and equality for blacks in wages, employment opportunities, and working conditions." MFLU relied upon the fund-raising resources of SNCC and "by that fall had developed its own sources of financial support." As "We Shall Overcome" gave ground to "Black Power" in the mid-1960s, a wave of nationalist activism seized the new generation of Black urban workers and students. Militant Black construction unions were formed, such as the Trade Union Local 124 in Detroit, and United Community Construction Workers of Boston. Black steelworkers at Sparrows Point, Maryland, formed the Shipyard Workers for Job Equality, pressuring Bethlehem Steel to halt its policies of hiring and promotion discrimination against Blacks. In most of the protest actions, there was the recognition that racism in the plants also undercut the "economic status of white workers. For example, when the United Black Brothers struck at Mahwah's auto plant in April, 1969, they urged white workers to "stay out and support us in this fight."
By the 1980s much of the political terrain had shifted to the right. White blue collar workers voted strongly for Ronald Reagan in 1980. The League of Revolutionary Black Workers, The Black Panther Labor Caucuses and other revolutionary nationalist organizations within the Black working class no longer existed. The late A. Philip Randolph had campaigned for the election of a white racist, neoconservative, Daniel Patrick Moynihan, to the U.S. Senate in 1976. Andrew Young, running for mayor in Atlanta in 1981, advised patience to the Black community's demands in ending the murders of its children. Abernathy and Williams supported Reagan's candidacy. An entire class of Black farmers, sharecroppers and rural laborers almost completely disappeared, eliminating part of the social foundation for the civil rights struggles in the Deep South a generation ago. As an activist in the Amalgamated Clothing Workers Union, Coleman Young led the creation of the fiercely independent National Negro Labor Council in the 1950s; years later, as mayor of Detroit, he forged a conservative political alliance with corporate capital at the expense of Black and poor constituents. Mahwah's huge automobile plant, the site of Black labor militancy, has been shut down permanently, along with hundreds of other industrial plants in the Northeast and Midwest.
In a recent essay, labor historian Philip S. Foner outlines the dimensions of the organic crisis confronting Black workers. Despite considerable gains, Black workers in the early 1970s were largely concentrated in the lowest paid, semi-skilled and unskilled sectors of the workforce. Those Blacks in skilled trade union positions usually had low levels of seniority. According to Foner, the recession of 1973-1975, combined with the political drift to the right in national politics, greatly worsened the position of the Black working class in several ways. The exportation of capital and jobs, especially by multi-national corporations, reduced the number of available jobs. Capital intensive industries, particularly auto and steel, sharply cut back the number of workers with low levels of seniority. Despite the creation of pressure groups like the Coalition of Black Trade Unionists, Foner notes, Blacks still have "an infinitesimal percentage" of top to middle-level representatives within the trade union bureaucracy. In 1977 the Supreme Court reinforced racism and sexism within unions by insisting that Blacks and women must prove that seniority systems were designed to "intentionally discriminate" against them. For these reasons the tenuous relationship between Black progressive groups and organized labor was increasingly antagonistic and bitter.
The acceleration of Black unemployment and underemployment, the capitulation of many civil rights and Black Power leaders to the Right, the demise of militant Black working class institutions and labor caucuses, and the growing dependency of broad segments of the Black community upon public assistance programs and transfer payments of various kinds, are not mutually exclusive phenomena. These interdependent realities within the contemporary Black political economy are the beginnings of a new and profound crisis for Black labor in America. As Harold Baron once noted, the capitalist class historically has needed "black workers, yet the conditions of satisfying this need compel it to bring together the potential forces for the most effective opposition to its policies, and even for a threat to its very existence. Even if the capitalists were willing to forego their economic and status gains from racial oppression, they could not do so without shaking up all of the intricate concessions and consensual arrangements through which the State now exercises legitimate authority." Despite the destruction of de jure segregation, the white capitalist class has not abandoned racism. Instead, it has transformed its political economy in such a way as to make the historic "demand for black labor" less essential than at any previous stage of its development. In the production of new goods and services, from semi-conductors to petroleum products, the necessity for lowly paid operatives, semi-skilled laborers and service workers becomes progressively less with advances in new technology. Simultaneously it has succeeded in developing a strong Black political current against Black participation in unions. Leading representatives of the Black petty bourgeoisie are in outspoken opposition to public sector union activities in metropolitan centers dominated by newly elected Black officials. These immediate political and economic problems, and the prospects for the Black working class beyond the 1980s, are the concern of this chapter.
III
The making of the Black industrial working class is a relatively recent historical phenomena, spanning only three generations. Throughout this period of Black proletarianization, advocates of Black economic equality and civil rights maintained an uneasy and ambiguous relationship with the labor movement. At most times, the overtly racist practices and policies of white labor leaders proved to be major obstacles to biracial labor unity. A brief historical sketch of the evolution of this uneasy relationship indicates the ideological and political tensions which comprise part of the contemporary crisis for Black labor in the U.S.
The longest and most durable labor Blacks have performed within the American experience was, of course, in the area of agriculture. From the American Revolution until the eve of World War I, about 90 percent of all Black people lived in the South. As late as 1940, 77 percent of all Blacks resided in the former slave states, while only 27 percent of all white Americans lived there. The majority of Black male workers ploughed and planted the fields, harvesting the annual yields of cotton or corn, usually for the benefit of an absent white landlord. In 1910, 57 percent of all Black men and 52 percent of all Black women workers were farmers. Eight percent of the men and 42 percent of the women were employed as domestics or personal servants. Only one sixth of the Black population worked in manufacturing or industries. During the early decades of the twentieth century, the disparity in income between Blacks and whites was nothing but extraordinary. This was particularly the case in the burgeoning commercial districts of Southern and border states, industrial and urban centers where the rural Black immigrants first arrived in their trek north. In Atlanta during the winter months of 1935-36, the median income for Black husband-wife families was $632; the median for white husband-wife families in the city was $1,876, creating a Black-white income ratio of 34 percent. Income disparities below 25 percent were not uncommon. Black families headed by women in Atlanta earned median incomes in 1935-36 of $332. In Columbia, South Carolina, these families earned only $254 per year.
The actual beginnings of the Black industrial working class are found with the massive migrations of Black humanity from the Deep South to the North after 1915. Most economists explain Black migrations after 1915 and again subsequently in 1940s as a result of the pull of wartime production in the factories of the North. However, the collapse of the cotton market and the epidemic of Black-owned bank failures in the autumn of 1914, combined with the curse of the boll weevil and the omnipresent fear of white lynch mobs, were also powerful factors pushing Blacks out of Dixie. The number of Black people who left the South rose from 454,000 from 1910-1920, 749,000 from 1920-1930, to 1,599,000 from 1940-1950. Most of these rural farmers and sharecroppers settled in the crowded yet bustling ghettoes like Cleveland's Hough district and Chicago's Southside. This was the first generation of Black workers who earned a living primarily from manufacturing, industrial and commercial labor. In 1940, 28 percent were service workers. Farm employment had dropped to 32 percent. Twenty years later, blue collar employment increased to 38 percent, and the number of operatives more than doubled. Thirty-two percent were service workers and only 8 percent of all Blacks employed worked on farms. (See Table I)
Labor unions were slow in their efforts to help organize the new Black proletariat. Until the Civil Rights Movement, the percentage of Black workers within organized labor was always significantly lower than the percentage of Blacks within the general U.S. population. In 1902, about 30,000 Blacks were in the AFL, only 3 percent of its total membership. During the Great Depression, Black membership actually declined to 2 percent. As the Congress of Industrial Organizations (CIO) recruited members in basic industries—electrical, auto, steel, rubber—the number of Black trade unions increased dramatically. Black membership in trade unions exceeded 700,000 in 1945, 5 percent of all members. In the early 1950s A. Philip Randolph initiated the Negro-American Labor Council to force all-white craft unions to desegregate and to abolish racially segregated locals. With the rapid expansion of public sector employment, where the percentage of Black workers was particularly high, more Blacks became members of unions. By 1970 Black trade union membership totalled 2 million, one-tenth of all union members. Ironically, even this figure does not indicate a historic breakthrough in biracial labor cooperation. In the late 1880s and 1890s the Knights of Labor had practiced a policy of building an effective biracial organization, and claimed Black workers as almost 15 percent of its 600,000 membership. In the assessment of political economist Victor Perlo, the Knights of Labor "represented a high point of an approach in industrial unionism and of black-white labor unity." In short, organized labor had only begun to reach the level of numerical parity for Blacks within its own ranks, an equality that had existed for a brief moment a century before.
Yet many instances of biracial cooperation within the labor movement occurred, even during the long night of Jim Crow. In September, 1920, between 12,000 to 15,000 bituminous coal miners, mostly Black, led an Alabama-wide walkout in demand for higher wages. The state militia was called to break the strike, and thousands of Black members of the United Mine Workers were beaten, arrested, or evicted from company houses. Coal company executives vowed to "fight for their property rights on high social, moral and legal grounds" and to crush the UMW, a union guilty "of associating the black man on terms of perfect equality with the white man." During the Depression, the Communist Party succeeded in establishing the Sharecroppers Union. By 1934, the mostly Black union acquired six thousand members in the Carolinas, Alabama, Florida and Georgia. CIO affiliates created in the South usually required integrated locals, and Blacks were encouraged to participate in local union decisions. A few Southern unions in the 1940s followed the example of the UMW, developing "a standard pattern of mixed locals in which the two races shared the offices." In a totalitarian social environment that was implacably hostile to both racial desegregation and labor organizing, it was abundantly clear to most Blacks at that historical moment that trade unions, for all their faults, were a positive force in the struggle for civil rights and Black economic advancement.
But as more Blacks occupied positions in industrial production, working conditions seemed to become worse. On the job accident and death rates were particularly high for Black workers, who were relegated by unions and bosses alike to the most unsafe and lowest paid work. As the number of Blacks increased in Detroit's automobile plants, for example, demands for higher productivity levels were made by management. In 1946, 550,000 Detroit auto-workers produced three million automobiles; by 1970, 750,000 workers were making over eight million automobiles every year. White union leaders were generally unsympathetic to demands raised by Black union members to improve the desperate workplace situation.
Management declared that this rapid increase in productivity was achieved by technological advances, "management techniques," and automation. Black Detroit workers responded, in turn, that these brutal methods of industrial exploitation were not "automation but Niggermation." After labor unions purged leftists from their ranks in the Cold War, they lost their "innovative dynamism and became narrowly wage-oriented," writes Harold Baron. Shop grievances were neglected, and "the black officials who arose as representatives of their race were converted into justifiers of the union administration to the black workers." Black labor leaders like Randolph and Bayard Rustin actually subordinated Black militancy "to maneuvers at the top level of the AFL-CIO."
And as in their domestic policies, the labor aristocracy pursued foreign policies in nonwhite countries that were overtly racist. The AFL-CIO played a major role, for example, in the CIA-sponsored subversion of Guyana and the Peoples Progressive Party of Cheddi Jagan. In 1964 the AFL-CIO sent Gene Meakins, former vice president of the American Newspaper Guild, to coordinate propaganda for the anti-Jagan forces. Between 1958 to 1964 the American Federation of State, County and Municipal Employees (AFSCME), then under president Arnold Zandler, received $60,000 or more annually from the CIA—much of which was spent "in the campaign of rioting and sabotage against the Jagan government." When Jagan was finally defeated in 1966, George Meany authorized the American Institute for Free Labor Development to initiate a housing project with loans from U.S. union coffers. Throughout the 1940s and 1950s, white labor leaders voiced opposition to the immediate independence of African nations. In a Federationist editorial published in July, 1952, for example, AFL leader William Green supported white minority rule in Northern and Southern Rhodesia and Nyasaland, declaring that only whites were "competent in government." The best that the "natives" could achieve was colonial patronage and "gradual development." In the 1960s the AFL-CIO helped to establish a school to train "moderate" African trade union leaders in Kampala, Uganda. Progressive African nations were attacked by Meany for their "totalitarian methods in labor relations."
By the late 1960s many Black activists concluded that most white-dominated unions would continue indefinitely to be unsympathetic to Blacks' economic plight. In Black Awakening in Capitalist America, Black social theorist Robert Allen predicted that many unions in the future would become more hostile to Federal government-sponsored "training programs for the hard-core jobless." Unemployed minority workers were, in their view, the "economic enemies" of white workers:
Labor leaders increasingly stress the need for protecting and preserving the existing jobs held by union members. The unemployed are seen as a great mass of potential strike breakers and scabs, ready on a moment's notice to take the union member's job and upset the wage scales for which the unions have so bitterly fought. That this narrow-minded policy is ultimately self destructive has not occurred to most union leaders and their rank-and-file followers. The labor unions perceive the advance of automation and mechanization as a threat to their interests, but the union leaders, once militant fighters for social change, have no program other than a panicky defensive reaction for meeting this challenge. Pleas to labor leaders to organize the jobless go unheeded as the unions watch their power base erode; the prospect of their eventual impotence seems ever more certain.
A consensus began to emerge among many Black middle-class leaders, many of whom were veterans of civil rights struggles, that unions were at best unreliable allies, and perhaps even structural impediments to Black socioeconomic advancement under capitalism. This growing hostility is particularly evident in the relationship between Black elected officials in municipal governments and the mostly white leaders of public service unions. Although many public sector workers are nonwhites in urban areas, Black mayors and city officials tend to rely on management techniques to limit wage demands. As Paul Johnston notes, "the union serves as a convenient political scapegoat for public officials caught between relatively declining tax revenues, spiraling demand for public services, and the taxpayers' rebellion. The union as villain takes the heat off management for its ineptitude, its criminal priorities, corporate profiteering, etc." The classic example of the budding unity of Black politicians—chamber of commerce vs. Black public employees occurred in Atlanta in 1977. Atlanta's 900 Black sanitation workers, members of AFSCME, had campaigned aggressively to elect Maynard Jackson as that city's first Black mayor. Under Jackson's tenure in office, the sanitation workers averaged annual salaries of $7,500, and received no wage increases in three years. After negotiations failed, the Black public employees went out on strike. Jackson's immediate response—to fire the Black workers—won the praise of Atlanta's corporations, media and leaders of the Black petty bourgeoisie. AFSCME president Jerry Wurf, a social democrat with a history of support for civil rights causes, was condemned as a "racist manipulator" who sought the demise of Black political power in Atlanta. Reverend Martin Luther King, Sr., informed the media that Jackson should "fire the hell out of" the Black public employees.
However, the most conservative Black expression of this antiunion view was published in 1980 by the Lincoln Institute for Research and Education, a Black think-tank in Washington, D.C. Two of the authors of the widely-circulated monograph, entitled Black American and Organized Labor: A Fair Deal? were Walter E. Williams, economics professor at George Mason University and a leading proponent of Black Reaganism, and Wendell Wilkie Gunn, assistant treasurer of Pepsi Corporation. The authors argue that capitalism is inherently democratic and amiable to Black advancement. The primary source of racism in the workplace comes from labor unions. The monograph implies that Black equality cannot be achieved unless trade unions are abolished. Failing that, Black workers should resist joining unions wherever possible. "It is only by providing real freedom of choice to workers with regard to whether or not they wish to join a labor union," the Institute declared, "that black workers will be given an opportunity to advance." Williams also has suggested that Blacks' interests would be better served in an alliance with Reagan Republicans and corporate interests. High Black unemployment rates are not the responsibility of business, in any event, since the Blacks' lack of educational preparation and low productivity are almost as much to blame as union racism.
Although progressive labor historians would dissent from this interpretation, many leftists would agree that labor's long prejudice towards Blacks was the direct result of the fact that all white workers have benefited in absolute terms from racism. A "whites only" labor strategy supposedly increases the wages and ultimately the bargaining power of white union members at the expense of superexploited Blacks. Paul L. Riedesel argued in 1979 that census data indicates "an overall pattern of white gain" in spite of great income dispersion within the white group. White racism is "endemic" to the AFL-CIO, and racially divisive policies and practices of the white labor aristocracy are designed consciously to promote the interests of all whites. It is true that segregationist policies can benefit whites in some unions, particularly racial restrictions in certain crafts or highly technical skills sectors. Craft unions historically discriminated against all Blacks with the desired intent to increase their own bargaining power. But even this does not prove that white workers as a group benefit in absolute, rather than in relative terms, from the perpetuation of racism. In a critique of Riedesel, Marxist economist Al Szymanski writes that where racism is dominant in labor relations, working class cohesiveness declines, creating a net loss in incomes for all whites, although less in real terms than to Black labor. But even after the election of Ronald Reagan, and the successful Solidarity demonstration in Washington, D.C., involving the coordinated efforts of both Black and labor groups in September, 1981, the issue was not resolved—at least not within the Black community.
The historic evolution of the Black working class in advanced capitalism, and the ambiguous relations between Blacks and organized labor, raise a series of difficult questions. Is there any real basis for Black-white working class unity within the trade union movement, and more generally, within American politics? Does unionization help or hinder Black economic advancement vis-à-vis whites? Are unions "structurally racist" in a racist/capitalist state, unable by their very existence to advance the material interests of Black laborers? To arrive at some conclusions, one must assess whether any real gains in Black income were derived in part from unionization.
IV
There is no question but that the large majority of the Black working class supports unions. Both in public opinion polls and in their support for "pro-labor" political candidates, most Blacks continue to express support for legislation favorable to union growth, despite organized labor's shoddy record on racial issues. The central reason for this is that the majority of Afro-American people—blue collar and service workers, public sector employees and clerical workers—understand that unionization has historically produced higher wages, both in absolute terms and in relative terms compared to white employees with similar educational backgrounds and skills. Unionization means improved working conditions, and a greater likelihood of upward income mobility. An analysis of the percentage of median earnings of Black male workers to the median earnings of all male workers for selected industries in 1969 illustrates this point. In industries with heavy union representation, the income disparity between Black and white males is relatively low: automobile industries, 84 percent; iron and steel, 83 percent; rubber products, 78 percent; primary nonferrous metals, 82 percent. In industrial sectors dominated by craft unions, or in industries that remain largely unorganized, the median income gap between Black and white males is more severe: yarn, thread and fabric mills, 75 percent; furniture and fixtures, 69 percent; printing and publishing, 68 percent; professional and photographic equipment, 67 percent. By comparison, the median income ratio of Black to white males for all workers in 1969 was 58 percent. Racism still exists within all unions, and most white union leaders tolerate if not encourage the systemic exclusion of their Black members from the highest paid and skilled positions. Nevertheless, it remains clear that "the relative wages of black workers to those of white workers are considerably better in industries where powerful industrial unions with a militant tradition embrace the majority of production workers, than in industries where craft unions, or weak industrial unions, or no unions at all prevail."
Another way of viewing the impact of unionization as a factor in reducing the economic inequality of Blacks is evident in census data comparing the relative incomes of nonwhite full-time male workers both in and outside labor unions. The ratio of nonwhite males' to white males' median incomes for all occupations in 1970 was 83 percent in unions, and 62 percent outside unions. For blue collar male workers, the ratio is 90 percent in unions, 72 percent outside unions. For white collar employees, the ratio is 85 percent in labor unions, 70 percent outside unions. Only for service workers are the figures for nonunion members higher than those of union members, 77 percent to 73 percent. The ratio for nonwhite females' to white females' median incomes for all occupations in 1970 was 91 percent for union members, and 82 percent for nonunion employees.
There is also a substantial body of research indicating the egalitarian or progressive effects of trade unionism on the dispersion of wages and fringe benefits. The option for personal wage differentials based on favoritism or white racism within specific job categories is greater in nonunion firms than in the unionized sectors of the economy. Harvard economist Richard B. Freeman argues that union wage policies which are designed to set standard rates across and within firms "significantly reduces wage dispersion among workers covered by union contracts and that unions further reduce wage dispersion by narrowing the white collar/blue collar differential within establishments." The dispersion of compensation "is also lower among establishments that are unionized than among those that are not." Because unions are fundamentally political institutions which are "sensitive to the intensities of preference," unionism raises the fringe shares of all workers. Union workers are usually more knowledgeable about retirement policies in their companies than nonunion workers, and generally expect to "receive a pension higher than that expected by" nonunion employees. Particularly in capital intensive industries, unions are able to achieve significantly higher wage increases for workers—so long as political unity exists between Blacks and whites within specific unions.
The divergent attitudes expressed by some Black petty bourgeois leaders as opposed to the great majority of Black workers towards unionization and biracial labor alliances can be explained in part by unemployment statistics. Blacks with college educations and professional degrees, who are employed in white collar work as professionals, technicians, managers and administrators, uniformly experience relatively low rates of unemployment. During the recession year of 1975, when the overall unemployment rate stood at 14.7 percent for Black men and 14.8 percent for Black women, only 7.4 percent of Black males employed as professional or technical workers were out of work. Black males and females employed as managers and administrators had unemployment rates in 1975 of 4.7 percent and 5.9 percent respectively. By contrast, white males and females working as managers and administrators experienced 1975 unemployment rates of 2.6 percent and 4.3 percent. The greater burden of joblessness always falls squarely on the shoulders of Black blue collar and service workers. The unemployment rates for Black male craft workers was 13.1 percent; Black male and female operatives, excluding transport equipment workers, 17.3 percent and 21.9 percent; Black male nonfarm laborers, 19.2 percent. The pattern of permanent Black working class unemployment persists. In 1977, the unemployment rates for Black male and female workers in wholesale and retail trade were 15.9 percent and 21.6 percent, while white males and females in this sector had unemployment rates of 6.1 percent and 8.6 percent, respectively. The immediate spectre of unemployment forces most Blacks in blue collar and service jobs, both within unions and outside of them, to view unionization as a step toward greater job security. Elements of the Black elite, reasonably comfortable in their own job positions, can afford the luxury of exigent condemnations of the future political utility of unions to the Black movement.
The critical irony here is that neither the material interests of white workers nor those of labor unions as a whole are advanced by white racism. There are at least several ways to document this. Perhaps the simplest is the lower rate of unionization in the South in virtually every industry. The strength of racial segregation both within the civil society as a whole as well as within broad elements of the trade union movement in the region is commonly recognized by historians as the major reason for Southern labor's failure to organize. Second, racism dilutes the bargaining power of unions for higher wages, fringe benefits and better working conditions. White workers who have greater seniority than many Blacks often accept contracts with decreasing benefits simply to maintain their own positions vis-à-vis Blacks within the labor market. In the long term, however, this racist strategy inhibits "union bargaining strength and militancy," according to economist Michael Reich, "thereby reducing the total income share of labor." Again, the political economy of the South provides an example. By the 1970s 75 percent of all textile workers in the U.S. worked in the Southern states. Only ten percent of this workforce of nearly 600,000 was unionized. The average hourly wage of Southern textile workers in the late 1970s was $3.46, near the bottom of the national wage scale for all industrial workers.
Probably the greatest negative impact of racism upon the material interests of labor and more generally of all workers is in the area of public policy. The massive spending reductions of the Reagan Administration are "racist" in that they have a disproportionately higher affect on Blacks as a group than upon all whites. It is crucial to observe, however, that by far the largest population targeted for cutbacks is the lower income, white working class.
Three illustrations will suffice to document this claim—food stamps, public housing and Medicaid. The 1977 Food Stamp Act was originally designed to "permit low-income households to obtain a more nutritious diet." According to the Bureau of the Census research, about 5.9 million households in the U.S. received food stamps in 1979. The median annual income of these families was a meager $5,300. Seventy-seven percent had total personal incomes below $10,000 a year. The average face value of food stamps received in 1979 was only $810 per household. Sixty—three percent of all household recipients of food stamps were white, 3.7 million families; 2.1 million, 35 percent, were Black; another 600,000 families were Latino, 10 percent.* One million householders were 65 years or older. Two-thirds of these households had children 18 years old and under.
The first public housing act passed by Congress in 1937, was initiated "to remedy the unsafe and unsanitary housing conditions and the acute shortage of decent, safe, and sanitary dwellings for families of low income." Rents for public housing are set not to exceed 25 percent of net monthly incomes for families or individuals served. In 1979, about 3 percent of all U.S. households, 2.5 million families, lived in federally subsidized or public housing. The median annual income for these households was $4,980. Almost half of all families living in public or subsidized housing had incomes below the official poverty line. 1.5 million households, 59 percent, were white; 1.0 million households, 39 percent, were Black; 200,000 households, 8 percent, were Hispanic. Two-thirds of these households were maintained by women householders without husbands present; one-third had householders who were 65 years or older.
Medicaid was created by the Federal government in 1965 "to furnish Medical assistance on behalf of needy families with dependent children, and of aged, blind, or permanently and totally disabled individuals whose incomes and resources are insufficient to meet the costs of necessary medical services." 18.1 million individuals, 8.0 million households, were enrolled in the Medicaid program in 1979—that is, they had a Medicaid assistance card or had medical bills which were paid for by Medicaid. Of these, 68 percent were white; 30 percent were Black; 700,000 or 9 percent were Latino. 36 percent were 65 years or over; 61 percent of all householder recipients had not worked during the year.
The chief beneficiaries of several decades of liberal and reformist Federal intervention programs have been individuals and families with annual incomes below $20,000 (1982 dollars); those without postsecondary education or technical skills, national minorities; blue collar and service workers; and the elderly. Mathematically these diverse groupings have the potential for becoming, in the new age of fiscal austerity, a left-of-center coalition that could be forced to articulate minimally a left social democratic public policy agenda, simply for their own survival. Yet the centrifugal forces of white racism, cultural conservatism and political reaction, embodied in the emergence of the New Right and the election of Reagan, now threaten the realization of such a majority.
The basic issue here is an old problem which can be traced to the very beginnings of U.S. history. White populists, labor leaders and leftists have long made the argument that racism actually reduces the absolute living standards of white workers, retards their unions, and undermines the institutional stability of their communities. Racial divisions within the working class accelerate the processes of exploitation in the workplace for Blacks and whites alike. Yet given clear political options, white workers have frequently sacrificed their own material and political interests to engage in the mass-mania of racist violence, terrorism and prejudice. White workers have organized lynchmobs, raped Black women, mutilated Black children, engaged in strikes to protest the employment of Black co-workers, voted for white supremacist candidates in overwhelming numbers (e.g., George Wallace in the Democratic Party's presidential primaries in 1972), and have created all-white unions. How and why does this process happen? We can gain some insights here from Georg Lukács. In History and Class Consciousness, Lukács writes that "Marx repeatedly emphasized that the capitalist is nothing but a puppet. And when, for example, he compares his instinct to enrich himself with that of the miser, he stresses the fact that 'what in the miser is a mere idiosyncrasy, is, in the capitalist, the effect of the social mechanism, of which he is but one of the wheels.'" In a racist/capitalist state and economy, the instinct among whites to exhibit racist behaviors and practices is not a psychological aberration. To be racist in a racist society is to be normal; to reject racism, denounce lynchings, and to fight for Black political and economic rights is to be in a symbolic sense "abnormal." Racism benefits the bourgeoisie absolutely and relatively; working class whites are usually part of the larger "social mechanism" of racist accumulation and Black underdevelopment, serving as uncritical cogs in the wheels of Black exploitation.
For many working class whites, the Afro-American is less a person and more a symbolic index between themselves and the abyss of absolute poverty. All whites at virtually every job level are the relative beneficiaries of racism in the labor force: Blacks, Puerto Ricans, Chicanos, etc., supply the basic "draftees" in the permanent and semi-permanent reserve army of labor. In the capitalist economy's periodic downturns, whites benefit relative to Blacks by not being Black. Moreover, lowly paid white workers, particularly in semi-skilled occupations, can "justify" their low wages, poor working conditions, and deteriorating standards of living with the racist view, "At least I am not living like the niggers." Another perspective on this process is provided by Jean-Paul Sartre. Anti-Semitism in the West, Sartre suggested, is "a poor man's snobbery. By treating the Jew as an inferior and pernicious being, I affirm at the same time that I belong to the elite." The philosophical foundations of "redneck racism" are the same dynamic. For generations, many white American workers refused certain menial jobs on the principal that they refused to do "nigger work." Psychologically, the Black was not simply a cultural "symbol of Evil and Ugliness," as Frantz Fanon attests. "The Negro (also) represents the sexual instinct (in its raw state). The Negro is the incarnation of a genital potency beyond all moralities and prohibitions." At a level of the collective unconscious, the Negro's demands for decent jobs, healthcare and voting rights could be opposed by the question, "Do you want your daughter/son to marry one?" In the workplace, labor union unity across the color line could be opposed as a contradictory coalition between white workers vs. beings who were somehow "less than human." The continued suppression of Blacks within the economy and across civil and political societies becomes the means through which many oppressed whites can derive cultural and psychological satisfaction without actually benefiting in an absolute material sense in super profits of racism.
The sad irony is that certain sectors of the white working class are also targeted for elimination and radical transformation. The identical processes which threaten the Black proletariat are confronting white autoworkers, steelworkers, rubberworkers, textileworkers, laborers and many millions more. Whether white workers as a self-conscious mass will perceive that their own "benefits" from racism are only relative to the oppressed conditions of Black labor, and that the social and psychological image of the Blacks-as-inferior beings actually promotes their own exploitation as well as that of Blacks, cannot be predetermined. A majoritatian bloc against the New Right and the interests of capital must at some initial point call for the protracted cultural and ideological transformation of the white working class.
V
The question of organized labor's relations with the Black movement acquired even greater significance with the recessions of 1980 and 1981-82. U.S. capitalism is in the midst of a major economic crisis. The serious character of the crisis has forced corporations to reevaluate their own assumptions about the internal workings of the capitalist system. The capitalist prognosis for restoring profits at the expense of the working class is old hat. However, it is how they plan on doing it and what sectors of the working class it will affect that is revealing. This strategy was spelled out in fine detail in Business Week (June 1, 1981).
In this special issue the editors observed that the American economy since 1977 "has been far stronger than anyone expected, it has refused to go into recession when predicted, it has been more inflationary than forecast, and it has created more new jobs than imagined." The reason for this, Business Week argued, is due to a radical transformation of the industrial and commercial economy since the 1960s. "The economy has developed into five separate economies that no longer act as one; these subeconomies do not grow together in periods of prosperity, nor do they decline together in periods of recession." The five subeconomies cited are: 1) old-line industry, which includes automobiles, steel, textiles, appliances, construction, electrical and non-electrical machinery, food and tobacco manufactures; 2) agriculture—livestock, vegetables, food grains, forestry, fishery products, cotton, and poultry; 3) energy—coal, oil, natural gas and utilities; 4) high-technology—semiconductor and computer technology, office machines, aircrafts, dental and optical supplies, surgical supplies, radio and television equipment; and 5) services—finances, personnel, consulting, information processing, education, healthcare, hotels and apartments, real estate, media, insurance and other social services.
Business Week noted that the rates of capital investment, relative prices and profits were strikingly divergent from one sector of the capitalist economy to another. Old-line industries employ about one-third of the U.S. work force, and once constituted the foundation for corporate growth. This is no longer true. Projected real growth in steel, autos and other older industries, with "Reagan's reforms" allowing for accelerated depreciation allowances, will be two percent, less than half the rate of growth achieved during the previous two decades. In 1975, the average return on equity for older industries was 14 percent; by 1980 return on equity was below 8 percent. Since 1973, 23 tire plants have shut down in the U.S.; 11 percent of America's steelmaking capability was "phased out" between 1977 and 1980. Defense-related firms, chemical food processing and steel industries will continue leaving the industrial Northeast and Midwest to pursue tax abatements and lower labor costs in the "sunbelt" or abroad. In New York City alone in the 1970s between 40-50,000 jobs in apparel and textile industries disappeared. About 400,000 U.S. workers, mostly employed in old-line industries, lost their jobs in 1979 alone because of plant closings or relocations.
Sectors of the private economy expected to do well in the 1980s include energy, high technology and many services, according to Business Week. Industry analysts predict that oil prices, currently about $34/barrel, will range between $77-$117/barrel by 1990. Despite reductions in the rate of U.S. petroleum consumption and an expansion of U.S. drilling, domestic oil and gas prices will go even higher.1980s record profits for the U.S. oil and gas corporations, $37.7 billion, will reach $100 billion by 1990. In semi-conductor and computer production, also, profits will be staggeringly high. With a growing worldwide demand for technology, annual sales of semi-conductor corporations alone should reach $40-50 billion. Many human service oriented corporations, particularly in the fields of advertising, travel, banking, credit, insurance and health care, will expand. Others, such as public education, automobile services, etc. will contract sharply in the next years. Government employment, particularly in lower paid white collar and blue collar service positions will be reduced significantly.
Perhaps the greatest rise in prices and profits in the 1980s will occur in agriculture. During the 1970s, U.S. exports of soybeans, corn, rice, wheat and truck produce reached all-time highs. Gross farm income rose 6 percent to almost $140 billion in 1980. But rising costs for fuel, pesticides and real estate have severely reduced agribusiness' profits. Business Week noted that "real profits plunged to $13.4 billion in 1980, from $31.5 billion in 1973." Farm liabilities tripled from $54 billion in 1970 to $180 billion in 1980. "Debt has jumped from 6 percent of overall cash flow in 1970 to about 19 percent today." Because of an accelerated demand for farm products and a growing debt, economists predict that agricultural prices will "explode" in the 1980s. Prices for food should increase about twice the rate of inflation. The continued high cost of commercial capital means that hundreds of thousands of small farmers will go out of business. Business Week observed, "the total number of farms will drop 25 percent to 1.8 million, and the largest 50,000 farms, about 3 percent of the total—will account for 58 percent of total cash sales." Overall farm assets will triple to an amount of $3.3 trillion by 1990.
What will be the position of the Black workers within the new capitalist macroeconomy? Blacks are being concentrated in exactly those industries that are undergoing rapid decline and conversely are excluded from the sectors of the economy targeted for growth. This labor force projection can be illustrated by a brief examination of Black employment patterns. (See Tables II, III) Of the eight and one-half million Blacks who found employment during the year 1977, 24 percent were in manufacturing. About 2 percent were employed in motor vehicle production; 12 percent made other durable goods, such as steel; 5 percent were in construction; 2 percent made food products. All of these sectors will experience harsh reductions in hiring, and hundreds of thousands of transport equipment operatives and nonfarm laborers will lose their jobs. In areas of potential economic growth, however, Blacks are underrepresented. 11 percent of all Black workers are in retail trade, and another 2 percent are in wholesale trade. Their numbers amount to only 8 percent of repair services, 7 percent of the employees in real estate, insurance and banking. 8 percent of all Black workers comprise 13 percent of the total work force in public administration or government—a sector targeted for major reductions in hiring in the wake of Proposition-13 style cut-backs.
At the same time the level of permanent Black unemployment, which increased from 8.1 percent in 1965 to 14.7 percent in 1975, will probably exceed 20-22 percent by the end of the 1980s. Black youth unemployment, which was only 16.5 percent in 1954 and 26.2 percent in 1965, will exceed the 51 percent figure of 1982. Growing numbers of Blacks, especially youth and adults under the age 35, will find few positions available to them in the work force. (See Table IV)
The economic plight of the Black labor force is symbolized best by the ironies of agricultural production. Only forty years ago, 41 percent of all Black male workers were either farmers or farm laborers. In 1949, Blacks owned 80,842 commercial cotton farms in Mississippi, a total of 66.0 percent of the segregated state's total. The number of Black-owned and operated cotton farms in 1949 ranged from 30,807 in Arkansas to 9, 727 in North Carolina, an amount that was still 45.4 percent of that state's cotton farms. Even as late as 1964, there were 21,939 Black-owned cotton farms in Mississippi, 61.7 percent of the total number. But by 1969, Black farmers were effectively swept from the fields. Only one thousand Black-owned cotton producing farms remained in Mississippi that year. In North Carolina, there were only 18 Black-owned cotton farms left. Between 1965-80, the amount of Black-owned agricultural land had been reduced by more than half. Thus, precisely as agricultural production has become as potentially profitable as high technology or natural gas production, Black agricultural workers/owners have been reduced to insignificance.
The fiscal projections of U.S. corporations have been wrong in the past, and nothing in the discussion above suggests that they will not be wrong in the immediate future. Little analysis in Business Week, Fortune or within the Council of Economic Advisors has been given to the central reason for the American economy's superficial vitality between 1976-80; the unprecedented explosion of public and private debt. In 1960, for example, the total net debt of all farms, banks, business, consumers and government amounted to $38.5 billion. This figure was equal to 7.6 percent of the nation's gross national product. By 1977, net additions to public and private debt came to $378.3 billion, about 20 percent of GNP. Much of this growth has been the indebtedness of consumers. Of the $378.3 billion figures, $107.7 billion was public debt, $103.1 billion was owed within business, and $130.0 billion debt was that of the consumer. Furthermore, the percentage of consumer debt vs. consumer income has grown from 4.4 percent in 1975 to 9.9 percent in 1977. The structural debt of even the most profitable sectors of the macroeconomy will continue to escalate. In agriculture alone, liabilities are projected to reach $600 billion by 1990. The upswing in the capitalist economy, in short, will be financed by borrowed funds, paid for at interest rates that will oscillate between 12 and 22 percent.
Surveying all possibilities, two conclusions can be drawn. First, there is a practical limit to the amount for mortgages and credit that individual and corporate consumers will be able or willing to pay for. Cutting the number of operatives, manual laborers and service workers will inevitably ease the pain for corporations, as they attempt to expand profit margins at the expense of growing unemployment. But as Paul Sweezy has observed, growth "rests on the continuous rise in consumer spending, mainly on durable goods, (and) an increasing flow of consumer credit will eventually—and sooner rather than later—turn back on itself as the stream of accompanying repayments grows inexorably larger." The second point is that one segment of the work force that is most vulnerable to these shifts in the macroeconomy is the Black working class. As many as one million could lose their jobs with the flight of capital in the form of plant closings in the "Frostbelt." Thousands of former Black farmers will not take part in the unprecedented expansion of agribusiness' profits, because they now lack the land and capital for reinvestment. Advancements in technology will replace thousands of manual laborers and service workers. Many white collar workers within government and those hired by affirmative action policies in the private sector may find it difficult if not impossible to keep the positions they have. As the economic crisis deepens, corporations will seek more innovative strategies to weaken unions, exacerbate differences between Black and white workers, and threaten financial chaos for entire cities. A number of predominantly working class communities are already subject to what United Auto Workers president Douglas Fraser has termed "industrial blackmail," where corporations threaten to leave an area if the local government does not grant extraordinary tax breaks. Union members are told that they must lower their expectations for wage increases and fringe benefits at contract negotiations, in order to keep the plant alive. The climate of fiscal austerity creates new tensions between those employees with greater seniority and those who have only recently entered the job market—often young people, women and Blacks.
An analysis of the evolution and current status of the Black working class leads us to several conclusions. More than any other social stratum within American society, Black workers would be the direct and immediate beneficiaries of the reorganization of the U.S. political economy. The contemporary and historical crisis which confronts the Black working class primarily, as well as the Black majority, cannot be resolved unless worker self-managed factories and the public ownership of the central means of production, transportation and the distribution of goods and services is won in our generation. There are two basic contradictions which present barriers to such a solution. The first, and most obvious, is the great (and still unanswered) question: will labor unions and the white working class wage unconditional war against its own contradictory history? The primitive bigotry, cultural exclusivity, social norms and explicit ideology of white supremacy have repeatedly undercut Black-white labor unity. If there is no attempt on the part of white labor to engage in extensive self-criticism, and to construct a common program for struggle against capital with nonwhites, the final emancipation of the American working class will be unattainable. The second problem relates to a more recent development within the overall political economy—the growth of a massive number of permanently unemployed men and women. The reserve army of labor is swelling the ranks of the American poor, and has created the socioeconomic conditions for an unpredictable "ghetto-class" whose political interests are not always identical to those of employed workers. As the contradictions within the capitalist economy and civil society deepen, millions of unemployed and desperate Americans may continue to ignore socialist alternatives for something that can promise jobs, food and domestic tranquility. That authoritarian alternative could be some form of fascism, as we shall discuss in chapter nine.
CHAPTER TWO
THE BLACK POOR: HIGHEST STAGE OF UNDERDEVELOPMENT
The economic relations of the ghetto to white America closely parallel those between third-world nations and the industrially advanced countries. The ghetto also has a relatively low per capita income and a high birth rate. Its residences are for the most part unskilled. Businesses lack capital and managerial know-how. Local markets are limited. The incidence of credit is high. Little savings takes place and what is saved is usually not invested locally. Goods and services tend to be 'imported' for the most part, only the simplest and the most labor-intensive being produced locally. The ghetto is dependent on one basic export—its unskilled labor power.
—William K. Tabb, The Political Economy of the Black Ghetto (New York: W. W. Norton, 1970), p. 22.
I
The citadel of world capitalism, the United States, has never liked to admit that millions of its citizens are poor. Yet the hub of international financial markets, Wall Street, is only blocks from some of the worst urban slums in the world. Atlanta's Omni and glittering convention center is walking distance from dilapidated shanties that are mirror images of eighteenth- and nineteenth-century slave quarters. The White House and the posh residential district of Georgetown are respectively less than twenty city blocks from rat-infested and crime-filled squalor. The percentage of the total U .S. population defined as impoverished increased from 11.1 percent in 1972 to 13.0 percent in 1980, the highest figure recorded by the Bureau of the Census since 1966. 1.3 million New York City residents were defined as poor in 1978, 18.7 percent of the city's populace. Chicago recorded 667,000 poor persons in 1978, 18.4 percent of its total population, and Philadelphia had 336,000 poor people, 19.8 percent of the city's total population. There were 2.6 million Latinos, 7.6 million Blacks and 16.3 million whites who were classified by the Federal government as poor in 1978. In a racist society, poverty is alloted unequally: 31 percent of all Blacks in the U.S. are poor, 22 percent of all Hispanics, but only 9 percent of all whites.
Poverty must be understood properly as a comparative relationship between those segments of classes who are deprived of basic human needs (e.g., food, shelter, clothing, medical care) vs. the most secure and affluent classes within a social and economic order. It does relatively little good to compare and contrast the family of a Puerto Rican welfare mother in the South Bronx with a poor family in Lagos, Sao Paulo or Bombay. Black American living conditions may be superior in a relative material sense to those of working class families in Poland—but we are not Poles. The process of impoverishment is profoundly national and regional, and it is in the light of capitalist America's remarkable success in producing an unprecedented standard of living for the majority of its indigenous white population that Blacks' and Hispanics' material realities must be judged.
The first dilemma confronting the researcher who explores the dimensions of American poverty involves the definition of class. Traditionally, American bourgeois social scientists have defined one's class status as a function of annual earned income, and not in terms of one's relationship to the means of production. Upper class Americans are not individuals who own the factories and the corporations, and who live without selling their labor power in the marketplace for a wage. Rather, the capitalist elite is delineated by its annual income of, let us say, $200,000 or more. Of course, this definition could include any number of persons who are not capitalists—from highly successful physicians to lucrative (and illegal) drugs dealers. Conversely, the Federal government has established a rather elaborate theoretical construct to define poverty, based again on an individual's or family's annual income—"the sum of the amounts received from earnings; Social Security and public assistance payments; dividends, interest and rent; unemployment and workmen's compensation; government and private employee pensions, and other periodic income." Certain non-monetary tranfers, such as healthcare benefits and food stamps, are not counted as income. The Federal government makes a distinction between "nonfarm" and "farm" residence in determining poverty status, weighs its analysis according to the number of persons who are in a particular family, and even considers whether a female is the nominal "head" of a particular household. Thus, widely varying standards emerge on what constitutes "the poor." An eighteen year old Black woman with a small child in Atlanta was considered poor in 1978 if her annual income was $4,268 or less. If she and her child lived in rural Georgia, her "poverty threshold" was $3,614. A Black family of seven persons in Chicago with both male and female parents would be poor at $11,038 or less. If their father was killed by the police, and the family returned to rural North Carolina, its poverty threshold would be $7,462; if it stayed in Chicago, $8,852. A blind and partially crippled 66 year old widow, living in a dangerous and drafty rowhouse in the slums of North Philadelphia, would not be considered poor if her yearly income exceeded $3,253. Sensible people of all political persuasions would have to admit that no single person can survive on an annual income of under $10,000 in a metropolitan area except at the precipice of despair and hunger. But as everything else in capitalist America, the state defines "poverty" to suit its own needs. Thus, the assertion that the percentage of all Americans who are "poor" declined from 22.4 percent in 1959 to 11.1 precent in 1973 must be viewed with a healthy degree of skepticism.
Even when one accepts the Federal government's definition of poverty, the general situation for millions of Americans becomes strikingly apparent. For the year 1978, there were 9.7 million children under the age of 18 who lived in families existing below the poverty level. 3.2 million persons 65 years or older were poor. 10.3 million poor persons, about 42 percent of the nation's total poor population, resided in the South. 62 percent of all poor people lived in metropolitan areas, and 62 percent of this population resided in the ghetto or central city. 5.4 million unrelated individuals over 14 years old, residing in the homes of nonrelatives or living alone, were poor. Most of these unrelated persons, 4.2 million, were white. 1.4 million white families with no husbands present were classified as poor, 23.5 percent of all such families. 15.7 percent of all families, Black, white and Hispanic—who lived in central cities were below the poverty level. 38.5 percent of all married women age 25 to 44 whose spouse was absent from the home in 1979 were poor, and 80.8 percent of all American women over 65 who are widowed are poor.
Statistically, the poor Black family differs from the impoverished white family in a number of critical respects. From 1959 to 1978, the number of whites classified by the Federal government as below the poverty level declined from 28,484,000 to 16,259,000. In terms of percentage to the general white population in the U.S., the decline cut the white poverty rate from 18.1 percent to 8.7 percent. During the same period, the number of poor Blacks also declined both in real numbers and in terms of their percentage to the Black population, but not as much as the whites' figures—9,927,000 persons and 55.1 percent in 1959 to 7,625,000 persons and 30.6 percent in 1978. In real terms, the number of poor Blacks actually increased slightly after 1969, from 6,245,000 that year to the current level. The number of poor white males with families declined from 4,952,000 to 2,132,000 between 1959 and 1978, for a drop in percentage terms of from 13.3 percent to 4.7 percent of all such white families. For Black male households, the decline was more marked, from 1,309,000 to 414,000. Even so, 13.4 percent of Black household heads were poor in 1979, a figure that exceeds the level of white male householders twenty years before.
Black families throughout the U.S., in every region and city, assume the unequal burden of poverty. In suburban districts outside the ghetto, 21.3 percent of all Black families are poor, vs. only 5.9 percent of white families. In central cities Black and white families below the poverty level comprise 28.6 percent vs. 7.6 percent of their total populations respectively. Outside metropolitan areas, 39.1 percent of all Black families are poor, while only 11.2 percent of white families are. When all American families are divided into fifths according to income, a much higher proportion of Blacks and Hispanics are located in the bottom two-fifths, and virtually disappear in the highest fifth of U.S. income earners. Using 1977 figures, 39.6 percent of all U.S. nonwhite families were in the lowest fifth of all income earners. 22.6 percent were located in the second lowest fifth. Only 9.4 percent of all nonwhite families earned yearly incomes to rank in the highest fifth, by way of contrast.
Although Blacks' incomes have increased over the past ten years, earners generally have not kept pace with inflation. One way of viewing the illusion of Black income mobility is by comparing Black median incomes between 1970 and 1977 in current dollars and in constant 1977 dollars. The median Black family income in 1970 was $6,279. Seven years later, Black family median income was $9,563, an increase of $3,284. In constant 1977 dollars, however, $6,279 was worth $9,799. Thus, the median Black family income actually declined—2.4 percent in the period 1970 and 1977. Using constant 1977 dollars, a pattern of growing impoverishment becomes clear. The median Black family incomes in Northeastern states declined by 15.2 percent between 1970 and 1977, from $12,132 to $10,285 annually; in the North Central States, the decline was 11.2 percent, $12,045 to $10,690; in the West, 20.6 percent, $12,487 to $9,917. Those families that suffered most were located in urban metropolitan areas. In central cities in excess of one million persons, Black median family income declined 13.6 percent, from $11,589 to $10,012. Even in the suburbs of major cities, Black median family income dropped 7.1 percent, $14,111 to $13,104. For Black families with no husband present, median incomes increased marginally, from $5,581 in 1970 to $5,598. Simultaneously, white median family incomes between 1970 and 1977 increased in constant 1977 dollars by 4.8 percent, and whites suburban families' median incomes passed the $20,000 mark by 1977.
Although the majority of Black poor families earned something between $3,000 to $5,000 in 1978, a frightening number of Blacks exist on virtually no financial reserves or resources. 78,000 Black families reported annual incomes between $1,000 and $1,499; 45,000 families earned between one dollar to $999 during 1978; 31,000 additional families actually had no cash income at all. For the most oppressed and destitute sector of the permanently unemployed, social services and public programs have provided little in the way of real additional income. Inside poverty areas, residential districts containing at least 20 percent of the population living below the official poverty level, 220,000 Black families survive solely on public assistance plus their meager salaries. 31,000 families in poor communities depend primarily on Social Security income. About one-third of a million Black poor families live in public housing, which reduces the amount of money they must pay toward their rent. 770,000 other Black poor families, however, are forced to find private accommodations usually at exorbitant rates.
Demographically, Black poor people are distinguished from poor whites by certain social characteristics: they are largely more female, younger, and usually reside in the urban ghetto. At all ages, Black women are much more likely to be poor than white females, white males, or Black males. Several examples can be used to illustrate this. Consider four categories of unmarried persons between the ages of 15 to 19: white males, white females, Black males and Black females. For these groups, the percentage of their total populations who would have been below the poverty level in 1978 was the following: white males, 8.5 percent; white females, 14.8 percent; Black males, 36.0 percent; Black females, 40.0 percent. For divorced women between the ages of 25 to 29, the poverty rates are white females, 19.7 percent; Black females, 41.2 percent. Among married women who are legally separated but not divorced, between age 35 to 44 years, those below the poverty line are white females, 40.6 percent; Black females, 52.5 percent. Overall poverty rates for all household heads 15 years and over, by race are white males, 5.3 percent; white females, 9.5 percent; Black males, 11.8 percent; Black females, 31.1 percent. For all persons of both sexes, the percentages of those in poverty are white males, 7.3 percent; white females, 10.0 percent; Black males, 26.5 percent; Black females, 34.1 percent. (See Table V)
Subproletarian status for Black women creates oppressive social conditions that inevitably include an absence of adequate birth control information and support services for young children. In residential areas where at least twenty percent of all persons exist below the poverty level, both birth and infant mortality rates are exceptionally high. In impoverished central cities, the number of Black children under 3 years old per 1,000 Black women between the ages of 15 to 44 was 327.93. In rural poverty areas, the rate is a staggeringly high 441.66. Again, these rates must be contrasted with both white and Black women who live above the poverty level, 173.61 and 184.69, respectively. There is a direct relationship between the number of children that are within a Black family with a sole female householder and family's likelihood of being below the poverty level. Only 14.8 percent of all Black women householders without children are in poverty. That percentage increases with each dependent: one child, 42.2 percent in poverty; two children, 59.8 percent; three children, 36.4 percent; four children, 82.5 percent; five children, 86.0 percent.
Poverty is also reinforced within the Black community by educational underdevelopment and academic inequality. By 1978, as an illustration, 74 percent of all Blacks between the ages of 22 to 34 were high school graduates, with 12.6 median years of school completed. 86.1 percent of all whites in this age group were high school graduates, with 12.9 median years of education. For Blacks below the poverty level between 22 and 34, both figures were significantly lower—53.0 percent high school graduates, with 12.1 years of schooling. Overall educational statistics for poor Blacks are much worse. The average poor Black person has completed only 10 years of school. Only 26.8 percent have been graduated from high school. Impoverished Blacks between 45 to 54 years of age recorded only 9.3 years of education, and Blacks between 55 to 64 years of age have but 8.4 years. Not a single Black man between age 60-64 in 1978 who lived in poverty had a high school diploma. 118,000 Black poor people have never attended school in their lives, 491,000 completed under five years, and another 585,000 had only a sixth or seventh grade education.
The strongest roots of Black poverty are anchored firmly in the capitalist marketplace, contrary to the opinions of most social scientists. The process of income erosion for Black families since the 1960s can be examined several ways. Perhaps the most effective is an assessment of the number of salaried workers per family by race, and the ratio of persons to income earners per family. (See Table VI) In 1967, the Black families were significantly larger than white families (4.35 persons vs. 3.59 persons). However, the economic conditions of the period allowed a relatively larger number of Blacks to enter the job market to support family members. The percentage of families with two income earners that year was 41.8 percent for Blacks and 38.4 percent for whites. 11.1 percent of all Black families had three earners, and 5.3 percent had four or more. There were overall slightly more income earners per family for Blacks (1.76) than for whites (1.67). By 1977, both Black and white families had dropped in size (3.74 persons vs. 3.25 persons). The percentage of white families having no earners increased during the decade, from 8.2 to 11.8 percent. For Black families without salaried workers, the percentage jumped about 70 percent, from 10.2 to 17.2 percent. The percentage of Black families with one only wage earner increased from 31.6 to 36.2 percent, while the figure for whites dropped, 39.5 to 31.7 percent. The percentage of Black families with two or more earners decreased, 58.2 to 46.6 percent, whereas the whites' percentage increased 52.3 to 56.5 percent. Only 3.8 percent of all Black families had four or more income earners by 1978. Most significantly, the ratio of persons to earners per family had remained roughly the same for Blacks, while the ratio declined for whites. These figures imply that the recessions of 1969-70 and 1973-75 forced at least 550,000 Black workers permanently out of the job market; that Black families who depended upon a second or third job to maintain their homes lost the opportunity to acquire employment; and that whites took the places of Blacks in most of these jobs.
Unemployment statistics provide another key in explaining the steady deterioration of Black economic life. In 1961 the official rate of unemployment for nonwhites and whites in the U.S. was 12.4 and 6.0 percent respectively. In the mid-1960s, nonwhite unemployment dropped sharply for several reasons: the continued relocation of rural Blacks to the North and West, where more jobs at higher wages were then available; the collapse of legal segregation; the Federal government's implementation of affirmative action guidelines which made jobs available to previously qualified Blacks; and a generally expanding capitalist economy. By 1969 nonwhite unemployment was 6.4 percent, and the rate for nonwhite married men who lived with a spouse declined from 7.9 percent in 1962 to only 2.5 percent in seven years. The crisis of U.S. capitalism in the 1970s contracted the number of available jobs in the labor market, with Black workers usually the first to be dismissed. In 1972 nonwhite unemployment reached 10 percent, and by 1975 the figure was almost 14 percent. (See Table VII) Nonwhite married men in 1975 had an unemployment rate of 8.3 percent, 170 percent higher than that for white married males. In 1975, 33 percent of all unemployed nonwhites were out of work for 15 weeks or more; 16 percent were jobless for more than half the year. Blacks below the poverty level were particularly victimized. Only 1.6 million of 4.7 million poor Blacks were able to work during 1978. Of this number, less than 950,000 were employed full-time. 508,000 of the employed Black poor held jobs for 26 weeks or less, and 689,000 more could only obtain part-time work. Hardest hit were poor, young Black men and women between 16 and 21 years of age. The mean number of weeks worked in 1978 for this group was a meager 17.2 weeks.
As the crisis of the capitalist economy became more severe, the rules for those unemployed workers, Black and white, to receive compensation became more restrictive. During the recession of 1973-1975, at least three-fourths of the unemployed received some sort of compensation. Workers losing their jobs because of foreign capital's growing shares of the U.S. consumer market were awarded a substantial share of their former wages for up to 18 months, with the passage of the Trade Adjustment Assistance Program. As late as December, 1980, almost one-quarter of a million unemployed workers obtained funds through the program; by December, 1981, only 12,100 were allowed to collect benefits. By the beginning of 1982, only 37 percent of the jobless were receiving any kind of compensation. Officially, Black overall unemployment reached 17.4 percent in late 1981, a percentage which does not even include those whom the Federal government calls "discouraged workers"—unemployed persons who have not looked for work actively for four weeks. Conservatively, the real rate of Black unemployment in the U.S. in the early 1980s easily exceeded 20 percent, and might surpass 30 percent under certain economic conditions. In many ghetto communities, Black youth unemployment surpassed 80 percent.
The pain of unemployment is magnified still further by the growing personal indebtedness that traps the Black poor. Black families below the poverty level had a median income deficit of $2,261 in 1978, compared to a median income deficit of $1,753 for poor white families. 261,000 Black families owed $3,000-$3,999. 146,000 were in debt between $4,000-$4,999; and 182,000 were behind by $5,000 or more. For Black families with related children under 18 years of age in 1978, the median income deficit was $3,781. Black families with female householders were behind by $2,440. 215,000 of these families owed $3,000-$3,999; 262,000 more female-headed households were in debt by at least $4,000.
Summarizing these statistics, one obtains at best a limited insight into the nature of Black poverty in the United States. To grasp the fact that the median annual income of a Black family consisting of one female adult and two children under 18 years of age who are below the poverty level is $3,260 does not and cannot tell us how she struggles every day to survive. Statistics report that 10,000 Black families in the U.S. that include a female householder, no husband, and three small children, reported no cash income in 1978. Beyond Aid to Families with Dependent Children, and beyond food stamps, how did these 10,000 impoverished Black families purchase school books, new clothing, shoes and other necessities? Did they have the luxury of going to the cinema on a Saturday afternoon, or jumping into the family automobile to take a leisurely ride down to the beach on a warm summer day? How did they cope when a sudden health problem struck one of the children in their family? What is the possibility of them ever overcoming their massive personal debt, and escaping the harassment of creditors and finance officers? Statistics cannot relate the human face of economic misery.
II
Oppressed people learn strategies—for survival: if they do not learn, they perish. The profile above indicates that in 1978 only 10.8 million out of 18.1 million Black persons over 14 years of age could find employment. What do several millions of these workers—the 2.2 million persons who have only found part-time jobs, and the 412,000 Black workers who are unemployed for more than 26 weeks during the year—do to survive? How do the other 7.3 million Black adults provide food, clothing, shelter, medical care and some measure of security to their families in the age of Reaganomics and racism? At the highest level of underdevelopment, the daily life of the Black poor becomes a continuous problematic, an unresolved set of dilemmas which confront each person at the most elementary core of their existence. The patterns of degradation are almost unrelenting, and thrust upon every individual and family a series of unavoidable choices which tend to dehumanize and destroy many of their efforts to create social stability or collective political integrity.
In recent decades, sociologists have described this growing social stratum as an "underclass" or "ghetto-class." Perhaps the best example of the literature on the subject was written by Douglas G. Glasgow, professor of social welfare at Howard University. Glasgow's Black Underclass examines the innercity Black youth of Los Angeles, from the Watts race uprising of 1965 to the late 1970s. Theoretically, he locates the center of Black unrest in the volatile group of 18- to 34-year-olds who were unified by "their common condition":
They were jobless and lacked salable skills and opportunities to get them; they had been rejected and labeled as social problems by the police, the schools, the employment and welfare agencies, they were victims of the new camouflaged racism.
Detached from the broader white society, even largely from the seemingly complacent working Blacks around them, they drank, gambled, fought a little, but mostly just generally 'hung out.' . . . They try to keep body and soul together and maintain a job, but they remain immobile, part of the static poor. Others who could make this adaptation fail to do so, often prefering to remain unemployed rather than accept a job that demands their involvement for the greater part of each day but provides only the barest minimum of financial reward. They seek other options for economic survival ranging from private entrepreneurial schemes to working the welfare system. Hustling, quasi-legitimate schemes, and outright deviant activity are also alternatives to work.
Glasgow separates the Black "underclass" from lower income Blacks by several rough social criteria: an absence of generational socioeconomic upward mobility, the "lack of real opportunities to succeed," and widespread "anger and despair" which "arises from contact with mainstream institutions, which, almost imperceptibly and very impersonally, reject them." The author also believes that "racism is probably the most basic cause of the underclass condition."
Conceptually, there are some problems inherent with the term "underclass." Using Glasgow's criteria, literally millions of Black Americans would have to be included with the underclass, since as I have illustrated previously, they have absolutely no meaningful prospects for future work. Glasgow emphasizes the subjective and superstructural factors related to underclass status—lack of decent education, widespread alienation from white civil order and society, the disintegration of stability within family life, and so forth. But these factors in and of themselves do not make this massive stratum a "class" in a real and decisive sense. These "subproletarians" include both marginal elements of the working class as well as those of whom Marxists have traditionally termed the lumpenproletariat: pimps and prostitutes, small-time criminals, drug dealers and "numbers" runners. The "work" that these elements perform is defined by capitalist society as illegal, but the profits it returns for a few ghetto entrepreneurs can be monumental. Moreover, the question of class must address the issue of consciousness. A class that is neither "self-conscious" nor acts collectively according to its material interests, is not worthy of the name. The general philosophy of the typical ghetto hustler is not collective, but profoundly individualistic. The goal of illegal work is to "make it for oneself," not for others. The means for making it comes at the expense of elderly Blacks, young Black women with children, youths and lower-income families who live at the bottom of working class hierarchy. The consciousness of the subproletariat is not so much that of a "class," but the sum total of destructive experiences that are conditioned by structural unemployment, the lack of meaningful participation within political or civil society, the dependency fostered by welfare agencies over two or three generations, functional illiteracy and the lack of marketable skills.
The pimp is one typical representative of innercity underdevelopment within the subproletariat, the personification of the individualistic hustler. He accumulates petty capital by brutalizing young women, who sell their sexuality on the open market to (usually white middle class male) "consumers." Methods of "labor discipline" invariably include naked force—rape, threats, physical and psychological assaults. Women who are coerced or who accept these crude terms of "employment" are expected to deliver a certain number of tricks with "Johns" per hour, day and week. Police in the ghetto are usually an integral part of the trade, and expect a regular cut from the women's profits for tolerating the traffic in their precincts. Local Black and white entrepreneurs in the inner-city motel and hotel business find room to expand and even to survive by orienting services to accommodate prostitution. The profits are also used to underwrite other illicit activities, from the ghetto's omnipresent drug traffic in elementary and secondary schools to small-time fencing operations.
Black women with young dependents are invariably touched by the process of lumpenization. A very small percentage may be forced at some point into prostitution simply to put food on the table for their children. Many more, however, supplement their inadequate incomes by a variety of illegal acts which carry relatively low levels of risk. "Boosting" or stealing clothing, shoes, small appliances and food from retail stores has become a regular and common occurence. Many poor people who maintain a high degree of public morality, and who actively participate in their churches, find little to no difficulty purchasing clothing, television sets, stereos, washing machines and even automobiles that they know are stolen. Children even below the age of twelve sometimes become numbers runners, or participate in marginal ways in the drug traffic. Teenagers who become skilled in drug transactions can accumulate literally thousands of dollars per month, and annual gross incomes above $20,000 for some high school students are not rare in major cities. In some urban Black communities, and especially in Chicago, over one-fourth of all Black youth between the ages of 14 to 25 belong to gangs, which often deal in small robberies, drugs and prostitution. A great many youth participate in gangs simply to survive daily life in urban high schools. Gang membership usually has little social stigma, and carries with it a limited guarantee of safety and security in their neighborhoods. The death of a gang member, the murder of a high school student during classes, or the random arrest of a young Black man by the police, are all integral factors of daily life. What is sad about the proliferating incidents of violence within the urban Black community's permanent reserve army of labor is that no one is surprised any more.
Substantial elements of the Black elite do not discuss the unique problems of the "underclass," either with whites or among themselves, because in doing so they would be forced to confront the common realities of racism that underlie the totality of America's social and economic order. They often do not like to be reminded that former friends and family members are on welfare, that their nieces may be prostitutes, or that their cousins peddle drugs, stolen fur coats and designer jeans. Even the expressions of popular culture among the Black ghetto poor are not seen as having any direct relationship to the Negro upper crust's aesthetics. In Certain People: America's Black Elite, author Stephen Birmingham recounts the acute embarrassment of one Black upper class matron from Washington, D.C. at the sight of a Black young man donning "Super Fly" pimp-type attire. "'Disgusting', she whispered. 'There is the cause of all our problems'. Her friend, more perceptive, said, 'No, that is the result of all our problems.'" Many Blacks who advanced into highly paid positions in the corporate world intensely dislike the mass cultural expressions of the Black poor and working classes, and refrain from any social relations with Blacks who rely on "transfer payments" to make ends meet. For several generations, the Black elite of Harlem's "Strivers' Row" effectively created a cordon sanitaire around their neighborhood to protect themselves and their property from contact with the Black "underclass." As late as the mid-1970s, the Strivers' Row's "two block associations (had) rigid rules which (were) rigidly enforced: no trash or litter thrown in streets; keep hedges uniformly clipped; keep brasswork polished; no children playing in the streets; no peddlers or solicitors; beautify gardens and window boxes." When well-heeled residents contemplated the plight of their distant relatives or neighbors outside Strivers' Row, the nearly universal attitude was one of contempt. The Black poor were characterized repeatedly as "lazy, shiftless, and no good." In employing low income Blacks as occasional domestic workers, the Negro elite can be every bit as paternalistic as the white ruling class. "One thing that can be said for the black upper class," one affluent Negro lady informed Birmingham, "is that we're always nice to our servants."
A central focus of subproletarian life is fear. Black elderly and handicapped persons are afraid to walk or visit friends in their own neighborhoods at night or travel on public transportation because they are convinced (with good reason) that they will be assaulted. Young Black women are often uncomfortable going to parties or social gatherings by themselves because they will invariably be harassed by Black men and even male youngsters barely into puberty. Parents who live in innercities are reluctant to send their children several blocks to attend school or to play outside after dark because they are afraid they might be harmed. Black-on-Black crime usually victimizes the working and poor, but it can paralyze virtually all Black people of whatever social class or neighborhood. It produces for capitalism and the state a deep despair, a destructive suspicion we hold against each other. It thwarts Blacks' ability to achieve collective class consciousness, to build political agencies which advance our material and cultural interests, and develop ourselves economically. It forces Black inner-city merchants to strap revolvers on their calves or shoulders, while serving poor patrons behind plexiglass shields. It stops Black doctors from making emergency calls to their patients who live in the midst of a tenement slum or ghetto highrise complex. It instills a subconscious apathy toward the political and economic hierarchy, and fosters the nihilistic conviction that nothing can ever be changed in the interests of the Black masses.
The permanent reserve army of Black workers, subproletarians or the "underclass," is the latest social culmination of the process of Black ghettoization, economic exploitation and urban decay. In one sense, it represents the highest stage of Black underdevelopment, because it eliminates millions of Blacks from belonging to working class organizations. The existence of a massive "ghettoclass" disrupts the internal functions of the mostly working class Black community, turning Blacks in blue collar jobs against those who have never had any job. The social institutions created by working class Blacks to preserve a sense of collective humanity, culture and decency within the narrow confines of the inner city are eroded and eventually overturned. Subproletarianization and the extension of permanent penury to broad segments of the Black majority provoke the disruption of Black families; increase the number of Black-on-Black murders, rapes, suicides and assaults; and make terror a way of life for all Blacks of every class background who live in or near the innercity.
CHAPTER THREE
GROUNDINGS WITH MY SISTERS: PATRIARCHY AND THE EXPLOITATION OF BLACK WOMEN
ain't I a woman? Look at me! Look at my arm! . . . I have plowed, and planted, and gathered into barns, and no man could head me—and ain't I a woman? I could work as much as any man (when I could get it), and bear de lash as well—and ain't I a woman? I have borne five children and seen 'em mos all sold off into slavery, and when I cried out with a mother's grief, none but Jesus hear—and ain't I a woman?
—Sojourner Truth, 1852
We are the slaves of slaves; we are exploited more ruthlessly than men.
—Lucy Parsons, 1905
I
The first two chapters of this book, which explore the history of the Black working class and subproletariat, do not examine in any great detail the largest single group within Afro-America—Black women. As noted earlier, Black women comprise a significant minority within the Black laboring population, and have for many years experienced higher rates of unemployment than their male counterparts. (See Table IV) Over one-third of all Black women are officially classified as "poor" by the Federal government. This economic profile graphically illustrates the effects of patriarchy, racism and capitalist exploitation. But it does not begin to present the unique dimensions of the Black woman's historical experience.
Black social history, as it has been written to date, has been profoundly patriarchal. The sexist critical framework of American white history has been accepted by Black male scholars; the reconstruction of our past, the reclamation of our history from the ruins, has been an enterprise wherein women have been too long segregated. Obligatory references are generally made to those "outstanding sisters" who gave some special contribution to the liberation of the "Black man." Even these token footnotes probably do more harm than good, because they reinforce the false belief that the most oppressed victim of white racial tyranny has been the Black man. It is true, as chapter four will cite, that the numerical majority of those Blacks who have been lynched, executed and forced to work in penal institutions have been males. But these numbers ignore a critical reality of racism and capitalist development. From the dawn of the slave trade until today, U.S. capitalism was both racist and deeply sexist. The superexploitation of Black women became a permanent feature in American social and economic life, because sisters were assaulted simultaneously as workers, as Blacks, and as women. This triple oppression escaped Black males entirely. To understand the history of all Blacks within the Black majority, the "domestic Black periphery," special emphasis is required in documenting the particular struggles, ideals and attitudes of Black women. To do less would be to reinforce capitalist patriarchy's ideological hegemony over the future struggles of all Black working people. Black male liberationists must relearn their own history, by grounding themselves in the wisdom of their sisters.
II
During the entire slave period in the U.S. a brutal kind of equality was thrust upon both sexes. This process was dictated by the conditions of slave production within the overall process of capital accumulation in the South. Black women working in the fields on rice, sugar and cotton plantations were expected to labor at least twelve hours a day without complaint, breaking their backs just like their sons, husbands and fathers. Angela Davis has recognized that "the slave system could not confer upon the Black man the appearance of a privileged position vis-à-vis the Black woman." Since slavery itself was authoritarianism in the extreme, with the white slaveowner exercising physical violence to maintain political hegemony, no "family provider" or Black patriarch could be allowed. "The attainment of slavery's intrinsic goals was contingent upon the fullest and most brutal utilization of the productive capacities of every man, woman and child. The Black woman was therefore wholly integrated into the productive force."
It must be remembered that the Afro-American slave was chattel: a thing, a privately owned commodity. Some slave masters tolerated the marriages of Blacks on their own farms or on their white neighbors' property to marry each other. But even the most "humane" master, when confronted with the inevitable economic declines that are a permanent feature of capitalism, would disrupt Black families by selling off a spouse or several children. "Here and there one can find sufficient respect for basic human rights or ample sentimentality to prevent the separation of families," John Hope Franklin indicates, "but it was not always good business to keep families together." Black women were sold separately to bring a more competitive price on the open market. Children over the age of fourteen were viewed as prime field hands, and were routinely taken from their mothers and fathers. Historians disagree on the precise number of families that were divided during slavery. One fair estimate is provided by Herbert Gutman, who describes the intersectional sale of slaves as "one of the great forced migrations in world history." 835,000 Afro-Americans were moved from the Upper South to Lower South between 1790 and 1860. Most of these persons were transported in the decades immediately before the Civil War, 575,000 slaves between 1830 and 1860. No fewer than one million Blacks were sold from 1820 to 1860, roughly one percent of the total slave population every year. Estimates of the number of Black women who were sold and thereby separated from their children, parents or husbands are, of course, difficult to assess. Gutman's work indicates that anywhere from 35 to 71 percent of marriage-age Black women who were sold in the interregional slave trade were involuntarily separated from their husbands. The public sale of young Black girls above the age of 12 who were bought to satisfy the sexual needs of white racist males was notorious. A few slavers even specialized in selling Black children between the ages of 8 to 12.
One decisive form of oppression which befell the Black woman was slave breeding. Here again, the overwhelming majority of white male historians insist that either slave breeding did not exist or that it was rarely attempted by white planters. Usually this volatile term is employed narrowly to describe owner-coerced matings, where little actual documentation exists. However, the concept of slave breeding should be extended to mean all and any forms of slavery which, in Kenneth Stampp's definition, "indicate that slaves were reared with an eye to their marketability." Massive evidence exists illustrating that "many masters counted the fecundity of Negro women as an economic asset and encouraged them to bear children as rapidly as possible. Masters who prized prolific Negro women not only tolerated but sometimes came close to promoting sexual promiscuity among them." Some white owners voided Blacks' marriages if they suspected that the men or women were sterile. In their own literature, Southern whites were absolutely candid about the centrality of slave breeding to the accumulation of profits. One Mississippian declared that fecund slave women "are the most profitable to their owners of any others. . . It is remarkable the number of slaves which may be raised from one woman in the course of forty or fifty years with the proper kind of attention." Nearly every Black woman interviewed by Fannie Kemble in her 1838-1839 journal on slavery had a number of children. One woman under thirty had borne ten children and had subsequently developed a "nervous disorder, brought on by frequent childbearing." Venus, a mulatto slave "terribly crippled with rhematism," had "eleven children, five of whom had died, and two miscarriages." U. B. Phillips observed that "one phenomenal slave mother born forty-one children, mostly of course as twins; and the records of many others ran well above a dozen each." One ingenious master, James Hammond of South Carolina, gave each of his Black slave mothers "a muslin or calico frock—but only when her newborn infant was thirteen months old." Another ordered that any Black "women with six children alive at any one time are allowed all Saturday to themselves."
Many masters did not wait for the slaves themselves to reproduce in sufficient numbers, and took matters into their own hands. As property, Black women were expected to produce wealth for their owners. But as females, Black women were also constantly subjected to the physical and sexual assault of white males. As Angela Davis observed, "the integration of rape (into slavery) harks back to the feudal 'right of the first night,' the jus primae noctis. The feudal lord manifested and reinforced his authority to have sexual intercourse with all the females." In the context of American slavery, in the United States and elsewhere, the white man sought to reduce Black women to the lowest level of biological being. "The act of copulation, reduced by the white man to an animal-like act, would be symbolic of the effort to conquer the resistance the Black woman could unloose." White American historians have usually been extremely reluctant to discuss this "normal" and universal aspect of any slave order. Brazilian sociologist Gilbert Freyre discussed the issue frankly with the initial observation that "there is no slavery without sexual depravity. Depravity is the essence of such a regime." Freyre noted that "one favorite saying of the planters was: 'The most productive feature of slave property is the generative belly.'" Brazilian whites had a casual attitude toward syphilis and gonorrhea and had no reservations about spreading their affliction into Black households. From the age of thirteen, the white boy "was subject to ridicule for not having had carnal knowledge of a woman and would be the butt of jests if he could not show the scars of syphilis on his body." Many older white men believed that the only method to cure themselves of gonorrhea was to have intercourse with a young Black virgin—"the surest means of extinguishing it in oneself." Black women who wet-nursed white infants who were already infected by their parents "thus convey(ed) from the Big House to the slave hut the blight of syphilis. It killed, blinded, deformed at will." Sadism and masochism were also an organic aspect of race relations, sometimes involving even small Black boys as well as females. Freyre noted that "the white lad was often initiated into the mysteries of "physical love" through sexual games of submission wherein Black youths were forced to "take a drubbing."
White males who settled the United States lacked the cultural and historic relations which characterize the evolution of Portuguese and Spanish slave societies vis-à-vis Africans. Their racism was more aggressive; their neurotic fantasies were more repressively checked by the religious heritage of Calvinism and Puritanism; their knowledge of Black culture was more limited; their desire for profits, greater. For the white male American, the Black women's vagina was his private property. Like his cotton fields, the fruit of its issue belonged to him alone. His half-white child by the Black woman was usually treated just like any other slave. Raping the Black woman was not unlike plowing up fertile ground; the realities of plantation labor descended into the beds of the slaves' quarters, where the violent ritual of rape paralleled the harsh political realities of slave agricultural production. As Davis noted:
In its political contours, the rape of the Black woman was not exclusively an attack upon her. Indirectly, its target was also the slave community as a whole.
In launching the sexual war on the woman, the master could not only assert his sovereignty over a critically important figure of the slave community, he would also be aiming a blow against the Black man . . . Clearly the master hoped that once the Black man was struck by his manifest inability to rescue his women from sexual assaults of the master, he would begin to experience deep-seated doubts about his ability to resist at all.
Many Black women fought these repeated sexual assaults, and an untold number sacrificed their lives to retain their humanity. Many more carried the scars of their rapes, both physical and psychological, with them for the rest of their lives. The children of such coerced owner-slave unions, and the omnipresence of white rape, is indicated in part by the swelling number of mulattoes in the South before the Civil War. By 1850 there were 245,000 mulatto slaves; by 1860, 411,000 mulattoes out of an enslaved Black population of 3,900,000.
For Black women, and their men, the only means to maintain their inner strength and integrity was through resistance. Black resistance assumed, first, the form of conscious, voluntary day-to-day protest: the destruction of agricultural implements, burning crops, stealing whites' personal food and property, deliberate slow-downs in the fields, and so forth. A number of Black women, far more than most Black historians have appreciated, ran away from their plantations or farms in search of freedom. Between 1736 and 1801 in Virginia alone, there were 141 documented instances of runaway African women. There was Hannah, a young woman of 19, "who when angered flashed a 'very passionate temper'"; Sarah, a "small and courageous girl of 14" who insisted in calling herself Mindingo; Milly, described by her owner as having grey eyes, "very large Breasts," and noted for being "a sly, subtle Wench, and a great Lyar." Cicley's master warned, "Beware to secure her Well, for she is very wicked and full of flattery." Only fifteen of the 141 women ran off in the company of slave men—a piece of evidence that indicates remarkable self-reliance in a patriarchal society. Yet many white owners, blinded by their entrenched sexism, could not contemplate that Black women by themselves would thirst for liberation. In 1772, a typical master lamented about one African woman who departed with her husband, "I imagine she is entirely governed by him."
The greatest indictment against slavery and white Southern patriarchy came from the voices of Black women. Jane Blake's Memoirs, written in 1897, provides all the evidence one needs to illustrate that slave breeding existed. Many slave women refused to have sex with men they did not love, and fought the sexual advances of their white owners. Blake wrote, if "all the bond women had been of the same mind, how soon the institution could have vanished from the earth, and all the misery belonging to it." Jane Brown's Narrative of 1856 asserted that virtually every slave longed for freedom, and that both freed and enslaved Blacks covertly discussed rebellion. Louisa Picquet was forced to become a concubine for white men. In her 1861 narrative, Inside Views of Southern Domestic Life, she argued that sexual exploitation of Black women constituted the core of white Southern hypocrisy. She observed that U.S. whites oppose the "heathenism of a Turkish harem. (But) is all this whit worse than what is constantly practiced, with scarce a word of unfavorable comment, in our Christian land? Our chivalrous 'southern gentlemen' beget thousands of slaves; and hundreds of children of our free white citizens are sold in the southern slave markets every year." When the moment of freedom arrived, Black women understood better than anyone else the ancien regime of rape and labor exploitation was at an end. The story of one young Black woman named Caroline Gordon, or "Caddy," bears witness:
Caddy had been sold to a man in Goodman, Mississippi. It was terrible to be sold in Mississippi. In fact, it was terrible to be sold anywhere. She had been put to work in the fields for running away again. She was hoeing a crop when she heard that General Lee surrendered . . . that meant that all the colored people were free! Caddy threw down that hoe, she marched herself up to the big house, then, she looked around and found the mistress. She went over to the mistress, she flipped up her dress and told the white woman to do something. She said it mean and ugly: Kiss my ass!"
III
From the very beginning of Black political activism in the United States, Afro-American men had real difficulty in considering the "triple oppression" (race/class/sex) of Black women with any degree of seriousness. Part of the problem stemmed from the evolution of patriarchal institutions within Black civil society. Black churches in the free states were involved in a variety of reform activities, from the creation of economic enterprises to the building of a network of Black schools. But these churches were invariably dominated by Black men, who served as pastors, evangelists and deacons. Black mutual benefit societies, first started in Newport, Rhode Island and Philadelphia, gave members recreational facilities, provided families with modest economic protection in case of sickness or death, and created the foundations for Black business development. Yet the major societies were funded, directed and controlled by Black males. The Black newspapers established in the nineteenth century, including John Russwurm's Freedom's Journal (1827), Martin Delany's Mystery (1843), Frederick Douglass' North Star (1848) and the Anglo-African of New York City (1859), tended to print the antislavery speeches, manifestos and essays of articulate Black men. The Negro Convention Movement, a series of Black political conferences beginning in 1830 in Philadelphia, almost always involved only Black men.
Many Black male activists identified the cause of Black liberation with the ultimate attainment of "Black manhood." This definition of freedom was a conditioned response evoked by white patriarchy, whether the Black men of the period recognized this or not. Henry Highland Garnet's famous "Address to the Slaves of the United States," delivered at the 1843 Negro Convention specifically called upon every Black "man" to "resist aggression." "In every man's mind the good seeds of liberty are planted, and he who brings his fellow down so long, as to make him contented with a condition of slavery, commits the highest crime against God and man." Garnet's audience was reminded of the racists' transgressions upon its manhood:
See your sons murdered, and your wives, mothers and sisters doomed to prostitution. . . And worse than all, you tamely submit while your lords tear your wives from your embraces and defile them before your eyes. In the name of God, we ask, are you men? Where is the blood of your fathers? Has it all run out of your veins?
Radical newspaper editor T. Thomas Fortune condemned whites as "the most consummate masters of hypocrisy, of roguery, of insolence, and of cowardice" in an 1887 polemic. Fortune was quick to add, however, that "many imagine that we are compelled to submit and have not the manhood necessary to resent such conduct. We shall labor as one man to wage relentless opposition to all men who would degrade our manhood." Pan-African scholar and clergyman Alexander Crummell reminded Blacks that the chief aim of civilization was the creation "of a true and lofty race of men. For manhood is the most majestic thing in God's creation." Even Frederick Douglass, the leading male proponent of women's rights in the nineteenth century, asserted in 1855 that the struggle for racial liberation meant that Blacks "must develop their manhood, and not be too modest to attempt such development."
Douglass was exceptional among all Black male activists in his open commitment to equality for women. Soon after his flight to freedom in the North, he identified himself with militant white and Black women in their struggle for suffrage and legal rights. In the initial issue of the North Star , he drew the obvious political parallels between the battles against racism and sexism, declaring that "Right is of no sex." He attended the first national women's rights convention held at Seneca Falls, New York, in July, 1848, and seconded the motion of Elizabeth Cady Stanton calling for women's voting rights. Douglass was the only male of thirty-seven men in attendance who supported women's suffrage. Douglass' advocacy for feminist causes was so well-known that both Stanton and Lucretia Mott urged women to elect him as a leader of their movement only two weeks after Seneca Falls. Susan B. Anthony notified friends to purchase the North Star "for announcements of women's rights gatherings." Douglass' partial break with white feminists occurred after the Civil War, when Anthony, Stanton and others opposed the ratification of the Fifteenth Amendment unless it also mandated universal suffrage. Politically pragmatic, Douglass urged his followers to support the winning of Black male voting rights first. By 1869, the Equal Rights Association split, and many white feminists began to gravitate toward racist slogans to support their own cause.
The struggle to destroy slavery, and the economic and political battles of Reconstruction, coincided with the entrenchment of patriarchal relations within the Black community. The rough equality of labor imposed by the brutalities of the slave regime did not extend into the slaves' quarters. Black men universally "regarded tasks like cooking, sewing, nursing, and even minor farm labor as woman's work," according to bell hooks. Black women after slavery seldom demanded social equality between themselves and their men. "Instead, they bitterly resented that they were not considered 'women' by the dominant culture. . ." With the establishment of sharecropping, the majority of Black women farm laborers and farmers ceased work in the fields, and retreated into the kitchens and homes of their families. They expected, as a point of honor and as an element of freedom, that they would be supported by their husbands, fathers and brothers. "White plantation owners were shocked when large numbers of Black female workers refused to work in the fields." Statistically this is illustrated by Census figures from 1890. Slightly less than half of all Black women between the ages of 15 to 24 years were employed in 1890; about half were domestic workers, and the remainder were field hands or farmers. Less than 40 percent of all Black women between the ages of 25 to 64 were workers, compared to 97-98 percent of all Black males. Of course, fewer white women were gainfully employed than Black women. Only 14 percent of all white women 10 years old and over were in the 1890 workforce, and the percentage dropped to 10 percent and below after age 35. (See Table VIII) Denied the right to work outside the home, the majority of Black women were expected to fulfill the "traditional" role of "mother" by giving birth to as many children as physically possible. For Black married women born between 1861 and 1865, the average number of children born to them by 1910 was 6.2. (See Table IX)
Although the Victorian era was inhospitable to intelligent and politically active females, a number of Black women succeeded in overcoming the institutional barriers of white and Black patriarchy. Frances Ellen Watkins Harper established herself as the nineteenth century's most popular Black poet/activist. Born in Baltimore of free parents in 1824, she became involved in the Underground Railroad, the illegal network by which slaves were channelled North. In September, 1854, the Maine Anti-Slavery Society recognized her talents as an orator and hired her to speak across New England. In 1857-1858 she worked for the Pennsylvania Anti-Slavery Society, speaking two or three times each day for the cause of Black freedom, attracting "large, enthusiastic audiences." In 1860 she married a Black Ohio farmer, Fenton Harper, and retired for several years to have a child. Within five months of her husband's death in 1864, Harper was again on the lecture circuit, speaking in support of the war effort. From 1865 until 1871 Harper travelled throughout the Southern United States at her own expense, living on meager donations, speaking endlessly "at Sunday schools, day schools, churches, town meetings, in homes and village squares," usually talking twice daily. During these years she also authored several popularly acclaimed books of poetry and wrote articles for the press. In the 1870s she became Assistant Superintendent of the YMCA school in Philadelphia, and was elected national officer in the National Council of Women and the National Association of Colored Women. Until her death in 1911, Harper was a noted advocate of women's suffrage, equal rights and Black freedom.
Sojourner Truth was, probably only second to Douglass, the outstanding orator of Black liberation during the mid-century. Born as "Isabella" in Ulster County, New York in 1797, she was one of twelve slave children who were sold away from their parents. Married at an early age, she gave birth to five children before she was freed; one of her sons was sold by her owner to an Alabama slavemaster. In 1843, she began to speak out on her personal ordeal as a slave at abolitionist gatherings, and assumed the name Sojourner Truth. During the Civil War Sojourner lived and worked in the "contraband" camps of Washington, D.C., teaching former slaves. She aided Black women "to protect their children against white Maryland raiders who sought to kidnap them and sell them into slavery." Appointed to work with the Freedman's hospital in Washington, she led the struggle to bar Jim Crow public transportation in the capital. In the late 1860s, Sojourner returned to the lecture circuit, speaking out in favor of a massive relocation of Black families from the South into the Great Plains states. In her view, no Black political solution was possible without a general reallocation of land. In 1879, Sojourner joined the wave of "Exodusters" who fled the post-Reconstruction era South and settled in Kansas City. Unlike most Black male leaders, she urged her people to buy land and to develop a sufficient economic base from which to wage their various struggles for social and political justice. One of the central tragedies of this period is that so few Black politicians listened seriously to Sojourner's ideas on Black economic development. Their ingrained sexism made it impossible, perhaps, for Black men to internalize the agenda of an eighty-two-year-old Black woman.
Two of the most progressive Black activists during the post Reconstruction period of political accommodation were Ida B. Wells and Mary Church Terrell. Wells was born in 1862, in Holly Springs, Mississippi and was educated at Rust College and Fisk University. Arriving in Memphis in the early 1880s, she soon acquired the reputation as the Black South's most militant journalist. Purchasing partial ownership in the Memphis Free Speech and Headlight, she used the press in a campaign against Southern lynchings. In a controversial editorial, she observed that "Nobody in this section of the country believes the old threadbare lies that Negro men rape white women. If Southern white men are not careful they will over-reach themselves and public sentiment will have a reaction, or a conclusion will be reached which will be very damaging to the moral reputation of their women." Wells' documentary on the near genocidal violence against Blacks, United States Atrocities (1893), is a valuable precursor to the works of William Patterson and Sidney Willhelm six decades later. Mary Church Terrell was the daughter of Robert R. Church of Memphis, a Southern Black real estate millionaire and political leader. Educated at Oberlin College, she taught at Wilberforce before settling in Washington, D.C. and, in 1891, marrying Robert H. Terrell, a lawyer and the principal of the District's M. Street High School. Mary Terrell was appointed a member of the Washington, D.C. Board of Education, and quickly became a leading critic of Booker T. Washington—the Black politician whom her husband closely supported. In fact, she created such a furor that one of the Tuskegeean's hacks penned a New York Age editorial declaring bitterly that "some one ought to muzzle Mary Church Terrell. What we now want as a race, is less agitators and more constructors." Terrell joined the NAACP and was promptly elected vice president of the Washington branch. In later years, Terrell became politically quite conservative, serving as director of the Republican National Committee's campaign to reach Black women voters on the East coast in 1920 and 1932. However, despite her support for Hoover and the Republican Party, Terrell continued to fight racial discrimination and Jim Crow laws until her death.
The first half of the twentieth century produced a new generation of creative and intellectually prolific Black women in education and the arts. Jessie Redmond Fauset, born in 1886, became famous both as the translator of Black poetry from the French West Indies, and for her novels There Is Confusion (1924), Plum Bun (1929), and The Chinaberry Tree (1931). Georgia Douglass Johnson was perhaps the most popular Black poet between Paul Laurence Dunbar and the rise of the Harlem Renaissance bards of the 1920s. Novelist Nella Larsen's Quicksand (1928) and Passing (1929) examined the "innumerable social problems of young Negro women in their efforts to struggle upward both in America and in Europe." Meta Warrick Fuller became renowned as a brilliant and innovative sculptor; Laura Wheeler Waring gained fame as a painter. Actresses Ida Anderson, Edna Thomas and Laura Bowman performed to rave reviews in Harlem's all-Black Lafayette Players' group during the 1920s. Among the most creative Black minds in aesthetics during the Great Depression was unquestionably Zora Neale Hurston—cultural anthropologist, novelist, essayist and folklorist. In a brief period of twelve years she authored seven important novels. In education and politics, Black women were ably represented by Mary McLeod Bethune. Founder of Cookman College in 1905, she became a master fund raiser and proponent of higher education for young Black women. During the 1930s Bethune was named Director of the Division of Negro Affairs for the National Youth Administration. In 1945 she was one of several Blacks named as members of the United States delegation at the creation of the United Nations in April, 1945, in San Francisco.
The decades after 1900 until the 1940s also produced gradual changes within both the employment patterns of Black women and in the size of Black families. More Black women were in the labor force than there were immediately after slavery: about 47 percent during the prime working ages of 20 to 54. Roughly twice the percentage of Black women were gainfully employed in 1930 as were white women (39 percent vs. 20 percent). (See Table VIII) By 1940, Black married women averaged only 2.3 children, the lowest number ever recorded for Blacks by the U.S. Census. Most married women were waiting longer to have their children, and between 22 to 29 percent of middle aged Black women were not bearing any children at all. The number of children ever born per married Black woman was reduced during this time by 53 percent. (See Table X) Black families during World War II were still slightly larger than those of whites, but as the Black woman acquired greater opportunities for post-secondary education, the number of her children dropped sharply. In 1940, married nonwhite women with one to three years of college training averaged only 1.7 children. With four or more years of college, nonwhite women had only 1.2 children—both figures that were below those for white college trained women. (See Table XI) More frequently than ever before, Black women were leaving the kitchens and earning their own wages in the labor force. Black women appeared no longer as "auxilliaries" or marginal participants in Black educational, social and political life. The leading figures of Bethune, Terrell, Hurston and others provided abundant role models for young Black girls to abandon the yoke of subordination and sexual subservience.
During these years, among Black men, W. E.B. DuBois largely filled the role of Douglass as the chief proponent of women's equality. DuBois' commitment to women's rights began as early as 1887, when as editor of the Fisk Herald he predicted that "the Age of Woman is surely dawning." In his essays in the Crisis and other periodicals, DuBois emphasized that the struggle for Black freedom must inevitably include the demand for "the emancipation of women." Constantly he chided Blacks for exhibiting any form of favoritism toward males over females. When one reader of the Crisis reported the birth of a girl, DuBois suggested "the ancient idea that boys are intrinsically and naturally better than girls is a relic of barbarism that dies a hard death . . . Be glad it's a girl and make life wider and safer and more equal in burden for all girls because of this one." The patriarchal attitudes of politicians was a particularly favorite topic for this Black scholar. "Every statesman who yells about Children, Church and Kitchen," he declared in January, 1934, "ought to be made to bear twins, to listen to as many sermons as we have, and to wash dishes and diapers for at least ten years." In 1912 DuBois drafted a pamphlet entitled Disfranchisement, published by the National American Woman Suffrage Association, which advanced women's right to vote as a necessary precondition to the realization of democracy. In states where universal enfranchisement was on the ballot, DuBois encouraged Black men to cast their support behind the women's rights movement. "Is there a single argument for the right of men to vote, that does not apply to the votes for women, and particularly for black women?" Although he was friendly toward feminist causes, DuBois would not hesitate to criticize the racism found within the white women 's political movement. In several Crisis articles, he condemned some leaders of the "Suffering Suffragettes" who advocated that white women, and not Blacks, should be allowed to vote. Despite these differences, DuBois enthusiastically supported the moves of women from the kitchens into the factory and business world. In March, 1941, he pointed with pride that many more Black women were in the labor force than white women. In January, 1947, he urged Black husbands to "share housework" and to shoulder the burdens of child-rearing equally. For half a century, he reminded Black men that "the hope of the Negro rests on its intelligent and incorruptible womanhood."
In contrast with DuBois, however, many Black men were disturbed with the evolutionary transformation in sex roles and the creation of political, educational and economic opportunities for Black women. Marcus Garvey's political approach toward Black women's issues was a curious mixture of romanticism, sexism and race nationalism. In the 1923 edition of the Philosophy and Opinions of Marcus Garvey, the Jamaican militant suggested that women were necessary yet contradictory beings: "She makes one happy, then miserable. You are to her kind, then unkind. Constant yet inconstant. Thus we have WOMAN. No real man can do without her." Like the Black activists of the nineteenth century, Garvey identified Black struggle with the attainment of manhood, the realization of a kind of masses' macho. He warned his followers, "There is always a turning point in the destiny of every race, every nation, of all peoples and we have come now to the turning point of the Negro, where we have changed from the old cringing weakling, and transformed into full-grown men, demanding our portion as MEN." In his Blackman journal, he cautioned affluent Black women not to marry white men, and urged Black men not to "insult our womanhood" by having sexual relations with whites. Garvey was profoundly concerned with statistics that showed a declining number of children in Black households. "By a decreasing birth rate and an increasing death rate," he warned in October, 1925, "it means the death of your race—the suicide of your race." In 1934, Garvey's Universal Negro Improvement Association issued a resolution condemning birth control for Blacks. "Any attempt to interfere with the natural function of life is a rebellion against the conceived purpose of divinity in making man a part of his spiritual self," the sexist manifesto declared. "The theory of birth control . . . interfered with the course of nature and with the purpose of the God in whom we believe." Simultaneously, DuBois authored a stirring statement endorsing planned parenthood in Birth Control Review, and invited Margaret Sanger, a "birth-control pioneer," to contribute to the pages of the Crisis.
From the 1930s to the 1950s, a number of Black men raised serious questions pertaining to the declining birth rate among Black women. University of Chicago pathologist Julian Lewis argued in 1945 that "the survival of the black race in the United States was dependent upon "a high birth rate." In subsequent articles, Lewis attacked the Planned Parenthood Federation for attempting to "improve the quality of the human race at the cost of numbers." Blacks who condoned birth control were sponsoring "race suicide." Some Blacks noted with apprehension that some states had sanctioned castrations and vasectomies on prison inmates and patients in mental hospitals in the 1890s, and suggested that racists now might be using birth control as a legal means to reduce the Black population. These fears were reinforced when a Mississippi state legislator introduced a bill in 1958 which would "provide for mandatory sterilization after a woman on welfare (had) given birth to a certain number of illegitimate children." By 1964 the Mississippi house ratified a law that "stipulated that any person who became the parent of a second out-of-wedlock child would be guilty of a felony punishable by a sentence of one to three years in the state penitentiary. A subsequent conviction would be punishable by three to five years in prison. However, a convicted parent had the option of submitting to sterilization in lieu of imprisonment." White Republicans and Democrats alike, particularly in the South, proposed punitive sterilization for Black welfare mothers. These same male politicians had no reservations, however, in denying legal abortions or contraceptive information to Black (or white) teenage girls and women.
Conservative Black nationalist formations often surpassed white reactionaries in their opposition to birth control. An extreme case is provided by the Nation of Islam. Patriarch Elijah Muhammad informed Black followers that their women were unprepared for the "tricks the devils are using to instill the idea of a false birth control in their clinics and hospitals." Black women were created by God to serve their husbands and sons. "The woman is man's field to produce his nation," Elijah Muhammad observed. The Nation of Islam's ministers frequently attacked Black women and men who supported freedom of choice regarding birth control. Minister Louis Farrakhan wrote in a Black woman's publication, Essence, that "when the black woman kills her unborn child, she is murdering the advancement of her nation." One Muhammad Speaks article declared that population control was a covert tactic in the general "war against the nonwhite people." Muslim woman Shirley Hazziez wrote in Muhammad Speaks that every Black woman should reject the pill as a "deadly poison," and that "Allah was able to feed and care for black infants." Birth control was, for the Black woman, "death for my babies and race."
Well before the Civil Rights Movement, a not-so-subtle reaction began to form within Black civil society which reinforced patriarchal relations between men and women. The Depression and war years produced within the popular culture the figure of Sapphire: a Black woman who was "evil, treacherous, bitchy, stubborn, and hateful." The Sapphire stereotype was utilized by white males, who "could justify their dehumanization and sexual exploitation of black women," and by Black males, who could reasonably "claim that they could not get along with black women because they were so evil." Black patriarchal society employed Sapphire to explain away any Black woman who exhibited tendencies of strength that were designated for males only. Furthermore, as greater numbers of Black women left agricultural work for domestic service employment, many Black men leaped to the illogical conclusion that white males "favored black women over black men" in all levels of the job market. As hooks observed, "white people did not perceive black women engaging in service jobs as performing significant work that deserved adequate economic reward. They saw domestic service jobs performed by black women as being merely an extension of the 'natural' female role and considered such jobs valueless." Unemployed Black men, desperate for work, perceived their wives' ability to gain employment an assault on their own manhood. At another level, Black women who adopted patriarchal perspectives "saw the black male who did not eagerly assume the breadwinner role as selfish, lazy, and irresponsible, or in white male sociological terms, 'emasculated'." These cultural, social and economic forces combined after 1945 to produce the conditions for a fundamental reaction.
Within the U.S. economy, this reaction was apparent in civilian labor force participation rates between 1945 and 1960. During the early 1940s, tens of thousands of Black women went into jobs previously held by men. By the end of World War II, almost half of all Black women (46 percent) were employed full-time, compared to only 31 percent of all white women. Fifty-one to 53 percent of Black women between the ages of 25 and 54 were wage earners. Sixty percent of the Black women were employed as private household workers, 7 percent were blue-collar laborers, and 16 percent were farmers or farm laborers. Fifteen years later, the percentage of Black women workers outside the home had increased by only 2 percent, while white women workers increased by 6 percent. Only 22 percent of all nonwhite teenage women who were actively in the job market could find work in 1960, compared to 30 percent for white female teenagers. By 1965, Black females with an eighth-grade education or less had a labor force participation rate of only 38 percent. Black men encouraged their wives and daughters to settle back, to return to the kitchen: the role of the husband was that of provider, and the task of wives was to produce offspring. After 1945, the birth rates for Black women climbed sharply. The percentage of all Black married women between the ages of 20 and 24 years who had two to four children increased from 34 percent in 1940 to 51 percent in 1960; in that same age group, those women with five or more children grew from 2 percent to 7 percent. The percentage of all Black married women between the ages of 25 and 29 who had five or more children doubled in two decades, from 11 percent in 1940 to 22 percent in 1960. Overall the number of children born per married Black woman increased from 2.3 percent in 1940 to 2.8 percent in 1960. (See Table X) Even outside of marriage, the number of Black children born during this period increased dramatically. The rate of childbirths for nonmarried nonwhite women per thousand, for women between ages 25 and 29, increased from 32. 5 in 1940 to 171.8 in 1960. Black fertility rates, which declined from 3.56 in 1920 to 2.62 in 1940, rebounded to 3.58 in 1950 and reached 4.54 by 1960. No Black female could become a real woman, in short, unless she had a child. Work outside the home should be a secondary goal. Black unmarried teenage girls could become women by bearing children "for the race."
IV
Sudden changes in the consciousness of oppressed people are often reflected in their poetry: the sexual and racial conflicts of the 1960s provided new directions for Black Americans in the arts. Occasionally, both Black liberation and patriarchal themes were woven together by the new Black women poets. Nikki Giovanni asked all Black men and women alike to develop their "manhood":
Can you kill
Can you piss on a blond head
Can you cut if off
Can you kill . . .
Can you splatter their brains in the street
Can you lure them to bed to kill them . . .
Can we learn to kill WHITE for BLACK
Learn to kill niggers
Learn to be Black men.
In "Beautiful Black Men," written in 1968, Giovanni praised "those beautiful beautiful outasight black men with their afros . . ." Her "brand new pleasure" was observing her men "running numbers, watching for their whores, preaching in churches," and "winking at me" in their "tight tight pants that hug what I like to hug." Other Black women embraced the image of the Black man as the urban guerilla, and created love poetry that expressed simultaneously their fertility and sensuality for their men:
My old man
tells me i'm
so full of sweet
pussy he can
smell me coming.
maybe i shd
bottle it and
sell it
when he goes.
Along more traditional romantic lines, poet Alice Lovelace's "Wedding Song" informs her husband-to-be: "You are my man/The part I've sought that makes me whole . . . we'll raise bubbling black babies/swathed in black culture." Carolyn Rogers' "For Some Black Men" counsels her brothers to recognize the inherent dependency and submissiveness of sisters: "Woman is softness, warm of warmth, need from need."
Among some Black women intellectuals, there was at one point a curious inversion of the "pedestal phenomenon," the cultural dynamic wherein white males had symbolically elevated white women to the heights of aesthetic and social predominance. These sisters not only acknowledged the innate or biological leadership of Black men, but literally placed their faith, their ontological existence, within the hegemonic corpus of the Black male. Romanticists were usually the worst offenders. Poet Ann DuCille's "Lady in Waiting" combined the African mythology of the cultural nationalists with the sexist acceptance of the woman-as-womb:
In dreams without sleep
I lie inside myself
waiting to be born . . .
I am a princess
goddess of the Nile
Nubian daughter of Nefertiti . . .
unsung
yet tuned in time
to take the milk of man
between my thighs.
Other Black women poets who reflected critically about their own "integrationist contradictions" sang high hosannas to the Black militant men who had delivered them from their former political beliefs. Lucille Clifton's "apology (to the panthers)" is reminiscent of a Catholic chant, evoking one's spiritual weaknesses before the holy altar, requesting absolution for the remission of sins:
i was obedient
but brothers i thank you
for these mannish days.
. . . brothers
i thank you
i praise you
i grieve my whiteful ways.
Most Black men accepted these mea culpas in stride. "The role of the black woman in the black liberation is an important one and cannot be forgotten," Black sociologist Robert Staples wrote in 1970. "From her womb have come the revolutionary warriors of our time." Thus, the Black woman's most significant factor to contribute to the Movement, in short, was her uterus.
But behind these glowing exhultations of the Black man there remained the bitter embers of sexual oppression and subordination. Half-hidden even during Black Power's hey-day, but becoming ever more dominant into the 1970s, were the contradictory stirrings of a Black feminist criticism. Often these expressions began in the form of an attack on all "brothers" who chose to have sexual relations with white females. Sonia Sanchez's "to all brothers" is a clear warning:
yeah.
they hang you up
those grey chicks
parading their tight asses
in front of you.
Some will say out right
baby I want
to ball you
while smoother ones
will integrate your
blackness
yeah.
brother
this sister knows and waits.
And in her finest work, "Woman Poem," Giovanni illustrates the basic exploitation of Black women within a patriarchal and racist social order:
a sex object if you're pretty
and no love
or love and no sex if you're fat
get back fat black woman be a mother
grandmother strong thing but not woman
manseeker dick eater sweat getter
fuck needing love seeking woman.
Poet/playwright Ntozake Shange, author of For Colored Girls Who Have Considered Suicide When the Rainbow Is Enuf, was one of the first major writers to examine the problems of abortion, alienation between Black women and men, and the hostilities between Black women over males.
she been there for years wid this dude
but he needed a change and well, she wd manage
nothin gonna last forever/
but i hesitated cuz she seemed so fragile
i wax fulla vitality and gall
'get ridda that bitch or leave me alone'
he did.
i ignored all that talk bout the woman who tried to
burn herself alive/waznt none of my business
what some weak bitch did to herself.
The obvious contradictions relating the issues of race and gender within these and other poems were, of course, a product of the turbulent politics of the period. The Civil Rights Movement had begun coming unglued by 1964, with the successful desegregation of Southern civil society. Young Black women and men, the vanguard of freedom fighters in the Student Nonviolent Coordinating Committee (SNCC), rejected integration as "subterfuge for the maintenance of white supremacy." Black nationalism as a cultural and political expression was seized by substantial elements of the Black petty bourgeoisie and working class. Across the country, hundreds of new political and educational institutions were created that were developed within the specious theoretical framework of Black Power. Yet remarkably few Black activists elevated the question of sexism to the level of primacy, within their practical political activities or in their intellectual work. Patriarchy had been historically more compatible with most Black nationalist groupings than among cultural pluralists or even integrationists. As a result, it is not surprising that the actual practice of Black militants did precious little to overturn the rampant sexism within Black life.
The fountainhead of contemporary Black nationalism, Malcolm X, was likewise not immune from this dynamic. For many young Black militants, both in the streets and the universities, Malcolm symbolized the best that Black humanity had produced. Black actor Ossie Davis eulogized Malcolm at his funeral, declaring that he "was our manhood . . . our own black shining Prince—who didn't hesitate to die, because he loved us so." Though Malcolm's views on Black women changed considerably for the better throughout his life, like so many other male leaders, he usually thought of politics as a preserve for men only; sisters were an invaluable but secondary factor in the race war. Even today, any serious criticism of Malcolm's views is akin to traitorous behavior in most Black activist circles. But it serves Malcolm's memory poorly if we simply reify the entire body of his ideas and actions without a detailed and serious analysis of his own contradictions. As bell hooks observes, "it is impossible to read his autobiography without becoming aware of the hatred and contempt he felt toward women for much of his life." At one point in his discussions with Alex Haley, the Black novelist/journalist, Malcolm admitted that "you never can fully trust any woman":
I've got the only one I ever met whom I would trust seventy five percent. I've told her that. . . . Too many men (have been) destroyed by their wives, or their women. Whatever else a woman is, I don't care who the woman is, it starts with her being vain. I'll prove it . . . You think of the hardest-looking, meanest-acting woman you know, one of those women who never smiles. Well, every day you see that woman you look her right in the eyes and tell her 'I think you're beautiful,' and you watch what happens. The first day she may curse you out, the second day, too—but you watch, you keep on, after a while one day she's going to start smiling just as soon as you come in sight.
Malcolm X was not the only, and certainly not the worst of the Black Power leaders with respect to the issue of gender. For Stokely Carmichael, leader of SNCC in 1966, young Black men had to assert themselves as males—politically, and sexually. "Every Negro is a potential black man," Carmichael taught nascent activists. Black militants cultivated a righteous contempt for white women as a sine qua non of activist practice. When whites asked Carmichael if integration meant interracial marriage, he replied that "the white woman is not the queen of the world, she is not the Virgin Mary, she can be made like any other woman." The revolutionary responsibilities of sisters in the cause of Black liberation were somewhat different. In a speech given at Morgan State on January 28, 1967, Carmichael outlined his thoughts on Black women:
Girls, are you ready? Obviously it is your responsibility to begin to define the criteria for black people concerning their beauty. You are running around with your Nadinola cream. The black campuses of this country are becoming infested with wigs and Mustangs and you are to blame for it. You are to blame for it. What is your responsibility to your fellow black brothers? So that you can become a social worker or so that you can kick down a door in the middle of the night to look for a pair of shoes? Is that what you come to college for? . . . Is it so that you can just get over? Do you not know that your black mothers scrubbed floors so you can get here—and the minute you get out, you turn your back on them?
Like the Garveyites, many later-day nationalists vigorously opposed contraceptives, abortions and planned parenthood measures. In 1970, Brenda Hyson, a female leader of the Black Panthers, attacked a New York state law which made legal abortions available to Black and poor women. The "oppressive ruling class will use this law to kill off Blacks and other opposed people before they are born," Hyson warned. Voluntary abortions would lead to forced sterilization. Black women had a political responsibility to oppose "legalized murder" and forced "family planning in the guise of pills and coils." The Black News, a nationalist publication based in Brooklyn, described birth control for sisters as "deceptive genocide" in one 1971 essay. Black women were too frequently "duped into having unnecessary hysterectomies and surgical sterilization." For the survival of "the Black man," Black women would have to put away all forms of contraceptives—even the traditional and most unreliable device, the condom. "The hidden meaning of the Trojan," Black News declared, "was to emasculate the Black man by convincing him that he should throw away his living sperm into the white man's rubber contraption rather than to put it into his woman's fertile womb." Haki Madhubuti, director of Chicago's Black Nationalist Institute of Positive Studies, argued that "the entire white system is geared toward the total destruction of the Black man first—mentally, physically and spiritually. If the Black man is not allowed to take care of and build his family, where is the Black woman?" Zero population growth campaigns and liberal abortion laws would destroy the Black race.
No single Black activist was more profoundly sexist that the celebrated ex-convict/writer of the Black Panther Party, Eldridge Cleaver. His infamous and bizarre expositions against Black women, gays, and others need no recounting here. What is most important about Cleaver's writing is that it falls squarely into the century-old tradition of viewing Black liberation first and last as the effort to assert one's manhood, in the sense of patriarchal hegemony exhibited by the old planter class. In a pathetic passage, Cleaver contemplates the impact of white racism upon the Black male:
Across the naked abyss of negated masculinity, of four hundred years minus my Balls, we face each other today, my Queen. I feel a deep, terrifying hurt, the pain of humiliation of the vanquished warrior. For four hundred years I have been unable to look squarely into your eyes . . . Instead of inciting the slaves to rebellion with eloquent oratory, I soothed their hurt and eloquently sang the Blues! Instead of hurling my life with contempt into the face of my Tormentor, I shed your precious blood! My spirit was unwilling and my flesh was weak. . . . Divested of my Balls, (I) walked the earth with my mind locked in Cold Storage. I would kill a black man or woman quicker than I'd smash a fly, while for the white man I would pick a thousand pounds of cotton a day."
From this standpoint, the white master had succeeded in erecting a barrier between all Black men and women. Cleaver's conclusion was to mimic the worst features of white patriarchy. "We shall have our manhood," he vowed. "We shall have it or the earth will be leveled by our attempts to gain it." This struggle for freedom did not involve Black women, since by their gender, they already possessed what Cleaver dubbed "pussy power."
Robert Staples merits special commentary at this juncture, for few Black sociologists writing about the Black woman have been more consistently wrong than he has. Writing on the "Mystique of Black Sexuality" in 1967, Staples gave his views on the "guilt-free attitude towards the sex act" among sisters. In a totally bankrupt interpretation of slavery historiography, Staples insisted first that "the women of Africa were brought to this country to service the lust of the white master class." Black men were unable to shield their women from "the carnal desires" of white males. Because virtually every Black woman experienced rape, "the worth of virginity" lost all its value. "What good was it to value something one was not allowed to have?" Staples reasoned. "As a consequence the deeply rooted feelings of guilt about sex never became entrenched in the psyche of Black women as they did in her white counterpart . . . Black women receive more satisfaction in marriage and are more aggressive partners during coitus than white women." Ergo, the collective rapes of Black women were, in retrospect, a liberating force which allowed sisters to "at least salvage the spirit of eros for their own." Black women were judged to have become slightly too aggressive, by Staples, as a result.
Further reflecting on the Black woman in a later publication, Staples writes: "Many black females assume that a male with an athletic build possesses large sex organs, which will guarantee them sexual pleasure." The term Staples employed to describe this process is surely a classic in the history of Black sociology: "the masculinization of female mate selection standards." "For those of us who are not built like athletes," he admitted, "this is a most disheartening trend." Describing the social phenomenon of "tipping out," or Black extramarital sex, the Black sociologist's fear of cuckoldry is plainly visible:
The independence of the black female leads her to sexual dalliance whenever things do not go right or she feels the desire to 'make it' with another male. This practice has become quasi-institutionalized . . . Sexual dalliance must, however, be discreet so as not to damage the male ego. It is most common among black females attending college some miles away from their boyfriends and in the lower class.
Regrettably, the historical legacy of racial and sexual oppression has also led some Black women to defend patriarchal definitions of manhood. In her 1968 essay in the Liberator, Black writer Gail Stokes denounced all Black men who were unable or unwilling to assume the role of provider and family patriarch. Stokes equated manhood with the economic function of "bringing home the bacon":
Of course you will say, "How can I love you and want to be with you when I come home and you're looking like a slob? Why, white women never open the door for their husbands the way you black bitches do." I should guess not, you ignorant man. Why should they be in such a state when they've got maids like me to do everything for them? There is no screaming at the kids for her, no standing over the hot stove; everything is done for her, and whether her man loves her or not, he provides . . . provides . . . do you hear that, nigger? PROVIDES
The material base that provided the impetus for such statements was the unprecedented proliferation of Black female one-parent households and growing Black unemployment. The percentage of Black families with no husband present increased from 21.7 percent in 1960 to 34.6 percent in 1973. The percentage of Black children who lived with both of their parents declined from 75 percent in 1960 to 54 percent by 1975. Single female-parent households within the Black community tended to become younger, with 42 percent of such homes having Black female householders between the ages of 14 and 34 years in 1975. Less than half of all Black women were married in 1975. As unemployment rates for nonwhite married men increased by 332 percent between 1969 and 1975, even Black households with two parents found it more difficult to provide the basic necessities of life. Black women who viewed themselves and their children through the prism of patriarchy could draw the conclusion that their male counterparts—unemployed, underemployed, or sometimes absent from home for indefinite periods of time—were somehow less than real men. The vicious cycle of sexism, fostered by white exploiters of the Black community, would be perpetuated in the actual social practices and relations between Black women and men.
As the contemporary women's movement gained impetus during the early 1970s, Black intellectuals and activists were forced to confront the rampant sexist traditions within their own community and underlying their own theoretical practice. At the outset, the majority of Blacks who wrote on feminism were decidedly hostile. In one widely read 1971 essay published in Ebony magazine, Helen King denounced "women's lib" as a white petty bourgeois fad that had little or nothing to do with the interests of Black women. In the Black Scholar, Elizabeth Hood charged that white feminists had opportunistically usurped issues such as affirmative action from Blacks. "It can be argued that women's liberation not only attached itself to the black movement," Hood explained, "but did so with only marginal concern for black women and black liberation, and functional concern for the rights of white women." Any coalition between Black and white women was unlikely because both groups had been socialized to perceive each other as the "enemy." Staples' view on the women's movement was decidedly antagonistic and betrayed a pathetic inability to grasp the essential character of the economic reforms feminists proposed that would have benefited poor and working class Black women. First, he suggested that "female liberation" was tantamount to a "hatred of men." Second, any discussion of the "sex-role antagonisms extant in the black community will only sow the seed of disunity and hinder the liberation struggle." Black women must tolerate, for the time being, any sexist behavior of their brothers and the patriarchal institutions developed by nationalists. "One must be cognizant of the need to avoid a diffusion of energy devoted to the liberation struggle lest it dilute the over-all effectiveness of the movement," Staples warned. "Black women cannot be free qua women until all blacks attain their liberation."
Perhaps the most "eloquent" assault against "white feminism" was written by Linda LaRue in 1970. Unlike other critics of the women's movement, LaRue attempted to put forward a clear theoretical argument against feminism. In her view, the basic dynamics of sexual exploitation were concretely different and secondary in nature to those of white racism. "Blacks are oppressed, and that means unreasonably, cruelly and harshly fettered by white authority. White women . . . are only suppressed," contrasted LaRue, "and that means checked, restrained, excluded from conscious and overt activity." For LaRue, it was a farce for Black women to align themselves with white women—a social group who benefited materially from white supremacy:
With few exceptions, the American white woman has had a better opportunity to live a free and fulfilling life. . .than any other group in the United States, with the exception of her white husband. Thus, any attempt to analogize black oppression with the plight of the American white woman has the validity of comparing the neck of a hanging man with the hands of an amateur mountain climber with rope burns. . . Is there any logical comparison between the oppression of the black woman on welfare who has difficulty feeding her children and the discontent of the suburban mother who has the luxury to protest the washing of the dishes on which her family's full meal was consumed.
LaRue's analysis rested solely on two other basic points. White women were, after all, white, and there was no reason to assume that they would be less racist or "more open-minded than their male counterparts." With millions of white housewives moving into the labor force, Black women and men would be forced inevitably to compete with them. "The black labor force, never fully employed and always representing a substantial percentage of the unemployed . . . will now be driven into greater unemployment as white women converge at every level on an already dwindling job market." What is interesting about LaRue and other Black critics of feminism was their perception that all white women were inside the "middle class." Statistically, the majority of women who depended on food stamps were, and are, white; the majority of women living in Federally-subsidized public housing were, and are, white. The poverty and educational backwardness of white female householders in the Appalachian hills of Kentucky is often worse than that of the South Bronx. There exists, in short, a unity of political and economic interests between women across the color line that LaRue and others failed to recognize. Furthermore, LaRue's economic analysis was premised on the incorrect belief that all white women benefited materially from the continuation of racism—a view which is not substantially supported by economic data. (See chapter 1)
At the founding convention of the Congress of African People, held in Atlanta in September, 1970, over 2,700 delegates gathered to chart the development of new Black social, political and economic institutions. One major feature at the convention included a series of workshops relating to Black women. Coordinator Bibi Amina Baraka set the tone for the sisters' dialogue, by first quoting West Coast cultural nationalist Maulana Ron Karenga: "What makes a woman appealing is femininity and she can't be feminine without being submissive." Baraka stated that Black females had to internalize "submitting to (their) natural roles" by studying their attitudes toward their "man, house, and children." Sisters needed to take cooking classes, learn to create tasty recipes, and improve their personal hygiene. In her paper on the Black family, Akiba ya Elimu suggested that Black males were the natural leaders of the Black community in all social, cultural and political relations. "He is the leader of the house/ nation because his knowledge of the world is broader, his awareness is greater, his understanding is fuller and his application of this information is wiser" than that of Black women. Kasisi Washao summarized the proceedings with a few appropriately sexist remarks. The Black family was "like an organ and the woman's function must be to inspire her man, to educate the children, and participate in social development. The man must provide security. . ." Black women fortunate enough to have a man in their lives should "be humble and loving, appreciative, and resourceful, faithful, respectful and understanding . . . to provide continuous inspiration" for their husbands.
Nationalists were aware of the climbing rate of Black single parent households and the economic pressures that fractured many of the relations between Black females and males. Madhubuti's Enemies: The Clash of Races, started from the assumption that "the destruction of the Black family was a crucial move in laying the ground for the destruction and total enslavement of Black people in America." If this destruction was a fait accompli, what evolved in the manner of social relations and male/female institutions among Blacks?
Madhubuti claimed that the most serious immediate effect of contemporary racism for Black women "depends upon and revolves around how they are able to effectively solve the problem of no men in their lives." The options available for Black women were unpleasant. Going "without Black men," sexual abstinence, was "unnatural and against life." Lesbianism, according to Madhubuti, "has only recently become popular among some Black women as a compensating move toward fulfilling their sexual desires, possible as a result of not having comfortable and non-frustrating relationships with a Black man." Homosexual activity among women was abnormal, "for it does not generate reproduction . . . with the opposite sex." The most dangerous option, of course, was the prospect of Black women/white men's sexual relationships. When "white men are pushed on Black women or if white men become the accepted option for Black women . . . there is a very serious consequence in terms of Black genocide." Miscegenation was a white supremacist/integrationist plot because the white man would eventually "control the reproductive process of Black women, which goes hand in hand with the physical destruction of Black men and Black families." The fourth option, prostitution, meant that the Black single woman would obtain some security by "(becoming) the property of her pimp." Within the Black community prostitution "is rampant not only for financial means but as (an acceptable) social norm" for Black females. The Black pimp was a kind of "semi-hero" for some, although the entire process "continues to degrade Black women . . . (who) end up as dead property. . ." The final option was in keeping with the African heritage of polygymy—the "quality of sharing" Black males by groups of Black females. Where a brother could economically support more than one household, and satisfy the sexual, emotional and social needs of more than one Black woman at once, such sharing agreements could be achieved for the mutual benefit of all. Sharing would "create a climate and conditions" wherein Black women would willingly permit "their men" to engage in extramarital sex and Black family-building, "while at the same time not damaging existing relationships."
Even outside the boundaries of cultural nationalism, Black political activities did little to challenge institutional sexism. The continuing patterns of Black patriarchy were evident within electoral politics in the 1960s and 1970s. A few Black women politicians gained national prominence after the Civil Rights Movement, including Yvonne Burke of California, Barbara Jordan of Houston, Shirley Chisholm of New York City, and Cardiss Collins of Chicago. The percentage of Black women holding elective office increased 522 percent between 1969 and 1976. Of 508 Black delegates and alternates who participated in the 1976 Democratic National Convention, 310 were women. This "success" in challenging patriarchy was more apparent than real, however. Only 22.2 percent of all Black Federal elected officials and 13.5 percent of all Black state representatives were Black women. Black women comprised only 9.5 percent of all Afro-American judges, and 11 percent of all county officials. 80.5 percent of all Black women who were elected officials in 1976 served either at the municipal level or on boards of education. Despite the formation of the National Association of Black Women Legislators by Tennessee politician Hannah Atkins, and the activities of Nellis Saunders' National Black Women's Leadership Caucus, the effective participation of Black women in electoral politics still grossly underrepresented the potential weight of Black women nationally and regionally. Both integrationist and nationalist-oriented Black men had little to say concretely about the exploitation of Black women by their own institutions. In theory and practice, the Black protest movemement was compromised and gutted by its inability to confront squarely the reality of patriarchy. Black leadership—in the workplace, in street demonstrations, in electoral politics and in the bedroom—was the province of Black men.
By the mid-1970s, a number of women emerged within the Black Movement who advocated key political and economic reforms suggested first by the feminist movement. Many, although by no means all, were also identified as socialists. Angela Davis' essays in the Black Scholar, her deep commitment to an antisexist and antiracist politics, were profoundly influential for many Black women. Cathy Sedgewick and Reba Williams, young Black women who were also members of the Trotskyist Socialist Workers Party, advocated Black support for the Equal Rights Amendment as a necessary and progressive reform which aided women of all races. Advocacy of feminism, they argued, aided and enriched the struggle for Black liberation. For Black women who were pessimistic about the viability of joint political work with white feminists, they pointed out that the real political and economic advances acquired by women of color involved in the women's movement more than made up for the very real problems and personal contradictions evident among certain petty bourgeois white women's "leaders."
Many of the theoretical gains achieved by Black feminists within the Black Movement and community were briefly compromised with the publication of Michele Wallace's controversial diatribe, Black Macho and the Myth of the Superwoman. Wallace emerged as a female version of Eldridge Cleaver, praised by Ms. magazine, the central publication of white liberal feminists, and exalted by pseudofeminist racists such as Susan Brownmiller. Her vulgar polemic combined historical truth with crude fiction, racial mythology with a neo-Freudian, psycho-sexual analysis of Black politics. "Come 1966, the Black man had two pressing tasks before him: a white woman in every bed and a Black woman under every foot," she pronounced. Wallace viewed the entire history of Black Power as "nothing more nor less than the Black man's struggle to attain his presumably lost 'manhood'":
To most of us Black Power meant wooly heads, big Black fists and stern Black faces, gargantuan omnipotent Black male organs, big Black rifles and foot-long combat boots, tight pants over young muscular asses, dashikis, and broad brown chests; Black men looting and rioting in the streets .. . [Stokely Carmichael] was a Black spokesman unlike any other that had come before him. He was a Black man with an erect phallus, and he was pushing it up in America's face.
Wallace contended that virtually every Black male leader of the 1960s accepted and perpetuated the idea of Black Macho, the notion that all political and social power was somehow sexual, and that the possession of a penis was the symbol of revolution. "Black Macho allowed for only the most primitive notion of women-women as possessions, women as the spoils of war, leaving Black women with no resale value," Wallace charged. "The Black woman was a symbol of defeat, and therefore of little use to the revolution except as the performer of drudgery (not unlike her role in slavery)." The Black man was a pathetic failure, and "when [he] went as far as the adoration of his own genitals could carry him, his revolution stopped." The obvious criticism of Wallace's work begins with her crude acceptance of Cleaver and the most blatantly sexist spokespersons of Black liberation as representative of all Black males. But the dilemma for genuine progressives was that her book served absolutely no purpose in facilitating an urgent dialogue between Black women and men on the very real and pressing questions of patriarchy within their community. Black Macho raised at its core several historically valid issues, but due to its distorted and acrid context, it actually reinforced sexism and a hostility towards feminism among many Blacks.
v
The emergence of a militant Black feminism since the mid-1970s, which has since continued and deepened in organizational character, is the product of the convergence of several specific social and economic factors. As illustrated previously, the actual practice of the Black Power Movement was the perpetuation of the structures of patriarchy, under the guise of "Blackness." With the passage of affirmative action legislation, many Black males drew the conclusion that Black women were now taking away newly-won middle income jobs from them. The vulgarly sexist thesis was based on the belief that Black women were indeed submissive, or less threatening to the white, male power apparatus than Black males. Their lack of a penis, in short, was an automatic ticket to employment and job advancement during economically austere times.
Black women knew better than men that the dynamics of sexist exploitation were not altered by bourgeois legislation: Black women remained at the very bottom of the income ladder within the U.S. social order. According to the 1979 Census statistics, for example, 68,000 Black males and only 8,000 Black females earned salaries between $30,000 to $35,000. 46,000 Black men and 6,000 Black women collected annual wages between $35,000 to $50,000 in 1979. 14,000 Black men and 2,000 Black women received wages between $50,000-$75,000. Within the highest income levels, in excess of $75,000, there were 548,000 white men and 4,000 Black men. Less than 500 Black women were in this category. The illusion that Black women, even within the so-called middle class, had achieved parity or had exceded Black men's earnings was not simply false, but a gross reversal of economic reality. Black female unemployment rates were generally higher than those of Black men, especially for all blue collar workers, clerical workers and sales personnel.
Responding to this chasm between Black liberation rhetoric and the harsh realities of Black women's existence, progressive Black female activists fought back. They helped to provide the political base for the fight to acquit Joanne Little, a North Carolina Black woman who was accused of murdering her jailer when he sexually assaulted her. They helped to rally a majority of the national Black community in favor of the Equal Rights Amendment. Progressive Black women in Boston formed the Combahee River Collective in 1974, to begin bringing together Black women who were "actively committed to struggling against racial, sexual, heterosexual, and class oppression" and who viewed as their "particular task the development of integrated analysis and practice based upon the fact that the major systems of oppression are interlocking."
They criticized white feminists who tended to ignore Black women's fears about forced sterilizations and who emphasized only abortion rights. Black female activist veterans of SNCC recalled with some bitterness that a few of the white women who now championed feminism and gave lip-service to antiracist politics had eagerly slept with Black male leaders and saddled Black women with the Movement's "shit work" a decade before. Lorraine Bethel's "What Chou Mean We, White Girl? Or, The Cullud Lesbian Feminist Declaration of Independence," spoke for thousands of Black women who view themselves as the historic victims of suppression by males (white and Black) and white females:
I bought a sweater at a yard sale from a white-skinned (as opposed to Anglo-Saxon) woman. When wearing it I am struck by the smell—it reeks of a soft, privileged life without stress, sweat, or struggle. When wearing it I often think to myself, this sweater smells of a comfort, a way of being in the world I have never known in my life, and never will. . . It is moments/infinities of conscious pain like these that make me want to cry/kill/roll my eyes suck my teeth hand on my hip scream at so-called radical white lesbians/feminists "WHAT CHOU MEAN WE, WHITE GIRL?"
The final history of the systematic exploitation of Black women in capitalist America will not be written by whites, or by Black men, no matter how sympathetic they might be to the struggle against racism and patriarchy. Historically, Black women have carried the greatest burden in the battle for democracy in this country.
Women have been the foundation of Black culture and society, yet their contributions have been generally ignored, or relegated to second class status by most Black male activists, historians and social scientists. They felt the sting of the lash upon their backs in Georgia's cotton fields; they knew the pain of losing children from lack of decent medical care; they felt the hot sun beating down upon their foreheads as they walked to work as maids in whites' homes; they fought to preserve their humanity from white and/or Black men's sexual abuse. The underdevelopment of Black America will end only when Black men begin to seriously challenge and uproot the patriarchal assumptions and institutions which still dominate Black civil and political society. In the words of Michele Barrett, the oppression of all women "is entrenched in the structure of capitalism. Just as we cannot conceive of women's liberation under the oppression of capitalism so we cannot conceive of a socialism whose principles of equality, freedom and dignity are vitiated by the familiar iniquities of gender." Similarly, no road toward the ultimate emancipation of the U.S. Black working class exists outside of a concomitant struggle, in theory and in practice, to destroy every vestige of sexual oppression within the Black community.
CHAPTER FOUR
BLACK PRISONERS AND PUNISHMENT IN A RACIST/CAPITALIST STATE
The Negro race . . . (has) been excluded from civilized Governments and the family of nations, and doomed to slavery. The unhappy black race were separated from the white by indelible marks . . . and were never thought of or spoken of except as property, and when the claims of the owner or the profit of the trader were supposed to need protection. Negroes were beings of an inferior order, and altogether unfit to associate with the white race, either in social or political relations; and so far inferior that they had no rights which the white man was bound to respect.
—Robert B. Tawney, Chief Justice of the United States Supreme Court, the Dred Scott decision, 1857.
Eastern guard tower
glints in sunset; convicts rest
like lizards on rocks . . .
Morning sun slants cell.
Drunks stagger like cripple flies
On Jailhouse floor.
To write a blues song
is to regiment riots
and pluck gems from graves . . .
—Etheridge Knight, "Haiku," in Dudley Randall, ed., The Black Poets (New York: Bantam, 1971), p. 206.
I
The Black domestic periphery in America is essentially imprisoned behind the walls of poverty, sexism, unemployment and workplace exploitation. Sometimes the barriers to freedom seem very real, as we observe a police assault against a random Black victim. At other moments they seem quite abstract. American democracy has at certain stages relished in its passion for racist violence, and at other times, paternalistically yielded to the demands of Black and white reformers. The Civil Rights and Voting Rights Acts thus replaced the Jim Crow signs and the legal stigma of second-class citizenship. But equal opportunity programs and affirmative action did not, and could not, obscure the brutal realities of "prison life" to those who were exploited. The Black majority in America is accepted in the lowest paying jobs, tolerated in public housing, and allowed to join the unemployment lines—but it is still barred from effective power within the corporate and political ruling class. Black workers experience workplace exploitation and racist assaults against their humanity, recognizing that this country's basic democratic creed of rule by law somehow does not apply to them. But it is necessary, at this point, to describe how this bizarre juxtaposition of public rights and private brutalities, of democracy and racism, comprises no aberration, but a system to facilitate oppression and the accumulation of capital from the Black masses. At the core of the capitalist accumulation process and institutional racism is coercion.
American capitalism is preserved by two essential and integral factors: fraud and force. Fraud is the ideological and cultural hegemony of the capitalist creed: that enterprise is free and competition exists for all in the marketplace; that success is available for all who work hard, accumulate capital, and participate as voters in the electoral process; that democratic government is dependent upon the freedom to own private property. Blacks, Latinos and white workers are barraged daily with illusions about the inherent justice and equal opportunity within the American System. The educational institutions, churches, media and popular culture all in their own way participate in creating the logical framework for a system that remains irrational and inhumane.
Beneath the velvet glove of fraud exists the iron fist of force. For reasons of history, Black people are more aware than whites of this delicate dichotomy between consensus vs. coercion. The essence of slavery was coercion of the most primitive kind—the relationships between master and slave were characterized by mutual distrust, fear, hatred and undisguised force. All slaves, whether the proverbial Uncle Toms or Nat Turners, recognized that production could not take place without the daily use of physical or psychological violence. Even the most paternalistic master had to divide Black families occasionally or employ the whip to get the crop to market on schedule. Under industrial capitalism, however, the essence of production involves force of a different kind: the extraction of surplus value from the labor power of the worker. Force is generally disguised within capitalist societies with democratic forms of government. The worker never receives the actual or real value of his/her own labor power, but is technically "free" to sell his/her skills or services to the highest bidder, or employer. Blue collar and service workers are "less free" than professional workers, but all are forced to accept the conditions of employment that the owners of capital are willing to grant. Capitalists and politicians in bourgeois democracies would prefer to mask their dictatorship over labor through a variety of means. They tolerate (and at times even encourage) the activities of labor unions, so long as profit margins are not reduced seriously. Most major public decisions impacting capital are made within the established channels of bourgeois discourse and legitimacy. It is only when a capitalist society is in deep crisis, when the dictatorship of capital over labor is questioned or threatened, that capitalists are pressured to employ brute force.
The oppressed Black majority is generally more subject to the violence of American capitalism than whites because (1) it is concentrated in the lowest paid, blue collar, unskilled and service sectors of the labor force; (2) it comprises a substantial portion of the total U.S. reserve army of labor, the last hired and the first fired during periodic recessions; and (3) it is the historic target of brutality within a racist culture and society, occupying an inferior racial position which has remained unaffected since the demise of slavery. America is not simply a capitalist state, but a racist state, a governmental apparatus which usually denies access and power to most Blacks solely on the basis of racial background. A capitalist/racist state still attempts to resolve problems within the Black community via fraud rather than force, just as it does for whites. Nevertheless, there remains a greater reliance on the omnipresence of coercion aimed at Blacks than at whites, and an even greater use of force aimed at the majority of poor and working class Blacks than at petty bourgeois Blacks. Force is the essence of Black underdevelopment under capitalism: to be Black in capitalist America is to be a prisoner to the reality of coercion.
II
Both during and immediately after slavery, whites seldom bothered to imprison Blacks for any real or imagined crimes. First, life in the South was for most Blacks a kind of imprisonment. No white, whether a drunkard, child-molester or criminal, was perceived to be beneath any Black person, no matter how upright and financially successful he/she happened to be. The strict racial code was an effective barrier to keep Blacks, with rare exceptions, outside positions of power and influence. A "salty" or "sassy" Black woman who objected to any of segregation's insanely strict restrictions could be raped by a white man with legal impunity. If her husband, lover, brother or son had anything to say about the matter, he might be castrated or lynched. Southerners established "Negro courts" which were separate from those dealing with whites by the eighteenth century. Such courts, according to historian Kenneth M. Stampp, "were usually less concerned about the formalities of traditional English justice than about speedy verdicts and certain punishments." Slaves charged with petty larceny usually did not appear in courts, but were simply lashed or punished by their owners or overseers. In misdemeanor or noncapital felony cases, Blacks were tried in courts that were, to say the least, highly prejudiced. In Mississippi, for instance, Blacks charged with noncapital felonies were tried before two justices and five slaveholders. Louisiana Blacks in noncapital felonies were judged by four slaveowners and only one justice. Some Southern whites recognized even then that their system of "Negro courts" was, in the words of one South Carolina judge, "the worst system that could be devised." Nevertheless, despite its obvious contradictions, the "Negro court system" became the basis for allocating "justice" in a biracial society.
Except in those instances when Blacks were accused of assaulting whites or stealing property, the slaveowners themselves presided over the majority of cases involving Black infractions. Punishments varied from the mundane to ingenious. For relatively minor offenses, field hands were forced to labor on Sundays or holidays. Black foremen were demoted to the status of field hand, and household servants were forced to leave the big house. One tobacco planter in Maryland ordered a slave "to eat the worms he failed to pick off the tobacco leaves." More serious infractions, such as failure to obey orders, meted out punishments of various kinds. Some large planters sentenced unruly slaves to spend days or even weeks in the local county jail. Others built jails ("nigger boxes") on their own plantations, small, windowless shacks in which Black workers were confined. Nearly every slave at some point in his/her life experienced the lash. Although castration was a legal and popular form of punishment in the eighteenth century, it declined in usage after 1800. A few planters resorted to the castration of a Black male, however, if they desired to take his slave wife. The greatest barrier to the imprisonment and/or execution of Black people was, ironically, slavery itself. It was not logical, in the view of most whites, for a man to "willingly destroy his own property." Racial atrocities existed in every state and on every plantation, but the loss of a prime fieldhand meant the loss of a capital investment of some importance. In rare cases, whites did not execute slaves who killed particularly brutal white foremen, especially when the white victims were from the "poor white" or lowest classes. The masters were racists, but as businessmen they also had to protect their investment. For these reasons, there were relatively few lynchings, public executions or imprisonment of Blacks prior to the Civil War. As a form of legal chattel, Blacks were the beneficiaries of a kind of perverse protection.
With emancipation and Reconstruction came an inevitable reaction in Southern race relations. Technically freed from the shackles of bondage, the Black man/woman was now just another "competitor" in the labor market. White laws had to be altered to compensate for the changing status of Black agricultural workers and artisans, to ensure their continued inferior caste status. In the autumn months of 1865, a series of Black Codes were ratified to guarantee Black labor subservience. It is important to note, however, that the Jim Crow laws which imprisoned Blacks for violations were originally developed in the North, not South. Many Northern restaurants, hotels and taverns were off-limits to Blacks throughout the eighteenth and nineteenth centuries. In North of Slavery, historian Leon Litwack describes the general pattern of race relations in Northern states between 1790 and 1860:
In virtually every phase of existence, Negroes found themselves systematically separated from whites. They were either excluded from railway cars, omnibuses, stagecoaches, and steamboats or assigned to special "Jim Crow" sections; they sat, when permitted, in secluded and remote corners of theaters and lecture halls; they could not enter most hotels, restaurants, and resorts, except as servants; they prayed in "Negro pews" in the white churches, and if partaking of the sacrament of the Lord's Supper, they waited until the whites had been served the bread and wine. Moreover, they were often educated in segregated schools, punished in segregated prisons, nursed in segregated hospitals, and buried in segregated cemeteries . . . Newspapers and public places prominently displayed cartoons and posters depicting (the Negro's) alleged physical deformities and poking fun at his manners and customs. Children often tormented (Negroes) in the streets and hurled insulting language and objects at them.
Many Midwestern states legally excluded anyone with a "visible admixture" of Negro blood from voting. Almost every major white leader of the Republican Party declared his unconditional opposition to "Negro equality." White women were not immune from attacking Blacks. In Indiana, for instance, a large prewar political rally was led by a large cadre of young white females who carried a banner reading, "Fathers, save us from nigger husbands." Thus the postbellum South after 1877 developed its public policies towards the punishment of Blacks primarily from the traditions and customs of the North.
During this period, the vast majority of Southern Blacks were legally imprisoned for three general offenses—any violation of segregation codes monitoring public behavior or activity; any violation of laws governing capitalist agricultural production; and any infraction (misdemeanors and noncapital felonies) against whites. In the first category, the most heinous crime was interracial marriage. The Mississippi Black Code of December, 1865, was specific:
. . . it shall not be lawful for any freedman, free negro or mulatto to intermarry with any white person, nor for any white person to intermarry with any freedman, free negro or mulatto, and any person who shall so intermarry shall be deemed guilty of felony, and on conviction thereof shall be confined in the State Penitentiary for life; free negroes and mulattoes are of pure negro blood, and those descended from a negro to the third generation inclusive, though one ancestor in each generation may have been a white person.
By the late 1870s, other Southern states ratified similar laws, calling marriages between the races "incestuous" and contrary to God's will. Other codes ordered Blacks off sidewalks to give way to white men, even segregating certain streets specifically for use by whites only. "Coons" were legally restricted "to keep their distance and mind their language in public gathering places," or they would find themselves behind bars.
To maintain the inferior position of Blacks within agricultural production, Southern whites developed the peonage system and convict leasing. Peonage was a logical byproduct of the sharecropping system that replaced slavery immediately after the Civil War. In principle, sharecropping represented a real step forward for Black rural workers. An industrious farmer would borrow farm utensils and seeds, and would divide the proceeds from the sale of the produce at year's end. Some Black farmers used the system to accumulate small amounts of capital, eventually buying their own farms. Many bitterly discovered at the end of a harvest that they actually owed more to the white planter than their share of the crop could pay for. Since virtually all white merchants and planters inflated the cost of their supplies, and kept all business records, illiterate Black farmers were caught in a never-ending cycle of debt. "Peonage occurred only when the planter forbade the cropper to leave the plantation because of debt," writes historian Pete Daniel. "A laborer who signed a contract and then abandoned his job could be arrested for a criminal offense. Ultimately his choice was simple: he could either work out his contract or go to the chain gang." Southern legislatures and courts always sided with owners in their disputes with Black sharecroppers. Once convicted of breaking their legal agreements with white planters, Black prisoners were sometimes bailed out of jail by other white businessmen, who in turn paid off the Blacks' fines and previous debts. But as convicts, these Blacks were now obliged to labor for their new "employer" in workgangs for long periods of years, often under the most brutal physical conditions.
The number of Black prisoners in Southern penitentiaries multiplied dramatically as the profitability of "convict leasing" became evident to white capitalists and politicians. In Mississippi the number of state prisoners grew from 272 in 1872 to 1,072 in 1877. Georgia's convict total increased from 432 in 1872 to 1,441 in 1877. This explosion of the Black prison population reflected an abrupt alteration of Southern laws. In 1872 Mississippi "defined the theft of any property over ten dollars in value, or any cattle or swine of whatever value, as grand larceny, with a sentence up to five years." Laws like this provided the legal foundation for a prison system that made millions of dollars for a small number of white politicians.
Colonel Arthur S. Colyar, editor of the Nashville American and a prominent Tennessee Democrat, who also served as director and general counsel for the Tennessee Coal, Iron, and Railroad Company, was one prominent beneficiary of the leasing program. Under Colyar's direction, the Tennessee Coal, Iron and Railroad Co. leased Black and white convicts to work in their various enterprises for a $101,000 annual fee, paid to the state. Arrangements like this were common and profitable for a number of reasons. Most states had no health or safety inspectors for the convicts, and sixteen-hour workdays were not uncommon. Leases to individual mining, railroad or other industrial companies varied from ten to thirty years. Companies often subleased their convicts to smaller white-owned firms at a profit. Prison wardens also became wealthy from the system, the beneficiaries of substantial "kickbacks" from politicians and company directors.
However, conditions for the prisoners became literally worse than under slavery. Black women who were chained together in straw bunks at night were often raped by white guards. Their children were also confined to the penitentiary with them. The annual death rates for Black convicts ranged from 11 percent in Mississippi to 25 percent in Arkansas in the 1880s. One 1887 grand jury study of a Mississippi prison hospital declared that all convicts bore "marks of the most inhuman and brutal treatments. Most of them have their backs cut in great wales, scars and blisters, some with the skin peeling off in pieces as the result of severe beatings. They were lying there dying, some of them on bare boards, so poor and emaciated that their bones almost came through their skin, many complaining for want of food. We actually saw live vermin crawling over their faces, and the little bedding and clothing they have is in tatters and stiff with filth." Historian Fletcher M. Green described the South's dreaded convict lease system in 1949 as a pattern of labor exploitation akin only to "the persecutions of the Middle Ages or in the prison camps of Nazi Germany."
The general conditions in Southern penitentiaries were, of course, scandalous (or at least should have been). The major prison in Virginia in 1900 was actually designed by Thomas Jefferson in 1797. The decayed penitentiary was so overcrowded, according to one Richmond newspaper editor, that "the feet of inmates tended to stick out the windows." Alabama's prisons in the 1880s were "packed with several times the number of convicts they could reasonably hold." Even that state's prison inspectors admitted that their penitentiaries "are filthy, as a rule . . . and both prisons and prisoners were infested with vermin. The convicts were excessively and sometimes cruelly punished . . . (and) were poorly clothed and fed." After World War I, conditions for Black and white convicts improved somewhat, but the essential brutalities of the penal system remained. Thousands of Black peons were routinely ordered to work in county chain gangs on public roads, in work camps, or in turpentine mills and mines. In Forced Labor in the United States, written in 1939, Walter Wilson discovered that chain gangs were a chief means of punishing Black and white offenders. "Prison camps ranged from portable steel cages to the neat brick and wooden buildings found in the road camps of North Carolina and Virginia."
Outside of imprisonment for debts owed to planters, or the "recruitment" of Blacks to replenish the numbers of convicts leased by counties or states, the frequency of arrests and imprisonment of Blacks was relatively low during the period of Jim Crow laws from 1890 to the 1930s. The reasons for this are rooted in the profoundly racist worldview most whites of all classes had adopted by this time. Writing in 1941, sociologists Allison Davis, Burleigh and Mary Gardner noted in Deep South that "the police, like the whites in general, believe that fighting, drinking, and gambling among Negroes are not crimes so long as they are strictly limited to the Negro group and are kept somewhat under cover. It is only when this behavior is brought out into the open and thrust upon the attention of the whites that it becomes a crime for which arrests are made." One white Southern woman of "upper middle class" origins explained to the researchers that "we have very little crime. Of course, Negroes knife each other occasionally, but there is little real crime. I mean Negroes against whites or whites against each other." The legal system was designed essentially for whites only, as was the rest of society. White policemen were encouraged to "pick up any Negro whose actions appear suspicious," viciously beating him/her, and then releasing the person without charges. Convinced that "formal punishments by fine or jail sentence fail to act as deterrents to Negro criminals," law-enforcement officials simply kept Blacks out of the court system entirely by "administer(ing) punishment themselves." Most Southern white police patrolmen lived in working class neighborhoods with Blacks as neighbors, and "a number of them have kept Negro women, usually on a more or less temporary arrangement, and are on a friendly footing with Negro proprietors of illegal establishments." Whites were also absolutely convinced that they could judge a "bad nigger" simply by his/her appearance. Blacks were thought to be inherently so stupid that they would readily admit to any infraction they had committed when confronted by white authority.
If Blacks were arrested by police for any minor or major crimes against whites, however, their eventual conviction and imprisonment were forgone conclusions. As Deep South explains:
The Negro is, from the very beginning, in a position subordinate to both the police and the court. His testimony will not be accepted if contradictory to that of the police. His witnesses carry little weight with the court, and he can wield no political influence. The Negro is less apt to have legal assistance in the police court or to appeal his case to the higher courts. . . . Negroes seldom prefer charges against whites. The police usually discourage such actions; and in trying such cases, the court protects the whites by technicalities and by attacking the truth of the Negro testimony. . . . There are no Negro officers, judges, lawyers, or jurymen. The only role a Negro can take is that of defendant or witness, except in a few types of civil cases. Furthermore, the Negro has no part in making the laws which the court system enforces. As a defendant, he faces the white man's court; he is tried not only on the evidence but also on the basis of the white man's concept of how a Negro would or should act. If he is found guilty, his sentence and punishment are determined by the same factors. The law is white.
Behind the peonage and convict-leasing system, behind the racist and undemocratic white court system, and behind all the powers of the brutal white police, rested what could be termed the Great Deterrent to Black crime: lynching. The segregationist South was steeped in violence. C. Vann Woodward documents that Alabama whites actually spent more money for rifles and pistols than they did for the state's entire supply of farming implements and tools. Into the twentieth century, white men often wore loaded revolvers "in banks, courtrooms and schoolhouses as well as in bars and ginhouses." Whites shot each other over the most "absurdly trivial" reasons. In 1923, 13 of the 15 cities with the highest homicide rates were Southern or border cities. The national homicide rate of 1926, 10.1 per hundred thousand, favorably contrasts with Jacksonville, Florida's 75.9, Birmingham's 58.8, Memphis' 42.4 and Nashville's 29.2 that same year. If whites in the South had few reservations about resorting to violence against each other, then the courts and police did little to protect Blacks from the wrath of that same violence. Blacks and whites alike understood that there were three crimes which would swiftly spark the flames of racist coercion: the killing or wounding of any white man; the real or suspected sexual assault against any white female; and perhaps the most serious offense of all, any overt political activity which challenged Jim Crow segregation and the basic system of caste/class rule upon which the entire economy and social order was based. Upon these acts, the massive weight of white vigilante "justice" would fall heavily upon any Black man/woman. No real trial would be held; no jail or state penitentiary would be secure enough to keep the Black man/woman from his/her certain fate. Lynching was the ultimate weapon used by whites to "keep the nigger in his place."
III
Lynching is a peculiarly American tradition. From the nineteenth to the late twentieth century, the modern auto-da-fé parallels the development and maturation of capitalism in an oppressive, biracial society. Technically, the term is often used to describe the hanging of a person outside the legal sanction of the police and criminal justice system. Historically, and in actual practice, it is the ultimate use of coercion against Blacks to insure white supremacy. The form it assumes—hanging by the neck, shooting, castration, burning at the stake, or other spontaneous and random forms of violence—is secondary to the actual terror it evokes among the Black masses, and the perverse satisfaction that it derives for white racists. Lynching is neither irrational nor illegal, in the sense that the white power elites tolerate and encourage its continued existence. Lynching in a racist society becomes a legitimate means to check the activities of the entire Black population in economics, culture and politics.
The creator of lynching was a Quaker, Charles Lynch, a well-to-do political leader of what is today Lynchburg, Virginia, and a member of the House of Burgesses. During the American Revolution, Lynch and his fellow patricians were disturbed with the outbreak of criminal activity in their area. Since the closest court was two hundred miles to the East, these early frontier people took legal matters into their own hands. An extra-legal court was established with Lynch presiding as chief magistrate. The arrested man was given an opportunity to defend himself. If he was declared guilty, punishments appropriate to the seriousness of his crimes were allotted: thirty-nine lashes in some cases, hanging by the thumbs in others, or in rare instances execution. These extra-legal courts became popular in the backwoods regions of Kentucky, Tennessee and the Carolinas after the Revolution. By the early 1800s, however, lynching became identified with the execution of an accused person. Southern whites of all classes tended to defend the system as honorable and as an efficient means of protecting private property. As Walter White observed, "the number of victims increased in direct proportion to the growth of the demand for cotton and to the growing sentiment in other parts of the country that slavery was not only morally wrong, but economically unsound."
Surprisingly few Blacks were lynched during the greatest period of slavery expansion. Between 1840 and 1860, only three hundred persons, Black and white, were lynched in the South. Again, the perverse paternalism and self-interest that slavery created provides one explanation. White slaveowners and politicians, being racists, had few reservations about administering the harshest punishments imaginable against their own slaves. There are several documented cases where Blacks accused of rape or murder were hanged or slowly burned to death, often in the presence of other slaves. One Alabama editor defended the occasional public burning of slaves by "the law of self-protection, which abrogates all other law . . . There was no passionate conduct here. The whole subject was disposed of with the coolest deliberation and with regard only to the interest of the public." After the Nat Turner rebellion of 1831, 17 slaves were lynched; other slaves were beheaded and their skulls were positioned on polls on the public roads; and Turner himself was hanged, his body given to surgeons for dissection, and souvenir purses were sewn from his dried skin. But the masters of the plantations were also the masters of the larger white society, which was itself plagued with serious internal class distinctions and divisions. In Roll, Jordan, Roll, Genovese captures the essential ambiguities of power which trapped the planter elite: "An easy attitude toward indiscriminate mob violence against blacks would do more than threaten slave property; it would also threaten the position of the master class in society and open the way to initiatives by the white lower classes that might not remain within racial bounds. The masters felt that their own direct action, buttressed by a legal system of their own construction, needed little or no support from poor white trash. Order meant order." The "compassion" that white planters felt toward Blacks was dictated not out of any abstract humanitarianism, but from simple economic self-interest. As one North Carolina planter who owned hundreds of slaves explained in 1850: "I should consider myself an unjust and unfeeling man if I did not have a proper regard for those who are making me so much money."
The demise of slavery, ironically, meant the collapse of an institutional check on violence against Black people. Whites from all social positions concurred that their continued supremacy had to depend upon the practice of lynching. Between 1882 and 1903 there was an unprecedented expansion in the number of Blacks lynched across the South. In Florida alone during these years 19 whites and 115 Blacks were lynched. Figures from other states in the region include Arkansas, 61 whites and 139 Blacks; Kentucky, 64 whites and 103 Blacks; Georgia, 28 whites and 241 Blacks; Maryland, 2 whites and 19 Blacks; North Carolina, 16 whites and 48 Blacks; Tennessee, 49 whites and 109 Blacks; Virginia, 21 whites and 70 Blacks; South Carolina, 8 whites and 109 Blacks. Texas led the nation in lynchings with 324, 199 of whom were Blacks. Louisiana had the highest number of lynchings in the Black Belt South, with 53 whites and 232 Blacks. Of the 2,060 Blacks lynched in the U.S. between 1882 and 1903, only 707 were actually charged with "attempted, alleged, or actual rape." 783 were lynched for allegedly murdering whites; 208 were charged with "minor offenses;" 104 were termed "arsonists;" 101 had stolen white property. Others were killed for "striking or talking back to a white man," testifying against whites in courts, "suing whites," or other related offenses. Between 1904 and 1924 the number of lynchings declined somewhat throughout the country, but still occurred in alarming numbers in the Deep South. Furthermore, lynching had become associated as a form of punishment almost specifically for Blacks only. During this later period, 11 whites and 269 Blacks in Georgia were same years. A total of 3,513 Blacks and 1,438 whites were lynched in the U.S. between 1882 and 1927. Fourteen former slave states (Mississippi, Georgia, Texas, Louisiana, Alabama, Arkansas, Florida, Tennessee, Kentucky, South Carolina, Missouri, Maryland, Virginia and North Carolina) were responsible for 80.8 percent of all lynchings and 94.7 percent of all lynchings against Blacks. (See Table XII)
White leaders justified lynching as an act to defend white racial supremacy. Most declared that rape was, in the words of Congress person James F. Byrnes (who would later become U.S. Secretary of State), "responsible directly and indirectly for most of the lynching in America." Racist demagogue Cole Blease explained, "Whenever the Constitution comes between me and the virtue of the white women of South Carolina, then I say 'to hell with the Constitution!'" Although rape accounted for only one-third of all statistics, the popular white view that Black sexuality was the sole cause of lynchings quickly was adopted at a mass level. By the 1920s, the overwhelming majority of white Southerners were convinced that the Black male was "always a potential rapist. Thus, white women are expected to fear strange Negro men, and they usually feel it unsafe to go alone in Negro districts or to stay alone at night in isolated houses." All Black men, from professionals to blue-collar workers, were regarded as "primitive being(s), emotionally unrestrained and sexually uncontrolled."
At this point, it is important to distinguish between the actual number of lynchings and the psychosocial and economic function of the terror it unleashed. After 1903, the number of lynchings receded gradually to only several dozen each year in the mid-1920s. The lynching of a Black man falsely accused of a crime might evoke sorrow and outrage, and perhaps the spirit of vengeance, among the Black masses. But executions per se, even accompanied with the passions of racist violence among whites, do not in themselves foster terror among Blacks. Terror is not the product of violence alone, but is created only by the random, senseless and even bestial use of coercion against an entire population. The coercion that takes place within a "normal" capitalist society, the exploitation of Blacks in the workplace, is insufficient to modify and control their collective behavior. Even the lynchings of thousands of Blacks across the South, for real and usually imagined crimes, could not guarantee a docile labor force. This recognition connoted a shift in racist tactics after 1900. As the absolute number of Black lynchings decreased, the level of crude indignities and bestial acts of random violence toward Blacks increased. Terror becomes real in one's mind only when a person recognizes that, at any moment and for any reason, he/she can be brutally tortured. Slavery left many Black people and their descendants unafraid of death. But there are many things that are indeed worse than death. It is the random, limited and spontaneous use of coercion that tends to afflict the mind and spirit of the oppressed. It is the omnipresent fear of a fate worse than death itself that creates the terror.
The lynchings committed against Blacks in the early twentieth century were designed specifically to evoke this special kind of terror. Walter White described these murders as being "executed with a bestiality unknown even in the most remote and uncivilized parts of the world." Between 1918 and 1927, 91.6 percent of all persons lynched in the U.S. were Black. Eleven were Black women, three of whom were pregnant. Forty-four Blacks were burned alive, and 18 others were burned after they had been executed. Some were simply tied to the backs of automobiles and dragged across city streets until they were unconscious. Many Black men were tied down and brutally castrated with knives or axes. In some cases, the families of the intended victims were seized physically, and delivered to the site to witness the series of atrocities. The purpose of the events was not to kill the Negro quickly or painlessly, but to derive sadistic satisfaction from the suffering of something that was less than human. In the twenties, lynchings became popular cultural events, not unlike circuses and dances. Hundreds of white women and children were invited to take part in the festivities. Fingers, ears and other body parts of the Black victims were eagerly seized for souvenirs.
Two examples of such brutalities are sufficient. One account from Mississippi at the turn of the century is typical:
When the two Negroes were captured, they were tied to trees and while the funeral pyres were being prepared they were forced to suffer the most fiendish tortures. The blacks were forced to hold out their hands while one finger at a time was chopped off. The fingers were distributed as souvenirs. The ears of the murderers were cut off. Holbert was beaten severely; his skull was fractured, and one of his eyes, knocked out with a stick, hung by a shred from the socket. The most excruciating form of punishment consisted in the use of a large corkscrew in the hands of some of the mob. This instrument was bored into the flesh of the man and woman. In the arms, legs and body, and then pulled out, the spirals tearing out big pieces of raw, quivering flesh every time it was withdrawn.
In Georgia, a Black sharecropper was lynched for the murder of his white landlord. When word arrived that the Black farmer's wife was going to swear out warrants against her husband's killers, the mob replied, "We'll teach the damn nigger wench some sense":
Securely they bound her ankles together and, by then, hanged her to a tree. Gasoline and motor oil were thrown upon her dangling clothes; a match wrapped her in sudden flames. Mocking ribald laughter from her tormentors answered the helpless woman's screams of pain and terror. The clothes burned from her crisply toasted body, in which, unfortunately, life still lingered, a man stepped towards the woman and, with his knife, ripped open the abdomen in a crude Caesarian operation. Out tumbled the pre maturely born child. Two feeble cries it gave—and received for answer the heel of a stalwart man, as life was ground out of the tiny form.
In the 1930s, the tradition of lynching and brutality was forced to submerge, and ultimately, to transform itself into a new phenomenon. Demographically, millions of Blacks left the rural South and travelled to the Northeast and Midwest, not just for employment opportunities, but to escape the reign of terror. The growth and influence of the National Association for the Advancement of Colored People in the South was another institutional safeguard that Blacks used to fight lynchings. As Black life and labor shifted toward urban and industrial areas, lynchings were made more difficult. The informal, vigilante-inspired techniques to suppress Blacks were no longer practical. Therefore, beginning with the Great Depression, and especially after 1945, white racists began to rely almost exclusively on the state apparatus to carry out the battle for white supremacy. Blacks charged with crimes would receive longer sentences than whites convicted of similar crimes. The police forces of municipal and metropolitan areas received a carte blanche in their daily acts of brutality against Blacks. The Federal and state government carefully monitored Blacks who advocated any kind of social or political change. Most important, capital punishment was used as a weapon against Blacks charged and convicted of major crimes. The criminal justice system, in short, became the modern instrument to perpetuate white hegemony. Extra-legal lynchings were replaced by "legal lynchings" and capital punishment.
IV
Neither through cold design nor quiet calculation did the racist/capitalist state choose to rely upon capital punishment as its new Great Deterrent to Black crime. Capital punishment, after all, is as old as human society. In European countries political dissidents, felons and beggars were beheaded or disemboweled by feudal governments for any number of crimes, great and small. In frontier America, the legal subtleties that separated lynchings from court-sanctioned executions were small indeed, at least so far as the populace was concerned. Both were bloody rituals evoking the worst passions (and prayers) that a culture claiming any degree of civilization can produce. At the last public execution in this nation, a Kentucky hanging in 1938, 20,000 people travelled to witness the event. But by the Great Depression, and continuing into the early 1960s, white capitalist society increasingly viewed capital punishment as its line of defense against the Negro.
The racial bias within the statistics on capital punishment speaks for itself. (See Table XIII) Although Blacks comprised about 9 to 10 percent of the U.S. population in the 1930s, almost 50 percent of all prisoners who were executed during the decade were Afro-Americans. Though 97.1 percent of all whites executed had been convicted for murder, only 10 white men were executed for rape during the entire ten-year period. And 115 Black men were sentenced to die for rape in the 1930s—14.1 percent of all Blacks executed. After 1940, the number of Blacks convicted and eventually killed for capital crimes increased significantly relative to whites. Between 1940 and 1959 the percentage of Blacks executed for rape compared to the total number of Blacks killed steadily climbed, reaching nearly one-fourth of the total. About 90 percent of all Americans executed for rape between 1930 and 1959 were Black, and all but two of the sentences occurred in the South. Georgia, one of the leading lynching states, has also executed the highest number of prisoners since 1930, 366 persons. The most important statistic to consider may be this: "no white has ever been executed for the rape of a black" in American history.
Advocates of capital punishment found themselves on the defensive in the 1960s. Research revealed that, between 1928 and 1949, the average homicide rates in states that allowed the death penalty were 200 to 300 percent higher than in states that had no capital punishment. Homicide rates in the early 1960s, when executions averaged 24 each year, were only 70 percent of the 1930s rate, when executions averaged 150 per year. Some states that switched to the death penalty actually experienced increases in their homicide rates. Confronted with mounting evidence that the death penalty was inherently racist and an ineffective deterrent against crime, white social scientists, police administrations and politicians launched an ideological "counteroffensive." The nation's leading crime stopper, FBI Director J. Edgar Hoover, spoke out repeatedly in favor of capital punishment. University of Chicago economist Isaac Ehrlich published a widely praised study which claimed that "every execution deterred approximately eight murders." Politicians in both the Democratic and Republican parties informed a budget-conscious public that executions would save taxpayers money over incarcerating prisoners for life terms. Convicted murderers were, as a group, dangerously antisocial individuals who would undoubtedly kill innocent people again once released. Evangelical white ministers even quoted Exodus 21:23-25 to justify capital punishment: You shall give "life for life, eye for eye, tooth for tooth, hand for hand, foot for foot, burn for burn, wound for wound, stripe for stripe."
The solid evidence against all these pro-death viewpoints is simple enough. In the mid-1970s a group of influential econometricians examined Ehrlich's research and declared that it was "fatally flawed with numerous methodological errors." Neither Hoover nor any social scientist has ever proven a direct relationship between capital punishment and crime deterrence. The public was told repeatedly that capital punishment is less costly to the state than life imprisonment. But in 1971, for example, it was estimated that "the commutation of death sentences of 15 Arkansas prisoners saved the state an estimated $1.5 million." The former assistant warden of Illinois's Cook County Jail noted that "on the average, a capital case, from the time of first commitment to the jail until the body is disposed of after an execution, costs about 25 percent more than the price of 30 years of imprisonment which, on the average, was the normal life expectancy at the age of conviction of capital cases. Capital punishment is by no means 'cheaper' than life imprisonment, and the jurisdiction that maintains it pays dearly, in both money and human costs." Even the biblical justification of capital punishment was found wanting on its own terms. Black and progressive white clergy observed correctly that the Bible also sanctions capital punishment "in cases of adultery (Lev. 20:10), blasphemy (Lev. 24:15), working on the sabbath (Ex. 35:2), refusing to obey a priest or judge (Deut. 17:12), disobedient children (Deut. 21:18), fornication (Deut. 22:23) and sixteen other offenses. Death penalty advocates who prided themselves on their Christianity conveniently forgot that Christ told his followers, "You have heard it said, 'An eye for an eye and a tooth for a tooth,' but I say unto you, Do not resist one who is evil." (Matthew 5:38-39) The apostle Paul wrote in the New Testament, "Beloved, never avenge yourselves, but leave it to the wrath of God; for it is written, 'Vengeance is mine, I will repay, says the Lord.'" (Romans 12:19)
White America continued to be unconvinced. By 1978, almost 70 percent of all white Americans favored capital punishment. After ending the death penalty in 1967, the Supreme Court reversed itself a decade later. By June, 1981, 827 men and women were on death row, the largest number in U.S. history and probably "the largest in the world.'' (See Table XIV) Since 1972, 62 percent of the prisoners sentenced to die "were unskilled, service, or domestic workers; 60 percent were unemployed at the time of their crimes." And again capital punishment has become a pivotal element in maintaining white supremacy. According to the Institute of Southern Studies, "in Georgia, between 1973 and 1977, over three times as many convicted defendants who had killed white victims received a death sentence as did those who had killed black victims." Three-fourths of the prisoners condemned were in the South, and almost half were Black. (See Tables XV and XVI) Blacks in the U.S. account for over half (54 percent) of all murder victims, and homicide is now the leading cause of death for Black people between the age of 25 and 34. Only 13 percent of all prisoners now on death row had Black victims. Legal activist Clare Jupiter has clearly linked racism, lynchings and the current use of capital punishment: "lynch mobs were ostensibly illegal, but the actions of juries are legally recognized as the will of the community. By their deliberations and selection of the proper victims for official murder, modern juries—especially Southern juries—echo a familiar message: white skin and wealth are still the best tools for beating the death penalty."
v
In the 1960s and 1970s, white public opinion on crime took a marked shift towards an authoritarian and "law-and-order" mentality. Polls commissioned by the American Institute of Public Opinion of Columbia University, and the National Opinion Research Center of the University of Chicago indicated that the percentage of Americans who were afraid to walk within a mile of their homes at night increased from 32 percent in 1967 to 45 percent in 1977. In national surveys taken in 1965, 57 percent of all Americans responded that the U.S. justice system was not "dealing harshly enough with criminals." Since then, that troubled majority has climbed—74 percent in 1972, 85 percent in 1975, and 90 percent in 1978.
Various governmental agencies responded to the anxiety of the white middle-to-upper class by increasing expenditures for public safety. Local government spending for police protection jumped from $1.8 billion in 1962 to $8.8 billion in 1977. States increased their police budgets in the fifteen-year period from $285 million to $1.6 billion. The Federal government followed suit, raising police protection spending between 1962 and 1977 from $177 million to $1.4 billion. Payments for police protection between 1962 and 1977 soared 375 percent, and annual government expenditures for prisons reached $4.6 billion in 1977. U.S. per capita expenditures for police protection jumped from $21.12 in 1960 to $34.50 in 1970 and $47.98 in 1977. States with substantial Black urban populations generally exceeded the national per capita average. In 1977, Michigan was spending $54.89; Illinois, $58.36; New Jersey, $58.82; California, $65.20; New York, $72.33. By 1974, cities with large numbers of Blacks were allotting substantial per capita sums to expand local police forces: Los Angeles, $60. 51; Baltimore, $64.29; Chicago, $73. 38; St. Louis, $74.11; Philadelphia, $74.98; Newark, $76.44; Detroit, $76.81; New York, $86.61; Washington, D.C., $123.60.
The U.S. Right was able to manipulate the public's anxiety by propagandizing crime statistics. The number of reported violent crimes climbed from 161,000 in 1960 to 487,000 in 1978. The various types of violent crime had increased across the board. The number of murders per 100,000 population, jumped from 5 in 1965 to 10 in 1975. In the same decade, reported instances of rape per 100,000 increased from 12 to 26; robbery, 72 to 218; and aggravated assaults, 111 to 227. White male victims of homicide increased from 5 to 9 per 100,000. The number of property crimes reported to the FBI had increased to 1,726 per 100,000 by 1975. Civil libertarians and civil rights supporters pointed out frequently that the huge increases in the money spent for police were not justified. For instance, the absolute number of homicides declined 3.5 percent between 1975 and 1978. In the same period, robberies dropped 4.4 percent, and property crimes reported to the FBI declined by 1.3 percent. In 1980, the Bureau of the Census reported that "the average annual growth rate was 17 percent between 1965 and 1970, but it was only 5 percent during the next five years, and it actually fell by 4 percent between 1975 and 1978. Similarly, the rate of motor vehicle thefts, which had risen by some 12 percent per year from 1965 to 1970, grew by less than 1 percent per year between 1970 and 1975." The data indicates that "most reported crime is either leveling off or diminishing . . . "
Crime statistics can always be interpreted in different ways, depending obviously upon one's political perspective. What neoauthoritarians failed to explore accurately was the factor of race within this unprecedented explosion of lawlessness. Several observations along the color line must be made. First and foremost, is the fact that the percentage of Black and Hispanic victims of violent crime has always been higher than for whites. From 1973 to 1978, white males were victimized by violent crime at rates between 42 and 45 per year per thousand. Hispanic male victims of violent crime had rates during these years between 49 to 54 per thousand. For Black men, the rate was between 53 and 57 per thousand. Nonwhite male homicide rates per 100,000 during the 1970s were between 60 and 83 annually. In other words, any Black man in the U.S. has a 6 to 8 times greater chance of being murdered than any white man. Second, Black working class and poor people, not white, are the most likely victims of household crimes. Between 1973 and 1978, Black families earning $7,500 to $9,999 annual income experienced burglary rates per 1,000 of from 132 to 159 annually. Black families earning under $3,000 in these years reported between 129 and 155 burglaries per year, and 83 to 90 household larcenies per year. According to the Bureau of the Census, 'The 1978 [burglary] rates per 1,000 households amounted to 115 (for blacks) and 83 (for whites) respectively." Third, the Black petty bourgeois strata has a greater chance of being victimized in most property crimes than whites of all income groups. In 1975 alone, almost one out of every ten Black families earning more than $25,000 annually lost their cars or motor vehicles to criminals, a rate 436 percent higher than that of whites of identical income. The irony of the newest "war against crime" is that white police, politicians and law enforcement officers have been nonchalant, at best, in aiding and defending Blacks' lives and personal property. The foundations of the modern U.S. police state are designed specifically to ensure that the killings, rapes and property thefts of Blacks continue unabated—so long as whites (especially in the upper classes) remain protected.
VI
Two other strategies emerged during the 1960s which increased the state's role in the suppression of Black leaders and the Black working class. The first, which involved the significant expansion of the Black prison population, was effectively used to maintain a high proportion of Blacks within capitalism's necessary reserve army of labor—a strategy not unlike that of convict-leasing in the 1800s. The second, established a sophisticated surveillance network and a police-state apparatus to blunt Blacks' criticisms of white supremacy and the political economy of capitalism. Both efforts combined to curtail the advances achieved by the Civil Rights and Black Power Movements.
In 1982, over 500,000 men, women and youths were incarcerated in more than 6,500 penal institutions of various types. Despite the growing recognition of scholars and some correction officials that mass imprisonments had not lowered the U.S. crime rate, many conservative white Americans pressed their elected officials and courts for increased jail terms for persons convicted of violent crime. A desire "to inflict severe punishment and to seek revenge and retribution," combined with the tradition of racism, sent the number of state prisoners soaring in the 1970s and 1980s. Between 1972 and 1978, for example, Florida almost doubled its state prison population. In the same six-year period, Delaware's prison population increased by 260 percent. Critics noted, without avail, that one-fourth of all persons imprisoned were alcoholics. One half million American youths every year spent some time locked away in a state reformatory or prison. Annually another 600,000 mentally ill persons are arrested and imprisoned for periods of months or even years, and few receive any psychiatric care. By the early 1980s the annual national incarceration rate of 250 per hundred thousand was the third highest in the world. Not surprisingly, the leader was South Africa, with 400; but some projections for U.S. prison growth could exceed that figure within a single decade.
Like South Africa, the American prison profile reflects the brutal realities of class exploitation and racism inherent in a modern racist/capitalist state. (See Tables XVII and XVIII) Almost half of all prisoners in the U.S., at any given time, are Black. Fifty-one percent of the entire prison population is 29 years old or less; and 30 percent is between the ages of 20 and 24; several thousand convicts are not even old enough to vote. Fifty-six percent of all prisoners never completed high school, and over one quarter have an eighth-grade education or less. The great majority of prisoners are from the working class: craftsmen (23 percent), operatives (29 percent), service workers (11 percent), nonfarm laborers (17 percent), and clerical employees (4 percent). Almost one-third of these men and women (31 percent) were unemployed during the four weeks prior to their arrest. Most inmates had difficulty finding steady employment, with 46 percent working at their last job for less than six months tenure. Only 14 percent of all prisoners had $10,000 or higher annual incomes, while 60 percent earned under $6,000. Such a large pool of "idle" workers did not escape the notice of many corporations and politicians, who put forward a prison "reform" program of "rehabilitative work" in the early 1980s. Prisoners would be hired to work at manufacturing jobs while still serving their sentences behind bars. Businesses would produce commodities at lower than normal wage rates, thereby saving money. Chief Justice Warren Burger, among others, endorsed the program to convert prisons into "factories with fences."
The American criminal justice system operates effectively as the conduit for enlarging the nonwhite prison population. Every year, over 8 percent of all Afro-Americans are arrested. As Lennox S. Hinds, former National Director of the National Conference of Black Lawyers, has observed, "someone black and poor tried for stealing a few hundred dollars has a 90 percent likelihood of being convicted of robbery with a sentence averaging between 94 and 138 months. A white business executive who has embezzled hundreds of thousands of dollars has only a 20 percent likelihood of conviction with a sentence averaging about 20 to 48 months." Blacks comprise over 25 percent of all Americans arrested in a given year. (See Table XIX) Although whites are charged with about 72 percent of all criminal offenses, the criminal justice system tends to "punish" them for certain less serious crimes more so than Blacks and other national minorities. For example, in 1975 whites constituted 87.8 of all persons arrested as runaway youths, 84 percent of all charged for driving while under the influence of alcohol, 88.6 percent of those who violated state liquor laws, and 83.3 percent of all vandals. Blacks comprised more than half of all Americans charged with murder and non-negligent homicide (54.4 percent), prostitution (53.6 percent), robbery (58.8 percent) and gambling (72 percent). Blacks also accounted for 45.4 percent of all Americans arrested for forcible rape, 39.5 percent of all aggravated assaults, and 41.4 percent of those carrying and/or receiving illegal weapons. The pattern of American "justice" that emerges is obvious: white middle class Americans are arrested generally for relatively minor property crimes, whereas Blacks are arrested for violent crimes which carry substantial penitentiary sentences.
Halting the emergence of Black political activism in the 1960s could not be left solely under the aegis of the criminal justice system. To accomplish this, the state developed an extraordinarily powerful and illegal apparatus—the COINTELPRO or "Counter Intelligence Program." Begun in 1956 by the FBI as a coordinated effort to undermine the Communist Party USA, COINTELPRO mushroomed into a wide ranging series of assaults against progressive and Black nationalist leaders and organizations. In its sordid fifteen-year history of operations, the FBI sent "anonymous mailings (reprints, Bureau-authored articles and letters) to group members criticizing a leader or an allied group;" encouraged "hostility up to and including gang warfare between rival groups;" engineered the firing of SNCC, Black Panther and even Urban League officials and members; ordered "federal, state, or local authorities to arrest, audit, raid, inspect (or) deport" Black activists; interfered with "judicial proceedings" by targeting Black and white progressive attorneys sympathetic to Black liberation; and used "politicians and investigating committees, sometimes without their knowledge to take action against targets." Two hundred and thirty-three of the total 295 authorized actions against so-called "Black Nationalist Hate Groups" were targeted against the Black Panther Party, declared by Hoover in September, 1968, to be "the greatest threat to the internal security of the country." Theoretically COINTELPRO ended in 1971, and the FBI was condemned by a Senate Select Committee for treading "on ground forbidden to it by the Constitution." Nevertheless, the FBI continued to operate COINTELPRO-type actions against Black activists, and under the Reagan Administration began to terrorize individual Blacks in a brazenly open manner. For example, the Black Press Institute learned in November, 1981, that the Federal government was planning a series of grand jury hearings to explore "possible linkages between respected black organizations and terrorist groups." Using a little-used regulation to investigate the Mafia, the grand jury probe targeted civil rights organizations, Black social and cultural groups, community organizations and Black student groups.
VII
The plight of the Black domestic periphery is symbolized by the life and death of George Jackson. At age 15, he was convicted for breaking into a department store, and served seven months in California's Paso Robles Youth Authority. At 18, he was charged with stealing $70 from a filling station. Bourgeois democracy is generous: the state provided Jackson a white public defender. On the lawyer's advice, he agreed to plead guilty, and was promised a short sentence. Unknowingly perhaps, Jackson forfeited his legal right to any appeal. The court issued its verdice: one year to life. Jackson's "release" from the penal system did not occur until he was assassinated at the age of 31. "America cannot let a black man steal $70 without severely punishing him," wrote former prisoner Eric Mann. "A system that demands that the poor work like dogs and accept what they are given while the rich throw away better meals than the poor eat, must treat stealing $70 as an insurrectionary act. The punishment, especially if that crime against property is committed by a black person, will usually involve throwing him in a cage for from one to five years."
Jackson's imprisonment and execution are mirrored in a thousand different acts of brutality that take place across the face of Black America everyday, in relative isolation and in broad daylight. These collective acts form the bars which imprison every individual member of the Black working class, every Black poor and unemployed person, and every Black woman. But George Jackson's life also provides a model for the directions of the inevitable revolutionary upsurge that must occur. Each oppressed person under capitalism must come to the realization that his/her death is a requirement for the continued life of the system. Corporate economics requires the existence of an undernourished, half-educated working class; millions of persons caught in perpetual penury, filth and disease; hundreds of thousands imprisoned, and millions more arrested annually; the development of the periphery, and the systematic elimination of the weak, the young, and the homeless. George Jackson recognized this dialectical unity as a one-sided process of death and destruction. "We always have done most of the dying, and still do: dying at the stake, through social neglect or in U.S. foreign wars. The point is now to construct a situation where someone else will join the dying," Jackson wrote. "If there must be funerals, then let there be funerals on both sides." This final verdict for militant action to the Black oppressed may appear unnecessarily apocalyptic, but it squares solidly with the process of change found in the pages of social history. Revolutionary transformations are not an orderly process, and violence is always an essential "midwife" in the birth of new societies. Moral suasion and plea-bargaining will not release the thousands of Black convicts in America's penitentiaries; gradual reforms within the criminal justice system will not blunt the razor's edge of police brutality. Underdevelopment and the imprisonment of the Black masses will not die a natural death until the real criminals within America's powerful ruling class taste something of the bitter anguish that distorts and cripples the Black majority.
SECTION TWO
THE BLACK ELITE: THE DOMESTIC CORE
CHAPTER FIVE
BLACK CAPITALISM: ENTREPRENEURS, CONSUMERS, AND THE HISTORICAL EVOLUTION OF THE BLACK MARKET
Having attained success in business
possessing three cars
one wife and two mistresses
a home and furniture
talked of by the town
and thrice ruler of the local Elks
Robert Whitmore
died of apoplexy
when a stranger from Georgia
mistook him
for a former Macon waiter.
—Frank Marshall Davis, "Robert Whitmore" in Dudley Randall, ed., The Black Poets (New York: Bantam, 1971), p. 121
I
Capital accumulation in the nonwhite periphery creates a number of social and political dislocations within the indigenous society. Businesses can operate at a profit only when there are adequate transportation systems—railroads, canals, highways, airports. Modern communication systems are required to link branch offices with the metropole, to facilitate the completion of orders. A steadily growing number of women and men from the indigenous population are needed to serve in clerical and lower-level administrative posts. Thus schools are a concomitant part of the developmental process, so long as both the content of its education and its pedagogy are oriented toward reinforcing the legitimacy of capitalism and Western civil society. The incessant drive for economic growth and expansion also sparks an inevitable transition within the religious ethos of the workers, since the Puritan work ethic promotes the proper ideological outlook for a hard-working, non-disruptive labor force. It is impossible, therefore, to talk about underdevelopment as a purely economic process, because the human content of that dynamic is profoundly social, cultural and political.
A decisive component of this underdevelopment process within the periphery is the nonwhite elite. This small social stratum is gathered from the masses, reeducated in colonial schools, and converted to the masters' faith. In political society, it serves as a necessary yet dependent buffer between those who wield power and those who have none. Within popular culture, it is the nonwhite mouthpiece of the new order, articulating in the media and in various aesthetic forums the ideals of the masters. In the context of modern Africa, for example, one can discern a direct correlation between increased agricultural and industrial production for overseas markets and the growth of the Black elite. In the Gold Coast (Ghana), for example, between 1891 and 1911 exports and the level of production of commercial enterprises increased 400 percent; the amount of currency or monetary resources increased by 1,000 percent; the amount of investments in cocoa production soared from £3,000 to £1,573,000. Gold exports to the West increased over 5,000 percent in a ten-year period, 1901-1911. Although the lion's share of wealth was controlled by British colonialists and businessmen, underdevelopment did result in the creation of a marginal Black petty bourgeoisie. By 1945, several thousand African small farmers produced 20 percent of the Gold Coast cocoa crop from their own land. As the capital city, Accra, expanded from a colonial village into an international port, the British were forced to hire Africans in a variety of petty managerial capacities—clerks, civil servants, teachers, skilled blue-collar workers. Hundreds of Africans became lawyers, doctors, dentists, newspaper editors and held other more influential posts. At the end of World War II, about 400,000 African small entrepreneurs owned residential stores selling clothing, food and household items to the growing rural and urban proletariat. This social strata was simultaneously "nationalist" and "integrationist," to use terms perhaps more suitable to Afro-American politics. It opposed British racism, and provided critical support for the radical elitists' demands for decolonialization. Yet it had also integrated the economic and social worldview of the British into its own raison d'être. The elite was a product of capitalism, colonialism and imperialism: its activities reinforced the process of Western capital accumulation and the underdevelopment of the African masses.
Across the nonwhite world, colonized elites have exhibited certain political and cultural tendencies which are, to repeat, a necessary part of the underdevelopmental dynamic. In The West and the Rest of Us: White Predators, Black Slavers and the African Elite, Chinweizu observes that this stratum is primarily the product of Western capitalist "liberalism":
African liberals, as agents of an international liberal imperialism, have a special job: to spread the liberal ideology in Africa, to maintain a black front there for a neocolonial world order run by the West, to administer the neocolonial African territories for the West, and to restore the imperialized status quo if any genuinely African nationalist regime should storm its way into power anywhere in Africa. To call them neocolonial administrators is not to say that they, like the former white colonial administrators, receive direct orders or mandatory guidelines from their masters overseas . . . But it is rather to say that, though they advertise themselves as serving Africa, they operate in an environment, with a mentality, and under conditioned attitudes and direct advice that all tend to yield policies that primarily serve the neocolonial powers, policies that often are in direct opposition to the genuine interests of the African peoples. Conditioned by a pro-western miseducation, they see their class interests as tied to those of their imperialist masters, and they readily abandon the interest of their people to protect those of their class.
Although the race/class dialectic of the United States cannot be adequately or accurately described as neocolonial, it is undeniable that the process that gave birth to a Black elite here is virtually identical to that of modern Africa. When Chinweizu writes bitterly, "those whom Africa expected to liberate her from the yoke of Europe have instead chained her to that yoke, perhaps even more tightly, in exchange for crumbs of wealth and privilege," a similar verdict must be levied against their American counterparts. When he dismisses neocolonial politicos as "British O.B.E.—Obedient Boys of the Empire," Black activists in the United States might include the names of Thomas Sowell, Benjamin Hooks and Vernon Jordan. The Afro-American majority has been systematically betrayed by its petty bourgeois stratum.
In Reconstruction, the masses demanded universal education and "forty acres and a mule"; they received instead political leadership of an uneven quality, sharecropping and convict-leasing. In the Civil Rights Movement, they demanded an end to racial discrimination, jobs, decent housing and education; they received instead temporary employment, an end to only the most blatant forms of legal segregation, and affirmative-action programs which directly benefited the Black elite. This is not to say that the Black elite has always consciously served the interests of the exploiters and racists. The key here is not one of intentions but of historical mission—a failure of the elite to comprehend its role as a necessary social force for basic change. As Frantz Fanon noted, "each generation must, out of relative obscurity, discover its mission, fulfil it, or betray it." It is here, on the scales of history, that our elites must be judged as inadequate.
Historically, within Black America, the Black elite has occupied four principal vocations—politicians, clergymen, educators, and entrepreneurs. By "politician," I mean a person who is directly involved in making, carrying out, or influencing state policies. A man/woman need not be an elected or appointed official to be described accurately as a politician. Booker T. Washington, A. Philip Randolph, Frederick Douglass and Martin Luther King, Jr., were all influential politicians, although none of these men were ever elected to public office. Even Adam Clayton Powell's profound impact within Black civil and political societies between 1945 and 1965 was perhaps only indirectly due to his position as a senior Black Congressional leader. Indeed, at the moment of the great 1963 March on Washington, there were fewer than 100 Black elected officials in the entire country. The acceptable role of a Black "politician" within a capitalist and racist society is to maximize the level of goods and services reaching the Black community. By definition, Black socialists or revolutionary nationalists are not "politicians" in this narrow bourgeois sense, because they are attempting through their practice to uproot racial hegemony and exploitative economic relations. The Negro politician is neither anticapitalist nor antiracist, except in his/her rhetoric.
The Black clergy comprise the bedrock of Black petty bourgeois politics, due to several historical and sociological reasons. The process of enslavement effectively eliminated the bonds of leadership which were part of indigenous African societies. The slaves who adopted the forms of the master's religion and who were granted the right to preach to their brothers and sisters became the ministers. These pastors were viewed by their white authorities as an ideological buffer between themselves and the often-dangerous Black masses. The Black messengers taught the Gospel of Christ to the weary, promising sweet visions of freedom in the afterlife. As in Africa, Black American preachers served a variety of roles—part-time politicians, social workers, indigenous intellectuals, spiritual comforters. Some were simply egotistical charlatans; others were reluctant revolutionaries. Because segregation eliminated any route of upward mobility for young Black men within the electoral arena between 1890 and 1960, the majority of Black would-be "politicians" ended up in the church. The church itself was, in many Black communities, the only institution in which a significant number of people regularly invested their time, energies and meager savings. The minister was particularly vulnerable to pressure from local white business and civic leaders, however, because they also recognized his central role in the daily life of his community. Through covert payments or through intimidation, the demands of white authorities were often incorporated into the political and even religious practices of many Black ministers.
The educators are still the largest single social group within the Black elite, but in many respects, they have been the least influential. During the nineteeth and early twentieth century, school for most Blacks consisted primarily of elementary level instruction. Within a patriarchal and agrarian society, public school teaching was often viewed as "women's work." The majority of Black male intellectuals were not found in the classroom; they tended to be businessmen, lawyers, newspaper editors and clergy. Even with the expansion of state-supported and private Black universities in the decades after the Civil War, the number of Black male teachers was surprisingly small. The economic demands of family life pressured Black men into vocations where the greatest possible financial compensation could be achieved. It was only in the 1940s, when the relative social status of the Black clergy had declined somewhat and the prospects for accumulating wealth through agricultural production had all but disappeared, that large number of Black males came to view teaching as a viable vocation. The status of intellectual work within the contemporary Black community still remains relatively low. This is particularly true for dissident voices among the Black intelligentsia. Revolutionary nationalists and Marxists are often persona non grata both at white and Black-operated universities and at white publishing houses. Mainstream Black intellectuals are usually politically integrationist and therefore more acceptable. Their Blackness is generally not part of their own intellectual praxis. The Black elite generally does not support Black institutions of higher learning as generously as other ethnic groups bankrole their own universities. Therefore, the economic terrain for Black intellectuals is always tenuous at best; Black academic institutions—particularly since desegregation—rock against the omnipresent shoals of bankruptcy; and Black education has become a marginal factor in influencing major public policy decisions that touch the lives of the Black majority.
Easily the most decisive element of the Black elite, both in the United States and in the Third World periphery, is the entrepreneur. The Black businessperson is the linchpin of underdevelopment and capital accumulation within the Black community. The goal of the Black entrepreneur is to make profits, period. How he/she accomplishes this task is secondary to the goal. The nonwhite businessperson is the personification of the legitimizing and rational character of capitalism. For white corporations, he/she serves to perpetuate the illusion that anyone can "make it" within the existing socioeconomic order, if only he/she works sufficiently at it. For the state, the Black enterpreneur represents the role model of proper civic behavior that the unruly and "nonproductive" Black masses should follow. The Black businessperson (which by definition here also includes persons involved in finance or banking, or who work as executives in a white-owned corporation) accepts and lives by the rules of the game. By nature and self-interest, the petty capitalist is profoundly individualistic. Profits can be made by exhorting Black consumers via Black nationalist appeals to "buy Black," or through NAACP-style pressures on the white private sector to subcontract goods, services or advertising through Black-owned firms: but profits must be made. My treatment of the elite will consist of all four major sectors described above. But it seems appropriate, writing this monograph during the period of "Reaganomics," to begin with the historical evolution of the entrepreneurs, and the theory of Black Capitalism.
Capitalism has always had proponents within the Black community. In fact, the historical evolution of the concept "Black Capitalism" provides one of the rare instances of ideological concensus among the fractious elements of the Black Movement, from the period of antebellum slavery to the present. Abolitionist leader Frederick Douglass, a strong integrationist, for example, encouraged newly emancipated Blacks to accumulate capital and to invest in their own enterprises. In 1874 Douglass even served briefly as president of the country's largest "Black" bank, Freedman's Savings and Trust Company. Racial accommodationist Booker T. Washington and Black nationalist leader Marcus Garvey developed detailed programs separately to coordinate small Black entrepreneurs. Conservative integrationists in the Urban League and nationalist-oriented members of the Nation of Islam advanced similar strategies for Black economic development within the U.S. capitalist system. At the 1968 Congress of Racial Equality (CORE) convention, leader Roy Innis, a militant Black nationalist, announced that his organization would build "a nation within a nation," attempting to develop Black community corporations and "Black ownership of capital instruments" to operate factories and to create job opportunities for thousands of unemployed Blacks.
For these leaders and the majority of Black political organizations of the last 100 years Black Capitalism connotes several key concepts: the accumulation of capital by individual Black entrepreneurs; strategies designed to maintain Black control over the Black consumer market in the U.S.; collective programs to improve the economic condition of all Blacks within the overall framework of U.S. capitalism. Beneath all of this is a theory of development, rooted in the often unchallenged assumption that U.S. capitalism is not structurally racist, and that the devastated condition of most Blacks throughout history could be alleviated through the acceleration of capital accumulation in the hands of a small number of Blacks.
This chapter begins with an alternate view of Black development, a thesis articulated by sociologist E. Franklin Frazier in his 1957 book Black Bourgeoisie. Black Capitalism was a "social myth," in Frazier's judgment, perpetuated by individual Black entrepreneurial "success stories" and by the economic barriers established by the system of segregation. The contemporary renaissance of Black Capitalist pro grams and ideology is fostered partially by the Reagan Administration and the emergence of a politically conservative sector of the Black elite. Beginning with Black economic history, this chapter documents some of the central components of the theory and practice of Black Capitalism, the evolution of the now highly profitable Black consumer market, and the current prospects for Black entrepreneurial activity in late capitalism. It will also reestablish that Frazier's initial critique is even more valid today than ever before in our history.
II
The origins of Black Capitalism are found in the development of a small but affluent propertied Black elite which emerged before the Civil War. In Northern cities, some Blacks owned surprisingly large amounts of real estate. Properties owned by Blacks in Philadelphia were valued at $400,000 in 1847 and $800,000 in 1856. In 1840, Blacks in Cincinnati had accumulated real property, excluding church and personal property, valued at $209,000. Real estate owned by Blacks in New York City and Brooklyn in 1853 was valued at $755,000 and $79,200 respectively. Black entrepreneurs were involved in a wide variety of antebellum commercial activities. In Manhattan, by 1840, Blacks owned one cleaning firm, two dry goods stores, two "first-class restaurants in the downtown financial district," four "pleasure gardens," six boarding houses, one confectionery and two coal yards. In the 1840s, one Black clothing and tailoring firm in Detroit, owned by James Garrett and Abner H. Frances, boasted annual gross profits of $60,000. Black entrepreneurs in Cincinnati were particularly successful. Samuel T. Wilcox, a Black boat steward on the Ohio River, initiated a wholesale grocery store in the downtown business district in 1850. Quickly he became "the largest dealer of provisions in the city," establishing commercial links with New Orleans and New York. By the mid-1850s Wilcox's annual gross profits were estimated at $140,000. In 1851 two Black businessmen acquired a contract with Hamilton County, Ohio, worth $10,000 to plaster all its public buildings. Henry Boyd, a former slave artisan, established a furniture store in the late 1830s in Cincinnati. By the 1850s he regularly employed 20 to 50 Black and white cabinet makers and workers, and was worth $26,000.
Under the slavery regime Black entrepreneurial activities were difficult, but not impossible in the South. In 1860, there were 348 free Blacks in Baltimore whose total property was worth $449,000. Eight hundred and fifty-five free Blacks in New Orleans owned 620 slaves and real estate worth $2,462,470 in 1836. By the outbreak of the Civil War, conservative estimates of property and business owned by the New Orleans free Black community exceeded $9 million. The vast majority of Blacks engaged in activities which provided goods and services to white patrons—tailoring establishments, saloons, eating houses, barbering and stables. The total value of all free Black-owned establishments and personal wealth in the U.S. in 1860 was at least $50 million dollars—half of which was based in the slave South.
Of course Black business was not without certain risks in a racist society. Northern and Southern whites found it difficult to tolerate the economic success of any individual Black person, fearing that even isolated instances of Black financial ability would threaten the racist order. In 1844, Virginia authorities revoked the license of mulatto innkeeper Jacob Sampson without explanation. In 1852 Maryland prohibited Black membership in building and homestead associations. Blacks who saved their money to purchase farms discovered that many white homesteaders did not want them in their states or regions. White insurance companies usually refused to do business with Blacks, and white bankers drew the color line against Blacks desiring credit. Black businessmen usually could not sue white creditors in Northern courts, and often were legally restricted from engaging in certain commercial activities. The political attitudes of wealthy Blacks were also subject to careful scrutiny. When a copy of Uncle Tom's Cabin was found in the possession of one Black merchant in Salisbury, Maryland, for instance, "the public hostility that resulted led to his financial ruin." In Cincinnati, white mobs periodically burned down Henry Boyd's furniture factory. "Three times he rebuilt, but the fourth blaze compelled him to yield since insurance companies refused to underwrite his risk."
Despite these risks, the relatively successful record of some early Black business efforts prompted many Blacks to conclude after the Civil War that private enterprise was the only means to achieve Black economic advancement. Booker T. Washington reflected upon these isolated instances and proceeded to postulate a general theory of group upward mobility via capitalism. Writing in 1906, the Black educator insisted that Black artisans "had a monopoly of the common and skilled labor throughout the South" in 1865. "By reason of contact (between) whites and blacks during slavery," Washington stated, "the Negro found business and commercial careers open to him at the beginning of his freedom."
In slavery, when the master wanted a pair of shoes made, he went to the Negro shoemaker for those shoes; when he wanted a suit of clothes, he went to the Negro tailor for those clothes; and when he wanted a house built, he consulted the Negro carpenter and mason about the plans and cost—thus the two races learned to do business with each other. It was an easy step from this to a higher plane of business; hence immediately after the war the Negro found that he could become a dry goods merchant, a grocery merchant, start a bank, go into real estate dealing, and secure the trade not only of his own people, but also of the white man, who was glad to do business with him and thought nothing of it.
Washington concluded, "for these reasons . . . the Negro in the South has not only found a practically free field in the commercial world, but in the world of skilled labor."
But emancipation and Reconstruction did not usher in a new period of Black economic expansion. Washington's interpretation of Black economic history is sharply contradicted by the evidence of the destruction of most Black artisans after the war. Several factors limiting Black economic opportunity were present. First, the vast majority of Black millers, blacksmiths, carpenters and other potential entrepreneurs were illiterate. According to figures from the Census of 1870, probably fewer than one-third of all urban Blacks in the South who were artisans or employed in commerce were literate. Any skilled Black artisan who lacked the ability to maintain correspondence with customers, to check accounts and to supervise payments to creditors was severely crippled. A second factor is suggested in DuBois' The Negro Artisan. Slavery permitted Blacks to develop skills as master craftsmen, but seldom permitted Black artisans to acquire training as entrepreneurs—placing advertisements in local newspapers, hiring and firing employees, purchasing supplies, and maintaining profit and loss records. The business of the Black artisan in slavery, DuBois observed, "had been to do work but not to get work." A third and decisive factor was white racism. In late 1865 many Southern states passed "Black Code" regulations declaring that any Black man who did not have an employer was subject to arrest as a "vagrant." Working independently got themselves, some Black artisans were fired, jailed and even sentenced to work as convict laborers. South Carolina's legislature declared in December, 1865, that "no person of color shall pursue or practice the art, trade, or business of an artisan, mechanic or shopkeeper, or any other trade, employment or business . . . on his own account and for his own benefit until he shall have obtained a license which shall be good for one year only." Black peddlers and merchants had to produce $100 annually to pay for the license, while whites paid nothing.
Historians Roger L. Ransom and Richard Sutch document that both before and immediately after slavery the number of Black artisans was extremely small. The percentage of slaves working as field hands in the Black Belt South in 1860 was between 80 and 92 percent in various states; rates for slave employment as blacksmiths ranged from under 1 to 3 percent; for all Black artisans, the percentages for states varied between 3 and 11 percent of the total slave workforce. These figures did not improve significantly by the 1890s. According to 1890 Census figures, in the five major cotton-producing states (Georgia, Alabama, South Carolina, Mississippi and Louisiana), the overwhelming majority of Black workers were employed as agricultural laborers, porters, laundresses, teamsters and personal servants. Over 90 percent of all male agricultural workers and almost 70 percent of all female agricultural laborers were Black, out of a total workforce of 594,700. The approximate number of Blacks gainfully employed in 1890 as painters in these five states was 2,272; butchers, 978; manufacturers, 256; printers, 234; bank employees, 108. More· importantly, the approximate number of Black lawyers and government officials in these states was 110 and 160, respectively. Aspiring Black businessmen had few allies in postbellum state and local governments to represent their interests, and had few if any friends in the banking industry to provide venture capital. The total number of Black businesses in the United States was approximately 2,000 in 1863, 4,000 in 1873, and only 10,000 in 1883. Growth rates in Black businesses declined abruptly between 1883 and 1903.
The older Black business elite—barbers, butlers, caterers, tailors, blacksmiths, carpenters, furniture makers and other skilled artisans—had been dependent upon white patrons for much if not all of its business. With the expansion of racial segregation after 1890, many of these artisans disappeared. The new generation of Black entrepreneurs was a byproduct of racial segregation, developing goods and services for Black consumers, embracing Washington's rhetoric of "self help" and racial upliftment. A conservative Black nationalist ideology was promoted aggressively by Black bankers, insurance agents and small merchants precisely because they "depended upon the Negro community for their support," observed historian August Meier. "The difficulties involved in obtaining credit from white banks, the discrimination practiced by white insurance companies and real estate firms, exclusion from white restaurants, hotels, and places of amusement, (and) the gradual elimination of skilled workers from employment" all combined to force Blacks to accept the Tuskegee economic theory. "Many (Blacks) were led to believe that only racially developed and supported business would solve their economic and other problems."
The number of Black Capitalist success stories multiplied with the proliferation of Jim Crow restrictions. In 1899 DuBois predicted that most Black barbers in Philadelphia would be eliminated, because they served whites. Eight years later he discovered that Black "barbers (were) more numerous than ever, but catering to Negroes." Between 1900 and 1914, the number of Black-owned banks increased from 4 to 51; Black retail merchants, 10,000 to 25,000; Black undertakers, 450 to 1,000. The total number of Black businesses in the U.S. doubled in a little more than a decade, reaching 40,000 in 1914.
Two of the most influential Black entrepreneurs of the period were John Merrick of North Carolina and Isaiah T. Montgomery of Mississippi. A former slave and brickmason, Merrick established the North Carolina Mutual Insurance Company. By 1915, the company was insuring Black customers in twelve states and the District of Columbia. Merrick and his Black partners also created Mechanics and Farmers Bank in 1908, and the Merrick-Moore-Spaulding Real Estate Company in Durham in 1910. They also briefly owned a textile mill, and managed two drug stores servicing Durham's Black population. In 1887, Montgomery, the former slave of Jefferson Davis' brother, established an all-Black town, Mound Bayou. In less than ten years the city possessed several banks and real estate firms, a trades and technical education school modeled after Tuskegee Institute, a newspaper, a power and light company and a sawmill.
But if the ideology and practice of Black Capitalism was to become a national force, it required political organizations. The leading advocate of this effort was Booker T. Washington. His influence in the Afro-American Council in the late 1890s was the beginning of the infrastructure which later became the Tuskegee Machine. The chief organization of Washington's power from 1900 to 1915 was the National Negro Business League. The original concept for the League came from the sociological studies of DuBois, who was at that time a professor at Atlanta University. In an 1899 conference, DuBois proposed "the organization in every town and hamlet where the colored people dwell, of Negro Business Men's Leagues." He also called upon Negroes to spend consumer dollars solely with Black entrepreneurs. Washington opportunistically expropriated the concept from DuBois, and within a year had created the organization. At its first annual conference in Boston, over 300 Black merchants, artisans, lawyers, doctors and newspaper editors gathered to promote the Tuskegee philosophy of self-help and Black private enterprise. For Washington, the development of the League would provide the basis for a gradual end to racial oppression and segregation. "Suppose there was a black man who had business for the railroads to the amount of $10,000 a year," he wrote. "Do you suppose that, when that black man takes his family aboard the train, they are going to put him in a Jim Crow car and run the risk of losing that $10,000 a year? No, they will put on a Pullman palace car for him." The road to eventual civil rights, in Washington's estimation, was clearly one of private capital accumulation.
Much of this sudden growth of Black businesses could not have occurred without the critical assistance of the Black press. Between 1865 and 1900 over 1,200 Black-owned newspapers were established, about 70 percent of them in the South. Without adequate advertising support, most of these papers disappeared within ten years. But in the age of Black business growth after 1900, a series of Black entrepreneurs succeeded in creating a number of politically influential news papers. Robert S. Abbott initiated the Chicago Defender in May, 1905, and within 15 years was printing 200,000 copies nationally. Virginia journalist P. Bernard Young started the upper South's most widely read Black newspaper, the Norfolk Journal and Guide, in 1909. Black lawyer Robert Lee Vann created the Pittsburgh Courier in 1910, which in three decades achieved a national circulation of 300,000 and became the largest Black publication in the U.S. In the Deep South, William A. Scott established a Black Republican newspaper, the Atlanta World, in 1928.
None of these newspapers could have survived without the continued support of Black business, since circulation revenues alone could not cover their normal expenses. As journalist-historian Henry G. LaBrie noted, "big business (in the 1920s) ignored the black press" because it was "unaware of the buying power of the black consumer." Thus, it was up to Black business to support the Black press. Accordingly, the National Afro-American Press Association usually selected officials who espoused the Tuskegee philosophy. At the peak of Washington's political power, the Tuskegee Machine even subsidized a number of Black newspapers, including the New York Age, the Boston Colored Citizen, the Colored American Magazine and the Washington, D.C. Colored American. Some Black newspaper owners and editors, particularly Fred R. Moore of the New York Age, not only became strong polemical advocates of racial accommodation but also became affluent business leaders in their own right. With these ties to Black business, the Black press became the chief vehicle to control and to exploit the Black consumer market, as well as to promote the ideology of Black Capitalism to the masses.
The "Golden Years" of Black business occurred in the decade 1919-1929, which not coincidentally was also the period of the most extensive racial segregation. By 1929 the number of Black-owned firms exceeded 70,000. Virtually every Black neighborhood or town in the United States could claim a number of independent Black entrepreneurs providing goods and services to an exclusively Black consumer market: barbers and beauty parlors, laundries, restaurants, grocery stores, newspapers, shoeshine and shoe repair shops, automotive service and repair, funeral parlors, insurance companies and small banks. It was this rapid petty capitalist development within a strictly segregated society that impressed and inspired the Black nationalist leader, Marcus Garvey. After only eight months in the United States, Garvey was convinced that Washington's strategy could be combined with race nationalism and political militancy to create a self-sustaining, Pan-Africanist economic order. Writing in 1916, Garvey declared:
The acme of American Negro enterprise is not yet reached. You still have a far way to go. You want more stores, more banks, and bigger enterprises. We (West Indians) have no banks of our own, no big stores and commercial undertakings; we depend on others as dealers while we remain customers. The file is there open and ready for anyone who has the training and ability to become a pioneer.
Garvey's Universal Negro Improvement Association (UNIA), which included commercial establishments, the Negro Factories Corporation and Black Star Line, was successful in part because it reflected the economic and political realities of the Jim Crow age. Even Garvey's harshest critics within the NAACP did not dissent from the general economic direction of the UNIA. In the Crisis, DuBois admitted that "the main lines of the Garvey plan are perfectly feasible. What he is trying to say and do is this: American Negroes can, by accumulating and ministering their own capital, organize industry, join the black centers of the south Atlantic by commercial enterprise and in this way ultimately redeem Africa . . . for black men. This is true. It is feasible."
Although DuBois considered himself an avowed socialist after 1904, his militancy was compromised with the optimistic spirit of the age. The Black entrepreneurial elite was basically a progressive, potentially powerful force in the battle against Jim Crow, in DuBois' view. He praised the rapid development of the Black business class in Durham, North Carolina, in 1912. In October, 1913, he commented on a conference of Black business leaders in Philadelphia, concluding that despite evidence of "a spirit of aggrandizement, lying, stealing and grafting" the general outlook for this stratum was "excellent." In articles written in 1922 and 1928, he applauded the development of Black-owned and directed banks. When two major Black businesses went bankrupt, Brown and Stevens Bank of Philadelphia and Standard Life Insurance in Atlanta, he urged readers of the Crisis not to lose confidence in Black enterprise. It was not until the Great Depression and its aftermath that DuBois grew pessimistic about the long-term possibility of a "Black Capitalist Solution" to the Negro's plight. In an October, 1942 newspaper column, DuBois lamented that Black entrepreneurs as a group had absolutely no ethics or morality regarding their own people. "What American Negro businessmen have got to remember," he urged, "is that a new economic morality is facing the world, and that emancipation from unfair private profit is going to be as great a crusade in the future as emancipation from Negro slavery was in the past." Again in May, 1943, he encouraged Black businesses to seek the general economic improvement of all Blacks, rather than simply the accumulation of capital at grossly high profit margins.
Few if any Black intellectuals and political leaders recognized the extreme economic instability of these expanding Black firms. A National Business League Survey of 1,534 Black enterprises in 33 large cities in 1928 found that 666—43.4 percent—recorded annual gross profits below $5,000, and only 137, or 8.9 percent, had annual gross receipts above $25,000.
For the Black banking industry, the Depression was disastrous. The Douglass National Bank of Chicago, which in 1929 had a capital investment of $293,212.70 and deposits totalling $1,507,336.70, failed in May, 1932, despite a $200,000 loan from the Reconstruction Finance Corporation. The Chicago African Methodist Episcopal Church lost $18,000 with Douglass' collapse; a Black fraternal order lost $20,500. Of the 134 Black banks founded between 1888 and 1934, not more than 12 were operating in 1938.
Thousands of other Black businesses also went bankrupt during the Great Depression. For the survivors, many managed by illegal means. In Chicago, for example, about one-fourth of all Black firms by the late 1930s were owned or controlled by "policy syndicates"—the "numbers" daily lotteries.
In World War II the number of Black enterprises resumed their pre-Depression growth, but at very low levels of capitalization. One 1944 survey of 3,866 Black businesses in 12 cities noted that the initial amount of capital for 64.4 percent of these firms was less than $1,000. The median value for Black business initial capitalization was $549. Some 86.3 percent of all enterprises were started solely with personal savings, and only 3.3 percent were initiated with bank loans. Almost 70 percent of all Black firms comprised only six types of businesses: restaurants (627); groceries (491); funeral parlors (126); shoe repair (130); laundries (288); barber shops and beauty parlors (1,004). Not until the late 1940s did Black businesses completely recover from the trauma of economic disaster.
III
As the Black sharecropper in the South became a blue collar or service worker in the East Coast and Middle West, the bulk of Black business activity moved with the massive migration North. Gradually, majority Black populations appeared where only two decades before emigrants from Eastern and Central Europe had settled. Georgia and Carolina Blacks moved into the traditional Italian neighborhood of East Harlem. In New York's lower East Side, Blacks and Puerto Ricans replaced Eastern European Jews. From the 1870s until World War I Harlem was primarily Jewish. The "ghetto," the term used in Europe to delineate the restricted residential boundaries for Jews, became attached to the Negro for all practical purposes by the 1930s. Black entrepreneurs who travelled north discovered that small Jewish, Irish, Italian and Slavic business owners did not often sell their establishments after their old ethnic neighborhoods had been racially transformed. Most of these firms were engaged in retail trade, had stable lines of credit with small banks established by their own ethnic groups, and they had absolutely no intention of surrendering the growing ghetto consumer market to upstart Black petty capitalists. Adding insult to injury, many of these Northern stores had an informal Jim Crow hiring policy well into the 1950s.
The Black response to white ethnic economic hegemony within the ghetto's retail market took distinct political form in the "Don't Buy Where You Can't Work Movement." Local Black leaders picketed white establishments first in Chicago in late 1931, demanding jobs for Blacks. The movement swept rapidly to Pittsburgh, Atlanta, Boston, Baltimore and Richmond. Blacks initiated the "Citizens' League for Fair Play of New York" and initiated selective boycotts of major white Harlem establishments. Black progressives were divided on the effectiveness of the "Don't Buy Where You Can't Work" boycotts. Adam Clayton Powell, Jr., rose to political prominence as Harlem's leading business boycott leader, and was elected to Congress in 1944. Black radical political economist Abram L. Harris thought that this Black nationalist-oriented strategy "would serve further to widen the breach between white and black labor." The boycotts "would merely meet the unemployment of Negroes with the displacement of whites. But in the final analysis it would be the hundreds of thousands of black workers in industry who would have to bear the cost of the movement's success in obtaining a few thousand jobs for Negro clerks, salesmen and managers. What would be more natural than a retaliatory movement of whites demanding that Negroes be employed only by those white capitalists whose income is mainly derived from Negro [sales]?"
The aspiring Black petty capitalists profited from this racial discontent. The closing of a single Jewish grocery store in a small Black neighborhood potentially meant thousands of dollars in added gross receipts to struggling Black entrepreneurs. To many Blacks in the middle strata within Jim Crow society, the existence of white businesses in a primarily Black community seemed essentially unfair. "Denied equal competition with whites in higher positions of the capitalist set-up and thwarted in its ambition to develop a miniature capitalism within its own segregated racial domain, the Negro middle class is being driven into a position of extreme racial chauvinism toward other minorities," Harris wrote in 1936. Black peddlers, loan sharks, retail store owners and real estate dealers not infrequently blamed Jews for Blacks' higher rents and exploitative consumer prices. The picture of the "money-grubbing, cheating Jew," to quote Paul Jacobs, soon became an integral part of Black urban folklore. In Los Angeles' Black ghetto, Watts, the vulgarism employed by unemployed Black teenagers for teasing Jewish shopkeepers was "pushing peanuts up Goldberg's nose." Jews, and after 1945, Lebanese, Palestinians, Latin Americans and Chinese were often the symbolic targets of Black economic animosity, primarily because they were the most visible non-Black entrepreneurs in ghetto life. But as Harris argued, racial chauvinism was no substitute for the development of an effective program to eliminate Black urban poverty, unemployment and hunger. "If there is exploitation of the black masses in Harlem, the Negro businessman participates in it as well as the Jew, while both the Jewish businessman and the Negro are governed by higher forces that are beyond their control."
In the 1950s and 1960s, the political prospects for Black Capitalism began to improve. White corporate leaders and politicians, anxious to improve their standing within the burgeoning Black urban communities of the North and West, began serious efforts to cultivate a stable and class-conscious Black elite. The general pattern that emerged was corporate and philanthropic support for local development corporations and "economic resource centers" which provided fiscal and technical assistance to Black businesses. In Los Angeles, for example, the Economic Resource Corporation was created with white corporate assistance. It guaranteed loans made by Black enterpreneurs at local banks, extended generous grants, and purchased property and machinery for Blacks. Chicago's Economic Development Corporation assisted Black businesspersons in their financial loan negotiations. The Interracial Council for Business Opportunity, a group of Black and white businesspersons in St. Louis, New Orleans, New York, Los Angeles, Chicago and other cities, gave technical symposiums to Black would-be corporatists, created the National New Enterprise Program—which helped Black businesses needing capitalization of over $100,000—and guaranteed "up to 50 percent loans made by banks to minority entrepreneurs." The Inner-City Business Improvement Forum of Detroit helped to arrange the finances of Black firms. Rochester, New York's Business Opportunities Corporation gave technical aid to Blacks just starting in business, and also guaranteed their bank loans. San Francisco's Program for Action in Changing Times provided most of the services available in other urban corporations of the type listed above, but it also acted "as a broker between minority job-seekers and large white corporations" and gave "counseling and technical assistance on a one-to-one basis for existing and potential businessmen." New York City's International Council of Shopping Centers encouraged Blacks who aspired to initiate their own shopping malls. New York's Association to Assist Negro Businesses (AANB) provided credit to Blacks "under a mechanism whereby pledges of $10,000 were solicited from each of twenty-nine white businessmen and used this as a basis for a $290,000 line of credit for ten years to be used against loan guarantees made by AANB to black enterprises."
This "benevolent" corporate strategy was actually a return to the policy of Andrew Carnegie and other business leaders vis-à-vis Washington and other Black accommodationists. It was Carnegie who financed the National Negro Business League's chapters; in 1904 the steel industrialist created a pseudo-civil rights organization, the Committee of Twelve for the Advancement of the Interests of the Negro Race, led by the politically pliable Washington. Similarly, years later, Richard Nixon appointed Black millionaire real estate developer and lawyer Gloria A. Toote to serve as Assistant Secretary for Equal Opportunity in the Department of Housing and Urban Development. Nixon also selected Black Capitalist proponent Jewel Lafontant to the post as Deputy Solicitor General in the Department of Justice. As women and as Blacks, both represented the newest version of the kind of personal success stories that perpetuate the myth of Black Capitalism. After Watergate and Nixon's political downfall, both women made the transition to symbolic posts in the upper sanctum of white corporate power. Lafontant became a member of the boards of TransWorld Airlines, Continental Illinois National Bank and Trust Corporation of Chicago, Equitable Life Assurance Society of the U.S. (New York City), Harte Hanks Communications, Foote, Cone and Belding, Jewel Companies, Inc., and the Bendix Corporation. Toote has emerged as the major Black female ideologue for Ronald Reagan and enjoys seemingly limitless access to the media to propagate her views.
Despite these and other paternalistic efforts, the general pattern of U.S. Black business today still reveals a systematic underdevelopment, a paucity of capital and employees, that extends across geographical and regional boundaries. A random selection of nine moderately sized cities where at least 100 Black businesses exist—three each in the South, North, and West—provides an illustration. The towns selected ranked between 70th to 90th in their size of Black population for U.S. metropolitan areas in 1977: Chattanooga, Tennessee (48,079 Blacks), Pensacola, Florida (43,458 Blacks), and Greenville, Mississippi (37,889 Blacks), in the South; Akron, Ohio (59,441 Blacks), Bridgeport, Connecticut (35,639 Blacks), and Harrisburg, Pennsylvania (33,605 Blacks), in the North; Sacramento, California (51,953 Blacks), Phoenix, Arizona (38,561 Blacks), and Austin, Texas (36,905 Blacks), in the West. Each town and region of the country exhibits different economic characteristics. Blacks comprise a higher percentage of a town's total population in middle-sized cities in the South than in the North and West. Akron, Harrisburg and Bridgeport have strong, industrial working class communities, with substantial Black membership in local trade unions. Sacramento, Harrisburg and Austin are state capitals, which traditionally have a higher percentage of Blacks employed in state government as white collar workers. Phoenix's Black community developed substantially later than in the other cities, with the sudden economic growth in the Southwest after 1950. (See Tables XX, XXI and XXII)
The data reveals some obvious divergences. The city recording the highest gross receipts in 1977 was Greenville, Mississippi, with $12,765,000. Greenville's gross receipts total is followed by Phoenix ($11,132,000) and Austin ($10,047,000). Cities with much larger Black populations, such as Sacramento ($6,920,000) and Akron ($7,666,000) actually recorded significantly lower gross profits. Greenville's Black economic development may be explained by history and geography. It is the largest town between Memphis and Baton Rouge on the Mississippi River. Situated between Arkansas and Louisiana to the Southwest, Greenville's Blacks are a high percentage of the town's population. Greenville is one of the largest commercial centers for what remains of the western Black Belt. It also retains a strong legacy of racial segregation. These points set Greenville apart from the two other Southern towns of similar size on the list. Chattanooga has some light industry, but is politically and socially more Appalachian white than Black Belt in character. Pensacola is part of the wiregrass region of western Florida and southeastern Alabama. George Wallace and his supporters still dominate the politics of the rural region, which is conservative, populist and technically outside the Black Belt. Blacks immigrating to Western cities like Phoenix and Austin after 1950 were generally better educated and more affluent than earlier Blacks who arrived between Reconstruction and World War II. Both cities, however, have recent histories of legal segregation ending only a generation ago. All three Black populations in the North have relatively small numbers of Black firms possessing paid employees, and rank fifth, seventh, and ninth in the group in 1977 amounts for gross receipts. Tentatively these figures suggest that cities with relatively high percentages of Blacks, having strong histories of legal segregation, and/or experiencing a rapid growth of middle class Blacks since 1950 will have a somewhat more developed Black petty capitalist infrastructure than towns of similar size without such characteristics. Black business communities are weakest in cities where no legal Jim Crow barriers have existed for a century or more, and/or where Blacks comprise a relatively small segment of the total metropolitan population.
There are far more similarities within these Black business profiles, however, than differences. The largest number of firms in all nine cities is in the area of "selected or human services," a broad category including housekeeping, repair shops, laundries, health services, amusement and recreational concerns, automotive repair and garages, hotels and educational services. Greenville has the lowest percentage of selected services within its entire number of firms, 35.2 percent. The other towns' percentages of selected services within the total number of Black firms range from 41 to 60 percent, roughly paralleling the Black national human services figure of 44 percent. In all cities selected, the number of human service firms without a single paid employee was much larger than those with workers. In Bridge port, only 14 out of 87 such firms have paid employees. The amount of gross receipts for firms without employees averages only $8,630 per year. Bridgeport's other 14 Black human services firms have staffs totalling 32 persons, pay annual payrolls averaging $10,214 per firm, and have average annual gross receipts of $55,714. The second leading number of Black firms in all nine cities is retail trade establishments: grocery stores, apparel and accessory shops, garden and building supply centers, general merchandise stores, restaurants, bars and furniture stores. Chattanooga and Austin have the largest number (both 108) of stores in the retail sector. The number of retail stores in both cities with paid workers is very low. Chattanooga's 79 Black retail stores without paid employees average annual gross receipts of $15,962. The city's 29 Black-owned retail establishments with employees (84 total) pay average annual payrolls of $12,689, and have average annual gross receipts of $139,931. Austin possesses 80 Black retail stores without paid workers, with average annual gross receipts of $14,925. The other 28 firms have a total of 46 employees, have average payrolls of $6,036, and average annual gross receipts of $63,679. Akron, the third ranking city (94) for Black retail firms, has similar totals: for the 77 Black retail firms without employees, average gross receipts were $10,597; the 17 other Black retail firms (43 employees) have average annual gross receipts of $130,058.
The lowest number of Black business enterprise in all of these cities is in the areas of manufacturing (food products, tobacco, lumber and wood products, electronic and electrical equipment, machinery, fabricated metal products, leather products, stone, glass and clay products, etc.) and wholesale trade (suppliers to food stores, general merchandise centers, furniture stores, etc.). Phoenix has only one Black manufacturer with paid employees, and 23 Black entrepreneurs who are wholesale merchants, most of whom (20) having no paid workers. Sacramento claims all of two Black manufacturers, neither of whom have employees, and only one out of a grand total of five Blacks involved in the wholesale business have any employees. Taken together, all nine cities listed here have a total of 2,933 Black-owned firms of various kinds. In this group, there are only 525 that have paid employees, 17.9 percent of the total number of enterprises. One thousand three hundred and seventy-one firms (46.7 percent of total) engage in human services. Some 687 businesses are in retail trade (23.4 percent). Over 70 percent of all modern Black enterprises, in summary, are in the same vulnerable sector of the segregated economy that was developed 80 years ago by Washington and the early proponents of Black Capitalism. Relatively few have made it into the big leagues of white corporate finance, manufacturing and wholesale commercial trading.
Census research on Black-owned businesses also indicates a profound pattern of concentrated wealth and power in the hands of a relatively small number of Black capitalists. Only 164,177 workers (mostly Blacks) found employment in the 39,968 Black firms which hired personnel in 1977. Within this figure, however, 32,581 businesses (81.5 percent of firms hiring workers) employed between one to four persons during the year. These firms hired an average workforce of 1.45 employees, paid average annual gross payrolls of $9,695, and recorded average gross receipts totaling $68,831. Moving up the employment scale, a different picture emerges. Only 230 Black firms in the U.S. in 1977 hired between 50 and 99 employees. This group retained an average workforce of 67.6 employees, had average annual gross payrolls of $540,035, and average yearly gross receipts of $2,357,909. At the pinnacle of Black Capitalism were the 113 Black U.S. firms which employed 100 or more workers in 1977. This tiny elite is marginally part of the dominant U.S. capitalist class. With an average workforce of 247.5 employees, these firms met average annual payrolls of $1,960,221. Average annual gross receipts for the elite in 1977 were $8,952,469. Throughout the U.S., there were 1,060 Black-owned corporations and partnerships that hired 20 or more employees. This small fraction of all Black entrepreneurs was only one half of one percent (00.46) of all Blacks engaged in private enterprise. These 1,060 affluent Black firms had gross receipts which totaled $2,467,958,000, 38.6 percent of all gross receipts acquired by Black firms with employees, and 28.5 percent of the gross receipts received by all Black-owned businesses. Only a few enterprises earn the vast majority of profits. One hundred and three manufacturing firms out of a total of 4,243 received 67.3 percent of all gross receipts in that sector, and employed 52.8 percent of all employees. In wholesale trade, 5 percent of the firms had 75.3 percent of all receipts and 58.3 percent of all paid workers. In finance, real estate and insurance, 90 firms (0.9 percent of the total number) earned 69.2 percent of all gross receipts and had 77.1 percent of all employees. Even within the Black commercial and industrial elite, the old patterns of the segregation era were stamped clearly on these profit patterns. Three hundred and forty three of the top 1,060 firms (32.4 percent) were involved in selected services, and another 277 businesses (26.1 percent) were large retail stores. Only two Black firms in the U.S. employing 100 or more workers were in wholesale trade. Only 5 construction firms and 3 transportation companies owned by Blacks hired 100 or more employees. (See Tables XXIII and XXIV)
Black Capitalism in the 1980s, whether considered as an economic force competing for a substantial share of Black consumer dollars or as a political force which advances a pro-corporate and "neo-Horatio Alger" ideology within Black society, must be subdivided into three distinct constituencies—the "proletarian periphery;" the intermediate Black petty entrepreneurs; and the Black corporate core. Over fourfifths of all Black-owned U.S. firms, 82.7 percent of the total number, belong to the proletarian periphery. These 191,235 enterprises have several common characteristics: (1) Almost all are sole proprietorships, unincorporated firms owned by a single Black individual; (2) most are started by Black blue-collar or marginally white-collar employees; (3) the firms are undercapitalized from the outset, and owners are forced to subsidize business activities by drawing upon personal savings, loans from friends and relatives, and by allocating a portion of their salaries at their other place of employment; (4) all of these firms have no paid employees; (5) the vast majority are concentrated in two traditional sectors of the segregated Black economy, human services and retail trade; (6) at least 75 percent become bankrupt within three years; and (7) their average annual gross receipts vary between $3,000 and $15,000. Economically and politically, these Blacks are essentially workers who are attempting to become small businesspersons, struggling against massive odds to leave the ranks of the proletariat.
These marginal worker-entrepreneurs must be viewed as part of the Black proletariat from which capitalism extracts surplus value. These small entrepreneurs uniformly pay higher rates for insurance, since majority-Black communities are defined as "high-risk" areas. They are exploited by banks which "redline" Black districts, making entire communities ineligible to receive loans at reasonable interest rates. The proletarian periphery falls victim to the economies of scale, wherein smaller retailers with low sales volume and a small number of commodities must charge Black consumers higher retail prices for goods or services than larger white companies. McDonald's and Kentucky Fried Chicken, for example, can sell their fast foods at nominally lower prices than the Black "mom-and-pop" chicken establishment, because of infinitely higher sales volume. Human service-oriented establishments initiated by Black workers who possess personal skills (hairdressers, cooks, barbers, caterers, etc.) can be established with little capital, but they are also extraordinarily vulnerable to capitalist recessions. Black workers and the unemployed have precious little discretionary income even during brief periods of high employment. At every periodic downturn in the capitalist economy, Black lower-to-middle income consumers cut back on their spending for services. As a result, in both 1973-75 and 1980-82 tens of thousands of small Black businesses failed.
Those fortunate enough to survive, by legal or even illegal means, became part of the Black petty bourgeoisie, the intermediate level of Black entrepreneurship. These Black businesses constitute about 38,900 firms, 16.8 percent of all Black enterprises. The common traits they share are the following: (1) All retain paid personnel, with an annual workforce between 1 and 19 employees; (2) average gross receipts are between $30,000 and $300,000; (3) almost all employers work full-time in their enterprises; (4) almost all firms receive loans from banks and savings and loan establishments to continue business expansion; and (5) a substantial minority of these firms are involved in real estate, finance, manufacturing, and other traditionally all-white sectors of private enterprise. In Black Capitalism, Timothy Bates outlines the financial characteristics of 285 Black "high-caliber" firms in Chicago, Boston and New York that received loans through the Small Business Administration in the early 1970s. Mean value for the group's total sales was $74,101; mean total assets, $30,029; the mean number of years of the Black owner's management experience, 8.45 years; mean total liabilities, $19,528; mean amount of Small Business Administration loan, $27,740.
The corporate core of Black Capitalism is the 1,060 Black businesses with a workforce of 20 or more employees, led by Black Enterprise magazine's top 100 firms. Number one is Motown Industries of Hollywood, producers of soul records, films and tapes, with 1979 gross receipts of $64.8 million. Numbers two through five are Johnson Publishers ($61 million), Fedco Foods supermarkets ($45 million), H.J. Russell Construction of Atlanta ($41 million), and Johnson Cosmetics of Chicago ($35.4 million). This select group also includes Independence Bank of Chicago ($98.3 million in 1979 assets); Seaway National Bank of Chicago ($80.9 million in assets); Industrial Bank of Washington, D.C. ($59.9 million in assets); Freedom National Bank of New York City ($57.9 million in assets); United National Bank of Washington, D.C. ($56.2 million in assets); North Carolina Mutual Life Insurance Company ($5.1 billion insurance policies in force); and Golden State Mutual Life of Los Angeles ($2.7 billion insurance policies in force). Although these figures seem impressive, all of these major Black corporations combined could be purchased, for instance, by Mobil Oil Corporation with its liquid assets. White corporations allow these Black companies to exist for symbolic value alone. John H. Johnson of Johnson Publishers, for instance, is a member of the Boards of Directors of Twentieth Century Fox, Greyhound Corporation, Zenith Radio Corporation and Marina City Bank. H.G. Parks, Jr., Black millionaire owner of Parks' Sausage Company of Baltimore, sits on the boards of First Pennsylvania Banking and Trust Company and W.R. Grace and Company. Former Tuskegee Institute President Luther H. Foster, the modern representative of Washington's conservative philosophy, was elected to the Boards of Directors of Sears, Roebuck and Company and Norton Simon, Inc. The modern equivalent of Fred R. Moore, Black Enterprise publisher Earl Graves, was rewarded with posts on the boards of International Telephone and Telegraph Corporation and the Liggett Group. Black millionaire and Atlanta Chamber of Commerce President Jesse Hill Jr. serves on the boards of Delta Airlines and Sperry and Hutchinson Company. The number of executives who truly dominate the Black corporate core within the Afro-American political economy amount to less than 200 individuals. They have earned the confidence of the white corporate hierarchy and the capitalist state by keeping alive the bogus illusion of Black Capitalism.
IV
Undoubtedly the greatest obstacle to a present-day Black Capitalist strategy is the newly found interest of white corporations in controlling and capturing the Black consumer market. Between 1960 and 1973 the estimated amount of goods and services purchased by Black Americans increased from $30 billion to almost $70 billion annually. By 1978 the Black consumer market was the ninth largest in the world. Twenty years ago, however, at the peak of the Civil Rights Movement, few corporations seemed interested or willing to make special efforts to appeal to Black consumers. Initial advertising strategies were poorly staged and more appropriate to the racial ideologies of the 1890s. In 1960, for example, Readers Digest decided to reprint Up from Slavery, and invited the United Negro College Fund to help it sponsor a creative writing contest to promote the ideals of Washington. In 1962 Greyhound Lines, Inc., the world's most profitable transportation company, hired baseball relief pitcher Joe Black as a special markets representative in New York City, to "recognize, identify and invite black passengers" to ride its buses. With much fanfare in press released to Black-oriented radio stations and to the Black press, Black was promoted in 1967 to vice president of special markets for Greyhound, becoming the first Black vice president in the U.S. transportation industry.
The white corporate strategy of gaining control of the Black consumer market occurred first with Pepsi-Cola Company. In the early 1950s the vast majority of Black soft-drink consumers purchased Pepsi, approximately three times more frequently than they selected Coca-Cola, Pepsi's chief competitor. Overall profits for Pepsi sagged from the Black market throughout the 1950s. In early 1961, Pepsi's management commissioned Elmo Roper and Associates to complete a detailed "breakout of black consumer preferences and attitudes, (giving) Pepsi its first overall picture of black consumer trends." The Roper study revealed a number of surprising facts:
1) Blacks comprised only 11 percent of the U.S. population, but made up 17 percent of the soft-drink market. Blacks purchased 300 million cases of soft drinks annually. White per capita consumption of soft drinks was 120 bottles, vs. 163 bottles for Blacks.
2) Blacks were far more "flavor-conscious" than whites. Forty-nine percent of all grape soda and over 33 percent of all orange soda sold in the U.S. was bought by Blacks.
3) Between 1951 and 1961, Blacks' consumption of Pepsi had remained constant, while Pepsi consumption among whites had increased 300 percent. "This lack of sales growth among blacks meant a loss of 60 million cases per year to Pepsi-Cola."
Reacting quickly, Pepsi elevated Harvey C. Russell as vice president of special markets. Russell's appointment, well publicized in both white and Black media, made him "the highest-ranking black executive of an international business firm." In January, 1962, Pepsi bought twelve four-color pages in Ebony, and ran advertisements in virtually every Black newspaper in the country. Pepsi donated money to over 30 annual Black conventions, cosponsored a tournament for Black golfers, and subsidized the casting of a special medallion for the president of the Black National Medical Association. The company urged its local bottlers to develop or expand programs for Black market development. In 1963 Pepsi hired Black historian John Hope Franklin and other prominent Black social scientists to develop an elaborate series of films and records entitled "Adventures in Negro History." By 1964, after spending several million dollars solely in Black-oriented advertising, the "bottom line" results were in. Pepsi-Cola's annual profits rose from $157.6 million to $250 million between 1960 and 1964. Market research indicated subsequently that after five purchases, six out of ten Black "heavy-user households" favored Pepsi, compared to only four out of ten white households.
The Pepsi-Cola campaign not only reaped almost $100 million, but illustrated to the entire white corporate and advertising world the enormous profits at stake in the Black consumer market. By the mid-to-late 1960s, advertisers produced exhaustive studies of Black consumer habits, finding key differences between Blacks and whites. Researchers discovered that Black women purchased over 50 percent more home cleaning products, particularly air fresheners, garbage bags, insecticides and oven cleaners, than white women on a per capita basis. In 1966, nonwhite consumers (11.5 percent of the U.S. population) purchased 15 percent of all cereal; 18.5 percent of the flour; 39 percent of the rice; 38 percent of the cornmeal; 17.5 percent of the poultry; 26 percent of the smoked sausage; 22 percent of the canned milk; 29 percent of the green beans; 32.5 percent of the lard; 14.5 percent of the molasses and syrup; 17 percent of the salt; 22.5 percent of the wool blankets; 15.5 percent of the cooking utensils; 14.5 percent of the overcoats; and 28.5 percent of the hats sold in the United States. The list of Black consumer preferences is, of course, almost endless. The data collected by market analysts can be interpreted in a number of ways, to promote greater profits from Black sales. For example, Procter and Gambel learned from its advertising agency that 22.4 percent of Black householders used Tide to wash dishes as well as the family laundry, compared to only 3.4 percent of white householders. The company developed two different marketing strategies: in white-oriented media, "the message referred only to Tide as a laundry detergent;" in majority Black areas, Tide is advertised as "an all-purpose detergent for dishes, in the bath, for washing fine fabrics, and in the laundry."
In the 1970s the level of corporate sophistication increased. Market analysts informed Pillsbury corporation that the purchasers of its "profit leader," Hungry Jack biscuits, were 46 percent Black and 54 percent white. Relatively few white householders outside the rural South regularly ate biscuits, whereas Black consumption was increasing. However, Pillsbury was dismayed to learn that only 11 percent of all Black consumers purchased Hungry Jack biscuits, which were then packaged in a ten-ounce, ten-biscuit can. Allocating $1.5 million for a new marketing strategy, Pillsbury decided to simply maintain its white consumer market while attempting to boost its sales to Blacks. A six-biscuit can was produced to appeal to smaller Black households. Black-oriented radio commercials were developed for Black stations with a "hearty endorsement of a black mother." Hungry Jack advertisements appeared in Essence and Ebony. By 1975, gross profits surged 56 percent. Brown and Williamson Tobacco Corporation of Louisville, Kentucky, hired a Black advertising firm for assistance in marketing its Kool cigarettes in the Black community. Research figures revealed that while Kool accounted for a meager 7 percent of the total U.S. cigarette market, Black smokers comprised about one-third of all Kool consumers. In the mid-1970s Brown and Williamson initiated the "Kool Jazz Festivals," featuring noted Black musicians and singers, playing only in cities where a significant number of Blacks resided. In its first year, the concerts reached 480,000 people, mostly Blacks. Much of the music presented in the Festivals by the late 1970s, ironically, was not jazz at all, but "disco." Kool producer George Wein admitted that this "has upset" some jazz artists, but "we will continue to present soul artists as long as the public wants to hear them." Authentic Black jazz or blues, in short, did not produce sufficient patrons or profits.
The impact of corporate America's massive exploitation of the Black consumer market has created a profoundly negative effect within Black culture and consciousness. When Schieffelin and Company, manufacturers of Teacher's Scotch, learned that Blacks consumed a 50 percent higher per capita rate of scotch than whites, it created a film narrated by Jesse Owens, The Black Athlete, in 1971. The film "premiered" in every U.S. city with a large Black consumer market. "Teacher's Scotch Sports Nights" were arranged by Black liquor salesmen, and the film was displayed in bars and nightspots in Detroit, New York, Baltimore, Chicago, Washington, D.C., Cleveland and Los Angeles. Prints of The Black Athlete were forwarded to Schieffelin distributors for showings in bars in smaller Black communities and in Black public libraries. The same ideological techniques devised by corporations are now used with greater effect by the U.S. military and other law-and-order agencies. In the aftermath of the urban rebellions of the late 1960s, for example, the National Guard recognized that it had a major "credibility problem" within the national Black community. In 1970 only 5,000 Black Americans were members of the National Guard. The military agency hired W.B. Doner and Company to devise a media strategy to help it "to overcome negative attitudes" among Blacks. With Doner's assistance, Black Guard membership exceeded 50,000 by 1976.
In addition to these specific marketing strategies, there has also been a general white corporate strategy to increase profitability at the expense of the Black consumer. The first aspect of this strategy concentrates on 50 percent of the total Black U.S. population, whose annual incomes fall below $13,000. White businessmen now recognize that the urban poor and lower-income consumers can be made to pay much higher prices than affluent white suburbanites for commodities, so long as adequate lines of credit are made available to them. In the 1960s, studies illustrated that personal debt-to-income ratios were quite high for all poor people, Blacks and whites alike. However, unlike low-income whites, Blacks' debts "tend to increase with income." Blacks with incomes of $5,000 actually had greater personal debt-to-income ratios than whites with virtually no income. Black low-income consumers also suffered because of low savings rates. For Black families with incomes below $2,500 in the early 1960s, only 25 percent had savings of $100 or more. Merchants designed their Black marketing strategy to make profits not only from the sale of the commodity, but primarily from the terms of the credit agreements. Almost two-thirds of all poor Blacks buy their household appliances either exclusively or primarily on credit, often on terms that exceed market credit rates by over 100 percent. David Caplovitz's observation of 1963, "the poor pay more," remains true today.
The second part of the profit-making corporate strategy concentrates on the 36.1 percent of the U.S. Black population with annual incomes above $15,000 in 1978. Segmented, this sector of the Black consumer market includes: the majority of Black two-parent households with both parents in the labor force, 1977 median income of $17,008; Black family heads with 4 or more years of college education, 1976 median income of $20,733; Black two-parent households under the age of 35 with both parents in the labor force, residing in the North and West, 1974 median income of $15,031. In 1974, the highest 20 percent of all Black families received 44.2 percent of the aggregate income earned by all Blacks, and the top 5 percent received 15.9 percent of all Blacks' aggregate income. Corporate market analysts learned that these "middle-class" Black families spent a larger share of disposable income on travel, certain foods, entertainment and luxury furnishings than whites at identical income levels. Mediamark Research, Inc., completed a detailed study of the purchasing patterns of Black families who earned over $15,000 in 1980. The research completed indicated that Black middle-class families not only were heavy consumers, but had spending patterns that were different from lower-income Blacks. Corporations and advertisers in the 1980s began to devise class-conscious propaganda, based on this type of information, to capture this new Black elite market. (See Table XXV)
v
The modern paradox confronting the prospective Black Capitalist is the process of desegregation. No Black nation in history has acquired the economic growth potential of the total Black consumer market in the U.S. Total Black income had grown from $98.6 billion in 1978 to $125.8 billion in 1980. Almost half of the aggregate Black income, roughly $56 billion in 1980, was earned by less than one-fifth of all Black families. Theoretically, Black enterprise activities should have entered an unprecedented period of capital growth in the 1970s and 1980s. But in real terms, the opposite occurred. Between 1900-1930, the number of Black firms increased 700 percent; between 1930-1969, the number of Black firms grew by 233 percent; between 1969-1977, growth was 70.5 percent. The number of Black businesses with paid employees in 1969—38,304—amounted to 23.4 percent of all Black firms in operation; by 1977, Black firms with employees totaled 39,968, only 17.3 percent of all Black businesses. Gross Black business receipts climbed from $4.5 billion in 1969 to $8.6 billion in 1977, but inflation and other factors actually reveal an overall stasis in real net profits. Historically, rapid Black business growth occurred only during the period of rigid racial segregation, when relatively few white corporations made any attempts to attract Black consumers. The Civil Rights Movement and desegregation permitted the white private sector to develop a variety of advertising strategies to extract billions in profits from Black consumers, all in the name of "equality." The net result was the increased marginalization of the Black entrepreneur, the manipulation of Black culture and social habits by white corporations, and a new kind of economic underdevelopment for all Blacks at all income levels.
Recognizing the crucial paradox, a number of Black advocates for capitalism have stepped forward with new approaches to this dilemma. In 1968, Andrew Brimmer, a member of the Board of Governors of the Federal Reserve System (and subsequently, a member of the Boards of Directors of Bank of America, American Security Bank, E.I. DuPont, United Air Lines, and International Harvester) admitted that "the wall of segregation which cut Negroes off from many public services" provided a "wall of protection (for) the Negro businessman." Washington's ambitious strategy was doomed to failure, however, because "in those areas in which Negro customers have relatively free access to retail establishments (such as department stores, hardware, furnishings and similar outlets), Negro businessmen have not found fertile ground." Complete desegregation would destroy the entire foundation of Black Capitalism. Therefore, Brimmer concluded, would-be Black entrepreneurs should leave the ghetto and become managers and consultants to multi-billion dollar U.S. corporations. As a conservative integrationist, Brimmer views all forms of racial separatism with utter contempt. As an integral spokesperson for corporate interests, he advances the necessity to develop a stable Black stratum within the upper-to-middle ranks of the managerial elite.
Other proponents of Black Capitalism are reluctant to yield to the modern realities of America's corporate system, yet they recognize that the old Washingtonian approach can no longer yield dividends. "It is obvious that black economic development, on the scale necessary, is impossible if it must rely solely on accumulated wealth possibilities in the black community," Black economist Flournoy A. Coles, Jr., wrote in 1975. "The black stock must be augmented with wealth from outside the black community—and this means wealth transfers." A combination of corporate property and Federal tax revenue, or perhaps "reparations payments" from white civil society, would be used to form the basis of a Black capitalism within the overall system of "white capitalism." The most ambitious and controversial scheme outlined to date that implements this strategy was written by economist Richard America. Since Blacks comprise over 10 percent of the total U.S. population, America observed, then in a truly "democratic capitalist" society, Blacks also should own 10 percent of all U.S. corporations. The Federal government should buy 125 of the largest industrial firms and corporations over a period of 15 years at fair market rates, and subsequently resell them to Black businesspersons at below market rates. The difference in purchase and resell price, literally hundreds of billions of dollars, would be absorbed by the Federal government. Coles favors the "America plan . . . because it addresses itself to the root cause of black powerlessness and black alienation from the economic mainstream of our society." Other Black theorists have extended the proposal to include 10 percent of all corporations and firms currently owned by whites.
Even when examined seriously, the America proposal is absurd. The total gross income received by all U.S. Blacks in 1980 was $125.8 billion, and the total gross receipts of all U.S. Black firms that same year was $8.6 billion. Let us assume, for the moment, that the Federal government agreed to such an arrangement—a deal that would significantly increase income tax rates and stimulate inflation tremendously. Let us assume further that every single Black income earner in the U.S. in 1980 set aside 3 percent of his/her gross income computed at $3.77 billion. Black firms with 20 or more employees would reserve 5 percent of all annual gross income ($123.4 million in 1977), and less affluent businesses with fewer than 20 workers would donate 3 percent of gross receipts ($117.9 million in 1977). The total amount of capital, excluding any costs for paperwork, etc., comes to $4 billion. The total number of all businesses in the U.S. in 1972, excluding corporations, was 7,053,000, of which Blacks owned 2. 7 percent. Gross 1972 receipts for all businesses, again excluding corporations, amounted to $289.3 billion. Even if the Federal government reallocated these small-to-medium sized sole proprietorships and partnerships at fantastic budget prices, it would take probably more than one hundred years to complete the payments. But one special problem emerges. In certain very profitable economic sectors, Blacks are not currently trained in adequate numbers to assume "leadership" for their 10 percent share of that particular area. Only 2.3 percent of all construction-firm owners are Black; only 0.4 percent of all wholesale trade owners are Black; Blacks comprise only 0.8 percent of all real estate, insurance and finance company owners. Should the Federal government pay the reeducational costs of Black factory workers, for example, to become chief executive officers of metropolitan banks and public utility companies? And will the transfer of these companies mean that more Blacks from the working class will have a greater possibility of jobs, eliminating the high Black unemployment rate? What America, Coles, et al., ignore is that the U.S. is not simply a capitalist state, but a racist state. Everything in U.S. history indicates that not a single major corporation would agree to liquidate its current directors and owners, rendering itself unto the desperate Black petty bourgeoisie.
There is yet another political reservation that must be registered about Black Capitalism. Historically within advanced capitalist societies it is the sector of petty capital that is often more inclined toward authoritarianism than large capital. Reactionary political movements within parliamentary democracies tend to develop their strongest support (although, I should add here, not their decisive support) among elements of the most economically insecure and marginal stratum within the capitalist class. Hitler's astonishingly rapid growth in Weimar Germany came not merely from the anti-Semitism of many German unemployed workers but also from the small shopkeepers and merchants of that country. In both 1976 and 1980, finance capital was extremely reserved about Ronald Reagan's candidacy for the Republican nomination. Reagan's delegates tended to be less well-educated and less wealthy than Ford's or Bush's delegates, respectively. Small business is usually less supportive of state intervention into the capitalist economy (e.g., its strong opposition to the Federal government's loan guarantees to Chrysler Corporation in 1980), and is far more hostile to unions than multinationals are. Large corporations agree to modest minimum wage laws and substantial wage and fringe benefits to workers because they desire long-term labor peace. Small corporations, sole preprietorships, and business partnerships, working with smaller profit margins, paying higher interest rates for borrowed capital for business expansion than the multinationals, cannot afford to take the "long view." The gross receipts of every single business day are much more crucial to them. Sole proprietors, Black or white, are much more likely to advocate strict laws to restrict the development of unions in their own workplace, and in their own states. The economic demands of day-to-day entrepreneurial struggle tend, in every capitalist society, to push the politics of small businesspersons to the right. This remains particularly the case for entrepreneurs engaged in human services and retail trade—the economic areas which have continued to be the decisive part of Black Capitalist development. In short, the crisis of modern capitalism may push the advocates of Black Capitalism squarely into the political camp of the most racist and conservative forces of white America. The logic of Black Capitalism could reinforce the politics of authoritarianism. The Black entrepreneurs' quest for profits could become part of the political drive to discipline the entire Black working class.
CHAPTER SIX
BLACK BRAHMINS: THE UNDERDEVELOPMENT OF BLACK POLITICAL LEADERSHIP
there's only two parties in this country
anti-nigger and pro-nigger
most of the pro-niggers are now dead
this second reconstruction is being aborted
as was the first
the pro-niggers council voting
the anti-niggers have guns. ..
—Nikki Giovanni, Black Feeling, Black Talk, Black Judgement (New York: William Morrow, 1970), p. 83.
It sometimes happens in a nation where opinions are divided that the balance between parties breaks down and one of them acquires an irresistible preponderence. It breaks all obstacles, crushes its adversary, and exploits the whole of society for its own benefit. But beneath this apparent unanimity deep divisions and real opposition still lie hidden. That is what has happened in America . . . It is easy to see that the rich have a great distaste for their country's democratic institutions. The people are a power whom they fear and scorn.
—Alexis de Tocqueville, Democracy in America (New York: Anchor, 1969), pp. 178-179.
I
There is something essentially absurd about a Negro politician in racist/capitalist America. The political apparatus was designed originally to exclude him/her. The rhetoric of the system is democratic, almost egalitarian: the practices are bluntly discriminatory. Any state cannot exist in and of itself; it rests upon the material base of a particular productive process, and in the last analysis, acts decisively to protect the propertied and powerful classes of that society. The Black majority has no real structural power, other than the productive capacity of its own hands. The Black elite retain the illusion of power, but are invested with little authority in its own right. The Black politician is locked in a world of meaningless symbols which perpetuate the hegemony of the white ruling class but that are not in themselves sufficient to maintain legitimacy. The Black elected official is essentially a vicar for a higher authority, a necessary buffer between the Black majority and the capitalist state, a kind of modern voo-doo priest, smelling of incense, pomp and pedigree, who promises much but delivers nothing. Frantz Kafka wrote of such people in this manner:
They were offered the choice between becoming kings or the couriers of kings. The way children would, they all wanted to be couriers. Therefore there are only couriers who hurry about the world, shouting to each other—since there are no kings—messages that have become meaningless. They would like to put an end to this miserable life of theirs but they dare not because of their oaths of service.
The instant that the Black politician accepts the legitimacy of the State, the rules of the game, his/her critical faculties are destroyed permanently, and all that follows are absurdities. Black petty bourgeois politics is by definition and practice an attempt to channel goods, services and jobs to Black voters. In this endeavor, not a single white corporate executive or power broker would raise a veto. The Black Brahmin, the representative of the Black elite in politics, is praised for his/her responsible activities, or is perhaps criticized for being "too liberal"; but all discourse takes place within the parameters of the system as it exists. After a period of years, the Black elected official actually believes that the meager level of services he/she provides for a constituency actually produces fundamental change for the Black masses. Perhaps bourgeois democracy is colorblind, after all. . . The Black majority, viewing the sordid process from the bottom up, retains few illusions about its inherent equality. But real political power is not yet in its hands. So the macabre dance of the absurd continues. And the agony of the masses is increased.
The hopelessly symbolic power of Black elected officials and politicians was never more apparent than in the wake of the election of Ronald Reagan to the Presidency in 1980. Most Black leaders immediately attacked Reagan's budget cuts and gross expenditures in military hardware as socially unproductive. But on fiscal policies, no real Black political consensus emerged as to the reasons for the emergence of Reaganomics at this time which could lead towards a general critique of modern American capitalism. Indeed, most Black politicians' criticisms of Reaganomics were at best highly confused, lacking any basic comprehension of the capitalist prerogatives behind the public policies of the Reagan Administration. Testifying before Congress, Chicago Urban League director James Compton suggested that he "could support" Reagan's agenda if it created "more employment opportunities for minorities." The board of directors of the NAACP proposed the adoption of an alternative Federal budget which increased defense expenditures and resulted in a $55 billion deficit, but also raised the income tax exemption for a family of four to $10,000 annually. The general direction of the proposal was a fairly conservative form of Keynesianism, not unlike the austere 1981 budget of Carter. Some Black commentators suggested that Blacks themselves were somehow to blame for the economic mess. "With the Reagan budget cuts in full swing some middle class Blacks are beginning to feel the razor's edge inching closer and closer to their necks," columnist Joyce Daniels Phillips wrote in the Jackson Advocate. The solution was developing a new set of austere socioeconomic values: "cutting back on material possessions, monthly mortgage payments, exorbitant car notes, and numerous charge accounts." A few Black politicians, such as Representative Harold Washington, attacked Reagan's budget cuts and tax policy as "nothing more than a transfer of wealth back to the rich from the poor," but professed no radical alternative program. Some Black politicians denounced Reaganomics by declaring that the President was racist—without a concomitant explanation suggesting why neither Nixon nor Carter, who were equally racist, had not advanced these specific fiscal policies. Still others asserted that Reaganomics was merely economic "evil," and that "Reagan is the antichrist."
Many Black politicians had consoled themselves in the wake of the "Reagan mandate" with the thought that Blacks must inevitably pull together to confront the common enemy. However, it was Reagan's Black friends that seemed to pull together first.
During the 1980 Presidential campaign, Reagan's Black apologists were few and far between. But in December, 1980, barely a month after Reagan's election, 125 Black academicians and business leaders caucused in San Francisco at a conference held by the Institute for Contemporary Studies to discuss the directions for Black conservatism. Organized by black economist Thomas Sowell, the conference featured Reagan advisors Edwin Meese and Milton Friedman as honored guests. This meeting marked a significant turning point for national Black politics, for it dramatized and made public the severe contradictions on major political, economic and educational issues which divided the members of the Black elite. By the autumn of 1981, differences within the elite had become so intense that any possibility of building a consensus position on major public policy issues was lost. Dissention within the ranks was the order of the day, as Black actors opportunistically seized the subordinated roles which were given to them. A new political current was born—Black Reaganism.
II
Easily the most striking thing about Black politics during the Reagan Administration was the sudden ascendancy of Sowell, Hoover Institution professor and eminent Black conservative. It occurred at a moment in history when the veterans of the Civil Rights Movement had become disillusioned and defensive in their language and public policy activities; a period when U.S. corporate hegemony was declining, and both white business and political leaders were calling for a conservative, supply side agenda. At the same time Black activists and militant nationalists seemed out of step with the masses of Black people. In the midst of this confusion Sowell stepped forward along with other Black conservatives, not to condemn the Reagan Administration, but to praise it. In a series of media events and public forums the new Black spokespersons railed against affirmative action, spending for social programs, the minimum wage law, and a host of New Deal and Great Society programs long cherished as necessities by millions of poor and working class Black people. Sowell's calculated program of submission and silence, his bombastic attacks on the NAACP, and his conciliatory demeanor toward the interests of capital won high marks from the most bitter and vitriolic opponents of the civil rights cause. We were told that the Black American professional and business elite would soon embrace the conservatives' programs in full, and that this shift toward Black Reaganism was inevitable and even a healthy step toward Black political power.
Black conservatives do not represent a monolithic political/social force, but rather have evolved from radically different sectors of Black society. In brief, there are at least four overlapping categories of Black Reaganites: conservative Black politicians; Black philosophical conservatives; Black corporate executives, business managers and Reagan administrative appointees; and former Black Power activists and nationalists who have not fully embraced Reaganism but nevertheless have become so closely aligned with this rightist trend that they merit the obloquy "fellow travellers." Some of the most prominent Black Republicans of the past two decades have been the late W.O. Walker, publisher of the Cleveland Call and Post and head of the national "Blacks for Reagan-Bush" organization in 1980; James Cummings, leader of the National Black Republican Council; Art Fletcher, former executive director of the United Negro College Fund and Labor Department officer under Nixon; Samuel Pierce, Reagan's Secretary of Housing and Urban Development; and William T. Coleman, Ford's Secretary of Transportation. These Blacks were subordinates within the Rockefeller wing of the Republican Party during the 1960s and early 1970s. During the Nixon Administration they consistently supported affirmative action programs, civil rights legislation and Federal assistance to Black-owned businesses. Coleman had been part of the legal team which successfully challenged school segregation laws in the 1954 Brown decision. Like other liberal Republicans, notably former New York Senator Jacob Javits and Illinois Senator Charles Percy, they strived to reconcile their belief in limited Federal government and unfettered capitalism with the desegregation of white civil society and equal opportunity legislation to promote the development of a Black petty capitalist class.
The philosophical conservatives properly belong to the rabid right wing of the Republican party, advocating Milton Friedman's version of laissez faire capitalism, state's rights, and a dogged hatred for left-of-center politics. This militantly rightist faction includes Walter Williams, professor of economics at George Mason University; J.A.Y. Parker, a former official of the anticommunist Young Americans For Freedom and currently president of Lincoln Institute and Educational Foundation; and Wendell Wilkie Gunn, assistant treasurer of Pepsi Corporation. The titular leader of this tendency is Sowell, Ronald Reagan's favorite "House Nigger." After serving in the Marines, Sowell attended Howard University. Considering himself a Marxist, Sowell eventually received graduate degrees at the University of Chicago and Columbia. As he moved up the academic ladder his ideological views grew increasingly conservative. By the late 1960s he had become a Goldwater Republican and a bitter opponent of the welfare state. He condemned the emergence of Black Studies and Black campus activism. By the election of Carter, Sowell had come to repudiate most of the ideals of the Civil Rights Movement. He condemned affirmative action legislation as detrimental to Blacks' interests. His prescription to the plight of poor education within the ghetto was the imposition of "strict discipline" and mandatory expulsion of "rowdies who disrupt education for the majority." Sowell attacked the NAACP/civil rights leadership as a "light-skinned elite" whose policies served to provide "access to whites" for themselves but not for the Black poor. In a major advertisement paid for by Smith Kline Corporation in 1981, Sowell praised capitalism as the vehicle for Blacks to gain acceptance and upward mobility. 'The rich are a red herring used by politicians to distract our attention," he declared. "There aren't enough rich people to make any real economic difference, whether they pay high taxes or low taxes. The great majority of the government's money comes from the great majority of the people." Like Reagan, Sowell believes that inflation, not unemployment, is the real problem within America's political economy. "Balancing the budget is not enough," Sowell warns. "Whether we yearn for government giveaways as the answer to our problems, we have to realize that every giveaway is also a takeaway. Anything the country can't afford without the giveaway, it can't afford with it."
Potentially the most influential faction among Black Reaganites are the coterie of Administration officials and middle level executives from major corporations. In the executive branch of government, the list includes Thelma Duggin, formerly the Republican Committee liaison to the National Black Voters Program in the 1980 election and currently serving as deputy to Presidential advisor Elizabeth Dole; Melvin Bradley, Senior Policy Advisor to Reagan, responsible for developing "public policy recommendations in the areas of food and agriculture, minority business development, urban affairs, free enterprise zones, small business administration, and Black colleges and universities"; and Thaddeus Garret, Vice Presidential assistant in charge of domestic policy and programs. Major Black corporate supporters of Reagan's policies include Gloria E.A. Toote, a New York attorney and millionaire real estate developer; William Pickard, owner of a lucrative McDonald's franchise in Detroit; Arthur McZier, president, National Business Services Enterprises, Inc.; Constance Newman, president, Newman and Associates; Abraham Venable, Vice Chairperson of the Business Policy Review Council and director of General Motor's Urban Affairs Division; Fred Blac, Business Policy Review Council Chairperson and corporate executive in General Electric; Cyrus Johnson of General Foods; Philip J. Davis of Norton Simon, Inc.; and John Millier of the United States Brewer's Association. These Black corporate executives and bureaucrats had no ideological commitment to civil rights, affirmative action, or to the defense of any traditional institutions within the Black community. They favor Reaganomics because it will generate greater profits for their client industries and monopolies. These corporate Black Reaganites are even more dangerous than Sowell, because their blatant and vigorous support for consevative public policies is rooted not in any ideological commitment, but is grounded purely in their own vicious desire for money and their hunger for power.
The "fellow travellers" of the Black Reaganites include a number of would-be Black militants who are disenchanted with liberalism and protest politics. At the top of the list are Charles V. Hamilton, professor of government at Columbia, and Black media commentator Tony Brown. Both Hamilton and Brown attended the San Francisco Conference of Black conservatives. The co-author of Black Power, Hamilton has experienced a radical metamorphosis since his days as mentor to Stokely Carmichael (Kwame Ture). Since Blacks are a "relatively powerless minority," he informed the New York Times, the rise of a new Black conservative trend was essential. "Frankly," Hamilton admitted, "I'd be very worried if we didn't have them." Brown criticized the NAACP's "hostile behavior towards President Reagan" when he appeared as a guest at their annual convention in Denver in 1981. Brown thought that Reagan really wants "to economically emancipate Black ghettos," and that the President's brutal budget cuts were tantamount to a request for Afro-Americans to "return to the fundamental nationalism of their past. Ironically," Brown explained, "Reagan's philosophy of a sound economic power base for Black America is more compatible with past Black leaders such as Marcus Garvey, Booker T. Washington, Elijah Muhammad and Frederick Douglass, than are the modern-day disciples of the Black establishment." This massive distortion of Black history by Brown scarcely masked his overt appeasement toward the forces of racism and political reaction." What all four tendencies hold in common is a firm belief that racism, in words of Reagan apoligist Nathan Wright, Jr., no longer has "a damn thing" to do with Black underdevelopment; that socialist, Marxist, Keynesian and/or liberal economic programs will not work; and that Black advancement is best served by initiatives of U.S. monopoly capitalism.
The emergence of a Black neoconservative tendency had not accompanied the reelection of Richard Nixon eight years before, despite the fact that Nixon had carefully cultivated a token program for Black Capitalism, and had even appointed a liberal Black Republican, James Farmer, to his cabinet in 1969. The sudden rise to prominence of the Black Reaganites can be explained, in part, by a decline in the internal organization and prominence of the Congressional Black Caucus during the interval between Watergate and the 1980 elections. In 1969, Charles Diggs, a progressive Democrat from Detroit, had initiated the process which culminated in the creation of the Caucus two years later. In the early 1970s, many Caucus members were either active or directly supportive of the Black nationalist political renaissance. Diggs served as a leader in the staging of the National Black Political Convention at Gary, Indiana, in 1972, was the influential vice chairperson of the House Committee on Africa, and chaired the House Committee on the District of Columbia. Walter Fauntroy of Washington, D.C., and Ron Dellums of Berkeley-Oakland, California, were also active at Gary; indeed, Dellums' close relationship between militant Black nationalists and the key organizers of the National Black Political Assembly, continued throughout the 1970s. The left wing of the Caucus, Dellums and Michigan Congressperson John Conyers, were open advocates of democratic socialism, and had little reservations in challenging the white leaders of their own party from the left on both foreign and domestic public policies.
Although the Caucus continued to exist (as of this writing), by the late 1970s it began to fracture internally due to ideological differences, egotistic power plays, and from external criticism from many moderate-to-conservative Black elite leaders. Critics pointed out that the Caucus was woefully inept in securing legislation favorable to minority interests. In the Ninety-fourth Congress, for example, of the 729 bills which became law, the Caucus members had sponsored only 16. Caucus efforts to identify itself as the "collective voice of the national black community" met opposition from nonelectoral Negro politicians and civil rights leaders, who jealously protected their political turf. Membership in the group was an unstable fact of life. During the Ninety-fifth Congress alone, two members resigned, one died, and another was defeated. Diggs was "forced from office by a prolonged scandal and finally a conviction for misappropriation of federal funds." The Caucus' most important achievement in their 13 year existence, the Humphrey-Hawkins Bill, was so "watered down" to meet the preferences of labor, liberals and moderates that it represented at best a defeat for the concept of universal employment. By 1980, seven Black Congress-persons had lost over 20 percent of their respective districts' populations during the decade, and were threatened with the very real prospect of losing their seats through redistricting. Shirley Chisholm's decision not to run for reelection in 1982 was dictated partially by the sobering loss of 32.1 percent of her Brooklyn constituency. By Reagan's election, a few Caucus members had climbed aboard the neoconservative bandwagon by supporting the latest corporate give-away project, the "free enterprise zones." With the outstanding exceptions of Dellums, Conyers, and Caucus newcomers such as George Crockett of Michigan, Gus Savage and Harold Washington of Chicago, the Caucus as a whole did not represent a coherent left bloc which could have pushed the Black Reaganites from media attention and public discourse.
The Old Guard civil rights leadership, likewise having been challenged effectively from the right, was also forced to move to the left in the early 1980s. Jesse Jackson, Southern Christian Leadership Conference president Joseph E. Lowery and Coretta Scott King participated in demonstrations involving 9,000 people in Mobile, Alabama on April 26, 1981, and 3,000 people in Montgomery, Alabama on August 9, 1981, to protest Congressional moves to repeal the Voting Rights Act of 1965. Georgia State Senator Julian Bond and the Institute for Southern Studies led a thorough investigation of the murders of the Communist Workers Party members in Greensboro, North Carolina in 1979, charging the police with "gross negligence." Benjamin Hooks, executive director of the NAACP, Vernon Jordan, Urban League head, and Coretta Scott King were speakers at the massive Solidarity march in Washington, D.C. on September 19, 1981, attracting hundreds of thousands of trade unionists and political opponents of Reaganism. One of the most publicized efforts of the Old Guard was the boycott of Coca-Cola products. Jesse Jackson's PUSH organization published information on the nonexistent affirmative action record of Coca-Cola, pointing out that not a single one of Coke's 550 bottlers or its 4,000 fountain wholesalers was Black. The corporate giant had on deposit only $254,000 in ten Black banks. When Coke executives balked during negotiations, PUSH and others initiated a Black nationwide boycott of the soft drink on July 11, 1981. Coca-Cola was removed from the shelves of four Black-owned Seven Eleven franchises in Washington, D.C., and white-owned franchises in that city did the same. Gary mayor Richard Hatcher, chairperson of the Black mayors conference, authorized a move to ban Coke machines from 194 Black controlled city halls. When more than one hundred stores in Chicago's metropolitan area joined the boycott, Coke president Donald R. Keough announced his readiness to give Black entrepreneurs "a piece of the action." The agreement represented a "promise that the free enterprise system can do more to develop opportunity for all elements of society."
Coke's "moral covenant" with PUSH included the following provisions: increase the number of Black-owned distributors to 32 within 12 months, establishment of a venture capital fund of $1.8 million for Black petty capitalists, the elevation of a Black to CocaCola's Board of Directors, double the amount of advertising capital spent with Black agencies, quadruple the amount of financial deposits within Black banks, and the hiring of 100 Black blue collar employees. The total package amounted to $34 million. Black newspapers widely publicized the boycott, calling it a "wonderful reunion fellowship" of Martin Luther King, Jr.'s old colleagues, including Mrs. King, Lowery, Hosea Williams, Andrew Young, Maynard Jackson and Jesse Jackson. Black columnist William Raspberry, never at a loss for words, proclaimed the historical deal "as important to Black America as the boycott of the Montgomery, Alabama, bus company a quarter of the century ago." The reality behind the rhetoric is somewhat different. Coke's white investors were furious with what was de scribed as "outright blackmail" and "a $30 million giveaway plan." On September 3, Coca-Cola President Keough informed the Atlanta Constitution that the corporation had neither bowed to "pressure" from Black leaders, nor had given the boycott more than "two minutes attention because we never considered it a real issue." By October, 1981, Coke officials informed the media that any money lent to Blacks for venture capital would be at high market rates. No forced changes in bottling franchise ownerships would occur. Black advertising was increased to only $2 million from the previous $1.2 million figure. No loans would be made to Black-owned banks except at competitive rates. Even the one hundred additional jobs would not materialize, because Coke "might be replacing Blacks with Blacks," declared a company executive. The conspicuous failure of the Coca-Cola boycott symbolized more than ever before the utter bankruptcy of "Black Capitalism."
The lack of any basic grassroots orientation or support of the Old Guard was illustrated at the 11th annual Congressional Black Caucus weekend in Washington, D.C., on September 25-27, 1981. The self-described "Black leadership family" included over 1,000 Black doctors, lawyers, politicians and bureaucrats. One participant suggested that the Black struggle in the 1980s would be led by "cadres of Black professionals." Joe Madison, an NAACP official, stated that the militancy of the old days "during the Montgomery bus boycott" were passe. "We've got to develop technical militants out of these middle class affluent Blacks who have received training, acquired good educations and have worked themselves into the mainstream of economic life." Neither the multitude of fashion shows nor the $150-a-plate awards banquet could provide the cultural cohesion necessary to forge new unity among this "Untalented Tenth." Frequently they quarreled among themselves on a variety of public issues. Representative Gus Savage correctly denounced Vernon Jordan, publisher John H. Johnson, NAACP president Margaret Bush Wilson and Rev. Leon Sullivan for sitting on corporate boards and sharing in the "ill-begotten super profits" from doing business in "fascist South Africa." At state levels, Black Democrats joined forces with white Republicans in reapportionment cases to increase the percentages of Blacks and/or whites within their respective Congressional districts. The most vocal advocate of the growing legislative detente between these unlikely forces is Julian Bond, a democratic socialist and the most "progressive" Black elected official in the South. The Atlanta Constitution charged that "the cynical coalition" of "ghetto Black politicians and country club Republicans" sought "to gut Atlanta for the sake of electing (Bond) to the Congress," while simultaneously extending GOP hegemony across the state.
Although the Black Reaganites and the civil rights leaders were at odds over public policy, both factions had greater similarities than either would acknowledge publicly. Both tendencies were firmly entrenched within the Black middle class, and received the greatest percentage of their financial support from dissenting sectors of the white establishment. Both tendencies were committed to political activity within the capitalist state and economic order as it exists. Both were clients of more powerful political interests which found it necessary to develop Black constituencies for their own public agendas. Black Democrats relied on the rhetoric of resistance, but in practical terms, tended heavily to favor tactical compromises and accommodation with powerful whites. Black Reaganites parroted the slogans of Milton Friedman and the Reagan Administration to facilitate their own socioeconomic mobility, at the expense of the Black masses. Neither tendency actually embodied in practice an effective social program which called for the structural or radical transformation of the inherently racist/capitalist state. The Black Brahmins waged war against each other, but not against the system that allowed them to exist.
III
Theoretically and programmatically, the sudden prominence of the Black Reaganites raises anew the historical question of accommodation and conservatism within Black America. In the 1960s, many Black and white social scientists and activist-oriented scholars tended to identify the cultural and social tradition of Black nationalism with political independence, public protests and militancy, while integration was portrayed as inherently a conservative and gradualist strategy to separate the Black elite from the Black working masses. Much of the political literature since Black Power has described the entire evolution of Black U.S. history as a clearcut division between Black nationalists and integrationists. According to this view, Black nationalists were rooted within the bowels of oppression, the leaders of Black workers and the poor, whereas integration was the aesthetic and cultural outlook of upper class Negroes. Black nationalist movements appealed to large audiences, with the primary cornerstone being Marcus Garvey's Universal Negro Improvement Association, and integrationist organizations were elitist and small (e.g., W. E. B. Du Bois' and W. Monroe Trotter's Niagara Movement or the National Urban League). Post-Black Power scholars describe integration itself as innately reformist, since its programmatic goal, the obliteration of barriers in political and social life that segregate Blacks from white Americans, is not a revolutionary demand. The nationalists identify their heroes as the real children of Martin Delany, Garvey and Malcolm X, while the integrationists remain adrift from the masses, hopelessly struggling for white recognition.
This dichotomy creates more problems than it resolves. First, it does not explain the career and legacy of the influential educator/politician, Booker T. Washington. Garvey constructed his economic and social program on the philosophy of Tuskegee, as we know. But what does this tell us about Washington, when we recognize the Garveyism was the highest expression of militant Black nationalism in the first half of the twentieth century? A closer reading of the subject also calls into question the Black nationalists' rejection of Frederick Douglass and Martin Luther King, Jr. Both men were committed to social equality and a closer sociocultural relationship between the races, but neither can be termed accommodationist in their political practice or "conservative" when contrasted with their contemporaries. More problems surface when the checkered and ambiguous careers of Congress of Racial Equality leaders Floyd McKissick and Roy Innis are reviewed. In 1966, McKissick demonstrated against the Vietnam War, and stood second only to Stokely Carmichael as the most articulate proponent of militant Black separatism. By 1972 he had endorsed the reelection of the politically and racially conservative Richard M. Nixon. Innis still advances a strong race-first philosophy, but combines his activist rhetoric with a close and cordial relationship with white capitalists and conservative corporate managers. When one surveys the single organization that is closest to the masses of Black people, the Black Church, one finds that the majority of Black religious leaders from the mid-nineteenth to late-twentieth centuries have been pragmatic or accommodationist in their politics, integrationists, and at times, profoundly conservative. Few ministers would hold much credence in the exhortations of Thomas Sowell or Ronald Reagan, but not many would consider themselves the descendents of Nat Turner or Malcolm X.
The singular service that the Black Reaganites provide is a new and more accurate understanding of what exactly constitutes conservatism within the Black experience. Generally speaking, conservatives from the Civil War to the present have agreed on a philosophy which can be outlined accordingly: first, a theoretical and programmatic commitment to capitalism as an economic system in which Blacks can take part as full and equal partners. Black conservatives are traditionally hostile to Black participation in trade unions, and urge a close cooperation with white business leaders. Hostile to the welfare state, they call for increased "self-help" programs run by Blacks at local and community levels. Conservatives often accept the institutionalized forms of patriarchy, acknowledging a secondary role for Black women within economics, political life and intellectual work. They usually advocate a specific social hierarchy within the Black community, and have a pronounced bias towards organizational authoritarianism and theoretical rigidity. Black conservatism as a definite ideological force can be found within both Black nationalism and integrationism. Conversely, a militant or political activist can be integrationist, particularly during periods when the consensus of white American society swings toward strict Jim Crow or racial segregation public policies. The internal logic of a Black nationalist who also is a rigid conservative, for example, is embodied in apartheid. But conservatism, in itself, should not be directly corrolated with accommodation as a political style. The entire terrain of Black politics since the Civil War can be characterized by a broad and uneven distribution of nationalists and integrationists at every end of the spectrum on questions of class, economic organization and state power. (See Table XXVI)
What few historians appreciate is that the contemporary foundations of Black conservatism and accommodation are not the responsibility of Booker T. Washington alone. The Tuskegee "wizard" (as his underlings called him) was neither a political theoretician nor an original thinker. Accommodation was a definite political response to the Compromise of 1877 and the extreme racist violence that accelerated across the South in the 1880s and early 1890s. J. C. Price, the president of Livingstone College of North Carolina and an influential Black postbellum leader, advanced a program in the 1880s that proposed the "sacrifice of nonessentials," such as Black political independence. Price's "mildly conciliatory policy toward the South" was also championed by C. H. J. Taylor. A newspaper editor in Kansas City and Atlanta, lawyer and minister resident in Liberia during Grover Cleveland's first administration, Taylor condemned Black advances achieved by radicals during Reconstruction. In his 1889 accommodationist polemic, Whites and Blacks, he urged Blacks to "(cease) exhibiting prejudice towards whites" and to accept "the olive branch of peace" offered them by political conservatives. The root of Black oppression, he declared, was the singular disaster of Afro-American politics during the 1865-1877 period. Blacks "voted in the white political scum they thought to be their dearest friends, but who . . . proved to be their greatest enemies." Like many conservative cultural nationalists a century later, Taylor chastized Blacks for hating the race, and urged an end to bleached skin and straightened hair. "We have no reason to complain until we take more pride in our own," he stated.
Black property owners, affluent small entrepreneurs and politicians helped to establish the conservative political terrain which made the subsequent rise of Booker T. Washington possible. These men adopted the aggressive, expansionist capitalist philosophy of Henry Grady by the mid-1880s. Black Mississippi planter Blanche K. Bruce resisted the "Republicans-only" politics of Frederick Douglass in 1876 by advocating the deliberate division of the Black vote in order to acquire leverage in both parties. By 1880 Bruce encouraged Blacks to deemphasize political work entirely, declaring in a series of public speeches "that the race needs now more than anything else . . . material and educational growth." In 1892, a meeting of Black educators and politicians at the Bethel Literary and Historical Association in Washington, D.C., advocated the immediate development of Black owned banks, insurance companies and service-related businesses as a means to promote racial uplift. All too frequently, this pro-business philosophy combined with a revisionist interpretation of slavery itself, leading its promulgators into a firm political coalition with white supremacy. A typical example of this is provided by a wealthy Black Mississippi landlord, Gilbert Myers. Testifying before a Senate committee only two years after the Compromise of 1877, he defended his decision to support the conservative Democratic party: "The South has always been kind to me. My master that I lived with I nursed him and slept at his mother's feet and nursed at her breast, so I thought my interest was to stay with the majority of the country who I expected to prosper with."
This is not to imply that the accommodationist philosophy was hegemonic before the demise of Populism and the Depression of the 1890s. The majority of Black Republicans and Democrats resisted whites' attempts to undermine the gains of Reconstruction throughout the period. Perhaps the leading Black militant of this era was T. Thomas Fortune. As editor of the New York Age, Fortune urged Blacks toward an independent political posture with the slogan "Race First: then party." Fortune condemned Isaiah Montgomery, founder of the all-Black city of Mount Bayou, Mississippi, for tacitly accepting the loss of the Black franchise in his state. He supported the creation of trade unions, and declared that "millionaires (were) the most dangerous enemies of society." As the founder of the Afro-American League in 1890, he revived the protest traditions of Martin R. Delany, declaring that "it is time to face the enemy and fight inch by inch for every right he denies us. Let us stand up like men in our own organization where color will not be a brand of odium." With the emergence of radical farmers and workers' movements, Fortune stood uncompromisingly on the side of liberation. "The revolution is upon us," he told his readers, "and since we are largely of the laboring population, it is very natural that we should take sides with the labor forces in the fight for a juster distribution of the results of labor." By the mid-1890s, Fortune's revolutionary ardor had cooled considerably. He began to accept financial contributions from the Tuskegee politician, and soon his militant voice was muted. With Fortune's active cooperation, Washington successfully plotted his election as president of the Afro-American Council and ratified an accommodationist program at the organization's meeting in St. Paul, Minnesota, in 1902. Black accommodationist Fred R. Moore was placed by Washington on the Age' s editorial staff in 1904, Three years later, Moore became editor; Fortune's career as a progessive spokesperson in the cause of Black civil rights was effectively ended.
Many historians have explored the striking prominence of Booker T. Washington, who it can be said was the most effective and influential politician that Black America has yet produced. In the light of Washington's eventual failure to achieve an "historic compromise" between the divergent interests of Southern conservatives, Northern capital, and the nascent Black middle class, he is sometimes accused of being simply the creature of white racism and oppression. His infamous Atlanta Compromise of 1895, close relationship with white millionaires like Collis P. Huntington and Andrew Carnegie, and his deprecating and even sycophantic remarks on the race question before white audiences seem to seal his fate before neo-abolitionist critics. Before we bury Booker T. as merely the compliant tool of racist reactionaries, let us make a few comments beside his grave. First, as illustrated above, Washington was the most successful practitioner of accommodation, yet the foundations of his success were forged in the years of defeatism and doubt after 1877. Without the C. J. Taylors and J. C. Prices, Washington's labor would have amounted to a futile and self-destructive errand in the political wilderness. Second, Washington's political genius was less "conservative" than tactically "accommodationist." He secretly funneled capitalists' donations for Tuskegee to a variety of civil rights causes. He paid his dues to white leaders by hiring a staff of talented ghost writers including Max Thrasher and Robert E. Park to articulate the cautious, conservative public policies of the age. For his public concessions, he achieved extraordinary influence in Federal appointments for Black members of his Tuskegee Machine. Finally, it must be emphasized the Washington was a popular figure within a significant segment of the Black community, an educator who inspired the development of schools based on the model of Tuskegee Institute in India, Panama, South Africa, Kenya, the Gold Coast and across the Black Belt South. Supporters of Washington's political organization included James Weldon Johnson, who later became Secretary of the NAACP; Benjamin J. Davis, Sr., the founder of the Atlanta Independent; W. H. Steward, a leading Black Baptist; and J. W. E. Bowen, president of Gammon Theological Seminary from 1906 to 1912 and senior editor of the influential Voice of the Negro.
The distinction between accommodation and cooptation must be emphasized here. In the light of history, we must judge the Tuskegee philosophy of tactical compromises and secret agitation against segregation a failure. Its achievements in the context of that bloody era—the creation of Tuskegee Institute, the appointment of Black officials in the Roosevelt and Taft administrations, the establishment of the National Negro Business League—should not be dismissed lightly, but in the end, do not and cannot make sufficient restitution for the forces of racist violence it also unwittingly unleashed. Washington's power was both real and an illusion; its inherent weakness was rooted not in his own body of politics, but within the racist practices of U.S. capitalism. Washington failed; but that does not make him an Uncle Tom. Had Washington's program been as servile as its critics claimed, it could not have inspired the development of Marcus Garvey's Universal Negro Improvement Association, or John Langalibalele Dube's African National Congress. Washington was a product of late nineteenth century Black cultural life, indeed as organic as the evolution of the blues at that identical historical moment.
Black American history's central axis is the tension between accommodation and struggle. Most prominent Black political spokespersons have embodied both contradictory positions within their respective programs. But a few "leaders" from the very beginning, went beyond accommodation and tactical concessions with racism, into what could properly be defined as true Black conservatism: a defense of the racist status quo as it exists. The Black conservative does not desire power; he/she has no independent program worthy of the name. The interests that the Black conservative defends have little or nothing to do with the realities of Black material and social life. No public position is too extreme, no statement is too ingratiating, no act too outrageous for the Black conservative, if in some minute way it serves the interests of whites in power. Accommodation as a political tactic is genuinely foolish, because tactical concessions and quiescent rhetoric seldom achieve long term gains. "Those in power never give way," C.L.R. James wrote in Black Jacobins, "and admit defeat only to plot and scheme to regain their lost power and privilege." The conquest of effective power may begin within the confines of parliamentary debate and moral suasion, but inevitably must end in the streets. "The struggle of classes ends either in the reconstruction of society or in the common ruin of the contending classes." Accommodation begins with the germ of doubt, a defeatist attitude which has afflicted the Black working class as well as the Black middle class. Conservatism is more clearly the attitude of sectors of the Black petty bourgeoisie, those who actively cooperate with the dominant white elites to oppress Blacks. Accommodation is "puttin' on ole massa"; conservatism for Blacks is actively doing "ole massa's" work. The former is an opportunist; the latter is a traitor.
During the "Age of Washington," the leading Black conservative was undoubtedly William Hooper Councill. After slavery, Councill became a leading Black Democrat in northern Alabama. He served as secretary for the National Equal Rights Convention in 1873, and three years later became president of the Black segregated state school at Huntsville. In 1887, he was excluded from a first-class railway car, and he appealed the case to the Interstate Commerce Commission. Alabama whites swiftly replaced Councill at the school, and he was prepared to retract his appeal. Reinstated as president, Councill began speaking out against integrated public facilities, railroads and accommodations. At the highpoint of lynchings, he praised the "love and attachment between the races at the South." He urged Blacks to accept positions as household workers, and he declared that employment discrimination toward Blacks was only "friendly advice" to start their own segregated establishments. Councill was as bankrupt morally as he was in politics: in May, 1885, he was charged with the rape of a twelve year old Black girl and the shooting of her uncle. Louis R. Harlan writes of Councill:
At the end of Reconstruction, Councill sold his Black soul for white Conservative favor. In return for his office he agreed not merely to stay out of politics but to speak out for the Democrats. This faustian bargain gave him great power, for he fulfilled the Alabama white man's conception of a Negro leader more com pletely than Washington. He could condemn the Yankee radical and proclaim the Southern white man to be the Negro's best friend without the restraints that inhibited Washington. He could out-Booker Booker, and he frequently did.
Washington could hardly tolerate the man. In 1899 he even informed a colleague that he could not bear to sit at the same public forum with Councill, because he "has the reputation of simply toadying to the Southern white people."
At the level of popular politics, Black electoral behavior is often characterized as monolithic behavior, with Afro-Americans casting their ballots for the Republicans between 1865 and the 1930s, and for the Democrats afterwards. In reality, the voting patterns of Blacks were uniform nowhere. The conservatives within the Black community tended to align themselves with whichever major party was ideologically and programmatically further to the right at a given time. Accommodationists, on the other hand, sought coalitions with the political party which controlled their own primary constituency's area. In the 1900s Washington quickly developed a strong national alliance with the Roosevelt administration, because the Republicans had become the majority party in the country by 1896. Locally, however, he supported Alabama conservative Democrats over Populists and the more radical agrarians from the poor white and Black classes. In the 1890s Black Republican leaders of Cincinnati threw their support to a local white Democratic boss, in order to gain petty patronage and economic development within that city. Black Republicans in Kansas City, Missouri consistently voted for the Democratic machine of Jim Pendergast, who repaid their allegiance by offering them local benefits to the city's services. For almost four decades, the Crum Democratic machine of Memphis controlled the Black vote in that city. A series of Black Republicans, the most prominent being Robert R. Church, consistently followed an accommodationist strategy by casting their weight behind local white segregationists. At the national level, a core of Black independents and former Republicans created the Negro National Democratic League in 1900, and actively attempted to increase among Blacks a new electoral loyalty for white Democrats. Even DuBois, in a rare moment of political confusion, endorsed the presidential candidacy of the Democratic governor of New Jersey, Woodrow Wilson. DuBois' support was repaid when Wilson ordered the most extreme racial segregation policies that had ever existed in the Federal government. The bitter fruits of Black accommodation to the Democratic Party during these years are illustrated by the single fact that not one Black delegate ever appeared at a national Democratic convention until 1936. It was not until 1948 that the Democratic party even took a lukewarm, public stand in favor of civil rights for Blacks.
The New Deal brought a general realignment to Black politics. Local Black Republican bosses, like Atlanta's A. T. Walden, shifted their organizations behind the Democratic Party. The percentage of Black votes for the Democrats increased dramatically in a remarkably short period of time. In Chicago, Democrats obtained 7 percent of the Black vote in the mayoral election of 1927, 16 percent percent in 1935. As early as 1932, 45 percent of Black voters in Baltimore were Democrats, 53.3 percent in Pittsburgh, and 79.8 percent in Kansas City. By 1936 the Black vote for Franklin Roosevelt exceeded 50 percent in most cities, and climbed to 75 percent in a few urban areas by 1940. As the Black working class shifted to the Democratic Party, Black accommodationists quickly followed suit. Chicago Black politician William L. Dawson had served as a city alderman from 1935 to 1939 as a Republican. Recognizing that political realities had changed, Dawson became a Democratic Ward Committeeman, and an ally of Chicago boss Edward Kelly. In 1942 he ran successfully for Congress, replacing another South Side Black Democrat, Arthur W. Mitchell. As Chuck Stone observes, "Dawson, a loyal 'organization man,' learned quickly that the organization was the wellspring from which all progress, jobs and favors flowed. Dawson exercised his power carefully, prudently and patiently. He quietly built a Black political machine that was as efficient and vicious as the city-wide Democratic machine." Like Booker T. Washington, Dawson's power was repeatedly compromised by the realities of racism and by the conformist demands that were placed upon him by whites. Dawson refused to support civil rights legislation, and was silent about the Emmett Till lynching. "As the Civil Rights Movement gathered," Stone writes, "Dawson retreated further into silence. He continued to do just three things: win re-election, control Black patronage in Chicago and keep his mouth shut." Through Dawson, the Tuskegee strategy was reborn within the Democratic Party.
For white Democrats after 1940, the Negro vote was not desired out of any abstract or altruistic commitment to social justice: it was born of the realization that Blacks now constituted what Henry Lee Moon termed "the balance of power." The implications of this were apparent as early as 1944, during the Roosevelt-Dewey election. Herbert Brownell, Jr., Republican National Committee Chairman, stated that a "shift of 303,414 votes in fifteen states outside of the South would have enabled (Dewey) to capture 175 additional electoral votes and to win the presidency with an eight electoral vote margin." In over half of the states mentioned by Brownell, Blacks comprised a significant and even decisive margin for Roosevelt's victory. In Michigan, Black voters cast 41,740 ballots for the Democratic nominee and Roosevelt carried that state by 22,500 votes; in Maryland "the 50,000 votes which Negro citizens in Baltimore alone cast for F.D.R. were more than double his 22,500 state plurality." Any effective power in which Blacks as a group could exercise electorally depended, of course, on whether white voters were evenly divided on the issues or candidates. In 1960 and 1976, Black voters did decide the Presidential election. About 77 percent of all Black voters supported Massachusetts Senator John F. Kennedy over Republican Vice President Richard M. Nixon in 1960, and in seven states—Illinois, Mississippi, New Jersey, Michigan, Texas, South Carolina, and Pennsylvania—the Black vote was greater than the Democratic candidate's margin of victory. Jimmy Carter received about nine out of every ten votes cast by Blacks in 1976. Democratic leaders had literally no other choice except to court the Black vote, particularly after the mid-1960s, as the New Deal coalition of organized labor and the South began drifting toward the Republican party. But white bosses, from Kelly's successor in Chicago, Richard Daley, to Democratic Senate leader Lyndon Johnson, mistrusted Blacks who expressed even modest tendencies towards political independence and militancy. They preferred to cut deals with Black pragmatists and accommodationists, Blacks clearly dependent upon the white power structure, men or women who understood and acquiesced to the rules of the game.
The tradition of accommodation had become so firmly grounded within Black politics that it affected even the most progressive Blacks elected to national office. Adam Clayton Powell's entire career stands as the greatest testimony to this unfortunate fact. Like Fortune, Powell began his political life as an uncompromising militant. In the depths of the Great Depression he led a series of successful boycotts of Harlem stores that refused to hire Blacks. Powell was frequently in the streets organizing Black workers, and set in motion a successful boycott of a bus company almost two decades before Martin Luther King, Jr. repeated the tactic in the Deep South. In 1941, Powell was elected to the New York City Council, and three years later won a Congressional seat from Harlem. Between 1945 and 1965, Powell was undoubtedly the most influential Black elected official in the country. Unlike Dawson, Powell won the praises of almost every major sector of the Black community. For older Black nationalists, Powell's streetwise rhetoric was reminiscent of earlier Harlem nationalists, from Hubert H. Harrison to Marcus Garvey. Integrationists from the Black middle class pointed out that Powell's leadership in the House Education and Labor Committee led to the adoption of sixty major bills which included increases in the minimum wage, school lunch program, Federal aid to public schools and the war on poverty. Black men with no discernable interest in electoral politics could identify with Powell's bombastic joi de vie, his succession of wives and mistresses. Even the most politically advanced spokesperson that Black nationalism produced in the 1960s, Malcolm X, considered Powell a true proponent of Black independence and activism. But throughout his public life, Powell made a series of questionable tactical concessions and compromises with the white power elite. In 1956 Powell endorsed the reelection of Dwight Eisenhower, although the former general had done virtually nothing in the area of civil rights. In return for the chairmanship of his Congressional committee, Powell endorsed the Presidential candidacy of Lyndon Johnson, a political protege of House Speaker Sam Rayburn. Powell's 1959 endorsement was a shock to most Blacks, since Johnson was a known southern segregationist. Despite his erratic and sexist personal conduct, Powell's eventual undoing may have had more to do with his inexplicably infantile attitude toward power. Had he possessed the seriousness of a Washington, who made accommodating overtures towards whites without ever forgetting once that covert action resided at the center of successful petty bourgeois politics, Powell would have never fallen in disgrace. Powell was no accommodationist certainly, but his claim to the credentials of militancy seems seriously inflated.
Since the Eisenhower Administration of 1953-61, many Black accommodationists and virtually every Black conservative joined the Republican Party. The most prominent Republican, and certainly the most successful, was Edward W. Brooke of Massachusetts. Brooke was "an authentic member" of the "Black bourgeoisie." After his graduation from Boston University, Brooke decided to run for the Massachusetts state legislature in both the Democratic and Republican primaries in 1950. Defeated in the former, he therefore became a Republican. After a series of electoral defeats, Brooke finally was elected Massachusetts attorney general in 1962. In 1966, Brooke campaigned and won a seat in the U.S. Senate over Endicott Peabody, a man described by observers as being "far more liberal on civil rights for black people than the black candidate himself." Of course, it may be unfair to classify Brooke as a Black politician, since he never made any attempts to identify himself as one. Stone condemned Brooke as "Mr. Non-Negro Politics," "the answer to the white man's prayers," "a political anomaly, (and) almost a political freak." After his election to the Senate, he hired only two Blacks out of a nineteen member staff. Brooke found little difficulty in campaigning for Nixon or Gerald R. Ford, despite both white politicians' antipathy toward Black political rights and socioeconomic progress. Unlike Thomas Sowell and the Black Reaganites of the 1980s, however, Brooke consistently obscured his essentially conservative economic and political philosophy by relying on the rhetoric of integration and civil rights. Even at the end of his career in 1978, when Massachusetts residents finally voted him out of office, Brooke used whatever leverage his "race" created for him within Back activist circles. Indeed, a group of Black nationalist militants from the National Black Political Assembly went so far as to campaign for Brooke that year, justifying their support solely on racial terms.
In How Europe Underdeveloped Africa, Walter Rodney observes that the most destructive idea within the expansion of Western societies into the nonwhite world was the concept of individualism. "It is a common myth within capitalist thought that the individual through drive and hard work can become a capitalist. The acquisition of wealth is not due to hard work alone," Rodney notes, "or the Africans working as slaves in America and the West Indies would have been the wealthiest group in the world. The individualism of the capitalist must be seen against the hard and unrewarded work of the masses." Individualism as an expression of Black politics is expressed as a commitment to oneself alone, a desire to transcend socioeconomic obstacles in order to become a power broker within the system. Blues artist B. B. King makes the point aesthetically: "You've got to pay the cost, to be the boss." Black accommodationists and many reformers with accommodationist tendencies such as Powell, acknowledge the centrality of individualism within their political practice. They developed a series of practical solutions, or answers, to resolve the dilemma of Black underdevelopment, from the placid politics of Dawson, to the Machiavellian agenda of Washington. Their basic flaw was that they had no theoretical or systemic analysis of what was to be done: they were asking the wrong questions. After a century of tactical compromises, Black accommodationists still retain an individualistic faith in the inherent justice of America's economic and social order.
Black conservatives from Councill to Sowell should not be considered accommodationists. They ceased asking any questions which relate to meaningful social and economic change for the Black working class and poor people. They are not willing to "pay the cost," because they do not wish to be the "boss"—that is, to transform the existing undemocratic, racist hierarchy in even miniscule ways. Like the Black radical journalist of the Harlem Renaissance, George Schuyler, some of the contemporary Black conservatives began their intellectual lives as socialists or militant reformers and gradually succumbed to anticommunism and a nihilistic view of Black activism as they reached middle age. Energetically, Sowell and his fellow Black conservatives—most notably Wendell Wilkie Gunn of Pepsi corporation, Black Republican leader J.A.Y. Parker and economist Walter Williams—claim to represent a "new" and unprecedented political tendency which has the potential for becoming dominant within Black civil society in the years ahead. But the Black majority recognizes that their agendas are not ours; their "supply-side" ideas are unoriginal; and their politics are simply the program of those forces that would crush the collective life from Black America. Black Reaganism is not an accommodation to white power, but a complete capitulation to racism. Thomas Sowell's extensive theoretical work is an apology for racism and Reaganism. Sowell does not even merit the mantle of Washington.
IV
History illustrates that the petty bourgeoisie of an oppressed nation or nationality is incapable by itself of struggling to achieve political and economic equality undercapitalism. In Class Struggle in Africa, Kwame Nkrumah asserted that during national liberation efforts the Black elite responds in three ways. "Firstly, there are those who are heavily committed to colonialism and to capitalist economic and social development." The second category, the nationalists, "want to end colonial rule" but oppose "a transformation of society." The third group simply "sits on the fence," supporting the militant actions of Black workers and the peasantry when it suits their own narrow interests. Politically, the Black Brahmin will go so far as to subvert its own institutions, betray its own representatives, and coalesce with the most vicious racists if conditions for progressive change seem temporarily remote. The modern "realignment" in Black politics is essentially a repetition of this classical pattern of petty bourgeois opportunism and accommodation.
The goals of the Civil Rights Movement, which promoted the necessity of social democratic reforms (e.g., food, public health care, child care, job training, free education, etc.) have been abandoned by major sectors of the Black elite. It becomes the task of Black progressives and Marxists in this period to complete this interrupted "revolution" for civil rights and social equality within the framework of the existing system. The burden of our history is two-fold. We must advance "reformist" programs within communities which reinforce Black owned socioeconomic and cultural institutions, advocating the maintenance of needed social service programs that affect the Black working class and the poor. But we must insist uncompromisingly that the social crises confronting Black people reflect a more fundamental contradiction created in part by the crisis of capital accumulation. Self-determination for the Black majority cannot be forged unless our politics, in theory and in practice, also opposes sexual exploitation, imperialism, and monopoly capitalism. The revolt for reforms within the capitalist state today transcends itself dialectically to become a revolution against the racist/capitalist system tomorrow.
Given this critique, the next logical question is—which sectors of the Black elite have the greatest potential for participating in the democratic reconstruction of capitalist America? As illustrated in chapter five, the Black entrepreneurs and executives are the greatest internal barrier to the achievement of a socialist political consensus within the Black community. The Black politicians, taken as a whole, are either clients of larger corporate interests, or excel in the electoral game for personal profit and ego gratification. We turn next to the Black Church for leadership, and find as with the politicians, a divided legacy—a history of struggle and accommodation.
CHAPTER SEVEN
THE AMBIGUOUS POLITICS OF THE BLACK CHURCH
The history of early Christianity offers noteworthy points of similarity with the modern labour movement. Like it, Christianity was in the beginning a movement of the oppressed. It appears first as a religion of slave and freedman, of the poor without rights and of peoples dominated or dispersed by the Romans.
—Friedrich Engels
Long-haired preachers come out every night,
Try to tell you what's wrong and what's right;
But when asked how ' bout something to eat
They will answer with voices so sweet:
You will eat, bye and bye ,
In that glorious land above the sky;
Work and pray, live on hay,
You' ll get pie in the sky when you die.
—Joe Hill, "The Preacher and the Slave," in Tristram Potter Coffin and Hennig Cohen, eds., Folklore: From the Working Folk of America (Garden City, New York: Anchor, 1974), pp. 401-402.
I
The Black Church occupies a unique position in the evolution of Black cultural and political life in capitalist America. From Reconstruction to Black Power, many significant political figures engaged in Black liberation struggles were either ministers or were profoundly influenced by religion: Nat Turner, Henry H. Garnet, David Walker, Elijah Muhammad, Malcolm X, Andrew Young, Jesse Jackson, John Lewis and hundreds more. The most influential minister in twentieth century American society, Black or white, was Martin Luther King, Jr. The majority of Black theologians and sociologists of religion tend to make a radical separation between Black faith and the specific political praxis of Black clergy. Most political science research on the Civil Rights Movement concentrates on King's role as a centrist within the broad and often fractious united front that constituted the desegregationist campaign, and ignores the historical relationship between Black politics and faith. Few historians have seriously explored the Movement's impact on the evolution of the Black Church.
In the decades immediately preceding the Second Reconstruction, Black clergy as a group experienced a decline in political influence and social status relative to other middle-class Blacks. The Civil Rights Movement provided an historic opportunity for activist preachers to direct their working class congregations in the practical struggle to overturn Jim Crow laws, improve housing conditions and to exercise the right to vote. King and other Black ministers succeeded in their efforts to achieve democratic reforms within the capitalist democratic system, but were unable to alleviate the sufferings of the Black masses caused by institutional racism and capitalism. As the Black Power and Vietnam War destroyed the fragile consensus among the petty bourgeois leadership of the Civil Rights Movement, King was pressured to move to the left. With the courage instilled by his nonviolent convictions, he advanced a progressive human rights agenda at home and abroad, and began to make the case for economic democracy. The majority of Black clergy were then, and still are today, unable to follow King's example established in 1966-1968.
It would be an error to discuss the politics of the Black Church, however, simply by concentrating on the life and death of King. King is important for us only in two specific respects; in his skillful use of Black faith and spirituality as a lever to motivate the consciousness of the Black working-class masses towards decisive action against the interests of racists and the state, and in his development of a certain praxis which was, although idealist in philosophy, clearly anticapitalist by the time of his assassination. In documenting the evolution of the Black Church, King represents the anticapitalist potential that is inherent within the Black clergy. Given the centrality of religion within the life of the Black masses, it is essential to discuss the potential and limitations of this decisive segment of the Black elite.
The foundations of modern Black politics are found within the Black Church. From the beginning periods of Afro-American slavery, the minister assumed a relatively privileged position within Black civil society, playing roles both spiritual and secular. Hundreds of Black Methodist and Baptist ministers were active in electoral politics during Reconstruction. In 1865, for example, the presiding officer of the African Methodist Episcopal Zion Church, the Reverend J.W. Hood, issued a series of radical reforms for Blacks which included the right to vote. There were a large number of Black ministers elected to their respective state constitutional conventions in the late 1860s. Some of the most influential included the Reverends Henry P. Jacobs, Baptist, Mississippi; T.W. Springer, AME, Mississippi; James Walker Hood, AME Zion, North Carolina; Richard Harvey Cain, AME, South Carolina; Francis Louis Cardozo, Presbyterian, South Carolina; and Henry McNeal Turner, AME, Georgia. In the 1880s, Black ministers like attorney T. McCants Stewart, pastor of New York City's Bethel African Methodist Episcopal Church, served on that city's school board and championed the necessity for Black political independence. Many Black religious leaders supported Black nationalist programs, including C.H. Philips, editor of the Colored Methodist Episcopal Christian Index, and Henry M. Turner. Without exaggeration, it can be stated that almost every Black minister was something of a politician, and that every aspiring Black politician had to be something of a minister. With the rise of Jim Crow and the electoral disenfranchisement of most Blacks after 1900, one of the few remaining roles in which articulate and militant young Black men could exercise political influence was as a preacher.
The twentieth century witnessed a gradual yet unmistakable decline in the political influence and social status of Black ministers. There were at least three basic reasons for this. The first is illustrated in U.S. Census statistics for the period 1890 to 1970. Four important vocations defined as "middle class" within American society were clergy, teachers, physicians and attorneys. In 1890 there were 12,159 Black ministers in the U.S.; that year, there were only 14,100 Black teachers, 909 doctors and 431 lawyers, out of a total Black population of about eight million. Relatively, a very large percentage of the Black intelligentsia and middle class was found within the church. By 1910 the number of Black ministers peaked at 17,495. Thirty years later, in 1940, the total number of Black clergy amounted to 17,102. That year, the U.S. Census counted 63,697 Black school teachers, 3,524 doctors and 1,052 lawyers and judges. The overall percentage of Black ministers within the Black professional stratum was greatly reduced. This decline accelerated after World War II and with the desegregation of white civil society. The U.S. Census of 1970 recorded only 12,850 Black clergy, compared to 235,436 Black school teachers, 3,728 lawyers and judges, and 6,106 physicians. The number of Black elected officials in the U.S. increased dramatically: 103 in 1964; 1,469 in 1970; and 5,003 in 1980. Many of these new and powerful representatives of the Black elite were not ministers, and owed no allegiance to the Black Church. The ministry itself ceased to be the choice vocation of the middle class, or even politically motivated Blacks. Thousands of other professional Blacks exerted, by their sheer numbers, an increasing significance within the Black community's political, social and economic development.
Second, throughout the period there was a sharp decline in the per capita rate of Black ministers to the general Black population. In 1890, 14 percent of all U.S. clergy were Afro-Americans. Using Census figures, the number of Black clergy per thousand Blacks in 1890 was a very high 1.62. This figure was relatively constant for several decades. For example, in 1910 the per capita number of Black ministers per thousand Blacks was 1.56; the per capita number of white ministers per thousand whites was 1.42. After World War I and the Great Depression, the per capita rate slipped for both Blacks and whites, but the decline is more pronounced among Blacks. In I940, the figures were .95 for Blacks and 1.11 for whites. In 1970 the per capita number dropped to .53 for Blacks, but increased slightly to 1.18 for whites. In other words, by 1970 there was about one Black minister for every 1,898 Black people—the smallest per capita figure in Black history. Only seven percent of all U.S. clergy were Black in 1960, and this figure dropped to six percent in 1970. The Census historically undercounts all Black people, so it is highly probable that the real number of Black clergy during these years was larger than reported. Nevertheless, even given a massive margin for error, there can be little doubt that both in numbers and in per capita percentage Black clergy declined after 1910.
The third and perhaps decisive factor was the escalation of Black political and social criticism levied at the Black clergy. Throughout his career as a political militant and social scientist, W. E. B. Du Bois repeatedly questioned the ambiguous role of the Black preacher as a progressive factor in the liberation of Afro-American people. In "The Religion of the Negro," written in 1900, DuBois suggested that the basic spirituality of Black folk "swept irresistibly toward the Goal (of) Liberty, Justice and Right." Black ministers had the obligation to preach a theology rooted in the practical political conditions of Black humanity. DuBois praised the Black Church as an expression of the "Negro's soul" and organizational ability. But he criticized the tendency of major Black churches to split and engage in fractious arguments over personalities and matters of doctrine. In 1928 DuBois attacked the Black ministers of Washington, D.C. for banning a lecture by Clarence Darrow because of his agnosticism. DuBois understood that the shortcomings of the Black Church were small in comparison to the massive hypocrisy and blatant racism evident within white denominations. In 1913, for instance, he used the pages of The Crisis to condemn the segregationist policies of the Episcopal Church, declaring "the church of John Pierpont Morgan" was not "the church of Jesus Christ." He denounced the Catholic Church in 1945 for maintaining "separate white and Negro congregations in the South" and for "(refusing) to receive colored students in a large number of their schools." DuBois believed that all white Christian churches expressed "a double standard of truth" towards the Negro, professing the highest ideals while carrying out "the most selfish and self-seeking" practices of race hatred and oppression. For these reasons, DuBois argued, the Black Clergy had no other alternative execpt to become an active agent for social justice and political transformation.
Other critics of the Black clergy were far less generous than DuBois. A. Philip Randolph and Chandler Owen, editors of the Black socialist journal The Messenger, declared in 1919 that the Black Church was an utter disaster. Black preachers as a group were silent on lynchings, political disenfranchisement in the South, and Black economic exploitation by white capitalists. Echoing Karl Marx, V.F. Calverton charged in 1927 that religion was a kind of "other-worldliness" among Blacks. The traditional Judeo-Christian ethic of forgiveness, submissive behavior, prayer for salvation and tolerance toward one's earthly oppressors simply perpetuated white racism and the brutal extraction of surplus value from the labor power of the Black proletariat. Many Northern Black ministers were secretly on the payroll of white industrialists such as Henry Ford, using their influence among working-class Blacks to counsel patience with low wages and to reject unionism. After World War II the level of criticism increased. Writing about that "special gray death that loiters in the streets" of Harlem, LeRoi Jones condemned the Black minister as representing a drug to blind Blacks from the frustrations of urban life. "You can go to church Saturday nights and Sundays and three or four times during the week," he stated in Home; "or you can stick a needle in your arm four or five times a day." In The Crisis of the Negro Intellectual, Harold Cruse suggested that the Black ministers of Harlem "vie with professional social workers and police chiefs over which brand of community uplift is best for soothing the tortured ghetto soul 'twixt Hell on earth and Heavenly hereafter. Many of them 'mean well' toward the 'masses' but they are frightened to death of power—others' and their own." Many, but not all Black ministers, were silent when DuBois, Paul Robeson and other Black socialists and progressives were slandered and arrested during the McCarthy era. The growing postwar successes of the NAACP and other more progressive biracial groups further reduced the power and prestige that the Black Church had once claimed.
The Black Church continued to serve its traditional function as a "refuge" and forum "to satisfy (the) deepest emotional yearnings" of Black people. However, the relationship between the first and second generation Black urban working class in the North with their Black clergy was becoming at best problematic. In The Negro's Church, published in 1933, the Reverend Dr. Benjamin E. Mays and Joseph W. Nicholson analyzed one hundred Black sermons at random, discovering that 20 were devoted to theological doctrine, 54 were vaguely "other-worldly" and only 26 centered on contemporary secular affairs. During the depths of the Great Depression, the Black working class had begun to "develop a more secular outlook on life" and increasingly complained "that the church and the ministers are not sufficiently concerned with the problems of the Negro race." By the dawn of the Civil Rights Movement, noted Black sociologist E. Franklin Frazier would observe that "the Negro church has lost much of its influence as an agency of social control. Its supervision over the marital and family life of Negroes has declined. The church has ceased to be the chief means of economic cooperation." Growing numbers of Black ministers in the North began to be selected by white politicians and business leaders to serve on municipal health and welfare boards. "In this capacity," wrote sociologist Daniel C. Thompson, these pastors "represent(ed) the Negro community" and served "as advisors to white groups where certain problems directly affecting Negroes are concerned." Nevertheless, the majority of Black clergy seemed ineffective or apathetic in the fight for meaningful economic and political reforms which would touch the daily lives of their congregations.
The Brown decision of the Supreme Court in May, 1954, presented new challenges to Black ministers. To the surprise and chagrin of many Negro clergy, a key element in the forces of "Massive Resistance" to desegregation were white ministers. Many more "liberal Southern Christian clergy cautioned their white congregations to obey the law, "improve communications between races," and advocated the "full privileges of first class citizenship" for all. But even Atlanta's white ministers, who were among the most tolerant and "liberal," warned in a public statement that "we do not believe in the wisdom of massive integration." Historian Numan V. Bartley has noted that "integrationist activity was not conducive to a smoothly functioning House of God in almost any part of the South." In Montgomery, Dr. G. Stanley Frazer, leader of Alabama's white Methodists, and R. Henry L. Lyon, twice president of the Alabama Southern Baptist Convention, "were two of the most prominent ministers in the city and both were outspoken proponents of "segregation." Dr. John H. Buchanan, Birmingham's leading white clergyman, declared in 1956 that "the good Lord set up customs and practices of segregation." Throughout the 1950s and 1960s the American Baptist Association Convention annually condemned desegregation. The American Council of Christian Churches, with a total membership of one million, declared solemnly in 1958 that integration "does violence to the true gospel of Jesus Christ." Episcopalians in South Carolina proclaimed publicly in 1956 "that there is nothing morally wrong in a voluntary recognition of racial differences and that voluntary alignment can be both natural and Christian." Mississippi Presbyterians refused to carry out church directives in 1957 to desegregate. The Alabama American Baptist Convention even proclaimed in October, 1959, that integration was a "Communist" plot. White Christian clergy and laymen expressed few reservations to become involved in the fight to preserve white supremacy.
The Montgomery Bus Boycott, initiated on December 1, 1955 by Rosa Parks, was the beginning of the Second Reconstruction, a massive, ethical movement by Blacks and their white liberal allies to destroy racial segregation. The idea for the nonviolent boycott had been that of E.D. Nixon, an experienced member of the 1941 March on Washington Movement and trade union activist in Randolph's Brotherhood of Sleeping Car Porters. A chief administrator in the boycott itself was Bayard Rustin, a Black Quaker and social democrat who had participated in the earliest "freedom rides," or Journey of Reconciliation in the late 1940s. Black ministers were a minority in the major Black political organization of the city, the Montgomery Improvement Association. Yet it was the Black clergy which provided the moral, social and political context for the entire struggle: the Reverend L. Roy Bennett, Reverend Ralph David Abernathy, Reverend Martin Luther King, Jr., and others. King's address at Montgomery's Holt Street Church at the outset of the boycott, established the popular framework for Black resistance:
One of the great glories of democracy is the right to protest for right . . . We are protesting for the birth of justice in the community. Our method will be that of persuasion, not coercion. Our actions must be guided by the deepest principles of our Christian faith. Love must be our regulating ideal. Once again we must hear the words of Jesus echoing across the centuries: 'Love your enemies, bless them that curse you, and pray for them that despitefully use you.' If we fail to do this our protest will end up as a meaningless drama on the stage of history, and its memory will be shrouded with the ugly garments of shame. In spite of the mistreatment that we have confronted, we must not become bitter and end up hating our white brothers. As Booker T. Washington said, 'Let no man pull you down so low as to make you hate him.'
Martin Luther King's life and martyrdom, long etched in Black history, and popularized within Black and U.S. culture, require little rehearsal here. Several important social factors within King's legacy, and in the history of the Black Freedom Movement, are however grossly ignored. The emergence of King, Ralph Abernathy, and other Black clergy in the forefront of the desegregation struggle was to an extent a progressive response to white clergy who had taken up the cause of white supremacy in Alabama and across the South generally. If Christ could be portrayed by white Baptists as a Ku Klux Klansman, then He could just as easily be enlisted in the ranks of bus boycotters and Freedom Riders by Black Baptists. The Civil Rights Movement occurred at a time when the social and political role of Black preachers was steadily diminishing. By participating in their people's struggles, the Black ministers could once again set the political and moral climate for millions of Blacks who over previous decades had become alienated or disillusioned with church inactivity in secular issues. As in the years of Reconstruction, from 1865-1877, the Black Church provided the necessary social space for political discussions, strategy sessions and effective protest. With the creation of the Southern Christian Leader ship Conference (SCLC) in 1957, King and other Black ministers forged an appropriate political vehicle for the battle to destroy Jim Crow. Not coincidentally, they created the political terrain essential to reclaim the prestige and class status the Black clergy had lost over the previous half century within the Negro petty bourgeoisie.
King was the most prominent Black minister of the Civil Rights Movement—yet his rise to greatness should not obscure the fact that hundreds of other Black preachers and laymen were responsible for many of the real accomplishments of the Movement. In Lynchburgh, Virginia, the SCLC affiliate led by the Reverend Virgil Wood initiated numerous nonviolent direct action campaigns. The Reverend Fred Shuttlesworth was responsible for many of the successes combating Bull Connor's racist police force and the white power structure in Birmingham. The Reverend Hosea Williams was an effective SCLC coordinator in the desegregation campaigns in Savannah, Georgia. The Reverend James Lawson assisted King in the founding conference of the Student Nonviolent Coordinating Committee (SNCC) at Shaw University, in Raleigh, North Carolina. The Reverend Matthew McCollum, one of the SCLC's founders, was a skilled veteran of desegregation struggles in Orangeburg, South Carolina. Other influential Black activist pastors included C.K. Steele of Tallahassee, Florida; C.T. Vivian, the central coordinator of the SCLC; Bernard Lafayette of Selma, Alabama; Walter Fauntroy, director of the SCLC Washington, D.C. Bureau; Wyatt Tee Walker of Petersburg, Virginia; and a host of younger Black divinity students and pastors like Jesse Jackson, Andrew Young and James Bevel. In Northern states, Black ministers who had previously done little in the way of political or economic protest were stirred to act. In May, 1960 in Philadelphia, four hundred Black clergymen decided to pressure white-owned corporations to hire Black employees in "decent positions." Confronting the racist policies of one company, the ministers initiated a boycott of the firm's products, an act supported by virtually every Black Masonic lodge, church organization and social club in Pennsylvania.
Yet it was King alone who captured the imagination of the Black masses, while earning the respect of the media and white establishment. In the early years of the sit-in movement, it was not unusual for teenage protestors to ask each other, "What do you suppose Martin Luther King would do in this situation?" King biographer William Robert Miller writes that by 1960 "King's symbolic role was supreme, his charismatic stature was universally recognized. In the flux of rapidly proliferating and chaotic events, he towered as a pillar of strength." For whites, confronted with the growing radicalism of SCLC and the Congress of Racial Equality (CORE), King made the "nonviolent direct action movement respectable." Historian August Meier recognized in 1965 that "King's very tendencies toward compromise and caution, his willingness to negotiate and bargain with White House emissaries, his hesitancy to risk the precipitation of mass violence upon demonstrators, further endear him to whites. He appears to them as a 'respectable' and 'moderate' man." As a minister, King constantly assumed the irreproachable posture of an ethical reformist committed to Gandhian political efforts. When white evangelist Billy Graham urged King "to put the brakes on a little bit" in the desegregation campaign in Birmingham, the SCLC leader relied solely upon Christian doctrines to justify the necessity for continued struggle. King's famous "Letter from Birmingham Jail," published in Christian Century and Liberation in June, 1963, was an eloquent rejection of white Birmingham clergymen's appeals to halt nonviolent demonstrations.
III
Historical memory is selective. Most Afro-Americans now fail to recall that the support provided for Black activist-oriented clergy by more powerful Black Church leaders was hardly unanimous. The outstanding example of neoaccommodation was the Reverend Joseph H. Jackson, president of the National Baptist Convention. In 1956 Jackson applauded King's protest activities, and was one of several speakers at a rally marking the first anniversary of the Montgomery Bus Boycott. Jackson soon disapproved of King's growing influence within political circles, and cautioned his ministers not to become actively involved in the Southern Christian Leadership Conference founded in 1957. When the Reverend George Taylor and the Reverend George Lawrence challenged Jackson's faction for leadership in the National Baptist Convention in 1960-1961, King supported Taylor and Lawrence. In 1961, 800 Black activist-oriented ministers finally broke with Jackson, establishing the Progressive Baptist Convention. Subsequently, Jackson had little to say in support of King, and took any opportunity to condemn nonviolent, direct action activities. At the 1962 National Baptist Convention, Jackson singled out fellow ministers who had assisted the SCLC drive to desegregate Albany, Georgia, criticizing the futility of their efforts. "It is hypocrisy," he charged, "for a delegation to leave Chicago and go to Albany to fight segregation." Four years later, when King, Abernathy, Jesse Jackson and other Black ministers followed his advice by staging a massive desegregation campaign in Chicago, Joseph Jackson "issued a public statement dissociating himself from the event and peppering its unnamed instigator with politely worded abuse."
The success of Montgomery not only boosted the protest potential of the Black Church, but it affected the political relations of almost every left-of-center group toward the Black clergy. Harold Cruse has argued that Black members of the Communist Party in the 1930s condemned the Black Church as hopelessly reactionary. "Twenty-five years later, with the emergence of Dr. Martin Luther King, the Negro church ceased to be a reactionary, as the Communists jumped on King's bandwagon." Actually, the leadership of the more conservative NAACP and Urban League, as well as King's SCLC and CORE eschewed public cooperation and joint work with Marxists and socialists. In 1961, for example, the Louisville branch of the NAACP attacked Louisville's CORE chapter for working with Carl and Anne Braden, officers in the Southern Conference Educational Fund which was "widely charged" as a Communist organization. James Farmer and CORE's national leadership "dealt with the Bradens most circumspectly, advising field personnel not to accept food or lodging from them." Two years later, when Black activists were confronted with a desperate shortage of lawyers in Mississippi who would take civil rights cases, the National Lawyers Guild "aggressively volunteered its help to various civil rights groups." SNCC accepted the Guild's offer, but CORE's leaders rejected "cooperation with the Guild, fearing that its identification as a Communist front might damage the movement." The Reverend Adam Clayton Powell, then the most influential Black elected official in the U.S., informed King in 1960 that he was willing to support him—on the condition that he fire Bayard Rustin, a moderate leftist, from his staff. Writing in Harper's, novelist James Baldwin charged that Martin "lost much moral credit . . . especially in the eyes of the young, when he allowed Powell to force Rustin's resignation. King was faced with the choice of defending his organizer, who was also his friend, or agreeing with Powell; and he chose the latter course."
The explicit anticommunism of many Black ministers, the NAACP and even more liberal civil rights groups existed throughout the postwar period. In 1946, the NAACP rejected cooperation with the leftist Civil Rights Congress' campaign to oust the notorious racist, Mississippi Senator Theodore Bilbo, from office. Walter White, NAACP leader, argued that "it was imperative that this (campaign) be done under non-Communist auspices." In 1948, CORE's Executive Committee issued a "Statement on Communism," ordering chapters not to affiliate with leftist organizations, and "enacted procedures for disaffiliating chapters which had fallen under Communist domination." In a different way, a contempt for a materialist analysis was also expressed by Black, middle class student radicals in the 1960s. Julius Lester wrote in 1968 that "many Blacks view Marxism and Communism as foreign ideologies. Young Black militants do not consider Marxism relevant" since Marx "was a white man." Liberal (and anticommunist) journalist Harry Golden suggested that Communists failed to attract Southern Blacks for two reasons. First, "they do not depend on nor incorporate Jesus and the Gospels." Second, "the great mass of the American Negroes do not reject the existing social order, they seek only to share fully in its bourgeois blessing." More than other Blacks, the clergy commonly shared an unstated antipathy for atheism in any form, and possessed a class-oriented commitment to the acquisition of private property and Black petty capitalism. "Historically, the Black preacher was the first member of the Black professional class, the Black elite," writes Robert Allen. "He frequently had some degree of education (and) enjoyed a semi-independent economic status." The unwillingness to unite with Marxists and militant social democrats who expressed a sincere commitment to destroy racial segregation eliminated any possibility that the Civil Rights Movement would transcend its theoretical parochialism and develop a legitimate agenda to reconstruct the political economy of the United States.
Legitimate criticisms of King, coming from Black activists and sympathetic intellectuals, began as early as 1958. In Présence Africaine, Cruse charged that King's theoretical foundations for social protest exemplified "the confusion of the Negro middle-class mind on (the) question of racial integration." For Cruse, King's assertion that the civil rights struggle would allow Negroes to lose their "racial identity" was both tragic and absurd. "It requires neither intellect, education, nor morality these days to howl for civil rights," Cruse declared, "but it does require some profundity of insight and honesty in racial matters to know what to do with civil rights after they are achieved." By late 1963, Rustin had begun to censure King for relying too heavily upon "the tactics of lying down in the streets to prevent the movement of trucks, and other forms of direct action." Rustin suggested that "heroism and ability to go to jail should not be substituted for an overall social reform program." In 1963 Black writer LeRoi Jones was perhaps the first critic to draw the historical analogy between King and Booker T. Washington. In Midstream magazine, Jones noted that "Washington solidified the separate but equal lie, when that lie was of value to the majority of intelligent white men. King's lie is that there is a moral requirement to be met before entrance into the secular kingdom of plenty." For Jones, King was a model missionary who helped to perpetuate racist hegemony:
In this sense King's main function (as was Washington's) is to be an agent of the middle-class power structure, Black and white. He has functioned in Montgomery, Albany, Birmingham, etc. (as has the Negro middle class in general) as a buffer, an informer, a cajoler against action not sanctioned by white Intelligence . . . He is screaming at the blimp with the loudspeaker of recent agonies. He is a hand-picked leader of the oppressed, but only the pickers are convinced.
In the summer months of 1964 and 1965, the patience fostered by Black ministers within ghetto communities began to wear thin. The absence of any "national organization which could speak to the growing militancy of young Black people in the urban ghettos and the black-belt South," in SNCC leader Stokely Carmichael's words, undermined "the struggle against racism." When innercity Blacks watched the news and "saw Dr. King get slapped they became angry. When they saw little Black girls bombed to death in a church and civil rights workers ambushed and murdered, they were angrier." The number of Black urban uprisings increased from nine in 1965, 38 in 1966, 128 in 1967, and 131 in the first six months of 1968. These urban disorders were not only a rejection of the Johnson Administration's limited "War on Poverty," but a break from the quiescence of Black middle class and Black preacher-dominated civil rights organizing efforts. The Black masses were prepared to "take to the streets and thereby declare their hatred for the bondage imposed on them."
With the sudden renaissance of Black nationalism in the guise of Black Power, both King and his entire generation of activist-ministers received a profound jolt. SNCC activist Julius Lester's Look Out, Whitey! Black Power's Gon' Get Your Mama! repeated Jones' denunciation of King as merely the "successor of Booker T. Washington." King's message of "love" was hypocritical, Lester declared. "What is love supposed to do? Wrap a bullet in a warm embrace? Caress the cattle prod?" For Black activist veterans of the Albany, Birmingham and Selma campaigns, the spirituality and ethos of nonviolence was dead. "We used to sing 'I Love Everybody' as we ducked bricks and bottles," Lester reflected. "Now we sing: Too much love, Too much love, Nothing kills a nigger like too much love." Robert Allen's Black Awakening in Capitalist America concluded that even the Black activist minister could not be expected to provide any effective, long-term leadership in the Black Movement. Although "the Black minister remains today an important, if not the most important, social force in most Black communities," he represents a prime "collaborator" and "force of conservatism." Allen noted:
While it must be said that the Black church has performed an essential function in maintaining social cohesion in Black communities through decades of travail and suffering, it cannot be denied that the Black preacher is often identified as an 'Uncle Tom' . . . He is seen as a traitor to the best interest of his people. .. The minister, in accepting Christianity, also in some degree identified with the major moral values and institutions of white society. Consequently it was relatively easy for him to work with whites, even though this sometimes amounted to a betrayal of Blacks.
As for Martin himself, the young Black nationalists had little sympathy. "As the crisis of Black America deepened," Allen wrote, King was converted into "a reluctant accomplice of the white power structure." The white elites discovered that King was useful "to restrain the threatening rebelliousness of the Black masses and the young militants." Furthermore, "King could not repudiate this role because he was convinced that the establishment could be pushed and pressured to implement his program." At a speech at the University of California-Berkeley in October, 1966, SNCC chairperson Stokely Carmichael expressed an ambiguous respect yet deep disillusionment toward King and his goals. Carmichael admitted that King was "full of love," "mercy and compassion," a man "who's desperately needed in this country. But every time I see (President) Lyndon (Johnson) on television, I say 'Martin, baby, you got a long way to go.'"
King's final years provide some parallels with the last months of the major Black nationalist of the 1960s, Malcolm X. Like the former Muslim minister, King had begun to reevaluate the goals of the Black struggle from the simple demand for civil rights to the pursuit of "human rights." His first public speech on the Vietnam War, given at a Virginia statewide meeting of SCLC affiliates in Petersburg in July, 1965, was a mixture of anticommunism, moral suasion and passivism. "I am certainly as concerned about seeing the defeat of communism as anyone else," King stated, "but we won't defeat communism by guns or bombs or gasses. We will do it by making democracy work." He called for an immediate end to U.S. military involvement in Southeast Asia and a "negotiated settlement even with the VietCong." By 1967 King was actively leading the U.S. peace movement, addressing rallies and proposing concrete details for U.S. disengagement from Vietnam. He became more concerned about the profound similarity between the oppressed material conditions of the unemployed, Blacks and whites, and proposed a "Poor People's March" on Washington, D.C. in October, 1967. Many of King's oldest friends rejected him, some visciously attacking his new political concerns in the media. Negro columnist Carl Rowan, who assisted King during the Montgomery Bus Boycott, charged that the leader's peace activities have "alienated many of the Negro's friends and armed the Negro's foes, in both parties, by creating the impression that the Negro is disloyal." Conservative representatives of the Black middle class, such as Whitney Young of the Urban League, NAACP director Roy Wilkins and former socialist Ralph Bunche bitterly condemned King, as did the only Black in the U.S. Senate, Edward Brooke. Many Black ministers within the SCLC privately criticized King for moving too far left, and publicly separated themselves from any antiwar demonstrations and religious peace services. On April 4, 1968, King was assassinated while assisting 1,375 Black sanitation workers in Local 1733 of the American Federation of State, County, and Municipal Employees, AFL-CIO in a strike in Memphis, Tennessee. The middle class reformer had become a militant proponent of peace, economic democracy and Black working class interests.
IV
King's strengths and weaknesses were not his alone, but those of his social group, the Black clergy. His moral appeals for nonviolence, racial harmony and desegregation were shared by previous generations of Black middle class reformers. His initial reluctance to emphasize economic issues, his implicit anticommunism and desire for compromise rather than confrontation with the white establishment was also the popular ideology of the Negro petty bourgeoisie. Where King departed from his contemporaries was his recognition that Black ministers as a group had to play a decisive role in the reconstruction of U.S. civil and political society. The greatest political contradiction confronting the masses of Blacks, the system of white supremacy, was of course the primary target of King's efforts. In the process of struggle, however, King concluded finally that the defeat of racial segregation in itself was insufficient for creating Americans. King followed the tradition of earlier Black activist-clergy—Henry Highland Garnet, Henry M. Turner, Nat Turner—by calling for radical and fundamental change. Without hesitation, he broke from many of his own advisors and supporters, and like Malcolm, raised many public policy issues which could not be easily resolved within the existing system. Congressperson Louis Stokes, chairperson of the U.S. House Select Committee on Assassinations, believes that King was murdered because "he had begun to wake up poor people in this country, not only poor Black people but also poor white people. (In) entering this dangerous area," King had to be killed.
Many of King's lieutenants in the Black clergy have failed to pursue King's vision. Abernathy, Hosea Williams and the brother of the martyred civil rights activist Medgar Evers, Charles Evers, endorsed the presidential candidacy of ultraconservative Ronald Reagan in 1980. Andrew Young, currently mayor of Atlanta, Georgia, served as U.N. ambassador in the Carter Administration.
Several ministers within the SCLC, including Fauntroy, have been elected to high office, and Jesse Jackson's Operation PUSH captures headlines with political maneuvers which are more style than substance. As a group, however, not a single member of King's generation has courageously pursued the logic of his final years. Part of their current dilemma is created by their conscious, class-oriented commitment to infuse the Negro middle class into the present economic order and to perpetuate the inert politics of bourgeois reform. They are not prepared to repudiate the system which rewards their own political accommodation at the expense of the continued exploitation of Black working class and poor people.
Even after the most detailed exploration of the politics of the Black Church, a series of contradictions remain. How has the Black Church as an institution failed repeatedly to evolve into a coherent agency promoting the liberation of Afro-American people, and why has it succeeded to reveal itself as an essential factor in Black struggles at certain difficult historical periods? Why is the stereotypical Black preacher the frequent object of embarrassment, ridicule and scorn for the Black petty bourgeoisie and to much of the Black working class, yet simultaneously he continues to be a critically important contributor to the total sum of Black social, cultural, economic and political life? How can such a church create Martin Luther King and Daddy Grace, Ben Chavis and Reverend Ike? Why, in short, does the Black Church continue to perform its fundamentally ambiguous role in the Black experience?
The insights of Marxist theorist Antonio Gramsci, and especially his critique of the role of Catholicism within Italian society and culture, have particular merit for our own situation. Religion for any society constitutes the most important element of the people's "common sense." But common sense "is not a single conception, identical in time and space: it is the folklore of philosophy . . . disintegrated, incoherent, inconsecutive." Organized religions attempt, first, to impose order out of the day-to-day chaos that is experienced in cultural, social and economic relations. Religion endeavors to transform "what the masses think embryonically and chaotically about the world and about life." Various social strata experience religion in diverse ways. "Every religion (is) a multiplicity of distinct and often contradictory religions: there is the Catholicism of the peasants, the Catholicism of the petty bourgeoisie and the town workers, the Catholicism of the women and the Catholicism of the intellectuals." The same could be claimed for Black America. The rural sharecroppers and urban poor are attracted to evangelical or fundamentalist denominations, with their physical and passionate expressions of faith and conversion. The Black working class for a century and more has consistently been Baptist and Methodist. The Black petty bourgeoisie are generally attracted to "high church" Anglicanism, Catholicism, Presbyterianism and Congregationalism. Substantial elements of the Black intelligentsia have been either Quakers, deists, agnostics or atheists. Nationalists have often been attracted to alternatives to Christianity, particularly Islam. Extreme integrationists have sometimes claimed Judaism. What unifies believers here is faith itself, "the most important element of a non-rational character" in all religious creeds.
"But (faith) in whom and for what?" Gramsci asks. "The power of religion has consisted and does consist in the fact that they feel strongly the need for the doctrinal unity of the whole 'religious' mass, and struggle to prevent the superior intellectual elements detaching themselves from the inferior ones. The struggle has not always been fought without serious inconvenience for the church itself, but this inconvenience is connected with the historical process which transforms the whole of civil society and which en bloc contains a criticism destructive of religion." Any and every religious organization is confronted with the problem of uneven ideological development and irregular commitments that the masses express toward the church and its dogma, an unevenness which is itself a direct product of class distinctions. Moreover, for historically oppressed groups, religion becomes a primary forum for the divisions that exploiters have pressed upon that people's socioeconomic reality. The church strives for unity in a material environment that cannot congeal itself.
The practical tasks of the Black Church have been (1) to provide an idealist, non-rational popular worldview to the Black masses, Christianity, which is achieved by the ritualistic acts of individuals who acknowledge Christ and the particular elements present within the theology of a denomination; (2) to preserve and to defend the actual material interests of one's congregation, and by extension, all Black people, by confronting the state apparatus, by taking calculated political risks, and by articulating the real grievances of Blacks from pulpits to public policy meetings; (3) to develop fraternal relations with white congregations and denominations, yet maintaining the unique character and independent spirit of the Black Church; and (4) to build cultural and social unity and a critical respect for Black history among Afro-Americans, while opposing the imposition of racial segregation, vigilante violence and racial hatred upon Blacks by whites. The Black Church is divided, because its raison d'être is divided. Confronting this nearly impossible challenge, Black churchmen have almost always set a series of priorities, either consciously or unconsciously. Those ministers who have emphasized material, day-to-day challenges of being Black in a racist/capitalist state, and those who have not hesitated to leave the cloistered halls of God to enter the turbulent and gritty realities of the streets are part of what I have called the tradition of Blackwater. Those ministers who emphasize prayer over politics, salvation over suffrage, the study of Ecclesiastes over the construction of economic cooperatives, represent the Other-Worldly position of Black faith. Both are legitimate and historically grounded within the Black Church, and are often expressed in contradictory ways by single individuals. The most conservative and accommodating Black itinerant preacher always has within him the capacity to become a Nat Turner.
Both traditional perspectives within the Black Church are flawed, however. The basic contradiction evident within the most elementary kernel of Christian theology is that "despite everything," the evil of the world is rooted within man himself, "that is, (Christianity) conceives of man as a clearly defined and limited individual. Man is conceived of as limited by his individuality and his spirit as well." We are all our "brother's keepers;" neither "good works" nor our "faith" can erase the primal sin of another man/woman. Each individual who wishes to be "saved" must, through his /her own accord, confront Christ as his/her personal savior, or acknowledge that "there is but one God and that is Allah," etc. Gramsci argues, "it is precisely on this point that a change in the conception of man is required. It is essential to conceive of man as a series of active relationships (a process) in which individuality, while of the greatest importance, is not the sole element to be considered. . . . man changes himself, modifies himself, to the same extent that he is a nexus."
The contemporary race/class crises within American society require that Black ministers confront the basic question that delienates humanity from all other forms of animal life—what is a human being, and what can hunanity become? Man/woman is the product of many ideological, political and economic forces. But in the end, collectively, humanity creates itself, its institutions and its common sense. The internalized patterns of a people's history becomes the basis of their class consciousness. By transforming ourselves, and our consciousness, we begin to make history. The next great challenge, the battle for socialism, will force the Black Church to place the collective needs of Black humanity ahead of the narrow individual needs of any single person. Whether the Black Church, and those courageous ministers who embody the militant tradition of Blackwater, can face this test remains to be seen.
Black ministers all too often have been content to interpret the scriptures in various ways and to preach salvation to the masses. The real point of Black faith, and the fundamental meaning of King's evolution toward more militant politics, is to change the conditions of the oppressed Black majority for the better. If Black ministers fail to learn from their own mistakes, they may as a social group decline still further in the esteem of their own people. If they succeed, they have the potential to spark anew the moral and ethical commitment that remains essential within the struggle against racism and capitalist exploitation. It is entirely possible that the most decisive ally of the Black working class in its struggle for democratic socialism, at least among the Black elite, will be the Black Church.
CHAPTER EIGHT
THE DESTRUCTION OF BLACK EDUCATION
The chief difficulty with the education of the Negro is that it has been largely imitation of his mind. Somebody outside of the race has desired to try out on Negroes some experiment which interested him and his coworkers; and Negroes, being objects of charity, have received them cordially and have done what they required . In fact , the keynote in the education of the Negro has been to do what he is told to do. Any Negro who has learned to do this is well prepared to function in the American social order as others would have him.
—Carter G. Woodson, The Mis-Education of the Negro (Washington, D.C.: Associated Publishers, 1933), p. 134.
I
The demand for Black education has probably been the most enthusiastically supported political reform among Afro-American people, from slavery to the present. Unlike "Black Capitalism," which appealed only to the Negro entrepreneur and segments of the Black nationalist faction, the call for increased state support for Black educational institutions has been a universal concern among all classes. The historical reasons for this can be stated briefly. Less than 10 percent of all former slaves in 1865 were literate. White racists from George Fitzhugh in the 1850s to George Wallace in the 1960s saw the Blacks' demand for access to the schoolhouse as a threat to the preservation of white supremacy. Free Blacks in the antebellum South who learned to read by various means usually hid this explosive secret from their masters—for obvious reasons. After the Civil War, Black women, men and children recognized that their lack of education permanently restricted them to a life of agricultural penury and economic exploitation. As DuBois observed, "there is no doubt but that the thirst of the Black man for knowledge—a thirst which has been too persistent and durable to be mere curiosity or whim—gave birth to the public free-school system of the South. It was the question upon which Black voters and legislators insisted more than anything else." Primary, secondary and university-level education was viewed as a decisive means to end the vicious cycle of racial underdevelopment.
Historically, the Black college is largely the direct product of racial segregation. Ninety-one of the 107 Black colleges were established before 1910. Generally underfinanced and inadequately staffed, Black higher education was permitted to exist only in skeletal form during the long night of white supremacy. As late as 1946, only four Black colleges—Howard University, Fisk University, Talladega College and North Carolina State-were accredited by the Association of American Universities. In the school year 1945-1946, Black undergraduate enrollment was 43,878 in the Black colleges. Less than 1,800 attended Black professional schools; only 116 were then training to become lawyers. Even after the passage of expanded educational legislation, the number of Afro-Americans who were financially able to attend universities was pitifully small. By 1950, 41,000 "minority" men and 42,000 "minority" women (Blacks, Asians, etc.) between ages 18-24 attended colleges, about 4.5 percent of the total Black age grouping. That same year, by way of contrast, 1,025,000 white males between 18-24 years old attended college, 15 percent of the total white age group. The function of the Black college was, at least from the view of white society, to train the Negro to accept a "separate and unequal" position within American life. (See Table XXVII)
Despite these institutional barriers to quality education, the Black schools did a remarkable job in preparing Black youth for productive careers in the natural and social sciences, the trades and humanities. A brief review of one Black college, Fisk University, provides an illustration. Fisk was the home for a major number of Black intellectuals during the era of segregation: DuBois, historian John Hope Franklin; sociologist E. Franklin Frazier; artists/novelists James Weldon Johnson, Arna Bontemps, Sterling Brown, Nikki Giovanni, John Oliver Killens, and Frank Yerby. A number of other Fisk alumni joined the ranks of the Black elite in the twentieth century as decisive leaders in public policy, representing a variety of political tendencies: U.S. Representative William L. Dawson; Marion Barry, mayor of Washington, D.C.; Wade H. McCree, U.S. Solicitor General during the Carter Administration; U.S. district judge Constance Baker Motley; civil rights activist John Lewis; Texas State Representative Wilhelmina Delco; Federal judge James Kimbrough. Other Fisk graduates moved into the private sector to establish an economic program for Black development along capitalist lines, such as A. Maceo Walker, president of Universal Life Insurance Company. And, within the professions, one out of every six Black physicians, lawyers and dentists in the United States today are Fisk graduates. A similar profile could be obtained from Atlanta University, Morehouse College of Atlanta, Spelman College of Atlanta, Tougaloo College of Mississippi, Tuskegee Institute of Alabama, Howard University of Washington, D.C., and other Black institutions of higher learning.
My point here is not that these schools ever developed a clear pedagogy for Black liberation, nor that they were organically linked to the daily struggles of the Black masses. The conservatism of many Black college administrators, as represented by Tuskegee's Booker T. Washington, is almost legend among Black people. These schools operated under the rigid constraints of race/class tyranny, and often suffered under benign-to-malignant administrations imposed by white trustees and state governments. But despite these and other contradictions, the Black universities have on the balance been much more open to progressive and liberal faculty—particularly during the period of the Cold War of the 1940s and 1950s. They created the intellectual and social space necessary for the development of militant political reformers, dedicated public school teachers, physicians, and other skilled professionals within the Black community. Without such institutions, the nightmare of Jim Crow might still exist, and the material conditions of the Black ghetto and working class would unquestionably be worse.
The Civil Rights and Black Power Movements, combined with a political shift of the U.S. government under the Johnson Administration toward implementation of some affirmative action guidelines within white civil society, accelerated this educational process. By 1970, 192,000 Black men and 225,000 Black women between ages 18-24 attended college. The overall percentage of Black youth enrolled in college, 15.5 percent, contrasted with white attendance ngures of 34 percent for males and 21 percent for females. Five years later, 294,000 Black men and 372,000 Black women between ages 18-24 were in college, respectively 20 and 21 percent of their age groups. The most recent available statistics, for the years 1976 and 1977, reveal a slight decline in Black college enrollment—a testament to the political assaults against Black educational opportunity of the 1970s. The total numbers of Black college youth slipped from 749,000 to 721,000, and the percentage of Black men who were college students within the 18-24 age group declined from 22.0 to 20.2 percent. Despite the desegregation of white universities, traditionally Black institutions, both private and public, continue to serve a majority of Blacks seeking college or professional training. Twenty-five percent of all Blacks in higher education attend the 35 state-supported Black colleges. Sixty-two percent of all Black M.D.'s and 73 percent of all Black Ph.D.'s are products of Black institutions. (See Table XXVIII)
For those Black students who did not go on to Black colleges but who struggled within the white university, a number of searching political, historical and cultural questions were raised—inquiries that could not be easily answered by the sterile discourse or conservative pedagogy of these white institutions. The struggle from the streets of America suddenly scaled the walls of the academy. "In the mid- and late 1960s, at the height of the burnings and when the assassinations sent death and rage through each of our hearts, we said we knew that we were inseparable from the searing life of the Black community," reflected historian Vincent Harding. "When the students rose on the campuses and demanded our presence, or pressed for greater visibility and recognition for our work, we claimed, with them, indissoluble bonds to the heaving life of the Black masses." The entire story of the Black Student Movement—the takeovers of computer centers, academic buildings and student unions; the creation of Black Student Unions and Black Cultural Centers; the emergence of Black nationalist ideology within the potential Black petty bourgeois stratum—remains to be told. It is sufficient to note that most white universities reacted first with fear, then anger, then finally with quiet calculation in the face of the Black revolt. Most white academicians viewed Black Studies as a tactical retreat on their part, an institutional maneuver to guarantee Black quiescence for a period of years. By the early and mid-1970s, many Black programs were reduced or eliminated entirely.
The demand for Black Studies was also a call toward the systemic reconstruction of American learning. Its most advanced advocates understood that the study of the African diaspora and its people could not simply be "added" into the standard curricula, merged within the mainstream of white thought. Rather, the social science, literary and creative contributions of Blacks to the whole of human knowledge charted new and different directions of critical inquiry. First, Black Studies demanded a pedagogical approach toward learning that deemphasized the "banking" concept of teaching, and advanced mixed methodological techniques, such as discussion, informal lecturing, debate and community studies. Black Studies theoreticians declared that interdisciplinary approaches toward learning were superior to narrow, selective teaching methods which concentrated on one single subject (e.g., history) at the exclusion of other related disciplines (sociology, political theory, political economy). Students were urged to devote some of their research activities towards the transformation and liberation of their own communities. Thus there was a basic relationship between theory and practice in the learning process that was missing from traditional white education. Students were urged to become active participants in their own education. For these theoretical and pedagogical reasons, therefore, Black Studies represented a basic and provocative challenge to the raison d'être of white universities.
But it was in the field of Black history that Black Studies evoked the greatest challenge to white bourgeois ideological hegemony. Prior to the 1960s, white historians approached the issue of race via two overlapping methods. The first approach, favored by ideological conservatives, could be termed "The Negro-as-Invisible Man." This school suggested that "the Negro had no history;" race relations studies, although interesting, properly belonged to the "secondary" discipline of sociology. Booker T. Washington and George Washington Carver were Negroes whose moderation merited some attention, but not W. E. B. Du Bois, Henry Highland Garnet or Marcus Garvey. The Civil War was interpreted as a sectional conflict sparked by disagreements over tariff regulations. The second approach, advanced ideologically by Cold War liberals, argued that the Negro had always been part of the Great American Melting Pot. The "patriotic" exploits of Crispus Attucks, Salem Poor and Peter Salem were invariably mentioned in texts on the American Revolution. The historical fact that more Afro-Americans fought with the British than on the side of the colonial rabble, and that over 25,000 former slaves departed the U.S. with the British army in 1781-83, was relegated to the dusty footnotes. The liberals maintained that, despite slavery and segregation, the Negro people had proven themselves as loyal Americans. A testimony to the liberal belief in the "Americanization" of the Negro is provided in Kenneth Stampp's classic The Peculiar Institution (1956). With some pride, Stampp wrote, "I have assumed that the slaves were merely ordinary human beings, that innately Negroes are, after all, only white men with black skins, nothing more, nothing less."
From the late nineteenth century, Black historians challenged both positions with intellectual courage and historiographical skill. George Washington Williams' History of the Negro Race in America, published in 1882, was the first exhaustive critique of the inferior position of Blacks in the U.S. This pioneering study was followed by William T. Alexander, History of the Colored Race in America (1887); Harold M. Tarver, The Negro in the History of the United States (1905); Benjamin Brawley, A Short History of the American Negro (1913); and Willis D. Weatherford, The Negro from Africa to America (1924). The most important works were produced by Carter G. Woodson, The Negro in Our History (1922), and by DuBois: The Negro (1915); Black Reconstruction in America (1935); and Black Folk, Then and Now (1939). These works set the direction for a new generation of Black and white historians writing after World War II.
Thus, by the late 1950s many white historians had begun to view the Negro as "the creator of his own history." This recognition of the legitimacy of the Black past was fatally flawed by an idealistic approach toward historiography. Black "heroes" were popularized as contributors to American civilization. The pharoahs and the pyramids were illustrative of early Black genius—without the observation that these societies were based on slave labor and financed by the systematic plundering of the Black Sudan. Black inventors like Jan E. Matzeliger and Granville T. Woods were discussed as making "contributions toward the growing industrialization of America," in the words of John Hope Franklin—without the recognition of the role of modern industrial capitalism as a socially disruptive force. From this vantage point, the history of the Black national minority group becomes devoid of struggle as the central motif. It was the conceptual framework designed to serve the secular goal of integrating petty bourgeois Blacks into late capitalist civil and political society.
The Black Power Movement brought these schools of interpretation to a temporary halt. For young Black historians and social scientists—Vincent Harding, Lerone Bennett, Sterling Stuckey, David Lewis, Robert Allen, William Strickland, and many others—the history of Black people was a history of continuous struggle. Their research was rooted in the philosophical concept that human beings collectively made their own history. Always in the face of adversity, often betrayed by their own leaders and the petty bourgeoisie, the Black majority fought to maintain its unique identity as a people and to secure by whatever means the economic and political tools for self-determination and self-reliance. The chief shortcoming of this school of Black historiography was, in retrospect, its lack of institutionalization. Few Black publishing houses were created in the 1960s or early 1970s; the emergence of the Institute of the Black World in Atlanta was one of the rare instances where Black activist/intellectuals could find the creative space to produce their works. By the mid- to late 1970s many white publishers ceased to solicit Black manuscripts, and the number of Black Studies and Black historical journals began to recede. The Black petty bourgeois stratum, the chief beneficiary of the affirmative action quotes of the 1960s, failed to provide adequate material resources for Black intellectual and cultural workers. Many Black social scientists who vowed never to teach at white universities during the nationalistic era found themselves within the confines of the white academy by the 1980s.
Desegregation proved to be both a blessing and a curse. It created the conditions for a virtual revolution in Black educational opportunities. Simultaneously, the liberalization of white educational institutions permitted many of the best Black intellectuals to leave the South for more prestigious posts at Northern and West Coast universities. The generation of Black middle class professionals trained at Howard and Fisk in the 1940s sent their children to Harvard and Berkeley. The Black Power explosion of white campuses from the mid-1960s to early 1970s accelerated the crisis as the most militant and progressive Black professionals began to work in Afro-American studies departments on white campuses.
The rapid growth of state-supported, two-year colleges and vocational schools in the 1960s and 1970s also contributed to the financial crisis of private Black institutions. By 1978, 41.8 percent of all Blacks were enrolled in two-year degree programs, vs. 34 percent for whites. The number of white students transferring or applying to Black campuses jumped sharply. For example, by 1981 the white enrollment at the engineering school at previously all-Black North Carolina Agricultural and Technical State University in Greensboro reached 40 percent. On the other hand, first-generation college students from low-to-middle-income Black families could not afford to pay the higher tuitions at private Black colleges. Private foundations cut back sharply in their donations to Black schools after the recession of 1973-1974. By the late 1970s, the traditionally Black colleges were facing the mounting financial costs of even maintaining essential services and buildings without sufficient support within the Black community as a whole.
II
One of the many promises made by Presidential-hopeful Ronald Reagan early in 1980 was a commitment "to improve and to defend" traditionally Black colleges. Unlike President Carter and independent candidate John Anderson, Reagan made substantial overtures to Black educators and administrators at predominantly Black Southern institutions. Reagan's chief Black aide, Art Fletcher, was the former executive director of the United Negro College Fund. The Republican nominee openly embraced the Black College Day demonstration held in Washington, D.C. on September 19, 1980, and charged that "the Carter Administration—in the name of desegregating Black colleges—is forcing them to become schools for training everybody but Blacks." Reagan also promised to encourage corporations to increase their financial support for Black universities and pledged "to work to increase the share of Title III budget allocated to Black colleges."
Under Carter's Administration, Black colleges received a smaller percentage of federal funds going to all universities than the Nixon Ford years. Black educators had denounced Carter's intention to desegregate two Black Texas colleges, Southern and Prairie View. By late 1979, Washington Post columnist William Raspberry expressed the widely held view among Blacks that Administration officials "are unfamiliar with the historical role of these (traditionally Black) colleges and are indifferent to the vital service they perform." Given this recent history, many Black college administrators perceived that Reagan's election would mean a real advance for Black higher educational opportunities, despite his economic austerity program and conservative social policies.
The Reagan Administration's first important announcement concerning the fate of Black colleges occurred, appropriately enough, at Tuskegee Institute. Institute President Luther Foster had invited Reagan to be the principal speaker at the April 12, 1981 "Founder's Day" program, marking the one-hundredth anniversary of Tuskegee. Reagan's hospitalization forced Vice President George Bush to substitute for the chief executive. Bush did not disappoint his Black audience. Before 3,000 people, the Vice President declared that his administration is "absolutely committed to supporting the nation's civil rights laws and to providing the resources necessary to make those laws work fairly and effectively for all Americans. We are committed to the principle of equal justice under the law." Interrupted repeatedly by loud applause, Bush promised to pressure public and private sources to grant greater financial support to traditionally Black universities. Bush was silent on whether the Reagan Administration would support the extension of the 1965 Voting Rights Act. But college administrators and local Black elected officials were generally pleased. Tuskegee mayor Johnny Ford stated that Bush's speech was "welcome by all of us who walked across the Edmund Pettus bridge" in nearby Selma, in the fight for Black equal rights and education.
During the spring and summer, 1981, the Reagan Administration worked aggressively to draft less stringent terms for integration within state-funded higher education programs. By mid-August, agreement for Florida, North Carolina, South Carolina, Missouri, Louisiana, and West Virginia were completed which would leave the old segregation era Black and white institutions virtually intact. In general, the plans eased pressures on the formerly whites-only systems to hire additional Black faculty and staff, and cut back any additional Black supervision within the governance of state universities. They also included provisions to improve both the academic program and physical facilities available at formerly all-Black colleges. The announcement of the newly relaxed desegregation policies had an immediate impact upon several court cases. Louisiana and Mississippi had consistently refused to alter their dual college systems, and were sued by the Federal Government for failing to enforce Title VI of the 1964 Civil Rights Act, barring racial discriminations. The Louisiana case was postponed as state and Federal officials were redrafting a settlement based on the North Carolina model.
The North Carolina agreement which was approved by Federal District Judge Franklin Dupree in Raleigh on July 10, after eleven years of litigation, quickly became the basic document for all other Southern states. The plan kept the dual educational system intact, and had no provisions which would upgrade or expand master's or doctoral programs at Black universities. It ignored any quotas for the hiring of minority faculty and staff at North Carolina's white universities. The plan committed the state to allocate $80 million "to upgrade the physical plants and academic programs" at the Black institutions, and provided some modest affirmative action guarantees to expand the number of Black graduate students in both systems. The plan also forbade the Federal government from suing North Carolina officials over the agreement for five years.
The North Carolina plan was quickly denounced as a return to "separate but equal" by the NAACP Legal Defense and Educational Fund, Inc., by former Carter Administration officials, and by Black alumni organizations from the traditional Black colleges in North Carolina. Leonard L. Haynes, director of the Office for the Advancement of Public Negro Colleges, informed the New York Times that the Reagan Administration "let North Carolina do whatever it wanted to do, thus abdicating its responsibility to enforce Title VI." Defenders of the agreement included all five Black chancellors of the state universities, and probably a majority of the Black college administrators and officials in the country. Clarence Thomas, a Black conservative attorney from Georgia who was appointed by Reagan as the Department of Education's Assistant Secretary for Civil Rights, justified the plan with the remark that "government fiat is not the only way to enforce civil rights laws." The road toward desegregation, initiated by the 1954 Brown decision, returned full circle to the Tuskegee-inspired dual educational structure.
Yet Bush's address at Tuskegee Institute had a disturbing historical precedent. In November, 1898, another conservative Republican, William McKinley, made a political sojourn to that Black college community. Tuskegee Institute President Booker T. Washington had come to national prominence several years before by issuing his "Atlanta Compromise" address which accepted the legal segregation of the races in return for Black economic and educational benefits. McKinley applauded Washington as "one of the great leaders of his race" and stated that Tuskegee Institute was a "generous and progressive" model for all Black education. McKinley's speech, like Bush's, was primarily symbolic, yet both provided political support for the construction and maintenance of all Black educational institutions. Within three years after McKinley's Tuskegee visit, Blacks were completely disfranchised in the state of Alabama, and the rule of "separate but equal" had become institutionalized throughout the South. The dual system of segregated higher education would exist for over sixty years. Would history repeat itself?
III
It is from this perspective of history that the North Carolina agreement must be judged. The state acquired the reputation as the most "liberal" throughout the South in its policies on Black public education. The first Black colleges in North Carolina, Barber-Scotia in Concord, Shaw University and St. Augustine's in Raleigh, and Johnson C. Smith in Charlotte, were started immediately after the Civil War. The number of schools expanded rapidly with the emergence of Jim Crow laws. Today, there are more Black colleges in North Carolina with substantial state support than in any other state. Nevertheless, Southern liberals always justified the necessity for state-supported Black higher education as a defense of white supremacy. In 1903 Gustavus R. Glenn, former Georgia public schools superintendent and an administrator of the Peabody Fund, informed a joint session of the North Carolina legislature that "the colored man will only be a danger to us when we leave him to be educated by outside philanthropists. You need not be afraid of the negro boy. It will take him a thousand years to get where your boy is." This racist tradition was preserved into the 1950s, when North Carolina Senator Sam Ervin drafted a "Southern Manifesto," asserting the intention to use every legal tactic to halt public school desegregation.
Caught in a seemingly hopeless dilemma, Black educators opted for what could be termed the lesser of two evils. An acceleration of the desegregation process would, in their view, simply transform traditionally Black colleges into majority white institutions. The North Carolina agreement, and others like it, promised to halt the growing numbers of white faculty, administrators and students of Black campuses, while providing millions of dollars for sorely needed physical plant expansion and research. Like Booker T. Washington, these college administrators are political accommodationists, and insist that the national mood has become profoundly conservative on racial matters. When the House of Representatives voted 265 to 122 on June 9, 1981, to prohibit the Justice Department from pursuing court cases that would lead to the busing of school children to promote desegregation, for example, it had a direct impact upon Black higher education officials' willingness to conciliate with Reagan's agenda.
The first real effects of the North Carolina agreement were a shock to Black college teachers. On August 24-25, 1981, between 70 to 90 instructors and assistant professors at North Carolina Central University were ordered to complete their doctoral degrees by November 30, 1981. Failure or inability to do so, under the terms of the consent decree, means that junior faculty members' contracts "would not be renewed and that they would not be considered for reappointment." The letter, signed by Vice Chancellor Charlie L. Patterson at Durham, was intended "to intensify the pressure" on mostly Black junior faculty members to complete their degree work. The agreement which promised to defend the legal and political stability of Black colleges quickly promised to radically transform them. As history professor Sylvia M. Jacobs complained, "I had no idea whatsoever that the results of a consent degree would be so extreme. It is feasible that under this policy, in the next two years we could have a predominantly white faculty" at North Carolina Central.
The only possibility to save the traditionally Black institutions without another "Atlanta Compromise" would be to reject both the liberal integrationist approach and the neo-segregationist North Carolina agreement. It is imperative that white higher educational systems be forced to accept strict quotas in hiring Black faculty and administrators, and that duplicate programs offered at various schools be eliminated. At the same time, traditionally Black public institutions should not be forced to integrate faculty and student bodies at a rate faster than white state universities have done. Black private colleges must remain Black, to fulfill their historic mandate of providing quality education to Black people. Given the absence of a radical Black critique in Black higher education circles, however, the prospects for the destruction of the remaining Black universities and a concomitant drop in the total number of Blacks admitted to all colleges are now very real.
IV
Nonwhite education, whether within the colonial administrations of preindependent Africa, or in the United States, has expressed a consistent duality of purpose. Capital accumulation within the Black community required the training of a select number of Blacks to fill positions in the economy. But to guarantee that their essential authority over Blacks could not be challenged, white educators deliberately and systematically fostered a pedagogy for Black subservience to capitalism. This process of educational underdevelopment was never entirely successful. As Walter Rodney asserted:
However much the colonialists tried, they could not succeed in shaping the minds of all the Africans whom they educated in schools. The most timid and the most brainwashed of educated Africans harboured some form of disagreement with the colonialists; and, in the pursuit of their own group or individual interests, the educated elite helped to expose and undermine the structure of colonial rule . . . (Colonial education) produced many 'loyal Kikuyu,' 'Capicornists,' (and) 'Anglophies' . . . but it also produced in spite of itself those Africans whom the colonialists called 'upstarts,' 'malcontents, ' 'agitators,' 'communists,' 'terrorists,' etc. Students who were taken to universities in the metropoles were most favoured and the most pampered of Africans selected by the white colonial overlords to become Europeans; and yet they were among the first to argue vocally and logically that liberty, equality and fraternity about which they were taught should apply to Africa.
The entire history of Black education is filled with examples which illustrate the central dynamic of Black civil society, the dual tendencies toward protest and accommodation. Washington and many Black educators consistently urged Black students and workers to "maintain peaceful and friendly relations with the best white people in the community who give our race employment and pay their wages." Other Black educators such as DuBois "saw education (to be truly education) as partisan and—given the realities of the social order—fundamentally subversive," writes Herbert Aptheker. Martin R. Delany was trained as a physician at Harvard; according to all white expectations, he should have become a non-threatening "credit to his race." Instead, this early nineteenth century product of the academy became an uncompromising abolitionist, a Black nationalist who declared that he "hoped the ground would refuse his body if a slaveholder crossed his threshold and he did not lay him a lifeless corpse at his feet."
Thus the process of Black educational underdevelopment has returned in a fashion to its original premises: the overt suppression of independent Black educational institutions, and the elimination of Black educators who call for the transformation of the racist/capitalist order. This is the reason why Black Studies had to be uprooted; this is the motivation behind the liquidation of Black colleges and universities which were created, ironically, to perpetuate segregation and Black inferiority. The false boundaries of Western education, and the pedagogy for replicating bourgeois life and labor are a vital aspect of the hegemony of capital. When the Black student or scholar seeks "to build black institutions which maintain and press forward truth," in the words of Vincent Harding, he/she raises a problematic which cannot easily or quietly be resolved within the present, inhumane order. The Black school becomes the background for the construction of a new society.
SECTION THREE
A QUESTION OF GENOCIDE
CHAPTER NINE
THE MEANING OF RACIST VIOLENCE IN LATE CAPITALISM
Fascism is a deformity of capitalism. It heightens the imperialist tendency towards domination which is inherent in capitalism, and it safeguards the principle of private property. At the same time, fascism immeasurably strengthens the institutional racism already bred by capitalism, whether it be against Jews (as in Hitler's case) or against African peoples (as in the ideology of Portugal's Salazar and the leaders of South Africa). Fascism reverses the political gains of the bourgeois democratic system such as free elections, equality before the law, parliaments, etc. ..
—Walter Rodney, How Europe Underdeveloped Africa, p. 216.
History has many cunning passages,
contrived corridors
And issues, deceives with whispering ambitions,
Guides us by vanities. Think now
She gives when our attention is distracted
And what she gives, gives with such
supple confusions
That the giving famishes the craving. Gives
too late
What's not believed in, or is still believed,
In memory only, reconsidered passion. Gives too soon
Into weak hands, what's thought can be
dispensed with
Till the refusal propagates a fear.
—T. S. Eliot, "Gerontion," in The Waste Land and Other Poems (New York: Harcourt, Brace, Jovanovich, 1979), p. 20.
I
Throughout his long and brilliant career as both a social scientist and political militant, DuBois speculated that the final solution to racial conflict in America might be the complete extermination of the Black race. In "The Future of the Negro Race," published in January, 1904, DuBois thought that extinction or "migration to foreign lands" might await Afro-Americans. Four decades later, in the pages of the Amsterdam News, DuBois shuddered at the horrors of the Nazi holocaust. "It is a case of race prejudice on a scale unknown and unconceived since the Emancipation Proclamation. What is happening to Jews," he warned, "may happen to us in the future. Unless (racism) is destroyed, rooted out, absolutely suppressed, modern civilization is doomed." Black writers in the 1960s flirted with the possibilities of Black genocide and emigration from the United States, sometimes with a reluctant ambiguity. Harold Cruse wrote in The Crisis of the Negro Intellectual that Garveyism and "impractical Back-to-Africa" schemes were ventures into "romantic escapism; for if the Afro-American does not find his salvation in the United States he will find it nowhere." Yet in the same book, 104 pages later, Cruse asserted, "there may well come a time when the race question in Africa will have to be solved by admitting specified numbers of white Rhodesians, Angolans and South Afrikaners into the United States, in exchange for an equal number of Afro-Americans to take their places in Africa." The most powerful thesis on the inevitability of whites' genocide of Blacks was Sidney M. Willhelm's Who Needs The Negro?
The life situation of Black Americans deteriorates with the passing of each year . . . technological efficiency makes possible the full realization of the nation's anti-Negro beliefs. The arrival of automation eliminates the need for Black labor, and racist values call for the Negro's removal from the American scene. . . As the races pull apart into life styles with greater polarity, the Black ghetto evolves into the equivalent of the Indian reservation. What is the point, demands White America, in tolerating an unwanted racial minority when there is no economic necessity for acceptance. With machines now replacing human labor, who needs the Negro?
The historical predictions of race war, genocide and destruction, the darkest fears of previous Black generations, seemed to many to have become reality in the 1980s. Beginning with the public execution of five members of the Communist Workers Party by Ku Klux Klansmen and Nazis on November 3, 1979 in Greensboro, North Carolina, there was an acceleration of racist violence across the country. Traditional leaders of the Black elite were convinced that "an informal coalition of white racist vigilantes, the police and government officials were conspiring to kill Blacks." Jesse Jackson declared to the New York Times in late November, 1980, that "there is almost a hysteria in Black communities because of the belief that there is a conspiracy. This country has taken a definite swing toward fascism." Even Blacks who discounted the possibility of a "national conspiracy to murder Blacks" usually prefaced their statements with the admission that "racism in the form of violence is sweeping the country."
Incidents of brutal violence against Blacks are reported infrequently. What usually is portrayed as an unusual or bizarre example of racism is only a small portion of the human tragedy. The lynching of nineteen-year-old Michael A. Donald in Mobile, Alabama, in March, 1981, was publicized as the first in the Deep South since the murder of Emmett Till in 1955. Almost completely ignored or suppressed by the white media were a series of barbaric incidents that have occurred in that region since 1979. In May, 1981, the Jackson Advocate reported in Mississippi alone there have been twelve murders "in as many months which are suspected by Blacks of being (racially motivated)." The tortured body of one unidentified Black man was found floating down a river in Cleveland, Mississippi. The man's sex organs had been hacked off, and the coroner later reported finding his penis in his stomach. On January 11, 1981, the body of 45-year-old Lloyd Douglas Gray was found hanging from a tree in Tallahatchie County, Mississippi. A. W. Hulett, Tallahatchie coroner, pronounced Gray's death a suicide, and no autopsy was performed. On February 28, 1981, the body of 32-year-old Roy Washington was found in Cypress Creek, in Holmes County, Mississippi. Washington had been "badly beaten in the head and face," his hands bound behind him, and then shot in the head at point-blank range. The corpse was weighed down with a scissor jack and wrapped by barbed wire. Scars around his neck indicated that he had also been lynched. Local white newspapers were silent on the murder. Police did not aggressively pursue leads in the case, and even followed a Black reporter around while he conducted his own investigation. The majority of the other Black men who have been found beaten or hanging in Mississippi counties have also been officially labeled suicides. Familiar with the pattern of racial violence, one Black resident of Tallachatchie County declared, "if they say it was suicide, it was probably a lynching."
Reaganites, Black and white, attempted to counter the growing perception that racism was out of control. Edwin Meese III, chief Presidential adviser, deplored the public statements of Jackson and others. "I guess what does disturb me, not from that standpoint of this administration as much as from society in general," he stated, "is that I think there are those people who are fomenting Black hysteria in order to preserve their own positions of so-called leadership." Many Black journalists agreed with Meese's condemnation of Black leadership. "The 1980 elections once again demonstrated that the group that designates itself as the Black leaders spent its political capital on a losing Democratic candidate and the failed politics of branding the winner as a warmongering racist," argued columnist Tony Brown. "As a result, there are fewer media opportunities, therefore a declining popularity for some of the traditional leaders." Both Brown and Meese concluded that "Black leaders were promoting hysteria for personal and selfish motives."
Only one instance of random violence against Blacks in the early 1980s attracted international attention—the systematic murders of at least 28 young men and children in Atlanta. The immediate questions that virtually every American asked—Who are the killers? What has the city government and police done to thwart the murders?—became almost secondary considerations. Neither the conviction of Wayne Williams, charged with the murder of two Black youth, nor the entry of the FBI in the case reduced the anxiety of millions of Black parents for the safety of their children. Why was Atlanta the site of these bizarre and inexplicable deaths? Were the murders only one small part of a pattern of racial violence which constitutes a national conspiracy? How have different social strata within the Black community responded politically to the killings?
Modern Atlanta is the product of the infusion of monopoly capital into a rapidly changing racial and political milieu. Until the Civil Rights Movement, the piedmont and Blackbelt South's central means of production were predominantly agricultural, construction and light industry. During the 1950s and 1960s Georgia experienced a massive economic transformation. The number of Black-owned and operated farms in the state dropped from 12,049 to 4,450 between 1954 to 1969, as agribusiness increased. Atlanta became a glittering convention center, and headquarters for virtually every major corporation in the Southeast. Jim Crow was gradually abandoned as Blacks comprised 51 percent of the city's population by 1970. Atlanta's Black elite, allied with liberal elements of the city's white private sector, successfully challenged the older racist hierarchy to become the new managers of the political apparatus. Maynard Jackson was elected mayor in 1973. By the mid-1970s the city projected the image of a successful, pro-business, biracial community.
Unresolved socioeconomic tensions created by the new realities of modern capital expansion and the older patterns of white Southern racism finally exploded in the late 1970s. Almost one quarter of Atlanta residents now exist below the poverty level. 26 percent of all households heads were unemployed in 1978. In recent years large numbers of middle-to-upper income whites fled to the suburbs. Between 1970-1980, 102,000 whites left Atlanta, and Blacks became two-thirds of the city's population. Incidents of violence between the remnants of the old segregationist police force and Blacks became more frequent. In 1973 and 1974, 23 Blacks were gunned down by police; 12 were under 14 years old. In the mid-1970s, Atlanta had the highest per capita police killings of civilians in the U.S. By 1979, Atlanta surpassed Detroit as the city with the highest murder rate in America.
Black Atlantans were poorly prepared to deal with their childrens' murders. The Black ministers and religious leaders, the backbone of the Black community's Civil Rights Movement, at first showed little concern in the case. Community groups did nothing to help resolve local tensions until the summer and autumn months of 1980. As the number of victims mounted, criticisms were raised against the Black petty bourgeoisie, and observers commented that only poor Black children were being singled out by the killer or killers. The local white-owned media branded the Jackson Administration hopelessly inept and promoted the racial slur that Blacks were intellectually incapable of governing a major metropolis. Television stations competed with each other to project tactlessly the anguish of Black parents, turning funerals into circus sideshows. One group of white patrolmen leaked to the media their view that Black police and government officials were simply "too stupid to solve the case." By the winter of 1981 Atlanta was by all accounts "a city under seige." Small school children from poor and middle class Black neighborhoods were actually arming themselves in school with homemade weapons. The white business community was convinced that a "racial blow-up would occur if a white was charged with the murders." Promising over 8,000 more jobs for inner city youths, the Atlanta Chamber of Commerce actually delivered only 2,000. Police repression escalated everywhere. 1,500 children in February, 1981, and 4,670 children in March, 1981, were stopped by authorities for violating a 7 p.m. citywide curfew. Ordered to cooperate with local officials, the FBI promptly infuriated Blacks by suggesting that some of the victims' mothers may have been the killers. With the arrest of Williams, the FBI left the city, and the attention of white capitalist America moved elsewhere.
Most Blacks recognized that the Atlanta murders signified a new level of terrorism which suppressed Black social and political development. Whether the racial identity of the killers was Black or white became secondary to what Jesse Jackson termed the conviction that "there is a cultural conspiracy to kill Black people." Blacks in Atlanta's Techwood Homes public housing project, armed with baseball bats and revolvers, organized self-defense patrols. Techwood community leader Israel Green stated that patrols were needed to protect the project's youth from "the crazed racist killers." Blacks and progressive whites organized solidarity demonstrations against the Atlanta murders across the nation. On March 13, 1981, almost 20,000 people marched down Harlem's Lenox Avenue in a candlelight demonstration. One reporter commented that "a certain religious atmosphere some organizers had called for, highlighted by candles, existed side by side with large pictures of Malcolm X, displays of revolutionary culture, and even an old 'Free the Panthers' banner from the sixties." An Atlanta-based association of parents of murder victims, the Committee to Stop Children's Murders, held a protest rally at the Lincoln Memorial on May 25, 1981. The five thousand participants included Black and white hospital workers from District 1199 in New York City, members of the United Auto Workers Local 99, several locals of the American Federation of State, County and Municipal Employees, and the United Mine Workers. Significantly, neither Washington, D.C. mayor Marion Barry nor Atlanta's Black Brahmins attended the demonstration. Speakers at the gathering, from Jesse Jackson, Victor Goode, president of the National Conference of Black Lawyers, and Bernice Krawczwk of the UAW emphasized that Atlanta was "the product of a racist society."
On several occasions Black speculation concerning the Atlanta crisis lapsed into a regrettable yet understandable (given the circumstances) level of paronoia. Social critic Dick Gregory developed a theory for the murders which asserted that "the missing children's bodies (are) drained of blood in order to create some miracle cure for cancer." Afro-Americans "have some special formula in their blood brought about because of the sickling traits which can be used in a formula to defeat cancer." Out of "sheer desperation," according to one Black source, some Blacks "have begun to accept Gregory's statement as fact and many (Black) Atlantans have begun to look strangely at all whites in the area." At the Washington demonstration Ella Collins, the sister of Malcolm X, reiterated Gregory's theory. She charged that the murders were the "work of white scientists" who were "performing experiments to discover what made the Black man so superior that he was able to withstand the abuses of 400 years." White journalists jumped at these and other statements to malign all progressive activities around the Atlanta murders. Chicago Tribune columnist Raymond Coffey denounced Collins' remarks as "dangerous, extremist, recklessly irresponsible, inflammatory, (and) abominably racist nonsense." The rally was a "political-racial-commercial jamboree," Coffey declared, dismissing the "End Genocide" placards carried by protestors as "preposterous." The Atlanta killings were not "racially motivated." Without missing a beat, some influential Blacks parroted this line. Big Red, one of New York City's major Black newspapers' informed readers that "there is no reason to doubt that all that can be done is being done." Statements implying that "if those kids were white" that the crimes would be solved do "far more harm than good." Talk about Black armed self-defense or revolt "plays into the hands of right-wing and left-wing extremists, both of whom constantly seek ways to undermine democracy. We should avoid all the kind of loose talk which adds to the insanity which that tragedy represents." Despite these arguments, the great majority of Blacks are now certain that the Atlanta murders will never be solved completely, and that the essense of the tragedy is both profoundly racial and political.
II
Atlanta represented the smallest fraction of random racist violence that had been mounting across the U.S. In every major city and small town, in virtually every part of the country, a shocking explosion of racist incidents occurred in the early 1980s. A small sample would include the following examples:
White police officers in New Orleans have shot at least 10 Blacks in 1980, killing eight. In one case, officers James Esposito and Robert Sedgeher shot Walter E. Brown on December 20, 1980, for cursing at them. They later resigned from the police force after admitting that they had planted a gun on Brown. An Orleans Parish grand jury cleared them of any wrong-doing.
On March 16, 1981, police in Roseville, Michigan pursued three young Black men driving what the officers mistakenly believed to be a stolen automobile. After a highspeed chase, police officers Rafael Perez and Thomas Lavender pursued one of the Black men, 20 year old Theodoric Johnson. Both policemen fired, killing Johnson. According to the Reverend Timothy Chambers, who had witnessed the shooting, one of the policemen bragged to the other, "I blew that nigger's head off"
Three Black women and one Black man were arrested in Summerville, South Carolina, on August 10, 1980, on shoplifting charges. The night of their transfer from the Summerville to Dorchester County Jail, police lieutenant Roger Hudson, 54 and white, forced the women "to perform sexual acts with and on him." The women filed charges through the sheriffs office charging Hudson with criminal sexual conduct, aggravated assault and official misconduct in office. A jury of ten whites and two Blacks acquitted Hudson. White jurors laughed and talked with Hudson, and the judge had told the jurors that "if (they) could not make up their minds, then the majority would rule." Two of the women and the man arrested for shoplifting were finally convicted and received sentences ranging from six to ten years.
In early 1981, white police officers in northwest Florida and southeast Mississippi circulated a mock hunting regulation document announcing "open season" for shooting "Porch Monkeys." The flyer continued: "Regionally known as Negro, Nigger, Saucer Lips, Yard Apes, Jungle Bunnies, Spear Chunkers, Burr Heads, Spooks, and the Pittsburgh Pirates." It is "unlawful to shoot any Porch Monkey in a Cadillac," to "trap within 25 feet of watermelon patches, or to bait traps with "pork chops, watermelons, mangoes, collards, cheap whiskey, fried chicken, chitlings [sic] or flashy clothes."
Cornelius Brown, a 42-year-old Black resident of Cleveland, was playing pool in a delicatessen on November 20, 1980. An off-duty white policeman, Napolean Dismuke, had left the pool table earlier and upon returning, demanded that Brown leave at once. Dismuke shot Brown with his .38 caliber revolver four times, killing him. Dismuke claimed that Brown had tried to assault him with a pool cue. In June, 1981, a jury found Dismuke innocent, and has since returned to active duty on the force.
Leroy Perry, a 48-year-old Black resident of Annapolis, Maryland, was halted for suspected drunken driving on July 20, 1981, by a white officer, David Hodge. Hodge shot and killed Perry when the latter left his car and came out holding "an ice pick or a pistol." Actually Perry had been holding a screwdriver which he needed to pry open the trunk, in which the car's registration was kept.
In Los Angeles, the police department was involved in a series of brutal citizen murders, where officers applied "chokeholds" across their victims' necks. In 1981 alone there were the following cases: Luel Marshall, 41 and Black, was stopped by police officers on February 3, 1981. While handcuffed, he was choked several times by police. Marshall suffered a massive heart attack, and died without gaining consciousness on March 17, 1981. Charles H. Hill, 40 and Black, was arrested after an altercation with police on March 14. Hill was beaten viciously with a baton and choked by officers. He subsequently stopped breathing in a Hollywood division cell tank prior to being booked, and was declared dead. The coroner's office declared that Hill had died from a "sickle cell crisis"! Arthur W. McNeil, 30 and Black, was arrested as a suspected prowler. Police choked McNeil, who died in a hospital on July 28. The coroner's inquest determined that McNeil died "at the hands of another, other than by accident," in February, 1982, and a $15 million lawsuit was filed against the city by McNeil's widow and daughter. When the press asked Daryl F. Gates, the police chief, why so many Blacks and Latinos were dying at the hands of his officers, he responded calmly that perhaps Blacks were not "normal people."
There were also a series of inexplicable hangings in jails of perhaps four dozen Black men in 1981 alone. Three such examples include 19 year old Eric Boyd, charged with armed robbery, and lynched in a Chicago precinct jail cell on March 13; Cleophus Powell, 31, serving a 10 day sentence for shoplifting in Chickasaw, Alabama, on March 31; and Grant Lee, 19, arrested for driving a stolen car by Cleveland police, on April 22, and found strangled by his socks attached to a crossbar section of the jail cell door. In most cases, the Black men were in relatively good spirits when contacted by family or friends hours before their "suicides."
Perhaps the largest number of racist incidents did not involve law enforcement officers at all, but were initiated by white youths. In 1981, there were at least 500 documented cases of random white teenage violence, including the following examples:
The drowning of John Stencil, a Black freshman at Farleigh Dickenson University on April 11, 1981. Two white youths pushed Stencil into the Hackensack River as he sat on a bridge railing. Stencil reportedly "shouted to them that he could not swim but they went away." Hackensack prosecutor Roger Breslin, a white lawyer, termed the drowning an "accident."
Five white youths in a car attempted to run down three Black women in Far Rockaway, New York on February 28, 1981. Charged with attempted murder, the youths pleaded innocent and were released on only $5,000 bail.
Five young white men were arrested by Maryland State Police on June 1, 1981, and charged with conspiring to burn a cross on the lawn of Harford NAACP president Joseph Bond of Churchville.
Gary Allen Smith, a 24-year-old Black student at Morgan State University in Baltimore, was viciously attacked by eight white youths in June, 1981, after Smith had argued with a white female employee where he worked. Smith was beaten with pool cue sticks and suffered "a broken left arm, contusions and swelling of the brain."
Three white men, ages 19, 21, and 23 tossed a pipebomb into the house of a Black Detroit family. Mrs. Synthia Steele had seen the bomb crash through the bathroom window, picked it up and was attempting to throw it away when it explocled in her hand. Three fingers of her right hand were blown off. The attack was the last in a series lasting two and a half years. Previously, white youths had thrown baseballs through Mrs. Steele's windows and painted KKK signs on her garage.
Michael Jarrett, a Black youth of 19, was killed by a gunshot wound to the head in Steubenville, Ohio on April 17, 1981, for allegedly dating white girls. Police traced the murder weapon to a white youth, who was eventually released. Over 500 people marched to protest police inaction in the case.
White students at Cass Technical High School in Detroit began calling themselves "the Junior KKKs" and "Baby Hitlers." In March 1981, the juvenile racists circulated white supremacist literature, spraypainted lockers with swastikas and assaulted a student with a knife.
At Wesleyan College, Connecticut, a racist campaign of terror mounted for months. White youths posted a series of "Wanted—Dead or Alive" flyers throughout the campus, with an ugly, twisted sketch of a spear-carrying Black man portrayed. One flyer charged "Jigaboo" with a variety of crimes, including "rape, murder, robbery. He (is) led by Communist Jews in a conspiracy to destroy America and the White race." Another flyer taunted: "All you fuckin' black sambas think you own the fuckin' campus—well I've got news for you. . . I hate you, Mr. Fuckin' nigger. Oh yes I do . . . get that white man's cock outta your mouth—I'm talkin to you. Mr. Nigger, you suck. You call yourselves brothers . . . well you're brothers of the gorillas. I have a dream . . . you-all gonna die in pain." Still another racist tract promoting a fraternity informed prospective white members that it was "dedicated to wiping all goddamned niggers off the face of the earth." By late October, 1981, KKK members visited Wesleyan's campus to recruit young racists.
The number of random racist incidents intensified to such an extent that it became a "normal" part of daily life for Blacks in the United States. Few Black parents were not concerned about the safety of their children during the 1980s. Few Black women did not worry about the possibility that their husbands, fathers, lovers and/or sons might be killed or horribly mutilated in Buffalo and dozens of other American cities. Even while writing this chapter in late 1981, I happened to return to my office at the Africana Center, Cornell University, early one morning. The windows on the first-floor of the building were punctured by an air-rifle. On the front door was printed clearly a single word—"NIGGER."
III
Simple recognition of the explosion in racially motivated random violence is no substitute for an analysis of the crisis. The current outbreak of racist attacks is a manifestation of a profound and fundamental crisis within the political economy of monopoly capitalism. Simultaneously it represents the logical culmination and popular expression of cultural/social patterns of race relations that increasingly pits the petty bourgeoisie, working class, and permanently unemployed of different ethnic groups against each other over increasingly scarce resources. What many Blacks perceive as a "white conspiracy," in the words of Jesse Jackson, is in reality the conjuncture of racist ideological hegemony in the U.S., an acceleration of the use of physical coercion and terrorism against Blacks by both the coercive apparatuses of the state (e.g., the police) and by paramilitary racist groups (the Ku Klux Klan, and many others), and the absence of a powerful, democratic and progressive movement by Blacks which challenges racism in the streets as well as in the courts.
In economic terms, the early 1980s are characterized in part by the crisis of capital accumulation and the steady erosion in the standard of living of the white petty bourgeoisie. The number of small business failures, to cite one example, reached epidemic proportions. During the first week of October, 1981, 468 U.S. companies—dry cleaners, lumber mills, restaurants, retail stores—closed permanently. From September, 1980 to September, 1981, commercial and industrial failures exceeded 12,600, a 250 percent increase over the bankruptcy rate of 1978. Median U.S. family incomes grew from $7,500 in the mid-1960s to over $22,000 in 1981. But inflation climbed from only 2 percent in 1965 to over 12 percent in 1980, negating any real income gains. As a result, many "middle class" whites believe that the Federal government's deficit spending, Keynesian economic policies since the Great Depression, and national, state and local taxes are the reasons for their economic plight.
In 1950 the U.S. manufacturing output totaled 62 percent of the combined output of the ten major capitalist nations. By 1965 the percentage dropped to 50 percent, and was 43 percent by 1976. A series of major bankruptcies and near-bankruptcies threatened to produce a chain of economic disasters, from Penn Central in 1970 to Chrysler, First Pennsylvania Bank and the Hunt brothers in 1980. For the automotive retail industry, including parts suppliers, service stations, new and used car dealers and repair shops, bankruptcies in 1980 rose more than 96 percent. Personal bankruptcies in the U.S. increased from 179,223 in 1977 to over 450,000 in 1981, with projected losses to creditors in excess of $6.4 billion. For white middle class families, even their solitary hedge against inflation, the home, ceased to provide any real security in the early 1980s. After adjustment for inflation and financing discounts, the average price of homes fell 10 percent in 1981, "the steepest drop since the Depression," according to the New York Times. The number of mortgage foreclosures instituted on homes financed by the Federal Housing Administration was over 2,000 each month in 1981, a 30 percent increase over 1980.
The crisis within capitalism is expressed within racial relations as a public repudiation of civil rights legislation passed in the 1960s and a vicious posture towards health care, welfare, job training and social service programs which benefit large numbers of Blacks and Hispanics. A decade ago, even so malignant a politician as Richard Nixon was forced to promote "Black Capitalism" by releasing Federal Reserve funds to Black-owned banks, appointing a moderate civil rights leader, James Farmer, to his cabinet, and expanding welfare and some social service programs. Under Reagan, all stops have been pulled. Daniel Moynihan's infamous 1970 memorandum to Nixon, justifying "benign neglect" of Blacks, has succumbed to a public policy posture which threatens to smash affirmative action, vocational programs, food stamps and a host of democratic reforms won by the Black masses over a half century of struggle.
Within civil and political society, a series of "Green Lights" has been signaled since 1978 which have been largely responsible for unleashing the racist terror. The first was the Bakke decision, which crystalized the anxieties of millions of whites of declining socioeconomic status to blame their misfortunes upon a scapegoat-Blacks and Hispanics. "The wide publicity given to the relatively small number of affirmative action programs instituted by government, by private corporations, and by unions, as well as the publicity given to Bakke, provided a highly distorted picture of undeserved Black gains to many white Americans," states Michael Reich in Racial Inequality. "The perception offended many white Americans' ethic of fair treatment and led to charges of 'racism in reverse.' It also provided a simple and emotionally appealing explanation of one of the principal causes of the economic deterioration that many households were experiencing in the 1970s."
The second "Green Light" was the vicious execution of five members of the Communist Workers' Party in Greensboro, North Carolina, November 3, 1979. The coordinated efforts of the Ku Klux Klan, American Nazi Party, and in all probability, the FBI and local law enforcement officers, were needed to blunt the momentum of antiracist forces in that state. Only sixteen of the forty racists were indicted, and just six were tried. One year later, the six white supremacists were declared innocent by an all-white jury. The lesson of Greensboro was not lost by any observer on the left. Marxist-Leninist journal Line of March noted grimly that "the state had given the Klan a hunting license against the anti-racist movement, particularly against any forces who attempted to link that movement up to a broader political perspective." In Monthly Review, Michael Parenti and Carolyn Kazdin charged that "the Klan and Nazis could not have done what they did in Greensboro had they not enjoyed the active support and passive complicity of state officials and agents. . . The Klan and Nazis were doing the work of the state."
The third "Green Light" was the election of Ronald Reagan in November, 1980, which represented the culmination of a sixteen year effort by the Right (beginning with Goldwater's Presidential campaign in 1964) to capture the executive branch of government. Reagan's campaign was based upon the same putrid ideology of racism, limited Federal government, sexism, anticommunism and states' rights that catapulted George Wallace to national prominence in the 1960s. Unlike Wallace, Reagan was able to win over Wall Street and monopoly capital, while maintaining his electoral base among small businessmen and sectors of labor. His greatest public relations victory in the area of race relations was the creation of "Black Reaganism," that tendency of the Black petty bourgeoisie which supported his election. Thus Reagan's Administration pursues what objectively amounts to an unprecedent, racist assault against national minorities while simultaneously appointing Blacks to prestigous positions and disclaiming any racist intentions. Thomas Sowell, Ralph D. Abernathy, Tony Brown, Walter Williams, Nathan Wright, ad nauseum therefore became essential to the destruction of the Black community.
The rise of Reaganism in electoral politics now has permitted the Right to openly question the utility of democracy for the 1980s. Whether Reagan's supply side version of restoring corporate profits or an alternative state-directed/corporatist strategy emerges which calls for the state to regulate prices and allocate government contracts to corporations which agree to reorganize themselves is almost a mute question. Marxist economist Sam Bowles was one of the first observers to note that either public policy strategy would be forced to impose massive political repression and civil terror upon workers. Thomas Weisskopf, writing in Socialist Review, suggested that the restoration of "a system more palatable to corporate capitalists, it might well be necessary to undermine the ability of others to function within that political framework. Such an effort at political repression could take the form of growing authoritarianism—the removal of major decisions from arenas where they are subject to some degree of popular influence. . ." Following this line of reasoning, California State Senator John Schmitz, a former Congressperson and colonel in the Marine Corps reserves, openly advanced the probability of a military coup in the U.S. as "the best we could hope for." In the October 30, 1981 issue of the Los Angeles Times, Schmitz sketched the following scenario: "Reagan's programs fail, the economy disintegrates, people are rioting in the streets, the Russians plan an invasion to take advantage of the domestic strife, the military recognizes the threat and the coup occurs." Schmitz stated that the coup will happen within several years, "definitely by 1986."
Rightwing ideologues are usually more tactful than Schmitz, but nevertheless are drawing similar conclusions. In a critically important essay published in the Wall Street Journal in October, 1979, Irving Kristol admitted a year before Reagan's election that his policies would be inadequate to resolve the crisis of capitalism. Kristol noted that an "increase in the growth of the private sector can be achieved only by a cut in tax rates for business" and upper-income families. 'Truly massive cuts" in social and educational programs, and a balanced Federal budget, would also help. In short, Kristol called for an austerity agenda "which will put America through the wringer. There is only one country," he noted, "where this economic policy seems to be working. That is Chile, where the nation has indeed been 'put through the wringer' these past couple of years and where the economic outlook is steadily improving." Commenting lightly upon Chile's bloody military junta, Kristol observed, "it would be ironic if it turned out that free-market economics .. . could only be achieved at the expense of a free society."
The function of the rise of racist attacks is the preparation of the ideological and cultural foundations necessary for a potential "Chilean Solution" to resolve the crisis of U.S. capitalism. This is not to predetermine the course of history. The capitalist ruling classes have not yet reached a stable consensus in their search for a strategy to accumulate capital and reduce Federal government intervention into the economy and society. Conversely, the emergence of a democratic and progressive front of national minorities, working people and the oppressed could reverse the present balance of forces. Another more probable option available to the state is the selection of key aspects of the "Chilean Solution" (e.g., brutal state repression of leftists, labor union activities, minorities) without moving toward the complete domination of the political apparatus by the Joint Chiefs of Staff and their subordinates. The open encouragement of police brutalities against Blacks by law enforcement officials and elected politicians, plus the proliferating civil violence by white youths and adults against nonwhites, sets the social and cultural climate necessary to establish an authoritarian regime. Whether this regime is "fascist" in the classical model of Nazi Germany, or "authoritarian," which would permit some democratic rights, could be simply a question of semantics.
Therefore, the existence of random violence against Blacks and civil terrorism is no accidental phenomenon. It is a necessary element in the establishment of any future authoritarian or rightwing government. Attacks by political rightists, small property owners and the police against workers and peasants in Chile during the early 1970s disrupted civil society and established the possibility for the military's coup over the democratic government of Salvador Allende in 1973. The fascist terrorism of Patria y Libertad, the Comando Rolando Matus of the rightist National Party and other paramilitary groups in Chile closely parallel the Ku Klux Klan, the American Nazi Party and other more mainstream, conservative, mass based forces in the U.S. In the United Kingdom, the rapid growth of the rightist National Front, founded in 1967, the neo Nazi British Movement and other racist parties constituted the essential right tendency for the emergence of Thatcherism. In late June, 1979, the chair of the National Front, John Tyndall, toured the U.S. at the invitation of the National States Rights Party. The "keynote of the tour," according to one British journalist, "was the unification of the far-right" in both English-speaking countries. Both the National Front and the U.S. Right are characterized by "authoritarianism, ethnocentrism, racism, biological naturalism and anti-intellectualism." Both have had recent success in attracting "white youngsters," have leaderships which are "firmly middle-class," and endeavor politically to appeal to both the white urban working class, petty enterpreneurs, and sections of the police. Thatcherism, like Reaganism, is "conservatism no longer content with pragmatism and compromise, vying with a social-democratic Labour Party for a middle ground, or with piecemeal retrenchment in public spending in the face of economic crisis." Both reactionary political movements unleash and rely upon the Klan and National Front/type movements to obliterate any possibility of unity between Black and white workers.
By late 1981 the State's repression of the Black Liberation Movement became conspiciously more overt than covert. The fourth "Green Light" was the arrest of Fulani Sunni Ali on October 27, 1981. Between 150 to 200 Federal agents, "a phalanx of four armored cars and a helicopter" descended on her farmhouse residence in Gallman, Mississippi. Charged with complicity in the New York robbery of a Brink's trunk, Ali was arrested and held under $500,000 bond by Federal magistrate John Countiss. Her arraignment to New York was under such intense security that one official described the courtroom as an "armed fortress." The FBI's "frameup" failed when witnesses testified that she was in New Orleans at the time of the holdup. Nevertheless immediately after Ali's release she was subpoenaed to appear before a federal grand jury on November 16. Federal Judge Irving Cooper, in an unprecedented move, granted the motion of U.S. Attorney John S. Martin to forbid one of Ali's attorney's, Chokwe Lumumba, to represent her in court. Although never accused or convicted of any crime, Lumumba's membership in the Republic of New Africa, [RNA] characterized by the FBI and media as a "terrorist organization," disqualified him as an attorney in the case. The New York Civil Liberties Union, the Center for Constitutional Rights, the National Lawyers Guild, the Central Committee of the National Black Independent Political Party (NBIPP), and other progressive groups denounced the FBI's attempt to smear Ali, the RNA and the State's efforts to bar Lumumba from representing his client."
This blatant assault designed to discredit Black nationalist and progressive forces was by no means an isolated event. In early morning raids on October, 16 and October 21, 1981, California Department of Corrections agents arrested four members of the Black August Organizing Committee, an "anti-imperialist and revolutionary prisoners' group" inspired by "the work of George Jackson and other martyrs of the prisoners' movement." The four Black men were charged with parole violations and conspiracy to assassinate California prison officials. Four radical activists, Vera Michelson of Albany, Aaron Estis of Massachusetts, Mike Young of New York City and John Spearman of Kansas were arrested by police in Albany, New York on September 21, the night before the Springboks antiapartheid demonstration and march. The arrests were part of a well-publicized effort by Democratic Governor Hugh Carey and other administrators to diffuse criticism of the appearance of the South African regime's rugby team in the state capital. In late October, 1981, the Youngstown, Ohio chapter of NBIPP was sued for $300,000 by the white owner of a local supermarket. Black Party members had organized a campaign to urge the Black community not to shop in stores where few or no Blacks were employed. The legal suit against NBIPP was curious in that the Party had previously achieved a tentative written agreement to hire more Black workers at the store in question. Charging that NBIPP was "conspiring to interrupt and destroy" his profits, the owner gave the Party no advance warning before filing the suit.
The wave of random racist violence and "legal lynchings" can be placed in perspective only in the light of these fundamental factors—the socioeconomic instability within the white middle to upper classes, the rise of Reaganism, the recent surge of FBI and local police terrorism to suppress dissent, and the growing probability of some kind of "Chilean Solution" by the ruling class to resolve the crisis of capital accumulation. Any authoritarian or even fascist regime in the U.S. would conform to the basic definition given by Georgi Dimitrov in 1935: "the terroristic dictatorship of the most reactionary, most chauvinistic and most imperialistic elements of finance capital." Reagan's base among white professionals and managers, the petty bourgeoisie and more affluent trade union members—and the emergence of virulent racist antagonisms which are manifested in their social and civil behavior towards Blacks—does not negate the basic and decisive corporate prerogatives behind Reaganism and contemporary racist violence. It is the interests of capital, in the final analysis, that permits the climate of racist terrorism to continue. It is the desire to restructure modern capitalism and to accumulate profits at the expense of Black, brown and white labor that is at the root of the current racial crisis.
IV
It is impossible to detach oneself from the spectre of racist violence and the inevitable emotions of outrage it created within the Black community. So many millions of Afro-Americans have become convinced that a racist conspiracy exists that whether it is real or simply a political phantom may no longer matter. The question of an American conspiracy to destroy the Black community must be approached historically. Almost twenty years ago social historian Richard Hofstader first perceived that white American politics has been frequently "illuminated by the lurid glare of paranoid visions." The paranoid style was a standard "psychological device for projecting various symbols of evil on an opponent and for building emotional unity through a common sense of alarm and peril." Colonial historian Bernard Bailyn illustrated in The Ideological Origins of the American Revolution that the belief in a British conspiracy against American colonists was a powerful force in creating the foundations for war. David B. Davis' The Slave Power Conspiracy and the Paranoid Style carried the thesis into the Civil War. Some Northern abolitionists were convinced that the slaveholder was quite literally the "antichrist." Paranoid polemics "awakened millenarian fantasies of persecution and suffering, of absolute power and absolute emancipation." Senator Joseph McCarthy and Vice President Richard Nixon manipulated the politics of postwar America through the demagoguery of the Red Scare in the late 1940s and 1950s. Black "paranoia" in the face of the white backlash against human dignity and civil rights, may be viewed as simply part of a largely American social/political response to fundamental change or conflict.
Perhaps a more productive approach to the problem of a racist conspiracy is suggested in the works of Louis Althusser. The solutions reached within any inquiry are predetermined by the paradigm from which one derives one's questions. A "problematic" exists, according to Althusser, "the objective internal reference system of its particular themes, the system of questions commanding the answers given." In Reading Capital he asserts that a social scientist "can only pose problems on the terrain and within the horizon of a definite theoretical structure, its problematic, which constitutes its absolute and definite condition of possibility, and hence the absolute determination of the forms in which all problems must be posed, at any given moment."
Using Althusser's problematic as a theoretical construct provides new insights into the contemporary reemergence of white racist atrocities. The theoretical common denominator of the variety of statements on Atlanta and other instances of violence raised by Blacks is the a priori assumption that whites as a group have adopted a more aggressive bigotry. The integrationist Old Guard (Vernon Jordan of the Urban League, Benjamin Hooks of the NAACP, Jesse Jackson, and others) relate the recent killings to a general political retreat of white American from the Great Society and Kennedy liberalism. This position suggests that a return to Keynesian economic policies, tougher affirmative action and civil rights legislation, and the successful election of a liberal Democrat into the White House would effectively reduce racial violence and social tensions—at best, an unlikely scenario. Black nationalists and community activists agree with the petty bourgeois integrationists that most whites are more overtly racist today than a decade ago, and that the current violence is a concrete manifestation of the level of racism tolerated by white civil society. But this approach starts from a false problematic that implies that all whites, to a greater or lesser extent, benefit materially from racism. Both problematics are profoundly superstructural—that is, the essential assumptions made by both paradigms exclude any serious recognition of the current crisis of U.S. capital accumulation. Both approaches emphasize racism as an ideology or consciousness which directs or dictates certain behaviors or public policies. Their "structured fields" that define the problem do not provide answers which will effectively combat racism, or even explain adequately the central reasons for the relatively recent series of incidents in which Black workers, the unemployed and the elite alike have become seemingly random victims.
Constructing a Black socialist problematic for analyzing contemporary racism might begin with four critical observations. The first, which has been illustrated, is that there has been in recent years an extreme racial polarization within U.S. civil society, accompanied by a pervading climate of fear and terrorism which has reached into virtually every Black neighborhood. Second, many Black institutions which were either developed in the brutal crucible of antebellum slavery or in the period of Jim Crow segregation are rapidly being destroyed. Two of these are the Black educational systems, especially the traditional Negro private and public colleges, and Black-owned and operated businesses. Third, a growing number of Black workers have become irrelevant to the U.S. economy. The level of permanent unemployment for Blacks under the age of 25 has reached staggering levels, and continues to climb. Fourth, an urban "ghetto-class" or underclass has emerged since the recession of 1970, consisting largely of women and children, who survive almost totally on transfer payments and the illegal, subterranean economy of the inner city. Reagan's budget cuts in food stamps, medicaid, and other social services are in reality akin to capital punishment for the millions of ghetto-class Blacks. The root cause of the last three factors is generated by the crisis of capital accumulation, wherein major corporations must demand the restructuring of the capitalist economy in order to preserve it. The capitalist state must drastically reduce social expenditures, and pass legislation to permit a more favorable climate for higher profits and reinvestment. The first factor is both a manifestation of popular white working class anxiety which accompanies any basic restructuring of the economic order, and an expression of the New Right's ideological and cultural commitment to provide the final solution to the Negro Problem in America.
Genocide is usually defined as the systemic and deliberate destruction of a racial, political or cultural group. Blacks have been brutally oppressed, unquestionably, since 1619 as chattel slaves, sharecroppers and industrial laborers. But the dynamic of racial prejudice traditionally has not culminated into a political demand to exterminate Blacks. The most dogmatically racist Southerners at the height of Jim Crow would have found the idea of Black genocide unworthy of cursory debate. Lynchings and terrorism of all kinds were used to suppress the Negro, to "keep him in his place." The goal was to insure a continued supply of relatively cheap laborers who were politically docile. Whites could be prejudiced toward Blacks, but absolutely intolerant of Jews, for instance. Racists could admire the Hitlerian solution to the Jewish problem, while at the same time could recognize the necessity to sustain the Black U.S. community as a racially segregated entity for the systematic exploitation of its labor power.
The scientific justification for the gradual eradication of "marginal" ethnic groups has been growing for two decades. In fall 1962 anthropologist Carleton Coon published The Origin of Races which proposed that Blacks were the youngest subspecies of Homo sapiens and therefore the least advanced intellectually and socially. In a similar vein, Dwight J. Ingle wrote a major article for the journal Science in October, 1964, entitled "Racial Differences and the Future." Ingles' thesis suggested that "equal representation of the Negro at the highest levels of job competence and in government will be deleterious to society." The greatest proponents of the neoracist scientific school are William Shockley and Arthur Jensen. Since 1965 Shockley has waged a relentless campaign, declaring that the soaring "crime and relief rates" are due to "some hereditary defect(s)." "The major deficit in Negro intellectual performance must be primarily of hereditary origin and thus relatively irremediable by practical improvements in environment," Shockley stated in 1968. Jensen's February, 1969 essay in Harvard Educational Review, "How much can we boost IQ and scholastic achievement?," was praised as "the most important paper in psychology since Pavlov and Freud, a masterful summary of evidence that has been gathering for several decades." Jensen's extension of Shockley's arguments was swiftly entered into the US Congressional Record by Louisiana Representative John R. Rarick. Copies of Jensen's polemic were sent to every member of the National Academy of Sciences with a letter from several prominent U.S. scientists, including Shockley, stating that "irrefutable evidence continues for the inheritance of genetically controlled, socially maladaptive traits. We fear that 'fatuous beliefs' in the power of welfare money, unaided by eugenic foresight, may contribute to the decline of human quality for both the Black and white segments of our society and that the fears of genetic deterioration expressed by Jensen are sound and significant."
What is qualitatively new about the current period is that the racist/capitalist state under Reagan has proceeded down a public policy road which could inevitably involve the complete obliteration of the entire Black reserve army of labor and sections of the Black working class. The decision to save capitalism at all costs, to provide adequate capital for the restructing of the private sector, fundamentally conflicts with the survival of millions of people who are now permanently outside the workplace. Reaganomics must, if it intends to succeed, place the onerous burden of unemployment on the shoulders of the poor (Blacks, Latinos and even whites) so securely that middle to upper income Americans will not protest in the vicious suppression of this stratum. Unlike classical fascism, Reaganism must pursue its policies without publicly attacking Blacks or Puerto Ricans by obvious racial slurs. The government's strategy must include a number of petty bourgeois minorities in responsible but low key positions to diffuse charges of white racism which would be levied by white liberal Democrats and progressives. But the final results of these socioeconomic policies, carried to their logical conclusions, would be the total destruction of all-Black institutions, the political separation of the Black elite and intelligentsia from the working class, and the benign but deadly elimination of the "parasitic" ghetto class that has ceased to be a necessary or productive element within modern capitalism.
Over a decade has passed since the Report of the National Advisory Commission on Civil Disorders published its devastating indictment against white racism. "What white Americans have never fully understood—but what the Negro can never forget—is that white society is deeply implicated in the ghetto. White institutions created it, white institutions maintain it, and white society condones it." With the failure of the Black Power Movement and the political collapse of white liberalism, the direction of America's political economy and social hierarchy is veering toward a kind of subtle apocalypse which promises to obliterate the lowest stratum of the Black and Latino poor. For the Right will not be satisfied with institutionalization of bureaucratic walls that surround and maintain the ghetto. The genocidal logic of the situation could demand, in the not too distant future, the rejection of the ghetto's right to survival in the new capitalist order. Without gas chambers or pogroms, the dark ghetto's economic and social institutions might be destroyed, and many of its residents would simply cease to exist.
CHAPTER TEN
CONCLUSION: TOWARD A SOCIALIST AMERICA
All phases of development are temporary and transient and are destined sooner or later to give way to something else . . . The capitalist epoch is not quite over and those who live at a particular point in time often fail to see that their way of life is in the process of transformation and elimination . . . Socialism has advanced on imperialism's weakest flanks—in the sector that is exploited, oppressed and reduced to dependency. Socialism aims at and has significantly achieved the creation of plenty, so that the principle of egalitarian distribution becomes consistent with the satisfaction of the wants of all members of society.
—Walter Rodney, How Europe Underdeveloped Africa, pp. 18-20.
How Capitalism Underdeveloped Black America evolved from a concern with the contemporary race/class situation in the United States. Like Rodney's seminal work, I have attempted to delve "into the past only because otherwise it would be impossible to understand how the present came into being and what the trends are for the near future." As we have seen, the basic social division within the Black community, the Black worker majority vs. the Black elite, was an essential by-product of primitive capital accumulation in slave societies. This class division became more pronounced in the twentieth century, and represented a tendency among many "middle class" Blacks in electoral politics, the church, small business and education to articulate a "capitalist road" to Black liberation. With Rodney, I have argued the thesis that Black economic, political and social development is possible "only on the basis of a radical break with . . . the capitalist system, which has been the principal agency of underdevelopment." The data and historical examples I have collected, in my judgment, more than justify the thesis. What remains to be developed, however, is the "formulation of a strategy and tactics" implied within the historical evaluation, which will uproot the hegemony of American capitalism. By necessity, such a strategy cannot be limited to Black Americans and their conditions, because the symbiotic processes of institutional racism and capital accumulation affect all American working and poor people.
The road to Black liberation must also be a road to socialist revolution. But what strategy is required, keeping in mind the special history of American society, and the convergence of racism, sexism and economic exploitation which comprises the material terrain of this nation? I would suggest ten points of departure, programmatically and theoretically, which may provide some tentative suggestions for social transformation and the end to the "underdevelopment" of Black America:
1) Any authentic social revolution in the United States must be both democratic and popular in character and composition. A majority of Americans, Black, Latino and white, must endorse socialism. By this statement, I do not imply that a majority of Americans will become socialists or Marxists. I mean that a clear majority of American people, with a large base in the working class, will support the general program of socialist construction. That expression of support may be electoral, but it should not be interpreted narrowly by social democrats to mean a constitutional majority within the electoral apparatus as it now exists. Visions of a revolutionary Black, radical feminist, or "Marxist President of the United States" are illusions fostered by the implicit acquisition of the logic of the bourgeois "democratic" process among some American progressives.
2) The American state apparatus is capitalist and racist in its operations and social trajectory, yet it also manifests the class contradictions and struggles which are always present within bourgeois civil society as a whole. U.S. bourgeois "democracy" is oppressive and under Reagan is even moving toward unambiguous authoritarianism, yet is not specifically fascist in the classical sense. Progressives can have a direct impact upon public policies and the behavior of the state in certain respects, via electoral participation, lobbying, civil disobedience, mass demonstrations, etc. The state bureaucracy under a bourgeois "democracy" often accommodates the demands of the left into its own public policies. Progressives can gain positions within the state, especially at municipal and state levels, which can help fund and support grassroots interests and indirectly assist in the development of a socialist majority.
Critical support for progressive and anticapitalist politicians (e.g. Ronald Dellums) who run for office within the Democratic Party, at the present time, may be a necessary and constructive activity in building an anticorporate consensus within the working class. Yet to view either major capitalist party as the primary or fundamental terrain for building socialism would be to court disaster. The Democratic Party will never be transformed into an appropriate vehicle for achieving the political hegemony of Blacks, Latinos, feminists and the working class. This requires the creation of an antiracist and antisexist political formation which is distinctly anticapitalist, and represents the interests of working and poor people.
3) Direct confrontations with the coercive agencies of state order are inevitable in the future. Yet any socialist strategy which deliberately provokes the repressive powers of the capitalist/racist state against working and poor people cannot win in the U.S. A series of urban rebellions can shake the perception of the American working class in capitalism as an inherently "fair" and "democratic" system, but these will not topple the powers of the State. The U.S. government cannot be directly equated, in short, with czarist Russia or Somoza's Nicaragua. A putschist strategy by the left will not only fail in overthrowing the racist/capitalist state, but will create the chaotic political conditions essential for the installation of U.S. fascism. From Gracchus Babeuf to Auguste Blanqui, ultraleftists have confused social revolution with conspiratorial coups which implicitly express an unstated distrust and even hatred for the people. "When most Americans think about a revolution, all they can think of is a coup d'état," write James and Grace Lee Boggs. "But people do not make anything as serious as a revolution to rub out a government or system. The only justification for a revolution is the fact that social, political and economic contradictions have accumulated to the point that the existing government and the existing institutions obviously cannot resolve them. Therefore it is not so much that the revolution overthrows the government and the system as that the government and the system, by their failure and their misdeeds, drive the people to rescind their mandate to rule."
4) A long and painful ideological struggle must be mounted by progressives to create a "counter-hegemony" essential for socialism. Every aspect of the capitalist civil society—educational institutions, the church, the media, social and cultural organizations—must be undermined. This "war of position," to use Antonio Gramsci's concept, must be viewed as the development of a popular "historic bloc" or "revolutionary social bloc" which is comprised of all progressive forces of divergent class and racial groups: women, Blacks, Hispanics, trade unions, Native Americans, antinuclear energy groups, environmentalists, anticorporate "populists," socialists, Communists, community and neighborhood associations, etc. A Common Program among these divergent forces would not be an informal alliance or a temporary convergence of formations as in a classical popular front. It would become the crystalization of a mass revolutionary bloc which would explicitly call for the transformation of the system as it now exists. It would wage a "war of position" for state legitimacy, for the majoritarian mandate to overturn the State. Within its structured forms, the embryonic models of what a socialist society would look like would be developed.
5) The immediate and preliminary goal of this historic bloc would be the achievement of "nonreformist reforms" which can be won within the present capitalist state. These would include, for instance, the passage of: the Equal Rights Amendment; abortion rights; antidiscriminatory legislation against gays and lesbians; strict restrictions to halt plant closings; affirmative action; massive job training programs; universal health care; the abandonment of nuclear power plant construction, and so forth. The successful achievement of these legislative socioeconomic reforms does not create a socialist society or state. But combined with legislation which restricts the legal prerogatives of private capital, and a mass mobilization of popular forces in the streets as well as in the legislatures, it will create the social and material foundations for a logical "alternative" to the bourgeois authority and hegemony. Throughout this initial process, a transitional program must be devised to divide and "win over" proletarian sections of the coercive apparatuses of the state, such as working class volunteers within the armed forces. The essential base of the historic bloc, however, must be the working class—not the petty bourgeoisie.
6) Progressives can only succeed in constructing this historic bloc if they articulate their demands in a popular and historical discourse, in a language readily accessible to the majority of American workers and nonwhite people. This is not an issue of "public relations." The symbols of the American tradition of struggle from past generations must be planted deeply in the socialist praxis of the future. Thomas Paine's moving essays which denounced British tyranny must become our contemporary anti-imperialist vision. Frederick Douglass' belief in the humanity of Blacks and women must become our own worldview. Ida B. Wells' courage in the face of the Memphis lynch mob must become our inner strength. Osceola's fierce determination to fight for the preservation of the Seminole nation must become our will.
The "Other America" of Nat Turner, Malcolm X, Fannie Lou Hamer, Eugene V. Debs, Sojourner Truth, and Harry Bridges must be the historical starting point for our fresh efforts to build a genuine peoples' democracy, and a socialist economic system. We cannot create a revolution in the United States if we mistakenly view the enemy as Reagan alone, or all males, or all white people, rather than the State. In the midst of another social revolution, Amílcar Cabral observed that the people of Guinea-Bissau "criticise Salazar and say bad things about him. He is a man like any other. . . But we are not fighting against Salazar, we are fighting against the Portuguese colonial system. We don't dream that when Salazar disappears Portuguese colonialism will disappear." The Boggs make the same observation somewhat differently. "A revolutionist does not hate the country in which the illegitimate and oppressive system and government continues to rule. Far less does the revolutionist hate the people of the country. On the contrary, a revolutionist loves the country and the people, but hates what some people are doing to the country and to the people."
7) Any Common Program or set of "transitional demands" developed by the anticapitalist bloc must be based from the beginning on the basic contradictions which have dominated American political and civil societies throughout the twentieth century. This program must be a) uncompromisingly antiracist h) antisexist c) anticorporate—that is, it must call for fundamental and powerful restrictions on the rights of private capital, and d) it must promote the necessity for world peace, and advocate an end to the escalating conventional and nuclear arms race with the Soviet Union. Support must be given to all legitimate national liberation struggles, and opposition to any wars of imperialist aggression waged by Western capitalist nations and their clients against the Third World (e.g., the El Salvadorian junta's bloody suppression of that nation's peasantry and working class); the South African reich's terror against the peoples of Angola, Namibia and Azania. In short, the bloc must commit itself in theory and practice to struggle against racism, sexism, U.S. imperialism and capitalism. The principal force for oppression in the world is not the Soviet Union: it is the racist/capitalist state, best represented by the United States and South Africa.
8) Racism and patriarchy are both precapitalist in their social and ideological origin. The successful seizure of state power by the U.S. working class and the creation of workers' democracy within the economic sphere would destroy the modern foundations for racial prejudice and sexism; however, it would not obliterate the massive ideological burden of either form of oppression in the practices of millions of whites and males. Separate and even autonomous apparatuses must be created after the revolution to effectively uproot racism and patriarchy. In practice, this means that the historic bloc in the presocialist period, the war of position, must build antiracist and antisexist structures within their own organizations. Organizations comprised solely of Blacks, Hispanics, and/or women must be an essential part of the struggle to build a new society.
9) Every decisive gain achieved by the anticapitalist forces will be countered by the state against the working class. This repression will be significantly greater against Blacks and other national minorities than experienced by other sectors of the working class. Socialists must come to the conclusion at the outset that there will be no peaceful culmination in the achievement of state power. If every Congressional district elected a socialist, and if the executive and judicial branches of government were dominated by Marxists, capital would not sit by benignly and watch its power erode or be destroyed through legal measures. Chile illustrated this feature of capitalist "democracy" decisively. Major corporations will not turn over the keys to their factories willingly to the workers.
The final question of power will be determined in a "war of maneuver," at a point in history wherein the capitalist ruling class will find no alternatives left except raw coercion. C.L.R. James makes his point in his brief discussion of the past European revolutions. "Why did not Charles I and his followers behave resonably to Cromwell? As late as 1646, two years after Marston Moor, Mrs. Cromwell and Mrs. Ireton had tea with Charles at Hampton Court. Cromwell, great revolutionary but great bourgeois, was willing to come to terms. Why did not Louis and Marie Antoinette and the court behave reasonably to the moderate revolutionaries?" James asked. "Why indeed? The monarchy in France had to be torn up by the roots." The racist/capitalist ruling elite in this country will do whatever is necessary to stay in power. Today it uses racist ideology to divide Blacks and whites, relies upon patriarchy to perpetuate males' suppression of women, and urges white workers to literally destroy a half century of labor reforms in the workplace through unionization by the relocation of factories and by pressuring the rank-and-file to accept contractual "give-backs" to corporate directors and owners. Tomorrow it may cloak itself in the flag and the Constitution while negating the civil liberties of millions of nonwhite, poor and working people.
There can be no long term "Historic Compromise" with capitalism. The choice for Blacks is either socialism or some selective form of genocide; for the U.S. proletariat, workers' democracy or some form of authoritarianism or fascism.
10) We must always remind ourselves that history is an organic process, the evolution of the forces of production as they affect and in turn are influenced by the civil and political institutions, ideologies and the cultures of human beings. Nothing in Black history, American history, or world history has ever been predetermined by any single factor or force. "Underdevelopment" and "socialism," when reduced to bare economic categories, outside of a particular history, become meaningless abstractions. The socialism we construct will have to encounter racial, sexual, and class components which do not exist anywhere else in the world, exactly as they appear here. If we apply some rigid "iron laws" of revolution gleaned from the dusty textbooks of other revolutionaries, in the name of Marxism, we will not only succumb to a left form of economic determinism but will fail to build an alternative to the oppressive state which we seek to overturn. "Men make their own history," Marx observed in The Eighteenth Brumaire of Louis Bonaparte, "but they do not make it just as they please; they do not make it under circumstances chosen by themselves, but under circumstances directly encountered, given and transmitted from the past." I have devoted a great deal of space in these pages toward analyzing Black history, therefore, because the transition to socialism and an end to Black underdevelopment did not begin in the 1980s, but in the racial and class struggles of past generations.
Our challenge is to interpret society in order to change it. But we must grasp that the particular manifestations of the American war of maneuver, the transition to socialism, will not be fixed or predetermined. C.L.R. James emphasized this point in his discussion of the Russian revolution. "The thing that we have to remember" about the development of the Petrograd's Soviet or workers' council of 1905, James noted, "is that nobody invented it. Nobody organized it. Nobody taught it to the workers. It was formed spontaneously. . ." A workers' democracy in America will not look precisely like anything we can ever imagine at this moment. A revolutionary rupture with the petty bourgeoisie's tendencies toward accommodation within Black America will generate new Black social organizations, new Black political institutions and workers' councils which many Marxists and revolutionary Black nationalists will not comprehend, and may at some point even oppose as "deviations" from their "master plan." We must consciously learn from other peoples' revolutionary experiences without reifying them into a pseudo-revolutionary catechism.
A final word: progressive white Americans must succeed in overturning their own racism, in theory and practice, if a successful revolution can be achieved in this country, which will in the process write the final page on Black underdevelopment. Nothing short of a commitment to racial equality and Black freedom such as that exhibited by the militant white abolitionist John Brown will be sufficient. Nothing less than the political recognition that white racism is an essential and primary component in the continued exploitation of all American working people will be enough to defeat the capitalist class. And to the Black working class, the historic victim of slavery and sharecropping, rape and lynching, capital punishment and imprisonment, I leave the advice of C.L.R. James:
Marxism is the doctrine which believes that freedom, equality and democracy are today possible for all mankind. If this (book) has stimulated you to pursue the further study of Marxism, we will have struck a blow for the emergence of mankind from the darkness into which capitalism has plunged the world.
Endnotes
Foreword: How Capitalism Underdeveloped Black America and Beyond
. Justin Wolfers with David Leonhardt and Kevin Quealy, "1.5 Million Missing Black Men," New York Times, April 20, 2015.
. Walter Rodney, How Europe Underdeveloped Africa (Washington, DC: Howard University Press, 1972).
. Eric E.Williams, Capitalism and Slavery (Chapel Hill: University of North Carolina Press, 1994).
. Lawrence D. Bobo, "Somewhere between Jim Crow and Post-Racialism: Reflections of the Racial Divide in America Today," Daedalus 140, no. 2 (2011): 14. See also Carmen DeNavas-Walt and Bernadette D. Proctor, Income and Poverty in the United States: 2013, U.S. Census Bureau, Current Population Reports (Washington, DC: U.S. Government Printing Office, 2014), 60–249.
. Michael I. Norton and Samuel R. Sommers, "Whites See Racism as a Zero-Sum Game That They Are Now Losing," Perspectives on Psychological Science 6, no. 3 (2011): 215–18.
. Shelby County, Alabama v. Holder, Attorney General, et al. 133 S. Ct. 2612 (2013).
. Chris Cillizza, "How Citizens United Changed Politics, in 7 Charts," Washington Post, January 22, 2014; Citizens United v. Federal Election Commission, 588 U.S. 50 (2010).
. Khalilah Brown-Dean, with Zoltan Hajnal, Christina Rivers and Ismail White, 50 Years of the Voting Rights Act: The State of Race in Politics (Joint Center for Political and Economic Studies, 2015).
. Bobo, "Somewhere between Jim Crow," 11.
. U.S. Census Bureau, "A Half Century of Learning: Historical Census Statistics on Educational Attainment in the United States, 1940 to 2000," Table 11 and Table 12, 2000, http://www.census.gov/hhes/socdemo/education/data/census/half-century/tables.html (accessed June 2, 2015).
. DeNavas-Walt and Proctor, Income and Poverty.
. U.S. Census Bureau 2013 Survey of Income and Program Participation. Table 1: Median Value Assets for Households. (accessed July 2, 2015).
. Thomas Gage, "Poverty in the United States: 2013," States Library of Congress, Congressional Research Service, CRS Report RL33069 (Washington, DC: Office of Congressional Information and Publishing, September 25, 2014).
. DeNavas-Walt and Proctor, Income and Poverty.
. Rakesh Kochhar and Richard Fry, Wealth Inequality Has Widened Along Racial, Ethnic Lines since End of Great Recession (Pew Research Center, December 12, 2014).
. Hall, Matthew, Kyle Crowder and Amy Spring, "Neighborhood Foreclosures, Racial/Ethnic Transitions, and Residential Segregation," American Sociological Review 80, no. 3 (2015): 526–49.
. The Sentencing Project, "Facts About Prisons and People in Prison," The Sentencing Project, January 2014, http://sentencingproject.org/doc/publications/inc_Facts%20About%20Prisons.pdf (accessed June 3, 2015).
. Michelle Alexander, The New Jim Crow: Mass Incarceration in the Age of Colorblindness (New York: New Press, 2012).
. Marc Mauer and Nazgol Ghandnoosh, "Incorporating Racial Equity into Criminal Justice Reform," The Sentencing Project, October 2014.
. Ann E. Carson, "Prisoners in 2013," US Department of Justice, Bureau of Justice Statistics, September 30, 2014.
. Drug Policy Alliance, The Drug War, Mass Incarceration and Race, June 2015.
. United States Sentencing Commission, "Report on the Continuing Impact of United States v. Booker on Federal Sentencing," December 2012.
. Vera Institute of Justice, A Prosecutor's Guide for Advancing Racial Equity (New York: Vera Institute of Justice, 2014), 17.
. Andrea Morrell, "Municipal Welfare or Carceral Reindustrialization: Thinking Through the 1980's Rust Belt Prison Boom," Paper presented at the Meeting of the Society for the Anthropology of North America, John Jay College CUNY, April 2015.
. Leith Mullings, "Losing Ground: Harlem, the 'War on Drugs' and the Prison-Industrial Complex," Souls: A Critical Journal of Black Politics, Culture and Society 5, no. 2 (2002): 22–41. 2005
. United States Department of Justice, Civil Rights Division, Investigation of the Ferguson Police Department, March 4, 2015.
. Human Rights Watch, Profiting from Probation: America's "Offender-Funded" Probation Industry, February 2, 2014, https://www.hrw.org/report/2014/02/05/profiting-probation/americas-offender-funded-probation-industry.
. Brent Staples, "The Ferguson Nightmare," New York Times, March 5, 2015.
. Heidi Beirich, "Anti-Black Hate Crimes Rise, Data Remains Flawed," Southern Poverty Law Center, November 24, 2009.
. Kevin Johnson, "Police Killings Highest in Two Decades," USA Today, November 11, 2014.
. Kimberly Kindy, Julies Tate, Jennifer Jenkins, Steven Rich, Keith L. Alexander and Wesley Lowery, "Fatal Police Shootings in 2015 Approaching 400 Nationwide," Washington Post, May 30, 2015.
. Robin D. G. Kelley, "Why We Won't Wait: Resisting the War Against the Black and Brown Underclass," CounterPunch, November 25, 2014.
. Protests have had some results. Dunn was sentenced to life in prison and Wafer was sentenced to prison for second-degree murder and manslaughter.
. Civil Rights Congress, We Charge Genocide: The Historic Petition to the United Nations for Relief from a Crime of the United States Government Against the Negro People (New York: Civil Rights Congress, 1951), 3–10; William Patterson, We Charge Genocide: The Crime of Government Against the Negro People (New York: International Publishers, 1970).
. Human Rights Council, "Draft Report of the Working Group on the Universal Periodic Review: United States of America," Twenty-second session, Geneva, May 4, 2015.
. Marx, Karl [1886] "Theses on Feuerbach," Appendix in Ludwig Feuerbach and the End of Classical German Philosophy, Marx-Engels Internet Archive, 1994, 65, https://www.marxists
.org/archive/marx/works/1886/ludwig-feuerbach/ (accessed July 3, 2015).
. Manning Marable and Leith Mullings, eds., [2000] Let Nobody Turn Us Around: Voices of Resistance, Reform, and Renewal, an African-American Anthology, 2nd rev. ed. (Lanham, MD: Rowman and Littlefield, 2009), 59.
. Cited in ibid., 595–99.
. Salih Booker and William Minter, "Global Apartheid: The Concept Captures Fundamental Characteristics of Today's World Order," Nation, June 21, 2001.
. Manning Marable, "An Idea Whose Time Has Come . . . Whites Have an Obligation to Recognize Slavery's Legacy," Newsweek, August 27, 2001.
. Zaheer Ali, "Analog Man with a Digital Plan: The Digital Legacy of Manning Marable," Souls 13, no. 4 (2011): 409–15.
. Russell Rickford, "Dr. Manning Marable Memorial Program Obituary," Columbia University, April 29, 2011, 2.
. Manning Marable, Race, Reform, and Rebellion: The Second Reconstruction and Beyond in Black America, 1945–2006, 3rd ed. (Jackson: University of Mississippi Press, 2006).
. Manning Marable, Black Leadership: Four Great American Leaders and the Struggle for Civil Rights (New York: Penguin Books, 1998).
. Manning Marable, African and Caribbean Politics: From Kwame Nkrumah to the Grenada Revolution, Volume II, Race, Politics and Power (London: Verso, 1987).
. Manning Marable, Speaking Truth to Power: Essays on Race, Radicalism and Resistance (Boulder, CO: Westview Press, 1996).
. Manning Marable, Living Black History: How Reimagining the African-American Past Can Remake America's Racial Future (New York: Basic Civitas, 2006).
. Manning Marable, W. E. B. Du Bois: Black Radical Democrat, rev. ed. (Boulder, CO: Paradigm Publishers, 2005).
. Myrlie Evers-Williams and Marable Manning, eds., The Autobiography of Medgar Evers: A Hero's Life and Legacy Revealed Through His Writings, Letters, and Speeches (New York: Basic Civitas, 2005).
. Finder's Guide, Manning Marable's Malcolm X Project, Columbia University.
. Amílcar Cabral, Return to the Source: Selected Speeches of Amílcar Cabral (New York: Africa Information Service, 1973).
. Manning Marable, Malcolm X: A Life of Reinvention (New York: Viking Penguin, 2011), 12, 13.
. Ibid., 493.
. Marable's notes for How Capitalism Underdeveloped Black America—now in his archive at Columbia University—demonstrate his extensive thinking about and interrogation of the state, power, and resistance.
. Thomas Piketty, Capital in the Twenty-First Century, trans. Arthur Goldhammer (Cambridge, MA: Belknap Press of Harvard University Press, 2014).
. Noam Scheiber and Dalia Sussman, "Inequality Troubles Americans Across Party Lines, Times/CBS Poll Finds," New York Times, June 3, 2015.
. Don Robotham, "Neoliberalism and Its Other," Identities: Global Studies in Culture and Power 18, no. 1 (2011): 47–53.
. In addition to the protests, as incarceration as a tool to manage redundant workers becomes massively expensive, right-wing organizations such as the Koch Brothers Industries, Americans for Tax Reform, and Freedom Works have joined forces with more liberal organizations such as the Center for American Progress and the American Civil Liberties Union to form an odd coalition "to make recommendations about criminal justice."
How Capitalism Underdeveloped Black America: A Critical Reassessment
. Manning Marable, Blackwater: Historical Studies in Race, Class Consciousness and Revolution (Dayton, OH: Black Praxis Press, 1981).
. See Manning Marable, How Capitalism Underdeveloped Black America: Problems in Race, Political Economy, and Society (Boston: South End Press, 1983), pp. 215-218.
. Walter Rodney, Groundings with My Brothers (London: Bogle-L'Ouberture Publications, 1983).
. Walter Rodney, How Europe Underdeveloped Africa (Washington, DC: Howard University Press, 1982), pp. 88-89, 223-226, 235. It is significant as well that Rodney hedges his class analysis with an acknowledgment of the powerful impact of racism on the collective behavior of whites, especially in the United States: "It can further be argued that by the nineteenth century white racism had become so institutionalized in the capitalist world (and notably in the U.S.A.) that it sometimes ranked above the maximization of profit as a motive for oppressing black people" (p. 89).
. Some of my writings on the Reagan military arms buildup at that time included: "Nuclear War and Black America," National Scene, Vol. 53 (January 1984), pp. 14, 18-19; and "The Future of the Cold War," in Leon Wofsky, ed., Before the Point of No Return: An Exchange of Views on the Cold War, the Reagan Doctrine, and What Is to Come (New York: Monthly Review Press, 1986), pp. 120-125.
. My own interpretation of the Reagan administration's policies, and especially its terrible relations with the African-American community, is presented in Race, Reform, and Rebellion: The Second Reconstruction in Black America, 1945-1990, Second Revised Edition (Jackson, Mississippi: University Press of Mississippi, 1991).
. See "Free South Africa Movement: Black America's Protest Connections with South Africa," in Manning Marable, Speaking Truth to Power: Essqys on Race, Resistance, and Radicalism (Boulder, Colorado: Westview Press, 1996), pp. 189-196.
. Marable, How Capitalism Underdeveloped Black America, pp. 209-228.
. Marable, How Capitalism Underdeveloped Black America, p. 154.
. Charles Hamilton, Black Power (New York: Vintage, 1967).
. See Manning Marable, "Why Black Americans Are Not Socialists," which first appeared in Phyllis Jacobson and Julius Jacobson, eds., Socialist Perspectives (Princeton: Karz-Cohl, 1983), pp. 63-95, and was later republished in Marable, Speaking Truth to Power, pp. 215- 241.
. Marable, How Capitalism Underdeveloped Black America, pp. 22-23.
. Rodney, How Europe Underdeveloped Africa, p. 182.
. Marable, How Capitalism Underdeveloped Black America, pp. 141-145.
. Rodney, How Europe Underdeveloped Africa, pp. 240-241.
. Marable, How Capitalism Underdeveloped Black America, p. 204.
. Marable, How Capitalism Underdeveloped Black America, p. 152.
. Marable, How Capitalism Underdeveloped Black America, p. 230-231.
. Marable, How Capitalism Underdeveloped Black America, pp. 225, 189.
. Marable, How Capitalism Underdeveloped Black America, p. 230.
. Marable, How Capitalism Underdeveloped Black America, p. 222.
. Manning Marable, Black American Politics: From the Washington Marches to Jesse Jackson (London, Verso, 1985).
. Marable, How Capitalism Underdeveloped Black America, p. 259.
. Angela Y. Davis, Women, Race, and Class (New York: Random House, 1983); Michele Wallace, Black Macho and the Myth of the Superwoman (New York: Verso, 1999); bell hooks, Ain't I a Woman: Black Women and Feminism (Boston: South End Press, 1981).
. Rodney, How Europe Underdeveloped Africa, p. 227.
. Marable, How Capitalism Underdeveloped Black America, p. 90.
. Marable, How Capitalism Underdeveloped Black America, pp. 111, 109.
. Marable, How Capitalism Underdeveloped Black America, p. ix.
Introduction to the First Edition: INEQUALITY AND THE BURDEN OF CAPITALIST DEMOCRACY
Author's Note: Sections from this introduction were published previously in "The Contradictory Legacy of American Democracy," Socialist Review, Vol. 43 (January-February, 1979), pp. 114-120.
. Fred R. von der Mehden, Politics of the Developing Nations (Englewood Cliffs, New Jersey: Prentice-Hall, 1964), p. 43.
. Ibid., p. 6.; David E. Apter, The Politics of Modernization (Chicago: University of Chicago Press, 1965), p. 43.
. Robert L. Heilbroner, The Great Ascent: The Struggle for Economic Development in Our Time (New York: Harper and Row, 1963), p. 10.
. Frank Tachau, ed., The Developing Nations: What Path to Modernization? (New York: Dodd, Mead, 1972). Other liberal perspectives on development include C. E. Black, The Dynamics of Modernization (New York: Harper and Row, 1966); Irving Louis Horowitz, Three Worlds of Development (Oxford University Press, 1966).
. Von der Mehden, Politics of the Developing Nations, p. 3.
. Harry Magdoff, The Age of Imperialism: The Economics of U.S. Foreign Policy (New York: Monthly Review, 1969), p. 23.
Karl Marx recognized the central role of slavery in the development of world capitalism. "Without slavery, no cotton; without cotton, no modern industry. Slavery has given value to the colonies; the colonies have created world trade; world trade is the necessary condition of large-scale machine industry. Thus before the traffic in Negroes began, the colonies supplied the Old World with only very few products and made no change in the face of the earth. Slavery is therefore an economic category of the highest importance." Karl Marx, in Marx, Frederich Engels, and V. I. Lenin, On Historical Materialism (New York: International Publishers, 1974), p. 279.
. Many Marxists tend to underestimate the role of civil society in the perpetuation of economic exploitation. The cultural chaos spawned by capitalists' disruption of traditional societies is in many respects the most apparent and decisive characteristic of underdeveloped societies. Under capitalist domination, as Noam Chomsky observers, "civil society is hardly more than a conspiracy by the rich to guarantee their plunder." Chomsky, For Reasons of State (New York: Vintage, 1973), p. 390.
. See Staughton Lynd, "Slavery and the Founding Fathers," in Melvin Drimmer, ed., Black History: A Reappraisal (Garden City, New York: Anchor, 1969), pp. 117-131.
. Richard Price, ed. , Maroon Societies: Rebel Slave Communities in the Americas (Baltimore: Johns Hopkins Press, 1979), p. 150; Herbert Aptheker, To Be Free: Studies in American Negro History (New York: International Publishers, 1948), pp. 11-30.
. See Price, Maroon Societies; C. L. R. James, The Black Jacobins: Toussaint L'Ouverture and the San Domingo Revolution (New York: Vintage, 1962). One illustration of the bravery of African people will suffice. James writes: "Far from being intimidated, the civil (Haitian) population met the terror with such courage and firmness as frightened the terrorists. Three blacks were condemned to be burnt alive. A huge crowd stood round while two of them were consumed, uttering horrible cries. But the third, a boy of 19, called to them in creole, 'You do not know how to die. Sec how to die.' By a great effort he twisted his body in his bonds, sat down and, placing his feet in the flames, let them burn without uttering a groan." p. 361.
. Ibid.; Kenneth Stampp, The Peculiar Institution: Slavery in the Antebellum South (New York: Vintage, 1956), pp. 180-181, 185-186.
. W. E. B. Du Bois, "Opinion," Crisis, Vol. 21 ( March, 1921), p. 197.
. DuBois, "The Negro in America Today," National Guardian (January 16, January 23, January 30, February 13, March 5, 1953).
. DuBois, "Opinion," Crisis, Vol. 28 (June, 1924), pp. 55-56.
The legal end of slavery in 1865 did not terminate the "peculiar institution" in the U.S. According to the New York Times, Federal authorities discovered a slave smuggling ring operating on the West Coast in early 1982 that sold 30 Indonesian adults to wealthy residents of Los Angeles and Beverly Hills. In North Carolina, three men were convicted of kidnapping, slavery and holding farm workers in "involuntary servitude" on February 2, 1982. Judith Cummings, "U.S. Says 30 Asians Were Sold as Slaves By Los Angeles Ring," New York Times (January 28, 1982); "Three Bosses of Migrant Crews Get Long Terms in Carolina Slavery Case," New York Times (February 3, 1982); Judith Cummings, "Recruiter Suspect in 'Slave' Case is Arrested," New York Times (February 4, 1982).
. DuBois, "The Election and Democracy," Crisis, Vol. 21 (February, 1921), pp. 156-160.
This is not to suggest, by any means, that the various legal victories achieved by Blacks and their progressive white allies during the period of Reconstruction (e.g., the thirteenth, fourteenth, and fifteenth amendments to the U.S. Constitution; the Freedman 's Bureau; the Civil Rights Act of 1875) were unimportant or undemocratic, or that the U.S. is a mirror image of Nazi Germany. "Democracy" for the majority of Afro-Americans has not and does not now exist because the political apparatus is a "bourgeois parliamentary democracy" and not a proletarian or "workers' democracy." Ernest Mandel noted that the majority of working people in the West usually "identify their democratic freedoms with the bourgeois-democratic, parliamentary state institutions." As a result, "the characteristic feature of bourgeois democracy is the tendency towards atomization of the working class—it is individual voters who are counted, and not social groups or classes who arc consulted. Moreover, the economic growth of the last twenty-five years has brought into the heart of the working class consumption habits—most serve to reprivatize leisure activity and thus to reinforce the atomization of the class." Within public discourse, socialism is usually identified with dictatorship and the loss of civil liberties; capitalism is portrayed as the ultimate in freedom (i.e., "free enterprise") and democratic decision-making. By attacking the consensus notion that real democracy exists for the American masses, DuBois established the possibility of elevating to national discussion the idea of socialist democracy. See "Ernest Mandel: a Political Interview," New Left Review, No. 100 (November, 1976-January, 1977), pp. 108-109.
. DuBois, "Is Man Free?" Scientific Monthly, Vol. 66 (May, 1948), pp. 432-433.
. DuBois, "The Winds of Time," Chicago Defender (August 17, 1946).
. DuBois, "The Winds of Time," Chicago Defender (September 15, 1945).
. DuBois, "Opinion," Crisis, Vol. 23 (March, 1922), pp. 199-200.
. DuBois, "The Case of Samuel Moore," Crisis, Vol. 23 (April, 1922), pp. 249-250.
. DuBois, "Postscript," Crisis, Vol. 38 (January, 1931), pp. 29-30.
. DuBois, "As the Crow Flies," Crisis, Vol. 26 (September, 1929), p. 293.
. C. Vann Woodward, The Strange Career of Jim Crow (New York: Oxford University Press, 1954).
. W. E. B. DuBois, The Autobiography of W. E. B. DuBois, (New York: International Publishers, 1968), pp. 304-305.
. DuBois, "Woman Suffrage," Crisis, Vol. 6 (May, 1913), pp. 28-29.
. DuBois, "As the Crow Flies," Amsterdam News (April 26, 1941).
. DuBois, "On the Right to Express and Hear Unpopular Opinion," National Guardian (May 25, 1953).
. DuBois, "Public School," Crisis, Vol. 12 (May, 1916), p. 32.
. DuBois, "As the Crow Flies," Amsterdam News (January 9, 1943).
. DuBois, "As the Crow Flies," Amsterdam News (September 11, 1943).
. DuBois, "Opinion," Crisis, Vol. 24 (August, 1922), pp. 154-155.
. DuBois, "As the Crow Flies," Amsterdam News (September 7, 1940).
. Julius K. Nyerere, Ujamaa: Essays on Socialism (London: Oxford University Press, 1968), pp. 38-39.
Nyerere's essential point is that "socialism is not for the benefit of black men, nor brown men, nor white man, nor yellow men. The purpose of socialism is the service of man. The man or woman who hates "Jews," or "Asians," or "Europeans," or even "Western Europeans and Americans" is not a socialist. "He is trying to divide mankind into groups . . . In either case he is denying the equality and brotherhood of man."
. W. E.B. DuBois, The Education of Black People (New York: Monthly Review Press, 1973), pp. 118-119.
. DuBois, "Socialism and Democracy," American Socialist, Vol. 4 (January, 1957), pp. 6-9.
. DuBois, "There Must Come a Vast Social Change in the United States," National Guardian (July 11, 1951).
THE CRISIS OF THE BLACK WORKING CLASS
Author's Note: Sections of this chapter were read in a paper at an international conference of political economists and social theorists at the Institute de Investigaciones Sociales, Universidad Nacional Autonoma de Mexico, Coyoacan, Mexico, July 29, 1981. A section of this paper was also published under the title, 'The Crisis of the Black Working Class," in Science and Society, Vol. 46 (Summer, 1982), pp. 130-161.
. Malcolm X, By Any Means Necessary (New York: Pathfinder, 1970), p. 183.
. Antonio Gramsci, Prison Notebooks (New York: International Publishers, 1971), p. xciii.
. W.E. B. DuBois, The Souls of Black Folk (Greenwich, Connecticut: Fawcett, 1961), p. 20.
. Afro-American writers have made this point repeatedly, in various ways. James Baldwin explains: "The history of the American Negro is unique also in this: that the question of his humanity, and of his rights therefore as a human being, became a burning one for several generations of Americans, so burning a question that it ultimately became one of those used to divide the nation. It is out of this argument that the venom of the epithet Nigger! is derived . . . In America, even as a slave, he was an inescapable part of the general social fabric and no American could escape having an attitude toward him." James Baldwin, Notes of A Native Son (New York: Bantam, 1964), pp. 144-145.
. Amilcar Cabral, Revolution in Guinea: Selected Texts (New York: Monthly Review Press, 1969), p. 86.
. Philip S. Foner, Organized Labor and the Black Worker, 1619-1973 (New York: International Publishers, 1976), Chapter 22.
. Manning Marable, From the Grassroots: Social and Political Essays Towards Afro- American Liberation (Boston: South End Press, 1980), pp. 144-146.
. Clayborne Carson, In Struggle: SNCC and The Black Awakening of the 1960s (Cambridge, Massachusetts: Harvard University Press, 1981), p. 104.
. Ibid., p. 172.
. Foner, Organized Labor and The Black Worker, passim.
. Philip S. Foner, "Organized Labor and The Black Worker in the 1970s," Insurgent Sociologist, Vol. 8 (Fall, 1978), pp. 87-95.
. Harold M. Baron, The Demand for Black Labor: Historical Notes on the Political Economy of Racism (Boston: New England Free Press, 1972), p. 39.
. Bureau of the Census, The Social and Economic Status of the Black Population in the United States: An Historical View, 1790-1978 (Washington, D.C.: Government Printing Office, 1980), pp. 30, 72. Hereafter this source will be cited as The Social and Economic Status of the Black Population.
. Ibid., p. 15.
. Victor Perla, Economics of Racism USA: Roots of Black Inequality (New York: International Publishers, 1975), pp. 198-201. Also see Philip S. Foner and Ronald L. Lewis. The Black Worker from 1900-1919, Vol. 5 (Philadelphia: Temple University Press, 1980).
. Horace R. Cayton and George S. Mitchell, Black Workers and the New Unions (Chapel Hill: University of North Carolina Press, 1939), pp. 317-320; George Brown Tindall, The Emergence of the New South, 1913-1945 (Baton Rouge: Louisiana State University Press, 1967), p. 337.
. Robert L. Allen, Black Awakening in Capitalist America: An Analytic History (Garden City, New York: Anchor Books, 1969), pp. 237-238.
. Tindall, The Emergence of the New South, p. 572.
. Dan Georgakas and Marvin Surkin, "Niggermation in Auto: Company Policy and the Rise of Black Caucuses," Radical America, Vol. 8 (January/February, 1975), pp. 31-57.
. Baron, The Demand for Black Labor, pp. 38-39.
. George Morris, CIA and American Labor: The Subversion of the AFL-CIO's Foreign Policy (New York: International Publishers, 1967), pp. 88-91, 149-150.
. Ibid., pp. 100-105.
. Allen, Black Awakening in Capitalist America, pp. 237-238.
Lack of union support for on-the-job training programs for Blacks and other national minorities is another sensitive issue for Black civil rights proponents. There is substantial evidence that federally supported corrective programs have reduced the income gap between Black and white workers, particularly for Black male workers with some secondary school education and with less than six years of actual work experience. See Daniel Taylor, "Education, On-The-Job Training, and the Black-White Earnings Gap," Monthly Labor Review, Vol. 104 (April l981), pp. 28-34.
. Paul Johnston, 'The Promise of Public-Service Unionism," Monthly Review, Vol. 30 (September 1978), pp. 9-10.
. Marable, From The Grassroots, pp. 42-43. The perception among some Blacks that unions were inherently racist was reinforced by the failure of AFSCME secretary-treasurer William Lucy to gain the presidency of the union upon Wurfs death in December, 1981. Although AFSCME's membership is estimated to be between 25 and 40 percent nonwhite, only three Blacks, one Hawaiian and one Native American served on the union's 25-member board. One AFSCME leader observed that "Lucy most likely would have gotten the job if he had been white." Ben Bedell, "AFSCME Elects New President," Guardian (December 30, 1981).
. Walter E. Williams, Loren A. Smith and Wendell W. Gunn, Black America and Organized Labor: A Fair Deal? (Washington, D.C.: Lincoln Institute for Research and Education, 1980).
With the exception of Thomas Sowell, Williams has become the most prominent Black apologist for the Reagan Administration and right-wing political causes. Not only is Williams a staunch defender of the open shop, but he also advocates the abolition of the minimum wage. The "minimum wage law systematically discriminates against the most disadvantaged members of the labor force," he argued in late 1980. Blacks, teenagers, and "any worker who cannot produce $3.10-an-hour's worth of goods and services" should have the "right" to work at jobs which pay below government wage mandates. See Walter E. Williams, "Legal Barriers to Black Economic Gains: Employment and Transportation," in Institute for Contemporary Studies, ed., The Fairmont Papers: Black Alternatives Conference, December, 1980 (San Francisco: Institute for Contemporary Studies, 1981), pp. 26-27.
. Williams' statements that high Black unemployment rates are a product of Blacks' lack of skills, an inability to work productively, and/or because of poor educational backgrounds, is absurd. Historically, Black males and females at all ages and in almost all sectors of employment have been overqualified. In 1976, the high school overqualification rate for Black males and females was 52 percent, and 27 percent higher than the rate for whites. For jobs requiring a college-level education, the Black male overqualification rate was 23 percent higher than for white males. U.S. Commission on Civil Rights, Social Indicators of Equality for Minorities and Women (Washington, D.C.: Government Printing Office, 1978), pp. 18-20.
. Paul L. Riedesel, "Racial Discrimination and White Economic Benefits," Social Science Quarterly, Vol. 60 (June, 1979), pp. 120-129.
. Michael Reich, Racial Inequality: A Political-Economic Analysis (Princeton: Princeton University Press, 1981), p. 271.
. Albert Szymanski, "Response to Riedesel," Social Science Quarterly, Vol. 60 (June 1979), pp. 130-134.
. See William Serrin, "Labor Group Girds For Capital Rally," New York Times (September 18, 1981).
. Perlo, Economics of Racism USA, pp. 206-207; see Table 31. "Median Income of Persons 14 Years Old and Over With Income, by Sex and Work Experience, for Selected Years: 1956 to 1974," in The Social and Economic Status of the Black Population , p. 47.
. U.S. Bureau of the Census, Social and Economic Status of Blacks in the United States, 1972, (Washington, D.C.: Government Printing Office, 1973), p. 55.
. Richard Freeman, "Unionism and the Dispersion of Wages," Industrial and Labor Relations Review, Vol. 34 (October, 1980), pp. 3-23.
. Richard Freeman, "The Effect of Unionism on Fringe Benefits," Industrial and Labor Relations Review, Vol. 34 (July, 1981), pp. 489-509; Duane Leigh, "The Effect of Unionism on Workers' Valuation of Future Pension Benefits," Industrial and Labor Relations Review, Vol. 34 (July 1981), pp. 510-521.
. The Social and Economic Status of the Black Population, pp. 214-215.
. Ray Marshall, Labor in the South (Cambridge: Harvard University Press, 1965) and J. Wayne Flint, Dixie's Forgotten People: The South's Poor Whites (Bloomington: Indiana University Press, 1979).
. Reich, Racial Inequality: A Political-Economic Analysis, p. 269.
The U.S. Department of Labor reported in 1974 that nonagricultural membership in unions was 26.2 percent in 1974. In the Southeast, the figure was 14 percent. Mississippi's union membership in 1974 was 12.1 percent, and North Carolina's rate of 6.8 percent was the lowest in the U.S. See Douglas Sease, "Many Northern Firms Seeking Sites in South Get Chilly Reception," Wall Street Journal (February 10, 1978).
. Marable, From The Grassroots, p. 141. On the plight of Black and white textile workers in the South, see Ed McConville, "The Southern Textile War,'' Nation (October 2, 1976), and The Struggle for Economic Justice at J.P. Stevens (New York: Amalgamated Clothing and Textile Workers Union, 1977).
. Bureau of the Census, Characteristics of Households and Persons Receiving Noncash Benefits: 1979 (Washington, D.C.: Government Printing Office, 1981), pp. 2-3. On January 2, 1982, the Reagan Administration announced plans to count food stamps as part of the income of poor people, a decision which would increase rents for families by 10 percent or more. Black Republican Samuel R. Pierce, Secretary of Housing and Urban Development, explained to the press that "food stamps should be counted as income. If somebody buys my food for me, that's income to me." Robert Pear, "Food Stamp Plan Could Increase Rents for The Poor," New York Times (January 3, 1982).
. Ibid., pp. 4-7.
. Ibid., pp. 7-9.
Studies completed by the National Center for Health Services Research indicates that the Federal government spends as much, if not more, to subsidize the health care of the rich than it does to assist lower-income people. In 1981 alone, the U .S. government lost between $17.5 billion and $24 billion in potential taxes on health insurance premium deductions. Sixty percent of the money, in the form of tax breaks, was received by the upper two percent of U.S. taxpayers. Only one percent of the tax deductions are received by the poor. "Report Finds High U.S. Aid for Health Care of Wealthy," New York Times (January 1, 1982).
. Georg Lukács, History and Class Consciousness: Studies in Marxist Dialectics (Cambridge: MIT Press, 1971), p. 133.
. Jean-Paul Sartre, Anti-Semite and Jew (New York: Grove Press, 1960), pp. 26-27.
. Frantz Fanon, Black Skin, White Masks: The Experiences of a Black Man in a White World (New York: Grove Press, 1967), pp. 177, 180.
. "America's Restructured Economy," Business Week (June 1, 1981), pp. 56-100. Business Week is not alone in its predictions. The recession of 1981-82 will create permanently high unemployment rates for employees in the rubber, construction, lumber, auto and steel industries. Any economic "recovery" after 1982, in the opinion of many Wall Street analysts, will not restore these jobs. Winston Williams, "The Jobs That Won't Come Back," New York Times (December 12, 1981). Liberal political economists, notably Robert Heilbroner and Lester Thurow, have also concluded that capitalism has entered a long period of deep structural recession. See Robert Heilbroner, "The New Economics: A Guide to Post-Keynesian Economics." New York Review of Books, Vol. 28 (February, 1980), pp. 19-22; Lester Thurow, The Zero-Sum Society: Distribution and the Possibilities for Economic Change (New York: Basic Books, 1980).
. "America's Restructural Economy," Business Week.
. Ibid.
The literature on the flight of capital from the industrial Northeast and Midwest is growing. Some excellent monographs and articles include Business Closing Legislation Won't Place Ohio at A Disadvantage (Cleveland: Ohio Public Interest Campaign, 1977); Stephen Mick, "Social and Personal Costs of Plant Shutdowns," Industrial Relations, Vol. 14 ( May, 1975), pp. 203-208; Barry Bluestone and Bennett Harrison, Capital and Communities: The Causes and Consequences of Private Disinvestment (Washington, D.C.: The Progressive Alliance, 1980); Reclaiming Our Future: A Citizen' s Conference on The Crisis of the Industrial States (Washington, D. C.: Conference on Alternative State and Local Policies, 1979); and Edward Kelley, Industrial Exodus: Public Strategies for Control of Corporate Relocation (Washington, D.C.: Conference for Alternative State and Public Policies, 1977).
The Reagan-inspired strategy to save industrial and commercial jobs in urban areas, the so-called "free enterprise zones"—where corporations receive massive tax reductions, zoning laws are relaxed, and minimum wage laws are perhaps suspended—is advanced in Stuart M. Butler, Enterprise Zones: Pioneering in the Inner City (Washington, D.C.: Heritage Foundation, 1980).
. Ibid.
. The Social and Economic Status of the Black Population, pp. 218-219.
. Ibid.
. Ray Marshall and Virgil L. Christian, Employment of Blacks in the South: A Perspective on the 1960s (Austin and London: University of Texas Press, 1978).
. Paul M. Sweezy, "The Present Global Crisis of Capitalism," Monthly Review, Vol. 29 (April, 1978), pp. 1-12; and Paul Sweezy and Harry Magdoff, "Debt and the Business Cycle," Monthly Review, Vol. 30 (June, 1978), pp. 1-ll.
. Ibid.
. See Bluestone and Harrison, Capital and Communities; Peter Dreier, "Plant closings are good business, but bad news," In These Times (February 13, 1980); Thomas Bodenheimer, "Taxes Do Not Cause Runaways," Our Socialism, (Spring, 1981); Douglass R. Sease and Robert L. Simison, "UAW Switch on Revising Contracts Reflects Growing Concern for Jobs,"Wall Street Journal (December 21, 1981).
. The thesis expressed in this paper is not a new idea. In 1911, W. E. B. Du Bois observed that the liberation of Black Americans was basically an economic, and not simply a political, question. He believed that the material interests of white workers objectively favored Black equality. DuBois stated that the goal of international capital was "to reduce human labor to the lowest depth in order to derive the greatest personal profit." DuBois, "The Economics of Negro Emancipation in the United States," Sociological Review, Vol. 4 (October, 1911), pp. 303—313.
THE BLACK POOR: HIGHEST STAGE OF UNDERDEVELOPMENT
. Bureau of the Census, Characteristics of the Population Below the Poverty Level: 1978 (Washington, D.C.: Government Printing Office, 1980), pp. 1-2, 50; John Herbers, "Poverty Rate on Rise Even Before Recession," New York Times (February 20, 1982).
Perhaps the most obvious manifestation of "lumpenization" in the 1980s was the growing army of homeless women and men who live on America's alleys, sidewalks and gutters. Gentrification in urban core areas has sharply reduced the number of single-room occupancy hotels for unemployed and poor persons. When the poor are locked out of their boarding houses, they often have nowhere else to turn except to the street. By 1982, New York City had an estimated 24,000 men and 6,000 women who were homeless. Chicago has an estimated 8,000 people homeless; Los Angeles, 7,500; and Washington, D.C., more than 6,000. Mary Ellen Schoonmaker, "Home on the Curb," In These Times (April 28–May 4, 1982)
. Ibid., p. 10.
. Bureau of the Census, Social Indicators III: Selected data on social conditions and trends in the United States (Washington, D.C.: Government Printing Office, 1980), p. 417.
. Ibid., p. 491.
The poverty index was adopted in 1969 to reflect the sex and age of the householder, family size, urban or rural residence and family composition. Rural standards for poverty are figured at 85 percent of urban or suburban living levels. A number of persons, including prison inmates, are not counted in poverty statistics.
Embarrassed by the recently growing number of poor Americans, the U.S. Commerce Department began to explore statistical maneuvers to redefine "poverty." On April 14, 1982, in what the Bureau of the Census admitted was a "highly exploratory procedure," the government suggested that many noncash benefits might be calculated in the determination of the poverty level. Such benefits under consideration are: Food Stamps, Medicaid, Medicare, subsidized school lunches, and public housing. The implications of this latest bureaucratic manipulation are alarming. For example, the number of poor persons in 1979 was 23.6 million, 11.1 percent of the total population. If assigned values of noncash government benefits were included in determining poverty status, the number of poor persons would drop between 13.6 million (6.4 percent) and 20.7 million (9.8 percent). For Black Americans, the number of persons classified as being poor would plummet from 7.5 million (30.8 percent of all Blacks) to as low as 3.7 million (15.1 percent). "Including Government Noncash Benefits Would Reduce Number of Poor," Bureau of the Census, U.S. Department of Commerce News (Aprill 4, 1982).
. Bureau of the Census, Characteristics of the Population Below the Poverty Level: 1978, pp. 2-4, 6.
. Bureau of the Census, Social Indicators III, pp. 491-493.
. Bureau of the Census, The Social and Economic Status of the Black Population, p. 201.
. Bureau of the Census, Social Indicators III, p. 483.
. Ibid., pp. 486-487.
. Bureau of the Census, Characteristics of the Population Below the Poverty Level: 1978, p. 97.
. Ibid., pp. 51, 101, 103.
. Ibid., pp. 54, 82.
. Ibid., pp. 56, 58.
. Bureau of the Census, Social Indicators III, p. 490.
. Bureau of the Census, The Social and Economic Status of the Black Population, pp. 69-71; and Bureau of the Census, Characteristics of the Population Below the Poverty Level: 1978, p. 71.
. Conservative estimates of the number of "discouraged workers" ranged from the Bureau of Labor Statistics' figure of 1.2 million in 1981 to over 2 million by independent observers of the labor force. The Federal government's number would still represent the largest total of discouraged workers in the U.S. since the mid-1940s. About one-third of this group is nonwhite, and almost two-thirds are females.
. Bureau of the Census, Characteristics of the Population Below the Poverty Level: 1978, p. 180.
. Douglas G. Glasgow, The Black Underclass: Poverty, Unemployment and the Entrapment of Ghetto Youth (New York: Vintage, 1981), pp. 1-9.
. Ibid. , pp. 10-11. There is a regrettable oversimplification of the dynamics of racism within the structural realities of late capitalism that mars what is otherwise an important contribution to the field of race relations. At one point, for instance, Glasgow issues this undocumented assertion: "In this country Blacks as a group represent the have-nots, whites the haves. The conflict between the two, although it has shifted from the open confrontation of the sixties, remains constant." This viewpoint all but negates the class component in the racial equation, which in turn creates sharply divergent interests within both the whites and Blacks as groups. (p. 31).
. Stephen Birmingham, Certain People: America' s Black Elite (Boston: Little, Brown and Company, 1977), p. 127.
. Ibid., pp. 127, 192-193, 288.
GROUNDINGS WITH MY SISTERS: PATRIARCHY AND THE EXPLOITATION OF BLACK WOMEN
. Angela Davis, "Reflections on the Black Woman's Role in the Community of Slaves," Black Scholar, Vol. 3 (December, 1971), p. 7.
. John Hope Franklin, From Slavery to Freedom: A History of Negro Americans (New York: Vintage, 1969), p. 179; Herbert Gutman, Slavery and the Numbers Game (Urbana: University of lllinois Press, 1975) pp. 102-103, 112, 126, 128.
. Kenneth M. Stampp, The Peculiar Institution, pp. 245-247.
. Ibid., p. 249.
. Frances Anne Kemble, Journal of a Residence on a Georgian Plantation in 1838-1839 (New York: New American Library, 1975), pp. 76, 245.
. Ulrich B. Philips, Life and Labor in the Old South, (Boston: Little, Brown and Company, 1963), p. 204.
. Gutman, Slavery and the Numbers Game, p. 98.
. Davis, "Reflections on the Black Woman," p. 13.
. Gilberto Freyre, The Masters and the Slaves (New York: Alfred A. Knopf, 1971), p. 324.
. Ibid., pp. 325-326.
. Ibid., pp. 74-75.
. Davis, "Reflections on the Black Woman," p. 13.
. Franklin, From Slavery to Freedom, p. 205.
. Gerald W. Mullin, Flight and Rebellion: Slave Resistance in Eighteenth Century Virginia (New York: Oxford University Press, 1972), pp. 103-105.
. Jane Blake, Memoirs of Margaret Jane Blake (Philadelphia: Innes and Son, 1897), p. 13.
. Jane Brown, Narrative of the Life of Jane Brown and Her Two Children (Hartford: G.W. Offley, 1860), pp. 47-49.
. Louisa Picquet, Louisa Picquet, the Octoroon; or, Inside Views of Southern Domestic Life (New York: the author, 1860), pp. 50-52.
Other slave narratives written by Black women include Annie L. Burton, Memories of Chidhood's Slavery Days (Boston: Ross Publishing Company, 1919); Elizabeth Keckley, Behind the Scenes (New York: G. W. Carlton , 1868); Sylvia Dubois, A Biography of the Slave Who Whipt Her Mistress and Gained Her Freedom (New Jersey: C.W. Larison, 1883).
. Lawrence W. Levine, Black Culture and Black Consciousness: Afro-American Folk Thought From Slavery To Freedom (New York: Oxford University Press, 1977), pp. 392-393.
. Quoted in John Bracey, August Meier, and Elliott Rudwick, eds., Black Nationalism in America (Indianapolis and New York: Bobbs-Merrill, 1970), pp. 70-71, 75-76
. Ibid., pp. 215-216.
. Ibid., pp. 14 141.
. Ibid., p. 62.
. Benjamin Quarles, Frederick Douglass (New York: Atheneum, 1969), pp. 131-136, 244-247.
bell hooks' treatment of Douglass in Ain't I a Woman seems somewhat monolithic. She argues that Douglass "saw the entire racial dilemma as a struggle between white man and black men. . . . By emphasizing that the right to vote was more important to men than [to] women, Douglass and other Black male activists allied themselves with white male patriarchs on the basis of shared sexism." hooks does not discuss Douglass' significant role in the early evolution of the suffragist cause, and does not mention DuBois even once in her study.
The record of white feminists and early supporters of women's suffrage on racism is more contradictory than hooks suggests. In 1851, white suffragists protested the appearance of Sojourner Truth at an Ohio women's convention because they opposed both "abolition and niggers." In her debate with Douglass, Elizabeth Cady Stanton asserted that she would not trust "the colored man with my rights; degraded, oppressed himself, he would be more despotic with the governing power than even our Saxon rulers are. If women are still to be represented by men, then I say let only the highest type of manhood stand at the helm of State." Robert L. Allen, Reluctant Reformers: Racism and Social Reform Movements in the United States (Garden City, New York: Anchor Books, 1975), pp. 141, 153-154; hooks, Ain't I a Woman (Boston: South End Press, 1981), pp. 89-90.
. hooks, Ain't I a Woman, pp. 44-45.
. Joan R. Sherman, Invisible Poets: Afro-Americans of the Nineteenth Century (Urbana: University of Illinois Press, 1974), pp. 62-74.
. John E. Fleming, "Slavery, Civil War and Reconstruction: A Study of Black Women in Microcosm," Negro History Bulletin, Vol. 38 (August-September, 1975), pp. 430-433; Hertha Ernestine Pauli, Her Name Was Sojourner Truth (New York: Appleton-Century Crofts, 1962); Sojourner Truth, Narrative of Sojourner Truth (Battle Creek, Michigan: the author, 1878); Marie Harlowe, "Sojourner Truth, the First Sit-In," Negro History Bulletin, Vol. 29 (Fall, 1966), pp. 173-174; E. Jay Ritter, "Sojourner Truth," Negro History Bulletin, Vol. 26 (May, 1963), p. 254; Arthur H. Fausett, Sojourner Truth: God's Faithful Pilgrim (New York: Russell and Russell, 1971).
. David M. Tucker, "Miss Ida B. Wells and the Memphis Lynching," Phylon, Vol. 32 (Summer, 1971), pp. ll1-122; Alfreda M. Duster, ed., Crusade for Justice: The Autobiography of Ida B. Wells (Chicago: University of Chicago Press, 1969).
. Elizabeth Chittenden, "As We Climb: Mary Church Terrell," Negro History Bulletin, Vol. 38 (February-March, 1975), pp. 351-354; August Meier, Negro Thought in America, 1880-1915 (Ann Arbor: University of Michigan Press, 1963), pp. 239-241; Human Relations Press, 1959); Mary Church Terrell, A Colored Woman in a White World (Washington, D.C.: Ransdell Publishing Company, 1940); Terrell, "Lynching From a Negro's Point of View," North American Review, Vol. 178 (July, 1904), pp. 853-898.
. Franklin, From Slavery to Freedom, pp. 505-506, 511.
A caveat must be registered concerning Hurston's views on politics. At the end of her career, Hurston drafted a letter attacking the 1954 Brown decision of the Surpeme Court as an "insult" to all Blacks. "Since the days of the never-to-be-sufficiently-deplored Reconstruction, there has been currently the belief that there is no greater delight to Negroes than physical association with whites . . . It is to be recalled that Moscow made it the main plank in their campaign to win the American Negro from 1920s on. It was the come-on stuff. Join the party and get yourself a white wife or husband." Not surprisingly, the viciously racist Mississippi State Sovereignty Commission reprinted and widely distributed her remarks. James Graham Cook, The Segregationists (New York: Appleton-Century Crofts, 1962), p. 311.
. Ibid., pp. 511, 532, 601-602; Rackham Holt, Mary McLeod Bethune: A Biography (New York: Doubleday, 1964); C.O. Pearce, Mary McLeod Bethune (New York: Vanguard Press, 1951); "Life of Mary McLeod Bethune," Our World, Vol. 5 (December, 1950), pp. 32-35; Bethune, "Clarifying Our Vision With the Facts," Journal of Negro History, Vol. 23 (January, 1938), pp. 12-15.
. W. E. B. Du Bois, editorial, Fisk Herald, Vol. 5 (December, 1887), p. 9.
. DuBois, "Fifty Years Among the Black Folk," New York Times (December 12, 1909).
. DuBois, "Postscript," Crisis, Vol. 40 (February, 1933), p. 45.
. DuBois, "As the Crow Flies," Crisis, Vol. 41 (January, 1934), p. 5.
. DuBois, Disfranchisement (New York: National American Woman Suffrage Association, 1912).
. DuBois, "Suffering Suffragettes," Crisis, Vol. 4 (June, 1912).
. DuBois, "As the Crow Flies," Amsterdam News (March 22, 1941); DuBois, "The Winds of Time," Chicago Defender (January 25, 1947).
. DuBois, "Ohio," Crisis, Vol. 4 (August, 1912), p. 182.
. DuBois, "Opinion," Crisis, Vol. 19 (March, 1920), p. 234.
DuBois' writings on women's rights and Black women include: An Attack (Atlanta: Published by author, 1906); "The Work of Negro Women in Society," Spelman Messenger, Vol. 18 (February, 1902), pp. 1-3; "Suffrage Workers," Crisis, Vol. 4 (September, 1912); "The Burden of Black Women," Crisis, Vol. 9 (November, 1914), p. 31; "A Question of Facts," Crisis, Vol. 21 (February, 1921), p. 151; The Gift of Black Folk: Negroes in the Making of America (Boston: Stratford Company, 1924); "Greetings to Women," Women of the Whole World (1959), p. 24.
. Amy Jacques-Garvey, ed., The Philosophy and Opinions of Marcus Garvey (New York: Reprinted, Atheneum, 1977), p. 7.
. Ibid., p. 9.
. John Henrik Clarke, ed., Marcus Garvey and the Vision of Africa (New York: Vintage, 1974), pp. 309-310.
. Garvey, ed., The Philosophy and Opinions of Marcus Garvey, p. 348.
. Robert G. Weisbord, Genocide? Birth Control and the Black American (Westport, Connecticut: Greenwood Press, 1975), p. 43.
This criticism of the sexist character of the Universal Negro Improvement Association's program should not be construed as a condemnation of the legitimate achievements of Garveyism. C.L.R. James is correct in his characterization of this Black nationalist leader: "Garvey is the only Negro who has succeeded in building a mass movement among American Negroes. Garvey never set foot in Africa. He spoke no African language . . . but Garvey managed to convey to Negroes everywhere (and to the rest of the world) his passionate belief that Africa was the home of a civilisation which had once been great and would be great again. When you bear in mind the slenderness of his resources, the vast material forces and the pervading social conceptions which automatically sought to destroy him, his achievement remains one of the propagandistic miracles of this century." James, The Black Jacobins, p. 396.
. W. E.B. DuBois, "Black Folk and Birth Control," Birth Control Review (June, 1932), pp. 166-167; Margaret Sanger, "The Case for Birth Control," Crisis, Vol. 41 (June, 1934).
. Weisbord, Genocide?, pp. 52-53.
. Ibid., pp. 141-142.
In some Southern counties, doctors refused to deliver a third or even a second child of a welfare mother unless she agreed to be sterilized. In a number of U.S. hospitals, particularly those with large numbers of Black and Latino patients, white doctors still perform sterilizations "without bothering to get permission." Linda Jenness, "Black Women Fight Sterilization," in Willie Mae Reid, ed., Black Women's Struggle For Equality (New York: Pathfinder Press, 1980), pp. 9-10.
. Ibid., pp. 96-104.
A note on the intimate relationship between religion and patriarchy is appropriate here. The ancient Jews stoned young brides to death "if the village elders agreed" with their husbands' charges that they were not virgins. The Orthodox Jewish prayer—"Blessed art Thou O Lord our God, King of the Universe who has not made me a woman"—speaks for itself. Muhammad taught his disciples, "When Eve was created, Satan rejoiced." The Hindu Code of Manu states: "In childhood a woman must be subject to her father; in youth to her husband; when her husband is dead, to her sons. A woman must never be free of subjugation." From its origins, Christianity promulgated misogyny. The Holy Bible taught that "all wickedness is but little to the wickedness of a woman." The woman was "an unescapable punishment" and "a necessary evil." In his correspondence to the Corinthians, St. Paul declared that "the head of every man is Christ, and the head of the woman is the man." St. Augustine commented that women were as a temple built over a sewer. Later-day Christian leaders were generally worse than their forefathers. John Calvin, the Protestant patriarch, argued that the sole function of women was to bear as many offspring as possible. Political responsibilities for females were a "deviation from the original and proper order of nature." Martin Luther "thought that sexual relations carried on Original Sin." In colonial America, evangelical ministers delivered solemn prayers while burning "witches" and "adulteresses" at the stake. At the level of popular ideology and cultural tradition, therefore, the various rituals of faith have often dictated an overtly hostile policy of suppressing women. The "good Christian" could beat his wife in "the name of the Father." The crude and often vicious practices of many Black male Christians and Muslims toward Afro-American women historically is to a degree an expression of a much older cultural heritage. See Lucy Komisar, The New Feminism (New York: Warner, 1972), pp. 69-72, 111-112.
. hooks, Ain't I a Woman, pp. 85-86.
. Ibid., pp. 91, 93.
. Bureau of the Census, The Social and Economic Status of the Black Population, pp. 67, 74.
. Ibid., pp. 124, 131.
Considerable sociological evidence exists indicating that Black women wanted to bear fewer children than white women. This was particularly true for low- to lower-middle-income Black women, even in the 1950s and 1960s. Researchers Adelaide Cromwell Hill and Frederick S. Jaffe point to a 1960 national survey demonstrating that "the average number [of children] wanted by nonwhite (women] was 2.9, compared to 3.3 by the white wives . . . Furthermore, 46 percent of nonwhites said they wanted no more than 2 children, compared to 29 percent of whites." They also noted a Chicago study in which "twice as many nonwhites as whites said they wanted only two children, and 90 percent of a group of A.F.D.C. mothers of out-of-wedlock children said they did not want to have the child." See Hill and Jaffe, "Negro Fertility and Family Size Preferences—Implications for Programming of Health and Social Services," in Talcott Parsons and Kenneth Clark, eds., The Negro American (Boston: Beacon Press, 1967), pp. 160-204.
. Nikki Giovanni, 'The True Import of Present Dialogue: Black vs. Negro," in Dudley Randall, ed., The Black Poets (New York: Bantam, 1972), pp. 318-319.
. Giovanni, "Beautiful Black Men," in Ibid., pp. 320-321.
. Sonia Sanchez, "Homecoming," in Don L. Lee, ed., Dynamite Voices (Detroit: Broadside Press, 1971), p. 48.
. Alice Lovelace, "Wedding Song," Gumbo Literary Anthology, Vol. 1 (Winter, 1978-1979); p. 46.
. Carolyn Rodgers, "For Some Black Men," in Lee ed. , Dynamite Voices, p. 57.
. Ann DuCille, "Lady in Waiting," in Pat Crutchfield Exum, ed., Keeping the Faith: Writings by Contemporary Black American Women (Greenwood, Connecticut: Fawcett, 1974), pp. 70-71.
. Lucille Clifton, "Apology (to the panthers)," in Ibid., pp. 67-68.
. Robert Staples, "The Myth of the Black Matriarchy," Black Scholar, Vol. I (January-February, 1970), p. 16.
. Sonia Sanchez, "to all brothers," in Randall, ed., The Black Poets, p. 231.
. Nikki Giovanni, "Woman Poem," in Lee, ed., Dynamite Voices, pp. 70-71.
. Ntozake Shange, poem in Black Scholar, Vol. 12 (November-December, 1981), p. 61.
. Stokely Carmichael, Stokely Speaks: Black Power Back to Pan-Africanism (New York: Vintage, 1971), p. 23.
. Malcolm X, The Autobiography of Malcolm X (New York: Grove Press, 1965), p. 454.
. hooks, Ain't l A Woman, p. 109.
. Malcolm X, The Autobiography of Malcolm X, pp. 389-390.
Following his second journey to Africa in 1964, Malcolm X began to question his profoundly sexist education via the Nation of Islam, and was gradually embracing more progressive thoughts on the role of women in political struggle. In a Paris interview in November, 1964, he contended: "The degree of progress (in the Third World) can never be separated from the woman. If you're in a country that's progressive . . . the woman is progressive . . . One of the things I became thoroughly convinced of in my recent travels is the importance of giving freedom to the woman, giving her education, and giving her the incentive to get out there and put that same spirit and understanding in her children." Despite the political advance, the discourse on women is still framed in a primarily patriarchal caste. Malcolm X, By Any Means Necessary, p. 179.
. Carmichael, Stokely Speaks, p. 114.
. Ibid., pp. 64-65.
. Ibid ., p. 73.
. Weisbord, Genocide?, pp. 94-95.
. Haki R. Madhubuti, Enemies: The Clash of Races (Chicago: Third World Press, 1978), p. 188.
. In Soul on Ice (New York: Delta, 1968), Cleaver described homosexuality as "a sickness, just as are baby-rape or wanting to become the head of General Motors . . . Many Negro homosexuals are outraged and frustrated because in their sickness they are unable to have a baby by a white man . . . . The fruit of their miscegenation is not the little half-white offspring of their dreams, though they redouble their efforts and intake of the white man's sperm. (pp. 102, 110).
. Eldridge Cleaver, Soul on Ice, pp. 206-209.
. Ibid., p. 61.
. Robert Staples, "Mystique of Black Sexuality," Liberator, Vol. 7 ( March, 1967), pp. 8-10.
. Staples, ed. The Black Family: Essays and Studies (Belmont, California: Wadsworth Publishing Company, 1971), p. 74.
Not surprisingly, Staples also justified the sexual relations between Black males and white females. "Since the interracial sex taboo is mostly centered around Negro men/white women, it is not strange that these two groups may have a certain curiosity about the sex ability of each other. Inflaming their curiosity" is the "common stereotype" that the Black man "possesses an overly large penis and has an abnormal sex drive." Many Black men "are preoccupied with the sexual conquest of women . . . Sexual conquest of women is generally seen as a sign of masculinity in American culture . . . being masculine, in a sexual sense, is very important to Negro males because the ordinary symbols of masculinity have often been denied them in the past." Staples, "Negro-White Sex: Fact and Fiction," Sexology Magazine, Vol. 35 (August, 1968), pp. 46-51.
. Quoted in hooks, Ain't I a Woman, pp. 92-93.
. Bureau of the Census, The Social and Economic Status of the Black Populatian, pp. 70, 103, 106, 107, 109.
. Helen King, 'The Black Woman and Women's Lib," Ebony (March, 1971), pp. 68-76.
. Elizabeth Hood, "Black Women, White Women: Separate Paths to Liberation," Black Scholar, Vol. 9 (April, 1978), pp. 45-46.
. Staples, "The Myth of the Black Matriarchy," pp. 15-16.
. Linda LaRue, "The Black Movement and Women's Liberation," Black Scholar Vol. 1 (May, 1970), pp. 36-42.
One root cause for dissention between elements of the Black activist intelligentsia and feminists was competition for white-collar jobs. Throughout the 1970s, many Black women and men argued that white women were seizing many of the avenues for upward mobility within the corporate and political hierarchies that had been offered originally as concessions to the Black Movement. Between 1966 and 1979, the percentage of total professional jobs that various groups held were: white women, 13 percent in 1966 to 31.6 percent in 1979; white men, 83.5 percent to 58.9 percent; Black women, 0.6 percent to 2.2 percent; Black men, 0.7 percent to 1.9 percent; and others (including Latinos, Asians, and Native Americans), 2.2 percent to 5.4 percent. White corporate executives and employment experts interviewed by the New York Times suggested several factors for the apparent preference for white women over Black women/men in executive hiring practices. "The white men who control advancement are more at ease with white women than with Blacks of either sex," some pointed out. Others noted that Blacks had a disturbing "lack of faith in the fairness" of capitalism whereas the majority of white middle-class females did not. See Sheila Rule, "Blacks Believe White Women Lead in Job Gains," New York Times (March 25, 1982).
. Bibi Amina Baraka, "Coordinator's Statement," in Imamu Amiri Baraka, ed., African Congress: A Documentary of the First Modern Pan-African Congress (New York: William Morrow, 1972), pp. 177-178.
. Akiba ya Elimu, "The Black Family," in Ibid., pp. 179-180.
. Kasisi Washao, "Marriage Ceremony," in Ibid., pp. 181-186.
. Madhubuti, Enemies: The Clash of Races, pp. 139-158.
The academic interest in polygyny transcended the Black Movement in the 1970s. Other works on the subject as it relates to Blacks include Jacquelyne Jackson, "But Where Are the Men?" Black Scholar, Vol. 2 (December, 1971), pp. 30-41; Melvin Ember, "Warfare, Sex Ratio, and Polygyny," Ethnology, Vol. 8 (1974), pp. 197-206; Joseph W. Scott, "Polygamy: A Futuristic Family Arrangement for African Americans," Black Books Bulletin (Summer, 1976), pp. 13-19; Leachim T. Semaj, "Male/Female Relationships: Polygamy Reconsidered," in Semaj, Working Papers in Cultural Science (Ithaca, New York: the author, 1980).
. Joint Center for Political Studies, National Roster of Black Elected Officials (Washington, D.C.: Joint Center, 1976), pp. xliii-li.
Works by or about Black women politicians include Shirley Chisholm Unbought and Unbossed (Boston: Houghton and Mifflin, 1970); Chisholm, The Good Fight (New York: Harper and Row, 1973); Herrington J. Bryce and Allan E. Warrick, "Black Women in Elective Offices," Black Scholar, Vol. 6 (October, 1974), pp. 17-20; Jewel L. Prestage, "Political Behavior of American Black Women: An Overview," in La Frances Rodgers-Rose, ed., The Black Woman (Beverly Hills and London: Sage Publications, 1980), pp. 233-245.
. Cathy Sedgewick and Reba Williams, "Black Women and the Equal Rights Amendment," Black Scholar, Vol. 7 (July-August, 1976), pp. 24-29.
. Michele Wallace, Black Macho and the Myth of the Superwoman (New York: Warner Books, 1980), pp. 52-53.
. Ibid., pp. 103-104, 118.
Predictably, the reviews of Black Macho were mixed. The bourgeois press embraced Wallace's analysis with gusto. "With this rude, witty polemic—part political broadside, part personal memoir—a 26-year-old Black writer makes a striking debut," declared Newsweek (February 5, 1979). The Library Journal (March 1, 1979, p. 616) was impressed with Wallace's "simple yet brilliant thesis . . . laser-like in its probing of Black sexual politics. Wallace ranges easily over a vast array of contemporary thought and culture." Kirkus Reviews judged Black Macho as "thoughtful and temperate." Former SNCC activist Julius Lester wrote in the Nation (February 17, 1979, pp. 181-182) that he liked "the book and agree with its thrust and energy when she calls for a Black feminism that is not imitative of what white feminists have done before." Most Black intellectuals' responses to Wallace were divided along feminist lines. Black males who were explicitly sexist provided the most caustic commentary. Harvard psychiatrist Alvin F. Poussaint bristled that "the Black macho response during the Black Liberation Movement was primarily and appropriately a response to white macho and was only secondarily directed at women." In Poussaint's view, Wallace and other Black women had now joined "with whites to destroy the number one object of racism—the Black male." Poussaint, "White Manipulation and Black Oppression," Black Scholar (May/June, 1979), p. 54.) Robert Staples' response was loaded with sexist stereotypes. "The attack on Black men is occurring when Black women threaten to overtake them, in terms of education, occupation, and income," he wrote. "True, lower-class Black women are not faring well. But lower-class Black men are in even worse condition." (Staples, ''The Myth of Black Macho," Black Scholar (May/June, 1979), pp. 24-33.) Antisexist Black males such as Kalamu ya Salaam recognized the problems with Wallace's polemic, but also insisted that a feminist perspective was imperative for progressive struggle. Salaam stated that "regardless of our [Black men's] power, the fact remains that we routinely act our sexist behavior and the controllers of society at large condone, seldom punish, and even sometimes reward such sexist behavior." (Salaam, "Revolutionary Struggle/Revolutionary Love," Black Scholar (May/June, 1979), p. 21.) Black women intellectuals Sherely A. Williams, Pauline Terrelonge Stone, Sarah Webster Fabio, and Julianne Malveaux critiqued both Black Macho and the obvious sexism inherent in Staples' and Poussaint's analysis of the Black community.
. In 1977, for example, Black women workers in sales jobs suffered more than twice the unemployment rate of Black men, 19.6 percent v. 9.2 percent. Black women in blue-collar jobs had an overall unemployment rate of 16.9 percent v. 11.8 percent for men. Bureau of the Census, The Social and Economic Status of the Black Population, p. 214.
. Cindy Jaquith, "Joanne Little's Victory," in Reid, ed., Black Women's Struggle For Equality, pp. 10-13.
. Sedgewick and Williams, "Black Women and the Equal Rights Amendment."
. hooks, Ain't I a Woman, p. 151.
. Ibid., pp. 152.
. Michele Barrett, Women's Oppression Today: Problems in Marxist Feminist Analysis (London: Verso Editions, 1980), pp. 258-259.
Sheila Rowbotham also provides some insights on the continuing contradictions between socialism and feminist politics: "Marxists have in general assumed that the overthrow of capitalist society will necessitate the fundamental transformation in the organization and control of production and the social relations which came from the capitalist mode of production. Women's liberation implies that, if the revolutionary movement is to involve women . . . as equals, then the scope of production must be seen in a wider sense and cover also the production undertaken by women in the family and the production of self through sexuality . . . The connection between the oppression of women and the central discovery of Marxism, the class exploitation of the worker in capitalism, is still forced. I believe the only way in which their combination will become living and evident is through a movement of working-class women, in conscious resistance to both, alongside black, yellow and brown women struggling against racialism and imperialism." Rowbotham, Women, Resistance and Revolution: A History of Women and Revolution in the Modern World (New York: Vintage, 1972), pp. 246-247.
BLACK PRISONERS AND PUNISHMENT IN A RACIST/CAPITALIST STATE
. Stampp, The Peculiar Institution, pp. 2, 24-25.
. Ibid., pp. 174-175; Eugene D. Genovese, Roll, Jordon, Roll: The World The Slaves Made (New York: Pantheon, 1974), pp. 36-37, 66-67.
. Leon Litwack, North of Slavery: The Negro in the Free States, 1790-1860 (Chicago: University of Chicago Press, 1961), pp. 97-99.
. Eric Foner, Free Soil, Free Labor, Free Men: The Ideology of the Republican Party before the Civil War (New York: Oxford University Press, 1970), pp. 263, 286.
. Vernon Lane Wharton, The Negro in Mississippi, 1865-1890 (Chapel Hill: University of North Carolina Press, 1964), pp. 227-233.
. Pete Daniel, The Shadow of Slavery: Peonage in the South, 1901-1969 (New York: Oxford University Press, 1972), pp. 23-25.
. C. Vann Woodward, Origins of the New South, 1877-1913 (Baton Rouge: Louisiana State University Press, 1951), pp. 3-5, 213-215.
. Fletcher M. Green, "Some Aspects of the Southern Convict Lease System in the Southern States," in Fletcher M. Green (ed.), Essays in Southern History (Chapel Hill: University of North Carolina Press, 1949), p. 122.
. Woodward, Origins of the New South, pp. 397-398.
. Ibid., pp. 213-214.
. Walter Wilson , "Twilight of the Chain Gang," Nation, Vol. 150 (1940), pp. 44-46; George Brown Tindall, The Emergence of the New South, pp. 214-215.
. Allison Davis, Burleigh B. Gardner, Mary R. Gardner, Deep South: A Social Anthropological Study of Caste and Class (Chicago: University of Chicago Press, 1941), pp. 297-301.
. Richard Wright provides a typical illustration of this in Black Boy:
"Do you want this job?" the woman asked.
"Yes, ma'am," I said, afraid to trust my own judgment.
"Now, boy, I want to ask you one question and I want you to tell me the truth," she said.
"Yes, ma'am," I said, all attention.
"Do you steal?" she asked me seriously.
I burst into a laugh, then checked myself.
"What' s so damn funny about that?" she asked.
"Lady, if I was a thief, I'd never tell anybody."
"What do you mean?" she blazed with a red face.
I had made a mistake during my first five minutes in the white world. I hung my head.
"No, ma'am," I mumbled. "I don't steal."
—Richard Wright, Black Boy: A Record of Childhood and Youth (New York: Harper and Row, 1945), p. 160.
. Davis, Gardner, and Gardner, Deep South, pp. 302, 310-311.
. Woodward, The Origins of the New South, p. 160.
. Even at the height of "gangland" killings in Chicago, immediately after World War I , the murder rate in that major Midwest city averaged a mere 11.8, slightly above the national homicide rate. Memphis' average homicide reached 88.2 in 1915. Walter White, Rope and Faggot: A Biography of Judge Lynch (New York: 1929, reprinted, Arno Press, 1969), pp. 238—244. Also see James H. Chadbourn, Lynching and the Law (Chapel Hill: University of North Carolina Press, 1933) and Arthur F. Roper, The Tragedy of Lynching (Chapel Hill: University of North Carolina Press, 1932).
. White, Rope and Faggott, pp. 83-87.
. Genovese, Roll , Jordan, Roll , p. 32; Stampp, The Peculiar Institution , p. 191.
. Manning Marable, Blackwater: Historical Studies in Race, Class Consciousness and Revolution (Dayton, Ohio: Black Praxis Press, 1981), p. 15.
. Genovese, Roll, Jordan, Roll, p. 33.
. Stampp, The Peculiar Institution , p. 191.
. White, Rope and Faggott, pp. 232-236, 252-259.
. Tindall , The Emergence of the New South, 1913-1945, pp. 170-171.
. Davis, Gardner, Gardner, Deep South, p. 25.
. White, Rope and Faggott, pp. 35-36.
. Ibid., pp. 27-29.
. "Surprising Facts About the Death Penalty," (Durham, North Carolina: Institute for Southern Studies, 1981). Other monographs cited on the death penalty and related data is collected from the Institute of Southern Studies, unless otherwise noted.
. Anthony G. Amsterdam, "The Case Against the Death Penalty," and "The Bible and the Death Sentence," Institute for Southern Studies, 1981.
. "Common Misconceptions About the Death Penalty," Institute of Southern Studies, 1981.
. Hans W. Mattick, "An Unsentimental View of Capital Punishment," Community, Vol. 36 (Summer, 1977), p. 11.
. "Common Misconceptions About the Death Penalty."
. Amsterdam, 'The Bible and the Death Sentence."
. "Surprising Facts About the Death Penalty."
. Ibid., and Clare Jupiter, "Lost Lives? A Profile of Death Row," Institute of Southern Studies monograph, 1981.
U.S. politicians have been forced recently to resort to outright lies in order to justify the death penalty. One small but typical example occurred in April, 1982, when President Ronald Reagan asserted to the press that Great Britain once hanged people if they used a gun in the commission of a crime, whether or not the gun was used. Reagan declared that this was a "cruel but effective system" that ended only when Britain ended capital punishment in 1965. Within days, a spokesperson for Britain's Law Society responded that the presidential assertion was "absolutely wrong." Researchers at the Library of Congress checked records dating back to the fourteenth century, and found nothing to support Reagan's brutal statement. When a White House press secretary was challenged for an explanation, he admitted that the story was untrue. He added for the record, "Well, it's a good story, though." "Briton Rebuts Reagan on Use of Guns and the Death Penalty," New York Times (April 17, 1982).
. Table 5/1, "Persons Afraid To Walk Alone at Night, Selected Years: 1965-1977," and Table 5/2, "Attitudes Toward Treatment of Criminals by the Courts, Selected Years: 1965—1978," in Bureau of the Census, Social Indicators III., p. 237.
. Table 5/3, "Public Safety Expenditures, by Function and Level of Government: 1952-1977;" Table 5/4, "Per Capita Expenditures for Police Protection, Selected Cities: 1974," in Ibid ., pp. 238-240.
. Table 5/6, "Violent Crimes by Type: 1960-1978;" Table 5/7, "Property Crimes by Type, 1960-1978;" Table 5/8, "Victims of Homicide, by Race and Sex: 1940-1977, in Ibid., pp. 206, 241-243.
. Table 5/8, "Victims of Homicide," and Table 5/10, "Personal Crimes of Violence and Theft: 1973—1978;" in Ibid., pp. 243—244. Black women are also more likely to be victims of violent crime than whites or Hispanics.
. Ibid., pp. 207, 246-247. Black families who rent their homes or apartments are also more likely to experience burglaries than all whites and those Blacks who own their own residences. Between 1973 and 1978, the instances of burglaries per 1,000 households for Black renters was between 139 to 154 annually.
. Ibid., p. 247. Between 1973 and 1978, white families earning $25,000 a year or more experienced household burglaries at a rate of 80 to 113 per 1,000. Black families in the same income bracket were victims of burglaries at a rate of 82 to 214 per 1,000 households annually.
. "Crisis and Cutbacks Stirring Fresh Concern on State of the Nation's Prisons," New York Times (January 5, 1982).
. Wall Street Journal (December 17, 1981).
Caught in a major crisis of capital accumulation, the corporations eagerly seized upon Burger's proposal as a step forward in penal reform. If one carries this model to its logical conclusions, half of all U.S. prisoners (250,000) could be employed in existing blue-collar jobs. At least 250,000 persons currently not in prison would no longer be necessary in the workplace. A sizeable number of now-unemployed Blacks, Hispanics and poor whites would have to commit petty crimes simply to survive. Once convicted, they could be added to the ever-expanding penal workforce at lower wage levels. Perhaps the final solution would simply be to imprison the entire working class, cutting wages in half, and turning the entire society into a kind of permanently armed camp. No proposal is too "extreme" in the pursuit of profits!
. Hinds, Illusions of Justice, pp. 36, 44.
. There is an unbroken political correlation between extreme bigotry and an opposition to socialism and communism. A fierce anticommunism was an integral part of white racist political culture by the Great Depression. At the famous trial of Black activist Angelo Herndon in 1937, the Georgia prosecutor informed the all-white jury that class played an equally important role with race in the conviction of alleged Black leftists. "This is not only a trial of Angelo Herndon, but of Lenin, Stalin, Trotsky and Kerensky, and every white person who believes that black and white should unite for the purpose of setting up a nigger Soviet Republic in the Black Belt . . . As fast as the Communists come [into Georgia], we shall indict them and I shall demand the death penalty in every case." Angelo Herndon, Let Me Live (New York: Reprinted from 1937 edition, Arno Press, 1969), p. 228.
. United States Senate, Final Report of the Select Committee to Study Governmental Operations with Respect to Intelligence Activities, Book III (Washington, D.C.: Government Printing Office, 1976), pp. 6, 40, 56, 57, 187-188.
The "long-range goals" of the "Black Nationalist-Hate Groups" program were outlined on March 4, 1968, and forwarded to 41 FBI offices nationwide:
"(1) to prevent the 'coalition of militant black nationalist groups' which might be the first step toward a real ' Mau Mau' in America;
(2) to prevent the rise of a 'messiah' who could 'unify, and electrify,' the movement, naming specifically Martin Luther King, Stokely Carmichael, and Elijah Muhammad;
(3) to prevent violence on the part of black nationalist groups, pinpointing 'potential troublemakers' and neutralizing them 'before they exercise their potential for violence';
(4) to prevent groups and leaders from gaining 'respectability' by discrediting them to the 'responsible' Negro community, to the white community (both the responsible community and the 'liberals') . . . and to Negro radicals; and (5) to prevent the long-range growth of these organizations, especially among youth, by developing specific tactics to 'prevent these groups from recruiting young people.' "(pp. 21-22)
. On December 4, 1981, "two FBI agents entered the home of black writer Sonia Sanchez and belligerently interrogated her . . . [and] threatened her with imprisonment for her alleged acquaintance with black militants, declaring that 'there will be no imprisonment; there will be no jail for them. We will kill." "FBI threatens Black writer," Militant (January 1, 1982).
. "Federal grand jury investigates Black groups," Portland Observer (December 31, 1981). One Black woman in New York City, Yaasmyn Fula, was sentenced in 1981 to an 18-month jail sentence because she refused "to tell a grand jury about her group."
. Eric Mann, Comrade George: An Investigation into the Life, Political Thought, and Assassination of George Jackson (New York: Harper and Row, 1974), pp. 21, 25.
. Ibid., p. 114.
BLACK CAPITALISM: ENTREPRENEURS, CONSUMERS AND THE HISTORICAL EVOLUTION
OF THE BLACK MARKET
. One of the best critiques of Gold Coast economic development is provided in Bob Fitch and Mary Oppenheimer, Ghana: End of an Illusion (New York: Monthly Review Press, 1966).
. Chinweizu, The West And The Rest of Us: White Predators, Black Slavers and the African Elite (New York: Vintage, 1975), pp. 355-356.
. Ibid., p. 382.
. Ibid., p. 385.
. Frantz Fanon, The Wretched of the Earth (New York: Grove Press, 1968), p. 167.
. I am tempted to assert that the most decisive "intellectuals" within Black history have always been found among the entrepreneurs. A solid argument could be made that racial segregation and an aggressive capitalist political economy fashioned the conditions for upwardly mobile, Black intellectuals in the traditional sense to flock to the marketplace instead of the academy. Gramsci's observation of Italian entrepreneurs provides a rough parallel to those in Black America: 'The entrepreneur himself represents a higher level of social elaboration . . . he must have a certain technical capacity, not only in the limited sphere of his activity and initiative but in other spheres as well, at least in those which are closest to economic production. He must be an organizer of masses of men; he must be an organizer of 'confidence' of investors in his business, of the customers for his products, etc. If not all entrepreneurs, at least an elite amongst them must have the capacity to be an organizer of society in general, including all its complex organism of services, right up to the state organism, because of the need to create the conditions most favorable to the expansion of their own class . . . " Gramsci, Prison Notebooks, pp. 5-6.
. August Meier and Elliott Rudwick, CORE: A Study in the Civil Rights Movement, 1942-1968 (New York: Oxford, 1973), p. 423; Benjamin Quarles, Frederick Douglass, pp. 269-270. Also see Roy Innis, "Separatist Economics: A New Social Contract," in G. Douglass Pugh and William F. Haddard, eds., Black Economic Development, (Englewood Cliffs, New Jersey: Prentice-Hall, 1969).
. E. Franklin Frazier, Black Bourgeoisie (Glencoe, Illinois: Free Press, 1957).
. Abram L. Harris, The Negro As Capitalist: A Study of Banking and Business Among American Negroes (New York: Haskell, 1936: Reprinted 1970), pp. 4-24.
. Ibid., pp. 8-9.
. Ibid., 12, 17-18.
. Booker T. Washington and W. E. B. Du Bois, The Negro In The South (New York: Reprinted from 1907 edition, Citadel Press, 1970), pp. 26-28.
. Roger L. Ransom and Richard Sutch, One Kind of Freedom: The Economic Consequences of Emancipation (Cambridge: Cambridge University Press, 1977), p. 35.
. W. E.B. DuBois, The Negro Artisan: A Social Study (Atlanta: Atlanta University Press, 1902), p. 22.
. Ransom and Sutch, One Kind of Freedom, p. 36.
. Ibid., pp. 37-38, 228-229.
. Bureau of the Census, The Social and Economic Status of the Black Population, p. 78.
. Meier, Negro Thought in America, pp. 140-141.
. Ibid., pp. 144-145, 148; Timothy Bates, Black Capitalism: A Quantitative Analysis (New York: Praeger, 1973), p. 9; Earl Ofari, The Myth of Black Capitalism (New York: Monthly Review Press, 1970), p. 30.
. Louis R. Harlan, Booker T. Washington: The Making of a Black Leader, 1856-1901 (New York: Oxford University Press, 1972), pp. 254, 266-270.
. Henry G. La Brie, III, A Survey of Black Newspapers (Kennebunkport, Maine: Mercer House, 1979), pp. 10-11.
. Meier, Negro Thought in America, pp. 225-228.
. Bates, Black Capitalism, p. 9.
. John Henrik Clark, ed., Marcus Garey and the Vision of Africa (New York: Vintage, 1974), pp. 89-91.
. Ibid., p. 207.
. W. E. B. Du Bois, "The Upbuilding of Black Durham," World's Work, Vol. 13 (January, 1912), pp. 334-338.
. DuBois, "The Business League," Crisis, Vol. 6 (October, 1913), p. 289.
. DuBois, "The Negro Bank," Crisis, Vol. 23 (April, 1922), pp. 253-254; DuBois, "Black Banks and White in Memphis," Crisis, Vol. 35 (May, 1928), pp. 154, 173-174.
. DuBois, "Opinion," Crisis, Vol. 29 (April, 1925), p. 252.
. DuBois, "As the Crow Flies," Amsterdam News (October 10, 1942).
. DuBois, "As the Crow Flies," Amsterdam News (May I, 1943).
. Harris, The Negro As Capitalist, p. 55.
. Ibid., pp. 145, 153, 60-61.
. Bates, Black Capitalism, pp. 10-13.
. David Caplovitz, The Poor Pay More: Consumer Practices of Low-Income Families (New York: The Free Press, 1963), pp. 4-5.
. Harris, The Negro As Capitalist, pp. 180-181.
. Ibid., p. 183; Paul Jacobs, "Negro and Jew," in Shlomo Katz (ed.), Negro and Jew: An Encounter in America (New York: MacMillan, 1967, pp. 74–80.
It would be a distortion of Black social history not to admit that many Blacks were profoundly influenced by the deep antisemitism of the dominant civil society. Richard Wright asserts: "All of us black people who lived in the neighborhood hated Jews, not because they taught at home and in Sunday school that Jews were 'Christ killers.' With the Jews thus singled out for us, we made them fair game for ridicule . . . No one ever thought of questioning our right to do this; our mothers and parents generally approved, either actively or passively. To hold an attitude of antagonism or distrust toward Jews was not merely racial prejudice, it was a part of our cultural heritage." Richard Wright, Black Boy, pp. 70-71.
. Flournoy A. Coles, Jr. Black Economic Development (Chicago: Nelson Hall, 1975), pp. 177-181.
. Meier, Negro Thought in America, pp. 124-177.
. Coles, Black Economic Development, p. 185; LeRoy W. Jeffries, Facts About Blacks, 1980-1981 (Los Angeles: Jeffries and Associates, 1980) pp. 11-14.
. D. Parke Gibson, $70 Billion in the Black (New York: MacMillan, 1978), p. 11.
. Another method to test the thesis that racially segregated cities help to support the development of Black Capitalism can be illustrated by a brief comparison between Dayton, Ohio (Black population 103,380 in 1977) and RaleighDurham, North Carolina (Black population 107,104). Dayton has 735 Black-owned firms, 130 of which (17.7 percent) have a total of 403 employees. Total gross receipts in Dayton, a Midwestern city with a strong Black petty bourgeoisie and a Black mayor, were $20.9 million in 1977. Raleigh-Durham has 921 Black-owned firms, 192 (20.8 percent) with 1826 workers. Gross receipts for Raleigh-Durham's firms without employees were $6.1 million. Black businesses with paid employees grossed $69.1 million, for a combined total of $75.2 million. See Bureau of the Census, 1977 Survey of Minority-Owned Business Enterprises (Washington, D.C.: Government Printing Office, 1979), pp. 129, 142-143.
. Ibid., pp. 169-173.
. Ibid., p· 169; Bates, Black Capitalism, pp. 24-25.
The real status of the Black entrepreneur within the proletarian periphery is not unlike that of a factory foreman. As Lenin observed, a foreman is not a boss; he/she is a worker who controls only a minute aspect of the process of production. His/her status, at least in the estimation of those who own the plant, is not as an equal partner or investor. The intermediate entrepreneur, only one out of every six Black businesspersons, is not a worker, but is also not part of the capitalist class. The periphery is sustained by "bourgeois illusions," whereas intermediate entrepreneurs do have a real material interest in private enterprise.
. LeRoy W. Jeffries, Facts About Blacks, 1980-1981, pp. 11-14, 21-23.
. Gibson, $70 Billion in the Black, pp. ix, 108-109, 152-153.
There is a substantial amount of research on the impact of advertising on Black consumers since 1970. Some informative sources are: T.R. Donohue, "Effect of Commercials on Black Children," Journal of Advertising Research (December, 1975), pp. 41-47; "Ethnic Marketing-So Much Opportunity, So Much To Learn," Product Marketing Magazine (June, 1977), pp. 29-34; "Selling to the Black Consumer: A Roundtable Discussion of the Increasing Black Impact on Corporate Economies," Black Enterprise (November, 1973), pp. 31-33; Thaddeus H. Spratlen, "The Black Consumer Response to Black Business," Review of Black Political Economy (Fall, 1973), pp. 73-105; Donald E. Sexton, "Black Buyer Behavior," Journal of Marketing (October, 1972), pp. 36—39; A.G. Woodside, "Credibility of Advertising Themes Among Blacks and Whites," Marquette Business Review (Fall, 1975), pp. 134-142; John H. Johnson, "Greening of the Black Consumer Market," Crisis (March, 1976), pp. 92-95; C. Marticorena, "Ethnic Market: Biggest Potential for Growth . . . " Chemical Marketing Reporter (June 23, 1975), pp. 37-39; "New Look at the Black Consumer," Sales Management (August 6, 1973), p. 13; C. Orphen, "Reactions to Black and White Models," Journal of Advertising Research (October, 1975), pp. 75-79.
. Ibid., pp. 132, 134-136.
Coca Cola launched a counterattack against Pepsi by hiring soul artists Ray Charles and the Supremes. Coke's advertising agency, McCann-Erickson, convinced the Atlanta-based billion dollar multinational that a blacker-than-thou approach was needed to boost profits at Pepsi's expense. Commercial tapes were cut and aired only on "Black-oriented" radio stations. Within a few months, Coke gross profits earned from Black consumers increased sharply. 'The Charles commercial even got fan mail and consumer requests of stations for its play." Gibson, $70 Billion In the Black, pp. 90-91.
. Ibid., pp. 40, 41, 202.
. Ibid., 89-90, 95-97.
. Ibid., pp. 4, 85, 159-162. Also see Gil Scott, "Blacks in the Liquor Industry," Black Enterprise (September, 1975), pp. 33-37.
By the mid-1970s Black entertainers and athletes were standard spokespersons for corporate products, something that would have been unthinkable twenty years before. A few on this ever-expanding list include: singer Nancy Wilson, Johnson and Johnson Disposable Diapers; Wilt Chamberlin, Deacon Jones, and Bubba Smith for Miller Lite beer; Pearl Bailey for Greyhound; O.J. Simpson for Hertz; Muhammad Ali for Brut; and Lou Rawls for Budweiser beer. Gibson, $70 Billion In the Black, p. 92.
. Caplovitz, The Poor Pay More, p. 126.
. Ibid., p. 96.
. Gibson, $70 Billion in the Black, pp. 34, 44, 250.
. Jeffries, Facts About Blacks, pp. 18-20.
. The Social and Economic Status of the Black Population, p. 175; Ibid., 21.
. The Social and Economic Status of the Black Population, p. 17; Jeffries, Facts About Blacks, pp. 11-14.
Since 1960, Brimmer has emerged as one of the ruling class' most prominent spokespersons on economic issues. Some of his essays include "Economic Trends in the Negro Market," Marketing Guide (May, 1964), pp. 2-7; "The Negro in the American Economy," monograph (Durham, North Carolina: North Carolina Life Insurance Company, 1966); "Outlook for Black Business," Black Enterprise (June, 1976), pp. 26-30; Brimmer and Henry Terrell, "The Economic Potential of Black Capitalism," Public Policy, Vol. 19 (Spring, 1971).
. Coles, Black Economic Development, p. 88.
. Ibid., pp. 88—89; Richard F. America, Jr., "What Do You People Want?" Harvard Business Review, Vol. 47 (March-April, 1969), pp. 103-112.
Economists who have proposed similar programs to aid in the development of Black Capitalism include Robert B. McKensie, "Vitalize Black Enterprise," Harvard Business Review, Vol. 46 (September, 1968); James M. Hund, Black Entrepreneurship (Belmont, California: Wadsworth, 1970); Theodore L. Cross, Black Capitalism (New York: Atheneum, 1969); Richard S. Rosenbloom, "Business, Technology, and the Urban Crisis," in Richard S. Rosenbloom and Robin Marris, eds. Social Innovation in the City (Cambridge, Mass.: Harvard University Press, 1969), pp. 51-61; George S. Odiorne, Green Power (New York: Pitman, 1969).
Other recent sources on Black Capitalism include Courtney N. Blackman, Black Capitalism in Economic Perspective (New York: Economic Research Department, Irving Trust Company, 1973); Edward D. Irons, "Black Entrepreneurship: Its Rationale, Its Problems, Its Prospects," Phylon (March, 1976), pp. 12-25; Arthur L. Tolson, "Historical and Modern Trends in Black Capitalism," Black Scholar (April, 1975), pp. 8-14.
. The Social and Economic Status of the Black Population, pp. 78-79; Jeffries, Facts About Blacks, p. 21.
. An ominous example is provided by Floyd McKissick, a prominent Black Powerite, supporter of Richard Nixon in 1972, and architect of Soul City, North Carolina. Defending Black Capitalism, McKissick justified his autocratic political practice by declaring his affinity with Marcus Garvey. In his view, Garvey "was not a democratic leader; in fact, he was a dictator." McKissick stated, "we need to study his style." Meier and Rudwick, CORE, p. 422.
Reaganism as a social and political force is clearly authoritarian, but is not fascist. The Reaganites' desire for law and order at any cost to civil liberties, extreme racism, the rightist libertarian demand to reduce the size of the welfare state, and the call for a balanced federal budget, do not constistitute fascism. Moreover, the politically conservative wing of Black Capitalism obviously would have nothing in common with the racist maneuvers of a Jesse Helms. Nevertheless, by calling for state intervention to assist in the development of a Black capitalist class, they must also embrace critical elements of an authoritarian and even proto-fascist ideology—crushing labor unions, passing right-to-work laws, increasing police in urban areas to protect Black-owned private property, reducing business taxes at the expense of higher taxes for Black workers, etc. As the most insecure and marginal element of the petty bourgeoisie and aspiring capitalist class, Black Reaganites and Black Capitalists alike have already repudiated the interests of the Black working class and the unemployed; whether their repudiation of Black liberation festers into an aggressive authoritarian political posture will only be decided by history.
BLACK BRAHMINS: THE UNDERDEVELOPMENT OF BLACK POLITICAL LEADERSHIP
Author's Note: A section of this chapter was published as "Black Conservation and Accommodation: Of Thomas Sowell and Others," Negro History Bulletin, Vol. 45 (April-June, 1982), pp. 32-35.
. Franz Kafka, "Couriers," in Walter Kaufman, ed., Existentialism From Dostoevsky to Sartre (New York: New American Library, 1956), p. 130.
. Gordon Crovitz, "Black Community Reviews Life With Reagan," Wall Street Journal (September 4, 1981).
. "NAACP Asserts Reagan Budget Profits the Rich at Expense of Poor," New York Times (April 14, 1981).
. Joyce Daniels Phillips, "Reaganomics Call For Values," Jackson Advocate (September 17-23, 1981).
. Crovitz, "Black Community Reviews Life with Reagan."
. Ivory Phillips, "Reaganism, Americanism and the Future," Jackson Advocate (September 17-23, 1981).
. Marable, Blackwater, pp. 16 161.
. Lee A. Daniels, "The New Black Conservatives," New York Times (October 4, 1981); Nathan Wright, Jr., "Dilemma of Black Republicans," Pensacola Voice (May 3-June 5, 1981).
. See Colin Campbell, "Conservative Economist Rides With the Reagan Tide," New York Times, (September 18, 1981).
Sowell's unbridled sycophancy was strikingly revealed in an October 12, 1981 interview in U.S. News and World Report. Beneath a large portrait of slaves laboring in the cotton fields, Sowell stated, "Blacks who suffered from slavery also suffered from its aftermath, in that many became hypersensitized against menial jobs. That's tragic." Sowell asserted that racial discrimination plays only a minor role "in holding back ethnic groups in America." Sowell's bankruptcy as a social theorist is matched only by his ability to debase himself as the witless tool of racist reactionaries.
. "Top Black Reagan Appointees Honored At Hill Reception," Pensacola Voice (June 6-12, 1981); "White House Names Minority Liaisons," Civil Rights Update (May, 1981), p. 4.
. Tony Brown, "NAACP Shuns Denver Blacks, Part II," Fort Lauderdale Westside Gazette (August 30, 1981).
Another prominent fellow traveler is Percy Sutton, former attorney for the family of Malcolm X and past Manhattan Borough president. At the San Francisco conference of Black conservatives, Sutton attacked "the environmental movement" and praised the Federal deregulation of corporations. Reagan's policy of urban enterprise zones, a massive corporate rip-off of taxpayers and inner city residents, received Sutton's endorsement with one qualification. "Free enterprise zones" will work, he declared, only if the state "[gave] us a lot [more] policemen." "Percy Sutton Calls For Help To 'Help Ourselves,'" Milwaukee Courier (June 13, 1981).
. Marguerite Ross Barnett, "The Congressional Black Caucus: Illusions and Realities of Power," in Michael B. Preston, Lenneal J. Henderson, Jr. and Paul Puryear, eds., The New Black Politics: The Search For Political Power (New York and London: Longman, 1982), pp. 28-54.
. Frank Elam, "Marchers Back Voting Rights,'' Guardian (May 6, 1981); "3,000 March in Montgomery," Guardian (August 19, 1981).
Jackson also led a major march in Natchez, Mississippi on May 31, 1981, in support of the Voting Rights Act. "Natchez March Begins Struggle," Jackson Advocate (June 4-10, 1981). Julian Bond hosted a Black conference on the significance of the Voting Rights Act in Jackson, Mississippi, on October 10, while Yolanda King, Martin's daughter, led a rally of over 1,000 people to defend a group of poor Black workers attempting to organize in Tylertown, Mississippi, on October 3, 1981. "Bond in Jackson for Voting Confab," and "Mass March At Tylertown," Jackson Advocate (October 8-14, 1981).
. "Bond Accuses Greensboro Police of 'Negligence,'" Atlanta Constitution (October 3, 1981).
. William Serrin, "Labor Group Girds For Capital Rally," New York Times (September 18, 1981); Seth S. King, "240,000 in Capital Rally For Protest of Reagan Policies,'' New York Times (September 20, 1981).
. William Raspberry, "Coke Deal: Reciprocity Rather Than Generosity," Miami Times (September 3, 1981).
Despite Jackson's failures, the Black capitalists' strategy continues on. In March, 1982, Heublein, Inc., a multi-billion-dollar beverage and food corporation, announced a $180 million program to develop Black business, in conjunction with Jackson and Operation PUSH Heublein's plans provided for $20 million in minority oriented programs in 1982, rising to about $50 million within five years. The program included: "$10 million in capital assistance to enable blacks to open 24 Kentucky Fried Chicken stores, with an additional 88 franchises to be made available to qualified investors who want to become owner-operators; a 50 percent increase (in 1982) in black ad agency expenditures; and increase in loan agreements with black-owned banks to at least $20 million; the placing of 15 percent of Heublein's group life insurance with a black-owned company; a plan to hire black-owned law and accounting firms; and a plan to spend $75 million in goods and services under a minority purchasing program." "Heublein Plan on Blacks," New York Times (March 17, 1982).
. Ibid.; and "Coke Covenant Brings King Followers Back Together," Miami Times (September 3, 1981).
The Black Brahmins joined forces once more when Ralph Abernathy, a prominent supporter of Reagan in 1980, and "Daddy" King endorsed the mayoral candidacy of Andrew Young in Atlanta, Georgia. Carole Ashkinaze, "Abernathy Endorses Young," Atlanta Constitution (October 3, 1981).
. Tony Brown, "The newest twist in the Coke Deal," Pensacola Voice (September 26–October 2, 1981).
. Sheila Rule, "Black Caucus in Capital Works to Develop Communal Leadership," New York Times (September 30, 1981).
. Gus Savage, syndicated column, Pensacola Voice (September 26–October 2, 1981).
. Reginald Stuart, "Georgia Blacks Join Battle on Legislative Redistricting," New York Times (September 28, 1981); Vernon Jarrett, "Black Democrats turn to the Republicans for help," In These Times (September 16-22, 1981).
The attitude of white Reaganites toward the Black Old Guard leadership was one of bitter denunciation. Richard Richards, Reagan's personal selection as national GOP chairperson, complained that his party did not win many Black votes because of "the so-called Black leaders, the so-called civil rights leaders, [and] the Black ministers." Richards attacked Benjamin Hooks by name, stating that "the NAACP hasn't been our friend at all," and declared that Reagan and other Republican politicians would go "around, through and over" traditional Black leaders to win a conservative Black constituency. Adam Clymer, "Black Leaders Criticized by GOP Chairman," New York Times (September 20, 1981).
. Stokely Carmichael's 1966 definition of integration, published in the New York Review of Books, represents the popular expression of Black nationalism during the Black Power period: "Integration speaks not at all to the problem of poverty—only to the problem of blackness. Integration today means the man who "makes it," leaving his black brothers behind in the ghetto. It has no relevance to the Harlem wino or to the cotton-picker making three dollars a day. .. integration is a subterfuge for the maintenance of white supremacy." It is based on a "lie: that black people inherently can't do the same thing white people do, unless white people help them." Carmichael, Stokely Speaks, p. 27.
. Meier, Negro Thought in America, pp. 32-33, 50.-51.
DuBois' views on Price are unclear. In The Souls of Black Folk, he relates that "Price and others had sought a way of honorable alliance with the best of the Southerners," thus paving the way for Booker T. Washington. In an unsigned editorial in the Crisis, Price is called a relatively progressive and successful educator who possessed "the quality of grit." Had Washington not existed, however, it seems likely that Price could have emerged in his place as the leading Black accommodationist. See DuBois, The Souls of Black Folk, p. 42; "The Ruling Passion," Crisis, Vol. 23 (March, 1922), pp. 224-225.
. Ibid., pp. 26, 27, 36, 45.
. Ibid., pp. 31, 38, 46-47, 128-129, 173-174, 228.
. DuBois' criticism of the Tuskegee philosophy remains the best analysis of the failures of accommodation: " . . . the way to truth and right lies in straightforward honesty, not in indiscriminate flattery; in praising those of the South who do well and criticising uncompromisingly those who do ill. . . . the way for a people to gain their reasonable rights is not be voluntarily throwing them away and insisting that they do not want them; the way for a people to gain their respect is not by continually belittling and ridiculing themselves." DuBois, The Souls of Black Folk, pp. 50-51.
. Lawrence W. Levine makes this connection between the Tuskegee philosophy and the blues: "It was not coincidental that a new emphasis upon the individual and individual expression was taking hold in black song at the very time that Booker T. Washington's philosophy was taking hold among black intellectuals and the black middle class. The individualist, ethos [influenced] the black school teachers produced by such new institutions as Hampton and Tuskegee, the popular press, and . . . preachers, businessmen, and leaders of every sort. This is not to suggest that the blues mirrored the moral and economic lessons of the [Horatio] Alger message; the opposition would be closer to the truth. But there was a direct relationship between the national ideological emphasis upon the individual, the popularity of Booker T. Washington's teachings, and the rise of the blues." Levine, Black Culture and Black Consciousness, pp. 222-223.
. James, The Black]acobins, pp. 127-128.
Black accommodationists and conservatives alike suffer from what Walter Rodney described as "a cultural and psychological crisis" of doubt, a failure to believe in the effective capacity of nonwhites to direct their own societies. "That means that the African himself has doubts about his capacity to transform and develop his natural environment. With such doubts, he even challenges those of his brothers who say that Africa can and will develop through the efforts of its own people." In a biracial capitalist social order, Black conservatives tacitly acknowledge the "higher" intellectual and cultural level of whites, identify with Western thought, and attempt to out-excel whites in the mental gymnastics that they have established for themselves. Rodney, How Europe Underdeveloped Africa (London: Bogle l'Ouverture, 1972), p. 30.
. Meier, Negro Thought ln America, pp. 72, 110, 209-210; Harlan, Booker T. Washington, pp. 168-169.
. K.L. Walgemoth, "Wilson and Federal Segregation," Journal of Negro History Vol. 44 (April, 1959), pp. 15S-173; Andrew Buni, The Negro in Virginia Politics, 1902-1965 (Charlottesville, Virginia: University of Virginia Press, 1967); Zane Miller, Boss Cox's Cincinnati: Urban Politics in the Progressive Era (New York: Oxford University Press, 1968); Lyle W. Dorsett, The Pendergast Machine (New York: Oxford University Press, 1968); Herbert Aptheker, A Documentary History of the Negro People in the United States (New York: Citadel Press, 1969), pp. 819-820.
. Chuck Stone, Black Political Power in America, Revised Edition (New York: Delta, 1970), pp. 177-179; Hanes Walton, Jr., Black Politics: A Theoretical and Structural Analysis (Philadelphia: J .B. Uppincott, 1972), pp. 67, 107, 111, 116.
. Henry Lee Moon, Balance of Power: The Negro Vote (Garden City, New York: Doubleday, 1948), pp. 35–36.
. Stone, Black Political Power in America, p. 52.
. Ibid., pp. 192-207.
Even Malcolm X was favorably impressed with Powell. In 1963 he informed Alex Haley, I'd think about retiring if the black man had ten like him in Washington." Malcolm X, The Autobiography of Malcolm X, p. 402.
. Ibid., pp. 174-175.
. Rodney, How Europe Underdeveloped Africa, p. 280.
. See George Schuyler, Black and Conservative (New Rochelle, New York: Arlington House, 1966).
. See Thomas Sowell, "The Uses of Government for Racial Equality," National Review, Vol. 33 (September 4, 1981), pp. 1009-1016; "Myths About Minorities," Commentary, Vol. 68 (August, 1979), pp. 33-37; Ethnic America: A History (New York: Basic Books, 1981); Markets and Minorities (New York: Basic Books, 1981); "Affirmative Action Reconsidered," Public Interest, Vol. 42 (Winter, 1976), pp. 47-65; Race and Economics (New York: McKay, 1975).
. Kwame Nkrumah, Class Struggle in Africa (New York: International Publishers, 1970), p. 56.
THE AMBIGUOUS POLITICS OF THE BLACK CHURCH
Author's Note: Sections of this chapter were published under the title, "King's Ambiguous Legacy," in WIN magazine, Vol. 18 (April 15, 1982), pp. 15–19.
. Meier, Negro Thought in America, pp. 6, 30, 49, 55-66; Lerone Bennett, Jr., Black Power USA: The Human Side of Reconstruction 1867-1877 (Baltimore: Penguin, 1967), p. 102.
. "Black Persons Employed in Selected Professional Occupations for Selected Years: 1890 to 1970," and "Black Elected Officials," in Bureau of the Census, The Social and Economic Status of the Black Population, pp. 76, 156.
. Ibid.
. W. E. B. Du Bois, "The Religion of the Negro," New World, Vol. 9 (December, 1900), pp. 614-625.
. DuBois, "The Negro Church," book review of Carter G. Woodson's The History of the Negro Church in The Freeman, Vol. 6 (October 4, 1922), pp. 92-93; editorial on "The Negro Church," in Crisis, Vol. 4 (May, 1912), pp. 24-27.
. "The Baptist Controversy," Crisis, Vol. 11 (April, 1916), pp. 314-316.
. "Postscript," Crisis, Vol. 35 (June, 1928), p. 203. Also see "Postscript," Crisis, Vol. 38 (June, 1931), pp. 207-208, in which DuBois critiques the religious views of Darrow and Bishop R. E. Jones.
. "The Three Wise Men," Crisis, Vol. 7 (December, 1913), pp. 80–82.
. W. E. B. Du Bois to the Reverend John R. Timpany, January 17, 1945, in Herbert Aptheker, ed., The Correspondence of W. E. B. Du Bois: Volume III (Amherst, Massachusetts: University of Massachusetts Press, 1978), pp. 26-27.
. W. E. B. Du Bois to the Reverend William Crowe, Jr., August 9, 1939, in Herbert Aptheker, ed., The Correspondence of W. E. B. Du Bois: Volume II (Amherst, Massachusetts: University of Massachusetts Press, 1976), pp. 144-145.
. "The Failure of the Negro Church," Messenger, Vol. 2 (October, 1919), p. 6.
. V. F. Calverton, "Orthodox Religion, Does It Handicap Negro Progress?" Messenger, Vol. 9 (July, 1927), pp. 221-236.
. LeRoi Jones, Home: Social Essays (New York: William Morrow, 1966), pp. 94-95.
. Harold Cruse, The Crisis of the Negro Intellectual (New York: William Morrow, 1967), p. 90.
. When the Truman Administration attempted to convict DuBois on the charge that he had "[failed] to register as agent of a foreign principal," the response of the Black Church was divided. The National Baptist Convention "took no action," but Black Baptists in Philadelphia voiced strong support for DuBois. Most AME and AMEZ church leaders were silent out of "the wide fear and intimidation" of the McCarthy period. However, Reverdy C. Ransom, former board trustee president of Wilberforce University and senior bishop of the AME Church publicly supported DuBois as "one of the best known Negroes in America or for that matter in the world. This blow at him looks like a strike at the intelligentsia of Negro Americans and the millions who trust and follow their leadership." See Reverdy C. Ransom to the National Council of the Arts, Sciences and Professions, October 26, 1951, copy of DuBois, in Aptheker, ed., The Correspondence of W. E. B. Du Bois, Volume III, pp. 317-318; also see DuBois, The Autobiography of W. E. B. Du Bois, p. 391.
. E. Franklin Frazier, The Negro Church in America (New York: Schocken Books, 1964), pp. 51, 72, 73; Benjamin E. Mays and Joseph W. Nicholson, The Negro' s Church (New York: Arno Press, 1969), p. 59.
. Daniel C. Thompson, The Negro Leadership Class (Englewood Cliffs, New Jersey: Prentice-Hall, 1963), p. 37.
. Numan V. Bartley, Massive Resistance: Race and Politics in the South During the 1950s (Baton Rouge: Louisiana State University Press, 1969), pp. 294-301.
Not a few Black ministers in the South, accommodationist in outlook, quickly joined forces with the white supremacists. The Reverend Dr. M.L. Young of Memphis was praised by the racists as a staunch opponent to integration and "one among the first of his race to combat communism." Young explained his political poverty in this fashion: "When the Supreme Court came out with its decision and the word was handed down that everybody's gonna be integrated now, a lot of these folks like to had a baby. But I want to know: will desegregation be the answer to the progress of the Negro universally? . . . My approach is like that of Booker T. Washington. In no section of the country does the Negro enjoy the education, employment, and economic opportunities which the Negroes in the South enjoy." James Graham Cook, The Segregationists (New York: Appleton-Century-Crofts, 1962), p. 322.
. William Robert Miller, Martin Luther King, Jr.: His Life, Martyrdom And Meaning for The World (New York: Avon Books, 1968), pp. 46-56.
. Ibid., pp. 56-58.
. Ibid., pp. 104, 109, 150, 191; Hannah Lees, "Boycott in Philadelphia," Jay David, ed., Black Defiance: Black Profiles in Courage (New York: William Morrow, 1972), pp. 162-169.
. Miller, Martin Luther King, Jr., p. 103.
. August Meier, "On the Role of Martin Luther King," New Politics, Vol. 4 (Winter, 1965), pp. 52-59.
. Martin Luther King, Jr., "Letter from Birmingham Jail," The Christian Century (June 12, 1963); Liberation (June, 1963); also see King, Why We Can't Wait (New York: Harper and Row, 1964), chapter five.
. Miller, Martin Luther King, Jr. pp. 66, 108, 137, 260.
. Cruse, The Crisis of the Negro Intellectual, p. 322.
. Meier and Rudwick, CORE, p. 120.
. Ibid., pp. 270-271.
. James Baldwin, 'The Dangerous Road Before Martin Luther King," Harper's Magazine (February, 1961), p. 42; Miller, Martin Luther King, Jr., pp. 107-108.
King's rejection of communism was based on his religious conviction that divine laws set all standards of justice. A Marxist society, he believed, is based on "no divine government, no absolute moral order." As a result, "almost anything—force, violence, murder, lying—is a justifiable means to the 'millenial' end." See Martin Luther King, Strength to Love, (New York: Pocket Books, 1964), pp. 114-118.
. Steven F. Lawson, Black Ballots: Voting Rights in the South, 1944-1969 (New York: Columbia University Press, 1976), pp. 104-105.
. Meier and Rudwick, CORE, pp. 64-65.
"It was the liberals," Hugh T. Murray argues, "who refused to compromise on the Communist issue. Liberals might compromise with anyone else, sheriffs of Mississippi, bombers of Vietnam, blockaders of Cuba, invaders of Santo Domingo, anyone else except Communists." Middle-class Blacks excluded "Communists and then anyone suspected of being one, even when the result was bitterness, dissension . . . or denial of needed aid." See Murray's review essay of Meier and Rudwick, CORE, in Freedomways, Vol. 14 (First Quarter, 1974), pp. 62-66.
. Julius Lester, Look Out, Whitey/ Black Power's Gon' Get Your Mama! (New York: Grove Press, 1968), p. 79.
. Harry Golden, Mr. Kennedy and the Negroes (Greenwich, Connecticut: Fawcett, 1964), p. 43.
. Allen, Black Awakening in Capitalist America, p. 12.
. Harold Cruse, Rebellion Or Revolution? (New York: William Morrow, 1968), pp. 60-62.
. Ibid., p. 128.
. Jones, Home: Social Essays, pp. 138-139.
. Stokely Carmichael and Charles V. Hamilton, Black Pawer: The Politics of Liberation in America (New York: Vintage, 1967), p. 50.
. Allen, Black Awakening in Capitalist America, pp. 126-127.
. Lester, Look Out, Whitey/ Black Power's Gon' Get Your Mama! pp. 79, 106-107.
Until 1966, King continued to consider the Johnson Administration, liberal corporate contributions to SCLC, NAACP, and other Black groups as allies in the desegregation struggle. SNCC, on the other hand, viewed "the liberal corporate Establishment as the main but often faraway enemy," and accepted Malcolm's definition of America as simply "one large Mississippi." See Paul Jacobs and Saul Landau, eds. The New Radicals (New York: Vintage, 1966), p. 17.
. Allen, Black Awakening in Capitalist America, p. 12.
. Ibid., p. 111.
. Carmichael, Stokely Speaks, p. 58.
. Miller, Martin Luther King, Jr., p. 236.
. Ibid., pp. 267, 272, 280; Carl T. Rowan, "Martin Luther King's Tragic Decision." Reader's Digest (September, 1967), p. 42.
. "Interview with Louis B. Stokes," in Emily Rovetch, ed., Like It ls (New York: E.P. Dutton, 1981), p. 42.
. Antonio Gramsci, The Modern Prince and Other Writings (New York: International Publishers, 1970), pp. 90-91.
. Ibid., pp. 63, 72.
. Marable, Blackwater, pp. 14-50.
. Gramsci, The Modern Prince, p. 77.
. Ibid., p. 76.
The great danger in Christianity as in all forms of human spirituality is that it all too often blocks the ability for the oppressed to comprehend the political and economic reasons for their victimization. A vivid and particularly sad example of this is illustrated in a letter of one Black man on Death Row in Mississippi, written to the Jackson Advocate: "I've been here at Parchman Prison on Death Row for five months and fifteen days. Twelve human beings sentenced me to the penalty of Death for a crime that I did not commit. And today I found out the true and real reason I'm here on Death Row. It's really a good reason; the reason has brought so much joy unto me this very day. I've found God. Yes, God sent me to Death Row so that I may see His light because but through Him only can a person be born again. I'm here in prison because I failed to see my true job in life and that job is to help God in the work that will never be finished and that is saving souls of lost sinners. Praise the Lord." Jackson Advocate (January 28-February 3, 1982).
THE DESTRUCTION OF BLACK EDUCATION
. DuBois' estimate of the number of Blacks who were literate in 1865 was 5 percent. DuBois, Black Reconstruction in America, 1860-1880 (New York: Atheneum, 1971), p. 638.
. DuBois, "Reconstruction and Its Benefits," American Historical Review, Vol. 15 (July, 1910), p. 797.
. "Table 66, Persons 18 to 24 Years Old Enrolled in College,"; and "Table 72, Historically Black Colleges and Universities by Region and Period Founded," in The Social and Economic Status of the Black Population, pp. 90, 96; W. Hardin Hughes, "The Negro and Education," in Jessie P. Guzman, ed., Negro Year Book: A Review of Events Affecting Negro Life 1941-1946 (Tuskegee Institute: Tuskegee Institute Department of Records, 1947), pp. 54-108.
. Marable, From The Grassroots, p. 194.
. Vincent Harding, "The Vocation of the Black Scholar," in Institute of the Black World, ed., Education and Black Struggle: Notes from the Colonized World (Cambridge: Harvard Educational Review, 1974), pp. 3-29.
. The inevitable retrenchment of the white university establishment against Black studies programs was not entirely unanticipated. In June, 1970, historian Eugene Genovese observed that "most campus liberals who were falling all over themselves to placate . . . Black students were unprincipled scoundrels whose fancy rhetoric disguised an overriding commitment to peace and quiet at any price. As soon as they realized their error in thinking that doles, third-rate educational programs, and fireworks would buy peace—as soon as they learned that black students wanted a serious education . . . then these same liberals would send for troops to restore the peace and quiet that alone interest them." Eugene D. Genovese, In Red and Black: Marxian Explorations in Southern and Afro-American History (New York: Vintage, 1971), pp. 228-229.
. Reginald Stuart, "New Trend in College Desegregation Emerges," New York Times (September 3, 1981).
. Marable, Blackwater, pp. 151-152.
. "Bush At Tuskegee," Black Belt Journal (April 20, 1981).
. Stuart, "New Trend in College Desegregation Emerges."
. Ibid.; and "Teachers on Mainly Black Campus Warned to Earn Doctorates," New York Times (August 26, 1981).
. Stuart, "New Trend in College Desegregation Emerges."
. Harlan, Booker T. Washington, p. 286.
. Louis R. Harlan, Separate and Unequal: Public School Campaigns and Racism in the Southern Seaboard States, 1901-1915 (Chapel Hill: University of North Carolina Press, 1958), pp. 104-105; Mary Berry, Black Resistance, White Law: A History of Constitutional Racism in America (Englewood Cliffs, New Jersey: Prentice-Hall, 1971), p. 180.
. Steven Roberts, "House, by 265 to 122, Votes to End Justice Department Role in Busing Case," New York Times (June 10, 1981).
. "Teachers on Mainly Black Campus Warned to Earn Doctorates."
. Rodney, How Europe Underdeveloped Africa, pp. 300-303.
. Thomas A. Brooks, Toil and Trouble: A History of American Labor (New York: Dell Publishing Company, 1971), p. 245.
. DuBois, The Education of Black People, p. xi.
. Benjamin Quarles, Black Abolitionists (New York: Oxford University Press, 1969), p. 201. Also see Martin R. Delaney, The Condition, Elevation, Emigration and Destiny of the Colored People of the United States (New York: Arno Press, Reprint of the 1852 edition, 1968).
. Harding, ''The Vocation of the Black Scholar," p. 25.
THE MEANING OF RACIST VIOLENCE IN LATE CAPITALISM
. W. E.B. DuBois, "The Future of the Negro Race in America," East and the West, (January, 1904), pp. 4-19.
. DuBois, syndicated column, Amsterdam News (September 18, 1943).
. Cruse, The Crisis of the Negro Intellectual, pp. 344, 448.
. Sidney M. Willhelm, Who Needs the Negro? (Garden City, New York: Anchor Books, 1971),pp. 332-334.
. Paul C. Bermanzohn and Sally A. Bermanzohn, The True Story of the Greensboro Massacre, (New York: Cesar Cause Publishers, 1980).
. Marable, Blackwater , p. 151.
. Vincent Baker, "Racism and Violence," Big Red (March 21, 1981).
. Frank Elam, "Mobile lynching: White men cleared," Guardian (June 17, 1981).
. "Lynchings in the Mississippi Delta, 1980-1981," Racially Motivated Random Violence, (May/June, 1981). Tallachatchie County was also the site of the famous Emmitt Till murder. The town of Tutwiler, where Gray's body was found, has no active NAACP chapter. No Blacks serve on the city council or the school board.
. Tony Brown, "57 Percent Say Some Black Leaders Selfishly Formented Hysteria," Jackson Advocate (September 17-23, 1981).
. See Mack Jones, "Black Political Empowerment in Atlanta: Myth and Reality," Annals (September, 1978), pp. 90-117.
. Stanley Crouch, "Atlanta Reconstructed," Village Voice (April 29, 1981), pp. 17-18; New York Daily News (May 3, 1981).
. "Atlanta Officials Harass Victims," Guardian (June 17, 1981); "Fear Alters Atlantans' Summer Plans," New York Times (June 5, 1981); interview with Jan Douglas, director, Community Relations, Atlanta, Georgia, September 30, 1981.
. Raymond Coffey, "Racial Views on Atlanta Killings," Chicago Tribune (May 29, 1981).
. Tom Fiske, "Atlanta Blacks Assert Right to Self-Defense," Militant (April 3, 1981).
. "Profound Outrage, Revolutionary Stirrings Over Atlanta," Revolutionary Worker (March 20, 1981); Lionel Cuffie, "Who's Killing Atlanta Children?" Militant (April 3, 1981).
. Frank Elam, "5000 Rally in D.C. to Defend Atlanta's Children," Guardian (June 3, 1981); Suzanne Haig, "D.C. Rally: Stop Racist Terror in Atlanta," Militant (June 5, 1981).
. James H. Cleaver, "Dick Gregory's Theory in Atlanta Deaths Gains Credence," Charleston Chronicle (May 30, 1981)
. Wendell Rawls, Jr., "Washington Rally Marks Atlanta Murders," New York Times (May 26, 1981).
. Coffey, "Racial Views on Atlanta Killings."
. Editorial, "If Those Kids Were White," Big Red (March 28, 1981). Columnist William Raspberry also denounced the Washington, D.C. rally as a "display of futility." Washington Post (June 1, 1981).
. Southern Advocate (April, 1981).
. Kevin O. Fitzpatrick, "Serious Questions Raised in Police Slaying Investigation," Michigan Chronicle (March 28, 1981).
. Barney Blakeney, "Minister Concerned With Lack of Local Interest for Charleston Women in Sex Abuse Case in Summerville," Charleston Chronicle (March 7, 1981).
. Racially Motivated Random Violence, (September/October, 1981), pp. 5-6.
. Cleveland Call and Post (June 27, 1981).
. Patricia Tatum, "FBI, NAACP enter case of county man slain by cop." Baltimore Afro-American (August 1, 1981).
. James H. Cleaver, "Chief Daryl Gates Must Go—Right Now!" Los Angeles Sentinel (May 13, 1982); Charles P. Wallace, "Blacks More Susceptible to Chokeholds?" Los Angeles Times, (May 8, 1982); David Johnston, "Bradley Orders Probe of Statements by Gates," Los Angeles Times (May 11, 1982).
Gates ordered his department's personnel and training division to determine if Blacks were more vulnerable to injury from chokeholds than whites. Gates declared to the press, "We may be finding that in some Blacks when it is applied the veins or arteries do not open up as fast as they do on normal people. There may be something arresting the ability of the blood to flow again (after the hold is applied)."
. Chicago Defender (March I6, 1981); Pat Bryant, "Racism Swings in Mobile Trees," Atlanta Voice (April 25, 1981); Cleveland Call and Post (May 2, 1981).
. The following examples are documented in Racially Motivated Random Violence (November, 1981).
. Tom Hentoff, "200 rally against racism and rightism," Wesleyan Argus (October 13, 1981); Mary Beth Bruno, "KKK reported on campus" and "Campbell addresses assembly on racism," Wesleyan Argus (November 3, 1981); Mark Sirota, Susan Lepselter and Melissa Hendricks, "Campus reacts to racist poster," Wesleyan Argus (October 27, 1981).
The events at Wesleyan were mirrored at dozens of other college campuses. In the winter of 1979, a group of white students at the University of San Francisco launched the "Society of White Students," a campus group dedicated to preserve and defend "white culture." Whites defaced Black students' posters with the racist epithets "nigger" and "jungle bunny." A series of cross burnings occurred at Purdue University in 1980, and the funds for Black Student Unions were reduced or eliminated at many institutions. See Manning Marable, "Neo-Racism: The White Shadow," Politics and Education, Vol. 2 (Spring, 1980), pp. 19-22; Marable, Blackwater, p. 151.
. Alexander L. Taylor, "Hard Times on Main Street," Time (October 26, 1981).
. Paul Sweezy and Harry Magdoff, "The Deepening Crisis of U.S. Capitalism," Monthly Review (October, 1981), pp. 12, 15.
. Kenneth B. Noble, "The Surge in Business Failures," New York Times (November 18, 1981); Thomas L. Friedman, "Sag in Home Prices May Affect Families' Investing," New York Times (November 16, 1981); Robert Lindsey, "More Families Losing Homes as Inflation and Jobless Rate Soar," New York Times (November 28, 1981.)
. Daniel Patrick Moynihan, "Memo to Nixon on the Status of Negroes, January 16, 1970." New York Times (March 1, 1970); U.S. Department of Labor, Bureau of Labor Statistics, The Social and Economic Status of Negroes in the United States , 1970, Report no. 394 (Washington, D.C.: Government Printing Office, 1971).
The urban fiscal crisis within the framework of a racist/capitalist state also manifests itself as a racial crisis. In New York City, for example, 3.5 million jobs were destroyed between 1953 and 1973, primarily in manufacturing. Significantly, the prime sectors of job growth during these two decades were in government and highly skilled selected services. The dual labor market process meant that whites continued to occupy positions in the most highly paid sectors, while Puerto Ricans and Afro-Americans assumed the burden of burgeoning unemployment in manufacturing. As petty bourgeois whites and the "professional-managerial class" fled to the suburbs, city tax revenues declined. New businesses that relocated in New York tended to be capital intensive, not labor intensive. The result of the transformation of the city's labor market meant higher Black-on-Black crime, diminished city services for minority communities, and an increased polarization between the races. See Arthur Paris, "Hidden Dimensions of the New York City Fiscal Crisis," Review of Black Political Economy, Vol. 10 (Spring, 1980), pp. 262-278; William K. Tabb. 'The New York City Fiscal Crisis," in William K. Tabb and Larry Sawers, eds., Marxism and the Metropolis: New Perspectives in Urban Political Economy (New York: Oxford University Press, 1978), pp. 241-266; Charles Brecher, Where Have All the Dollars Gone? Public Expenditures for Human Resource Development in New York City, 1961-1971 (New York: Praeger, 1974).
. Reich, Racial Inequality, p. 6.
. "A Communist Proposal for a United Front Against War and Racism," Line of March, Vol. I (March-April, 1981), p. 24; Michael Parenti and Carolyn Kazdin, "The Untold Story of the Greensboro Massacre," Monthly Review, Vol. 33 (November, 1981), pp. 42-50; Bermanzohn and Bermanzohn, The True Story of the Greensboro Massacre.
The closest historical parallel to the Greensboro slayings might be the execution of Leo Frank in Georgia, August 16, 1915. Frank, a Jew, was accused and convicted of slaying a white fourteen-year-old girl, in a trial characterized by the cry for the blood of the "Jew pervert." Governor John M. Slaton commuted the death sentence on the day before his term in office ended. Twenty five armed men entered the state prison, took Leo Frank out, and hanged him. "A heel was repeatedly ground into the dead man's face, and bits of his clothing and of the rope were distributed as souvenirs." The new Georgia governor and mayor of Atlanta defended the lynching. Former Populist Tom Watson declared, "The next Jew who does what Frank did is going to get exactly the same thing that we give to Negro rapists." The Frank case was a key reason for the resurrection of the Ku Klux Klan in 1915, and formed the ideological basis for the infamous "Red Summer of 1919." See C. Vann Woodward, Tom Watson: Agrarian Rebel (New York: Oxford University Press, 1970), pp. 435-450.
. Thomas Weisskopf, "The Current Economic Crisis in Historical Perspective," Socialist Review (May-June, 1981), p. 49; Sam Bowles, "The Trilateral Commission: Have Capitalism and Democracy Come to a Parting of the Ways?" URPE, ed., U.S. Capitalism in Crisis (New York: URPE, 1978). Also see Terry Cannon, "Reviving McCarthyism in Washington," Political Affairs, Vol. 60 (October, 1981), pp. 20-25.
. Harry Ring, "A Military Coup the best we could hope for?" Militant (November 27, 1981).
. Irving Kristol, "Will Conservative Economics Work?" Wall Street Journal (October 24, 1979). Yale professor James Tobin, the 1981 winner of the Nobel Prize, has predicted that Reaganomics "will have devastating effects on the finances of many state and local governments and on the services they render, especially to the poor. In the end, I think, a democratic policy will not tolerate in its government and central bank an economic strategy of indifference to the real state of the economy." This articulates the assumption, held by many liberal Democrats and democratic socialists in the U.S., that the capitalist state will not resort to extralegal or extraordinary means to discipline labor or to restore capitalist profits at the expense of the democratic process. James Tobin, "Reaganomics and Economics," New York Review of Books, Vol. 28 (December 3, 1981) p. 14.
. Les Evans, ed. Disaster in Chile: Allende's Strategy and Why it Failed (New York: Pathfinder, 1974), pp. 104-105; Paul E. Sigmund, The Overthrow of Allende and the Politics of Chile, 1964-1976 (Pittsburgh: University of Pittsburgh Press, 1977), p. 212; Luis Corvalan, "The Unarmed Road of the Revolution: How It Worked Out in Chile," Political Affairs, Vol. 58 (July, 1978), pp. 21-29.
It is of some importance to American progressives to analyze critically the U.S. state's role in the brutal murder of Allende, the military overthrow of Chile's democratic socialist government, and the subsequent installation of a pro-American, fascist regime. From the moment Allende achieved the presidency in a democratic election on September 4, 1970, U.S. ambassador Edward Korry wrote frantically to the Nixon administration: "Chile voted calmly to have a Marxist-Leninist state, the first nation in the world to make this choice freely and knowingly . . . It will have the most profound effect on Latin America and beyond; we have suffered a grievous defeat; the consequences will be domestic and international." Henry Kissinger, then Nixon's National Security Adviser, later wrote that "Allende's election was a challenge to our national interest. We did not find it easy to reconcile ourselves to a second Communist state in the Western Hemisphere." Covert action by the CIA was required to check Allende's "hostility to the United States and his patent intention to create in effect another Cuba . . . Allende's success would have had implications also for the future of Communist parties in Western Europe, whose policies would inevitably undermine the Western Alliance whatever claims of respectability." Kissinger, White House Years (Boston: Little, Brown, 1979), pp. 653, 654, 656-657.
. Michael Billig and Andrew Bell, "Fascist Parties in Post-War Britain," Race Relations Abstracts, Vol. 5 (February, 1980), pp. 1-30; G. Weightman, "Red roses and drums," New Society (April 28, 1977); "Right, righter, rightest," The Economist (April 14, 1979); "Tyndall's Sentimental Journey," Searchlight, No. 53 (September, 1979), pp. 3-5.
The politics of Reaganism and the New Right is a phenomenon of political retrenchment, crude racism and capitalist reaction that is evident not only in the U.K. and the U.S., but across Western Europe. In the Netherlands, Italy, France, West Germany and Switzerland, the extreme right since the late 1960s has been organized specifically against nonwhite or colored immigrants and migrant workers. The cutting edge of neoconservatism is not Nazism or fascism in the classical sense, but white supremacy. See Christopher T. Husbands, "Contemporary Right-Wing extremism in Western European Journal of Political Research, Vol. 9 (March, 1981), pp. 75-99.
. Peggy Kahn, "Thatcher's Assault on the Unions," Socialist Review, Vol. 10 (September-October, 1980), p. 55.
Thatcher's Conservative government has even gone as far as to deny that the racial uprisings in south London's Brixton neighborhood in April, 1981, were caused by racism. British police are "not on the whole racist." "London Melee Not Race Riot, Study Says," New York Times (November 26, 1981).
. Scott Anderson, "Black Liberation Army, White Left Ties Used to Justify Government Crackdown, Obadele Says," Milwaukee Courier (November 7, 1981); "Conflicts, Brinks, Boston and RNA," Jackson Advocate (November 5-11, 1981); "Case Against Fulani Ali Collapses," Mississippi Enterprise (November 14, 1981); Wes Miller, "Sunni-Ali Blames 'Fascist State' for Her Arrest," Jackson Advocate (November 12-18, 1981); Nelson Gonzalez, "Black Leaders Condemn FBI Terrorism Smear," Militant (November 13, 1981); Nelson Gonzales, "Black Activist released, terrorism smear continues," Militant (November 20, 1981).
. Mike Wyman, "Black August Activists Raided," Guardian (November 11, 1981).
. Michael Kozak, "Anti-Apartheid activists framed up in Albany," Militant (October 30, 1981); William Robinson, "Springboks Hounded Out of U.S. ," Guardian (October 7, 1981).
. Malik Miah, "Black Party Sued in Affirmative-Action Fight," Militant (November 27, 1981).
. Georgi Dimitrov, Report to Seventh Comintern Congress, 1935, quoted in Palmira Togliatti, Lectures on Fascism (New York: International Publishers, 1976), pp. 1-2.
. It is paramount to distinguish between the traditional racism of Jim Crow and Southern segregation of the late nineteenth to mid-twentieth century with the new racist "counter-revolutionary" movement that exists now. James Boggs correctly characterizes the current mood: "Every day that the crisis of inflation, mass unemployment and barbarism in all our social relationships grows worse, more and more Americans are joining or following these counter-revolutionary organizations. These organizations are led by very calculating and political individuals who are skillfully playing on the fears, frustrations and prejudices of middle America. There are a lot of white Americans who have the illusion that America can go back to where it used to be . . . just as there are a lot of Black Americans who have the illusion that we can go back to struggling only against racism when the only solution to our problems has become the struggle against capitalism." James Boggs, "From Racism to Counter-Revolution," speech in Milwaukee, Wisconsin, November 1, 1980.
. Bernard Bailyn, The Ideological Origins of the American Revolution (Cambridge: Harvard University Press, 1967), pp. 144-159; David B. Davis, The Slave Power Conspiracy and the Paranoid Style (Baton Rouge: Louisiana State University Press, 1969), pp. 3-5, 76.
. Louis Althusser, For Marx (New York: Vintage, 1970), p. 67; Louis Althusser and Etienne Balibar, Reading Capital (London: Verso, 1979), p. 25.
. Marable, Blackwater, pp. 69-77.
. See Jerry Hirsh, "To 'Unfrock the Charlatans'," Race Relations Abstracts, Vol. 6 (May, 1981), pp. 1-65.
. The National Advisory Commission on Civil Disorders, Report of the National Advisory Commission on Civil Disorders, (New York: Bantam Books, 1968), p.2.
CONCLUSION: TOWARD A SOCIALIST AMERICA
. Rodney, How Europe Underdeveloped Africa, p. 7.
. The extreme left wing of the French Revolution, the Babouvists, mapped out a plan to seize control of society without any real democratic participation of the working class. A half century later, the Blanquists argued that a militant vanguard should seize state power in the name of the masses. See Blanqui, Textes Choisis (Paris: Editions Sociales, 1955); Babeuf, Textes Choisis (Paris: Editions Sociales, 1965); David McLellan, Karl Marx: His Life and Thought (New York: Harper and Row, 1973), pp. 155, 168, 170, 187. An elitist dictatorship which exercises authority in the "name of the people" has no relationship with genuine socialist democracy or workers' power.
. Boggs and Boggs, Revolution and Evolution in the Twentieth Century, p. 260.
. Carl Boggs, "Gramsci and Eurocommunism," Radical America, Vol. 14 (May-June, 1980), pp. 15-16.
. Marable, Blackwater, pp. 171-186.
. This point cannot be overemphasized. Social democrats tend to substitute white students and professionals for the traditional working class. They develop reformist programs which concentrate on "quality of life concerns," such as the environment and the issue of nuclear power, which are valid issues, but not of the nature which can generate the immediate and profound concern of Blacks, Latinos and blue-collar workers. Neo-Bakuninists make the same error in the opposite direction by glorifying the "lumpenproletariat" as the motivative factor in socialist revolution.
. Cabral, Revolution in Guinea, p. 79.
. Boggs and Boggs, Revolution and Evolution in the Twentieth Century, pp. 260-261.
. James, The Black Jacobins, p. 127.
. Karl Marx, The Eighteenth Brumaire of Louis Bonaparte (New York: International Publishers, 1975), p. 15.
. C.L.R. James, Modem Politics (Detroit: Bewick, 1973), p. 46.
. Ibid., p. 155.
Tables
Census data on Black Americans is notoriously unreliable in many respects. Yet when taken into perspective with other factors, it can provide critical insights into the material conditions of Blacks in the United States. The social scientist who tacitly accepts the quantitative research of the U.S. government without this caveat will inevitably succumb to the ideological hegemony of the state vis-á-vis any alternative framework of analysis.
-Manning Marable
About the author
Manning Marable (1950–2011) was a professor of history, public affairs, and African-American Studies at Columbia University. Marable authored fifteen books including Malcolm X: A Life of Reinvention, for which he won the Pulitzer Prize for History.
Leith Mullings is a distinguished professor of anthropology at the Graduate Center CUNY. She is an anthropologist, author, lecturer and educator. Her Web site is http://leithmullings.com.
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\section{Introduction}
\noindent In 1968 George Mostow published his famous Rigidity Theorem \cite{MR0236383}: if $M_1$ and $M_2$ are two closed oriented hyperbolic manifolds of dimension $n\ge 3$ and $f\colon\pi_1(M_1)\to\pi_1(M_2)$ is a group isomorphism, then there exists a unique isometry $M_1\to M_2$ inducing $f$. This can be reformulated as a statement about lattices in the orientation-preserving isometry groups $\operatorname{PSO}(1,n)$ of hyperbolic $n$-space $\mathbf{H}^n$:
\begin{Thrm}[Mostow] Let $n\ge 3$ and let $\Gamma_1,\Gamma_2\subset\operatorname{PSO}(1,n)$ be cocompact lattices. Let $f\colon\Gamma_1\to\Gamma_2$ be an isomorphism of abstract groups. Then $f$ is conjugation by some element of the full isometry group $\operatorname{PO}(1,n)$ of $\mathbf{H}^n$, in particular $f$ extends to an algebraic automorphism of $\operatorname{PSO}(1,n)$.
\end{Thrm}
This has later been generalised by various authors; in particular, the condition that $\Gamma_j$ be cocompact can be weakened to having finite covolume, see \cite{MR0385005}. The condition that $n\neq 2$, however, is necessary: two-dimensional hyperbolic manifolds are the same as hyperbolic Riemann surfaces, which are well-known to admit deformations.
As a model for the hyperbolic plane take the upper half-plane $\mathfrak{H}=\{\tau\in\mathbb{C}\mid\operatorname{Im}\tau >0\}$, so its orientation-preserving isometry group becomes identified with $\operatorname{PSL} (2,\mathbb{R} )$ via M\"{o}bius transformations. In this article we prove that a variant of Mostow Rigidity does hold in $\operatorname{Isom}^+(\mathfrak{H})=\operatorname{PSL} (2,\mathbb{R} )$ if we restrict ourselves to a certain class of lattices, for which congruence subgroups are defined, and demand that the group isomorphism preserves congruence subgroups.
We first state our result in the simpler case of arithmetic groups. Recall that given a totally real number field $k\subset\mathbb{R}$, a quaternion algebra $B$ over $k$ which is split over the identity embedding $k\to\mathbb{R}$ and ramified over all other infinite places of $k$, an order $\mathrsfs{O}\subset B$ and an isomorphism $\varphi\colon B\otimes_k\mathbb{R}\to\mathrm{M}(2,\mathbb{R} )$ we obtain a group homomorphism $\varphi\colon\mathrsfs{O}^1\to\operatorname{PSL} (2,\mathbb{R} )$ whose image is a lattice, where $\mathrsfs{O}^1$ is the group of units in $\mathrsfs{O}$ with reduced norm one. A lattice $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ is called \emph{arithmetic} if $\Gamma$ is commensurable to some such $\varphi (\mathrsfs{O}^1)$.
For a nonzero ideal $\mathfrak{n}\subset\mathfrak{o}_k$ we then define the \emph{principal congruence subgroup}
$$\mathrsfs{O}^1(\mathfrak{n})=\{ b\in\mathrsfs{O}^1\mid b-1\in\mathfrak{n}\cdot\mathrsfs{O}\} .$$
If $\Gamma$ contains a subgroup of finite index in $\varphi (\mathrsfs{O}^1)$ we set $\Gamma (\mathfrak{n})=\Gamma \cap\varphi (\mathrsfs{O}^1(\mathfrak{n}))$, and a subgroup of $\Gamma$ is a \emph{congruence subgroup} if it contains some $\Gamma (\mathfrak{n})$.
\begin{Thrm}[special case of Theorem A below]
Let $\Gamma_1,\Gamma_2\subset\operatorname{PSL} (2,\mathbb{R} )$ be arithmetic Fuchsian groups, and let $f\colon\Gamma_1\to\Gamma_2$ be an isomorphism of abstract groups such that for every subgroup $\Delta\subseteq\Gamma_1$ of finite index, $\Delta$ is a congruence subgroup of $\Gamma_1$ if and only if $f(\Delta )$ is a congruence subgroup of $\Gamma_2$.
Then there exists $a\in\operatorname{PGL} (2,\mathbb{R} )$ such that $f$ is conjugation by $a$. In particular, $\Gamma_2=a\Gamma_1a^{-1}$.
\end{Thrm}
Now both the notion of congruence subgroup and our result can be extended to a larger class of Fuchsian groups.
For a subgroup $\Gamma\subseteq\operatorname{PSL} (2,\mathbb{R} )$ denote the preimage in $\operatorname{SL} (2,\mathbb{R} )$ by $\tilde{\Gamma }$. A lattice $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ is called \emph{semi-arithmetic} if $\operatorname{tr}^2\gamma$ is a totally real algebraic integer for each $\gamma\in\tilde{\Gamma }$; this notion is invariant under commensurability. It was introduced in \cite{MR1745404}, and many classes of Fuchsian groups are semi-arithmetic:
\begin{enumerate}
\item Arithmetic lattices are semi-arithmetic.
\item All Fuchsian triangle groups $\Delta (p,q,r)$ are semi-arithmetic. However, they fall into infinitely many commensurability classes, only finitely many of which are arithmetic, see \cite{MR0429744}.
\item In \cite{MR1745404} further examples of semi-arithmetic groups which are not arithmetic were constructed by giving explicit generators.
\item The theory of flat surfaces provides for another construction of semi-arithmetic groups. If $X$ is a closed Riemann surface and $\omega$ is a holomorphic one-form on $X$ which is not identically zero, a simple geometric construction yields the Veech group\footnote{The name first appeared in \cite{MR1397686} but these groups were studied before from different points of view, see \cite{MR1005006}.} $\operatorname{SL} (X,\omega )$ which is a discrete subgroup of $\operatorname{SL} (2,\mathbb{R} )$. In certain cases the Veech group is a lattice, and then its image in $\operatorname{PSL} (2,\mathbb{R} )$ is a semi-arithmetic group by \cite[Theorems 5.1, 5.2]{MR1992827} and \cite[Proposition 2.6]{MR2188128}. Veech groups are never cocompact, see \cite[p. 509]{MR2186246}, therefore a Veech group which is a lattice is arithmetic if and only if it is commensurable to $\operatorname{SL} (2,\mathbb{Z} )$.\footnote{For a complete characterisation of $(X,\omega )$ whose Veech group is arithmetic see \cite[Theorem 4]{MR1397686}.} In \cite{MR1992827} we find, for every real quadratic number field $k$, the construction of a lattice Veech group contained in $\operatorname{SL} (2,\mathfrak{o}_k)$ which is therefore semi-arithmetic but not arithmetic.
\end{enumerate}
Examples (ii) and (iv) intersect: in \cite[Theorem 6.12]{MR2680418} it is proved that all non-cocompact triangle groups $\Delta (p,q,\infty )$ are commensurable to some Veech group. On the other hand, cocompact triangle groups can never be Veech groups, and only finitely many of the examples in \cite{MR1992827} are commensurable with triangle groups.
The generalisation of the notion of congruence subgroups to semi-arithmetic groups is a bit involved; we refer the reader to section \ref{SectionSemiArithmetic}.
Now the conclusion of Theorem A does not hold for general semi-arithmetic groups; we need to impose one more condition which is the existence of a \emph{modular embedding}: let $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a semi-arithmetic subgroup and let $k$ be the number field generated by all $\operatorname{tr}^2\gamma$ with $\gamma\in\tilde{\Gamma }$. Then for every embedding $\sigma\colon k\to\mathbb{R}$ there exists a group embedding $i_{\sigma }\colon\tilde{\Gamma }\to\operatorname{SL} (2,\mathbb{R} )$, unique up to conjugation in $\operatorname{GL} (2,\mathbb{R} )$, such that $\operatorname{tr}^2i_{\sigma }(\gamma )=\sigma (\operatorname{tr}^2\gamma )$ for every $\gamma\in\tilde{\Gamma }$, see \cite[Remark 4]{MR1745404}. The original group $\Gamma$ is arithmetic precisely if no $i_{\sigma }(\tilde{\Gamma })$ for $\sigma$ different from the identity embedding contains a hyperbolic element. In general, let $\sigma_1,\ldots ,\sigma_r$ be those embeddings $\sigma$ for which $i_{\sigma }(\tilde{\Gamma })$ contains a hyperbolic element. Then the coordinate-wise embedding $(i_{\sigma_1},\ldots ,i_{\sigma_r})\colon\Gamma\to\operatorname{PSL} (2,\mathbb{R} )^r$ maps $\Gamma$ to an irreducible arithmetic group $\Lambda\subset\operatorname{PSL} (2,\mathbb{R} )^r$; for the precise construction see section \ref{SectionModularEmbedding}.
We note that if $\Gamma$ is not already arithmetic itself, it is mapped into $\Lambda$ with Zariski-dense image of infinite index; such groups are called \emph{thin}. This is essentially due to S.\ Geninska \cite[Proposition 2.1 and Corollary 2.2]{MR2968231}; we explain it below in Corollary \ref{SemiArithmeticAreThin}.
Now $\Lambda$ acts on $\mathfrak{H}^r$ by coordinate-wise M\"{o}bius transformations, and a \emph{modular embedding} for $\Gamma$ is then a holomorphic map $F\colon\mathfrak{H}\to\mathfrak{H}^r$ equivariant for $\Gamma\to\Lambda$.
\begin{enumerate}
\item If $\Gamma$ is arithmetic, then $r=1$ and $\Lambda$ contains $\Gamma$ as a finite index subgroup. We may take $F(\tau )=\tau$ as a modular embedding.
\item All Fuchsian triangle groups admit modular embeddings, see \cite[Theorem p. 96]{MR1075639}.
\item Most of the new examples of semi-arithmetic groups in \cite{MR1745404} do not admit modular embeddings, see \cite[Corollary 4]{MR1745404}.
\item Veech groups which are lattices always admit modular embeddings, see \cite[Corollary 2.11]{MR2188128}. This solves \cite[Problem 1]{MR1745404} which asks whether every Fuchsian group admitting a modular embedding is arithmetic or commensurable with a triangle group: there exist Veech groups which are neither\footnote{Almost all of McMullen's genus two examples in \cite{MR1992827} do the job: only finitely many real quadratic fields appear as invariant trace fields of triangle groups, so if $k$ is not among them, then any lattice Veech group with trace field $k$ cannot be commensurable to a triangle group, and it cannot be arithmetic either since it is not cocompact.}, but do admit modular embeddings.
\end{enumerate}
More generally, we say $\Gamma$ \emph{virtually admits a modular embedding} if some finite index subgroup of $\Gamma$ admits one.
\begin{MainTheorem}
For $j=1,2$, let $\Gamma_j\subset\operatorname{PSL} (2,\mathbb{R} )$ be semi-arithmetic lattices which virtually admit modular embeddings. Let $f\colon\Gamma_1\to\Gamma_2$ be an isomorphism of abstract groups such that for every subgroup $\Delta\subseteq\Gamma_1$ of finite index, $\Delta$ is a congruence subgroup of $\Gamma_1$ if and only if $f(\Delta )$ is a congruence subgroup of $\Gamma_2$.
Then there exists $a\in\operatorname{PGL} (2,\mathbb{R} )$ such that $f$ is conjugation by $a$. In particular, $\Gamma_2=a\Gamma_1a^{-1}$.
\end{MainTheorem}
This theorem will be proved in section \ref{SectionCongruenceRigidity}. It rests on the following result on congruence subgroups in semi-arithmetic groups, which may be of independent interest.
\begin{ThrmB}
Let $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a semi-arithmetic lattice satisfying the trace field condition\footnote{This is a technical condition which is always satisfied after passing to a finite index subgroup, see Definition \ref{DefTFC}.}, with trace field $k$. Then there exists a finite set $S(\Gamma )$ of rational primes with the following property:
\begin{enumerate}
\item If $\mathfrak{p}$ is a prime ideal in $k$ not dividing any element of $S(\Gamma )$, then $\Gamma /\Gamma (\mathfrak{p})\simeq\operatorname{PSL} (2,\mathfrak{o}_k/\mathfrak{p})$.
\item If $q$ is a rational prime power not divisible by any element of $S(\Gamma )$ and $\Delta$ is a normal congruence subgroup of $\Gamma$ with $\Gamma /\Delta \simeq\operatorname{PSL} (2,q)$, then there exists a unique prime ideal $\mathfrak{p}$ of $k$ of norm $q$ with $\Delta =\Gamma (\mathfrak{p})$.
\end{enumerate}
\end{ThrmB}
Here, (i) is a combination of Proposition \ref{CorollaryGammaLocallyCongruence} and Lemma \ref{OoneModOonepIsSLTwo}; (ii) is Proposition \ref{CongruenceQuotientsGivePrimes}.
In particular, the information which groups $\operatorname{PSL} (2,q)$ appear how often as congruence quotients determines the splitting behaviour of all but finitely many primes in $k$ (see Remark \ref{ReconstructionOfArithmeticSimilarityClass}). On the other hand, allowing noncongruence quotients we get many more finite groups. The collection of all these finite groups will determine the abstract isomorphism type of a Fuchsian lattice, but of course no more, see \cite[Theorem 1.1]{arxiv14013645}.
\begin{Outline}
In sections 2 and 3 we fix notations and recall standard results on the group $\operatorname{PSL} (2)$, both over the reals and over finite fields. In sections 4 and 5 we introduce semi-arithmetic subgroups of $\operatorname{PSL} (2,\mathbb{R} )$ and study their congruence subgroups. The object of section 6 is the deduction of a statement about $\operatorname{PSL} (2)$ from an analogous result for $\operatorname{SL} (2)$ by Culler and Shalen \cite[Proposition 1.5.2]{MR683804}: a finitely generated subgroup of $\operatorname{PSL} (2,\mathbb{R} )$ is determined up to conjugacy by its squared traces. This allows us to work with numbers instead of matrices in the remainder of the article. In section 7 we formally define modular embeddings and discuss some consequences of their existence. Then in section 8 the previous observations are used to prove Theorem A and the hard part of Theorem B. Section 9 presents an example with two arithmetic groups, sharpening the statement of Theorem A considerably in this special case. Finally section 10 discusses some possible and impossible generalisations.
\end{Outline}
\begin{Ackno}
This work is part of the author's ongoing dissertation project at the University of Bonn. He wishes to thank his supervisor, Ursula Hamenst\"{a}dt, for many fruitful discussions, and helpful comments on earlier versions of this article.
\end{Ackno}
\section{Traces on $\operatorname{PSL} (2)$ and M\"{o}bius Transformations}\label{SectionTraces}
\noindent For every ring $A$ we set $\operatorname{PGL} (2,A) = \operatorname{GL} (2,A) /A^{\times }$ where $A^{\times }$ is embedded by means of scalar matrices. We also set $\operatorname{PSL} (2,A)=\operatorname{SL} (2,A)/\{\pm\mathbf{1}\}$. There is an obvious homomorphism $\operatorname{PSL} (2,A)\to \operatorname{PGL} (2,A)$, but in general it is neither injective nor surjective.
Let $k$ be a field. The determinant homomorphism $\operatorname{GL} (2,k)\to k^{\times }$ descends to a homomorphism $\operatorname{PGL} (2,k)\to k^{\times }/(k^{\times })^2$, and we obtain a short exact sequence
\begin{equation}\label{SesPSL}
1\longrightarrow \operatorname{PSL} (2,k)\longrightarrow \operatorname{PGL} (2,k)\longrightarrow k^{\times }/(k^{\times })^2\longrightarrow 1.
\end{equation}
In particular, $\operatorname{PSL} (2,\mathbb{C} )$ and $\operatorname{PGL} (2,\mathbb{C} )$ are naturally isomorphic whereas for $k=\mathbb{R}$ or a finite field of odd characteristic, $\operatorname{PSL} (2,k)$ becomes identified with an index two normal subgroup of $\operatorname{PGL} (2,k)$.
Note that since $\operatorname{PSL} (2,k)$ is a normal subgroup of $\operatorname{PGL} (2,k)$, the latter operates faithfully on the former by conjugation. Since $\operatorname{tr} (-g)=-\operatorname{tr} g$, the squared trace map $\operatorname{tr}^2\colon\operatorname{SL} (2,k)\to k$ descends to a map
$$\operatorname{tr}^2\colon\operatorname{PSL} (2,k)\to k,\quad\{ g,-g\}\mapsto (\operatorname{tr} g)^2.$$
For $k=\mathbb{R}$ we also define
$$\lvert\operatorname{tr}\rvert\colon\operatorname{PSL} (2,\mathbb{R} )\to\mathbb{R},\quad \{ g,-g\}\mapsto\lvert\operatorname{tr} g\rvert .$$
Let $\mathfrak{H}=\{\tau\in\mathbb{C}\mid\operatorname{Im} (\tau )>0\}$ be the upper half-plane. The group $\operatorname{SL} (2,\mathbb{R} )$ operates on $\mathfrak{H}$ in the well-known way by M\"{o}bius transformations, descending to a faithful action by $\operatorname{PSL} (2,\mathbb{R} )$. This in fact identifies $\operatorname{PSL} (2,\mathbb{R} )$ with both the group of holomorphic automorphisms and that of orientation-preserving isometries (for the Poincar\'{e} metric) of $\mathfrak{H}$. Elements of $\operatorname{PSL} (2,\mathbb{R} )$ can be categorised by their behaviour on $\mathfrak{H}$, see \cite[section 1.3]{MR1177168}:
\begin{Proposition}
Let $\pm\mathbf{1}\neq g\in\operatorname{PSL} (2,\mathbb{R} )$. Then $g$ belongs to exactly one of the following classes:
\begin{enumerate}
\item $g$ is \emph{elliptic:} it has a unique fixed point in $\mathfrak{H}$, and $\operatorname{tr}^2 g<4$.
\item $g$ is \emph{parabolic:} it has a unique fixed point in $\mathbb{P}^1(\mathbb{R} )$, but not in $\mathfrak{H}$. Its squared trace satisfies $\operatorname{tr}^2 g=4$.
\item $g$ is \emph{hyperbolic:} it has two distinct fixed points in $\mathbb{P}^1(\mathbb{R} )$, one of them repelling and one of them attracting, but no fixed points in $\mathfrak{H}$. Its squared trace satisfies $\operatorname{tr}^2 g>4$.
\end{enumerate}
\end{Proposition}
\section{The Finite Groups $\operatorname{PSL} (2,q)$}\label{SectionFiniteGroups}
\noindent Next we study $\operatorname{PSL} (2)$ over finite fields. With $\mathbb{F}_q$ being the field of $q$ elements we also write $\operatorname{PSL} (2,q)$ instead of $\operatorname{PSL} (2,\mathbb{F}_q)$.
\begin{Proposition}
If $q>3$ is an odd prime power, $\operatorname{PSL} (2,q)$ is a simple group of order $\frac{1}{2}q(q^2-1)$. Furthermore $\operatorname{PSL} (2,q)\simeq\operatorname{PSL} (2,q')$ if and only if $q=q'$.
\end{Proposition}
\begin{proof}
The simplicity of $\operatorname{PSL} (2,q)$ is a well-known fact, see e.g.\ \cite[section 3.3.2]{MR2562037}. The order of $\operatorname{PSL} (2,q)$ is easily calculated using (\ref{SesPSL}), for instance. The function $q\mapsto \frac{1}{2}q(q^2-1)$ is strictly increasing on $\mathbb{N}$, therefore if $\operatorname{PSL} (2,q)$ and $\operatorname{PSL} (2,q')$ have the same orders, $q=q'$.
\end{proof}
As remarked in section \ref{SectionTraces}, $\operatorname{PGL} (2,q)$ operates by conjugation on $\operatorname{PSL} (2,q)$. Furthermore the Frobenius automorphism $\varphi\colon\mathbb{F}_q\to\mathbb{F}_q$ defined by $\varphi (x)=x^p$, where $p$ is the prime of which $q$ is a power, defines an automorphism $\varphi$ of $\operatorname{PSL} (2,q)$. The following is also well-known, see e.g.\ \cite[Theorem 3.2.(ii)]{MR2562037}:
\begin{Proposition}
The automorphism group of $\operatorname{PSL} (2,q)$ is generated by $\operatorname{PGL} (2,q)$ and $\varphi$.
\end{Proposition}
In particular if $q=p$ is a prime, then every automorphism of $\operatorname{PSL} (2,p)$ is the restriction of an inner automorphism of $\operatorname{PGL} (2,p)$, and the map $\operatorname{tr}^2\colon\operatorname{PSL} (2,p)\to\mathbb{F}_p$ is invariant under all automorphisms. So the following definition works:
\begin{Definition}\label{AbstractTraces}
Let $G$ be a finite group which is abstractly isomorphic to some $\operatorname{PSL} (2,p)$ for an odd prime $p$. Then the map $\operatorname{tr}_G^2\colon G\to\mathbb{F}_p$
is defined as follows: choose some automorphism $\alpha\colon G\to\operatorname{PSL} (2,p)$, then set $\operatorname{tr}_G^2=\operatorname{tr}^2\circ\alpha$.
\end{Definition}
If $p$ is replaced by a prime power $q$, the corresponding map on $G$ is only are well-defined up to automorphisms of $\mathbb{F}_q$, i.e.\ we may define a map $\operatorname{tr}_G^2\colon G\to\mathbb{F}_q/\operatorname{Aut}\mathbb{F}_q$.
\begin{Lemma}\label{LemmaOnFiniteGroups}
Let $n\in\mathbb{N}$ and let $q_1,\ldots ,q_n,q'$ be odd prime powers. Let
$$\beta\colon G=\operatorname{PSL} (2,q_1)\times\cdots\times\operatorname{PSL} (2,q_n)\to\operatorname{PSL} (2,q')$$
be a group epimorphism. Then there is a $1\le j\le n$ such that $q'=q_j$ and for some automorphism $\alpha$ of $\operatorname{PSL} (2,q')$ we can write $\beta =\alpha\circ\operatorname{pr}_j$, where $\operatorname{pr}_j$ is the projection on the $j$-th factor.
\end{Lemma}
\begin{proof}
By the Jordan--H\"{o}lder theorem, the only simple quotients of $G$ are the $\operatorname{PSL} (2,q_j)$, so $q'=q_j$ for some $j$.
We now proceed by induction on $n$. For $n=1$ the lemma is trivial, so assume the lemma has been proved for $n$. Let $\beta\colon G\to \operatorname{PSL} (2,q')$ be an epimorphism where $G$ has $n+1$ factors. For cardinality reasons it cannot be injective, so there exists some $g\in G\smallsetminus\{ 1\}$ with $\beta (g)=1$. Write $g=(g_1,\ldots ,g_{n+1})$, then $g_j\neq 1$ for some $j$; for simplicity of notation assume that $j=n+1$. Since $\operatorname{PSL} (2,q_{n+1})$ has trivial centre, there exists some $h_{n+1}\in G$ which does not commute with $g_{n+1}$. Then set
$$h=(1,\ldots ,1,h_{n+1})\in G$$
and compute
$$1=\beta(h)\beta(h^{-1})=\beta (ghg^{-1}h^{-1})=\beta (1,\ldots ,1,g_{n+1}h_{n+1}g_{n+1}^{-1}h_{n+1}^{-1})$$
using $\beta (g)=1$. That is, $\beta$ restricted to the $(n+1)$-st factor has nontrivial kernel. Since that factor is simple, the restriction of $\beta$ to the $(n+1)$-st factor has to be trivial, so $\beta$ factors through the projection onto the first $n$ factors, hence (by induction hypothesis) onto one of them.
\end{proof}
\section{Semi-Arithmetic Groups and their Congruence Subgroups}\label{SectionSemiArithmetic}
\noindent Let $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a lattice and let $\tilde{\Gamma }$ be its preimage in $\operatorname{SL} (2,\mathbb{R} )$. By $\Gamma^{(2)}$ we denote the subgroup of $\Gamma$ generated by all $\gamma^2$ with $\gamma\in\Gamma$. Since $\Gamma$ is finitely generated, $\Gamma^{(2)}$ is then a normal subgroup of finite index in $\Gamma$.
\begin{Definition}\label{DefTFC}
The \emph{trace field} of $\Gamma$ is the field $\mathbb{Q} (\operatorname{tr}\Gamma )\subset\mathbb{R}$ generated by all $\operatorname{tr}\gamma$ with $\gamma\in\tilde{\Gamma }$. The \emph{invariant trace field} of $\Gamma$ is the trace field of $\Gamma^{(2)}$.
A lattice $\Gamma$ satisfies the \emph{trace field condition} if its trace field and its invariant trace field agree.
\end{Definition}
Clearly the trace field contains the invariant trace field, but the two are not always equal. As the name suggests, the invariant trace field is the more useful invariant: commensurable lattices have the same invariant trace field, see \cite[Theorem 3.3.4]{MR1937957}, but not necessarily the same trace field.
Hence, if $\Gamma$ is any lattice then $\Gamma^{(2)}$ satisfies the trace field condition. Therefore any lattice has a finite index normal sublattice which satisfies the trace field condition.
\begin{Definition}
A lattice $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ is called \emph{semi-arithmetic} if its invariant trace field is a totally real number field and every trace $\operatorname{tr}\gamma$ for $\gamma\in\tilde{\Gamma }$ is an algebraic integer.\footnote{It follows from \cite[Lemma 3.5.6]{MR1937957} that this is equivalent to the definition given in the introduction.}
\end{Definition}
Being semi-arithmetic is stable under commensurability, therefore every semi-arithmetic lattice contains a semi-arithmetic lattice satisfying the trace field condition.
For the following constructions let $\Gamma$ be a semi-arithmetic lattice satisfying the trace field condition, and let $k=\mathbb{Q} (\operatorname{tr}\gamma )$. Then the sub-$k$-vector space $B=k[\Gamma ]$ of $\mathrm{M}(2,\mathbb{R} )$ generated by $\tilde{\Gamma}$ is in fact a sub-$k$-algebra, more precisely a quaternion algebra over $k$. The sub-$\mathfrak{o}_k$-algebra $\mathfrak{o}_k[\tilde{\Gamma }]$ of $B$ generated by $\tilde{\Gamma }$ is an order in $B$, though not necessarily a maximal one. We choose a maximal order $\mathrsfs{O}\supseteq\mathfrak{o}_k[\tilde{\Gamma }]$.
If $\mathrsfs{O}^1$ denotes the subgroup of $\mathrsfs{O}^{\times }$ consisting of elements with reduced norm one, $\tilde{\Gamma }$ becomes a subgroup of $\mathrsfs{O}^1$. Also write $\mathrm{P}\mathrsfs{O}^1 =\mathrsfs{O}^1/\{\pm\mathbf{1}\}$ so that $\Gamma$ is a subgroup of $\mathrm{P}\mathrsfs{O}^1$.
\begin{Proposition}\label{EquivalentCharacterisationsArithmetic}
Let $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a semi-arithmetic lattice satisfying the trace field condition. Then the following are equivalent:
\begin{enumerate}
\item $\Gamma$ is arithmetic.
\item Let $k=\mathbb{Q} (\operatorname{tr}\Gamma )\subset\mathbb{R}$. Then for every embedding $\sigma\colon k\to\mathbb{R}$ other than the identity inclusion and every $\gamma\in\tilde{\Gamma }$ one has $\lvert\sigma (\operatorname{tr}\gamma )\rvert\le 2$.
\item For every embedding $\sigma\colon k\to\mathbb{R}$ other than the identity inclusion, $B\otimes_{k,\sigma }\mathbb{R}$ is isomorphic to Hamilton's quaternions $\mathbb{H}$.
\item $\mathrm{P}\mathrsfs{O}^1$ is a discrete subgroup of $\operatorname{PSL} (2,\mathbb{R} )$.
\item The index $(\mathrm{P}\mathrsfs{O}^1 :\Gamma )$ is finite.
\end{enumerate}
\end{Proposition}
\begin{proof}
The equivalence (i) $\Leftrightarrow$ (ii) is the main result in \cite{MR0398991}; the other equivalences follow from the explicit classification of arithmetic lattices in $\operatorname{PSL} (2,\mathbb{R} )$, see e.g.\ \cite[chapter 5]{MR1177168} or \cite[chapter 8]{MR1937957}.
\end{proof}
Now we discuss congruence subgroups. For an elementary definition, let $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a semi-arithmetic lattice satisfying the trace field condition, and let $k$ and $\mathrsfs{O}$ be as above. Then every nonzero ideal $\mathfrak{a}$ of $\mathfrak{o}_k$ defines a subgroup
$$\tilde{\Gamma }(\mathfrak{a})=\{ \gamma\in\tilde{\Gamma }\mid\gamma-\mathbf{1}\in\mathfrak{a}\cdot\mathrsfs{O}\}$$
and its image $\Gamma (\mathfrak{a})$ in $\Gamma$, called the \emph{principal congruence subgroup} of level $\mathfrak{a}$. A \emph{congruence subgroup} of $\Gamma$ is then a subgroup containing some principal congruence subgroup. Similarly we define principal congruence subgroups $\mathrsfs{O}^1(\mathfrak{a})$ and congruence subgroups of $\mathrsfs{O}^1$.
These groups can also defined more abstractly using algebraic groups: there is a canonical linear algebraic group $H$ over $k$ with $H(k)=B^1$; we may define it functorially by setting $H(A)=(B\otimes_kA)^1$ for every $k$-algebra $A$. Then $H$ is a twisted form of $\operatorname{SL} (2)_k$. By Weil restriction of scalars we obtain an algebraic group $G=\operatorname{Res}_{k|\mathbb{Q} }H$ with a canonical identification $G(\mathbb{Q} )=H(k)=B^1$. Then $G$ is a twisted form of $\operatorname{SL} (2)_{\mathbb{Q} }^d$ where $d=[k:\mathbb{Q} ]$; in particular $G(\mathbb{C} )$ is isomorphic to $\operatorname{SL} (2,\mathbb{C} )^d$.
Choosing a faithful representation $G\to\operatorname{GL} (n)$ we can define a congruence subgroup in $G(\mathbb{Q} )$ to be one that contains the preimage of a congruence subgroup of $\operatorname{GL} (n,\mathbb{Z} )$ as a finite index subgroup. This notion of congruence subgroup is independent of the representation $G\to\operatorname{GL} (n)$, see \cite[Proposition 4.1]{MR2192012}; that it is equivalent to the more elementary one given before follows by taking the representation of $G\to\operatorname{GL} (4d)$ by left multiplication on $B$, the latter considered as a $(4d)$-dimensional $\mathbb{Q}$-vector space with the lattice $\mathrsfs{O}$.
Let $\mathbb{A}^f$ be the ring of finite ad\`{e}les of $\mathbb{Q}$ and endow $G(\mathbb{A}^f)$ with the ad\`{e}lic topology. Similarly let $\mathbb{A}_k^f$ be the ring of finite ad\`{e}les of $k$, then there is a canonical isomorphism $\mathbb{A}^f\otimes_{\mathbb{Q} }k=\mathbb{A}_k^f$ inducing $G(\mathbb{A}^f)=H(\mathbb{A}_k^f)$. The closure of $\mathrsfs{O}^1$ in $G(\mathbb{A}^f)$ can be identified with the completion of $\mathrsfs{O}^1$ with respect to all congruence subgroups; equivalently, with the group of elements of reduced norm one in the profinite completion of $\mathrsfs{O}$. Therefore we denote it by $\widehat{\mathrsfs{O}}^1$. It is a maximal compact open subgroup of $G(\mathbb{A}^f)$.
There is a canonical bijection between open subgroups of $\widehat{\mathrsfs{O}}^1$ and congruence subgroups of $\mathrsfs{O}^1$: with a congruence subgroup of $\mathrsfs{O}^1$ we associate its closure in $G(\mathbb{A}^f)$, and with an open subgroup of $\widehat{\mathrsfs{O}}^1$ we associate its intersection with $\mathrsfs{O}^1$. For the proof see again \cite[Proposition 4.1]{MR2192012}.
\begin{Proposition}[Strong Approximation for Semi-Arithmetic Groups]\label{StrongApproxSemiArithm}
The closure of $\tilde{\Gamma }$ in $G(\mathbb{A}^f)=H(\mathbb{A}_k^f)$ is open.
\end{Proposition}
\begin{proof}
First we claim that $\tilde{\Gamma }$ is Zariski-dense in $G$. It suffices to show that $\tilde{\Gamma }$ is Zariski-dense in $G(\mathbb{C} )\simeq\operatorname{SL} (2,\mathbb{C} )^d$, and the proof of an analogous but more complicated statement over the reals \cite[Proposition 2.1 and Corollary 2.2]{MR2968231} carries over mutatis mutandis.
Then we use a special case of a result of M.\ Nori \cite[Theorem 5.4]{MR880952}, see also \cite{MR735226}: if $G$ is an algebraic group over $\mathbb{Q}$ such that $G(\mathbb{C} )$ is connected and simply connected (which is the case for our $G$ since $\pi_1(\operatorname{SL} (2,\mathbb{C} ))=\pi_1(\operatorname{SU}(2))=\pi_1(S^3)=1$) and $\Gamma$ is a finitely generated Zariski-dense subgroup of $G(\mathbb{Q} )$ contained in some arithmetic subgroup of $G$, then the closure of $\Gamma$ in $G(\mathbb{A}^f)$ is open.
\end{proof}
\begin{Proposition}\label{CorollaryGammaLocallyCongruence}
There exists a nonzero ideal $\mathfrak{m}$ of $\mathfrak{o}_k$, depending on $\Gamma$, such that for every ideal $\mathfrak{a}$ of $\mathfrak{o}_k$ prime to $\mathfrak{m}$ the homomorphism
$$\tilde{\Gamma }\hookrightarrow\mathrsfs{O}^1\twoheadrightarrow\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{a})$$
is surjective, i.e.\ the canonical homomorphism
$$\Gamma /\Gamma (\mathfrak{a})\to\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{a})$$
is an isomorphism of finite groups.
\end{Proposition}
The proof uses several results that will be used later on, so we mention them separately.
\begin{Theorem}[Strong Approximation for Quaternion Algebras]
$G(\mathbb{Q} )=H(k)$ is dense in $G(\mathbb{A}^f)=H(\mathbb{A}_k^f)$.\footnote{Usually this result is phrased differently: if $\mathbb{A} =\mathbb{A}^f\times\mathbb{R}$ denotes the full ad\`{e}le ring, then $G(\mathbb{Q} )\cdot G(\mathbb{R} )$ is dense in $G(\mathbb{A} )$. But the latter is canonically isomorphic to $G(\mathbb{A}^f)\times G(\mathbb{R} )$ which shows the equivalence to our formulation.}
\end{Theorem}
For the proof see e.g.\ \cite[Theorem 7.12]{MR1278263}.
We shall now investigate the quotient groups $\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{a})$. These are best understood locally: if $\mathfrak{p}$ is a finite prime of $k$, we set $\mathrsfs{O}_{\mathfrak{p}}=\mathrsfs{O}\otimes_{\mathfrak{o}_k}\mathfrak{o}_{\mathfrak{p}}$. We can then consider the group $\mathrsfs{O}_{\mathfrak{p}}^1$ of its elements of norm one, and its congruence subgroups $\mathrsfs{O}_{\mathfrak{p}}^1(\hat{\mathfrak{p}}^r)$. Recall that $\mathrsfs{O}_{\mathfrak{p}}$ is a maximal order in $B_{\mathfrak{p}}$.
\begin{Proposition}
Let $\mathfrak{a}$ be an ideal of $k$ with prime factorisation $\mathfrak{a}=\mathfrak{p}_1^{r_1}\mathfrak{p}_2^{r_2}\cdots\mathfrak{p}_n^{r_n}$. Then the canonical homomorphism
\begin{equation}\label{CongruenceQuotientPrimeDecomposition}
\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{a})\to\prod_{j=1}^n\mathrsfs{O}_{\mathfrak{p}_j}^1/\mathrsfs{O}_{\mathfrak{p}_j}^1(\hat{\mathfrak{p}}_j^{r_j})
\end{equation}
is an isomorphism of groups.
\end{Proposition}
\begin{proof}
Injectivity is easy, so we only show surjectivity.
We use the description of $H(\mathbb{A}_k^f)$ as the restricted direct product of the completions $B_{\mathfrak{l}}^1=(B\otimes_kk_{\mathfrak{l}})^1$, restricted with respect to the compact subgroups $\mathrsfs{O}_{\mathfrak{l}}^1$. For $j=1,\ldots ,n$ take an element $x_j\in\mathrsfs{O}_{\mathfrak{p}_j}^1$. The Strong Approximation Theorem furnishes us with an element $\beta\in H(k)= B^1$ with the following properties:
\begin{itemize}
\item For $j=1,\ldots ,n$, $\beta$ considered as an element of $B_{\mathfrak{p}_j}^1$ is congruent to $x_j$ modulo $\mathrsfs{O}_{\mathfrak{p}_j}^1(\hat{\mathfrak{p}_j}^{r_j})$ (note that the latter is an open subgroup of $B_{\mathfrak{p}_j}^1$).
\item For each finite prime $\mathfrak{l}$ different from all $\mathfrak{p}_j$'s, $\beta$ is in $\mathrsfs{O}_{\mathfrak{l}}^1$.
\end{itemize}
Then $\beta\in\mathrsfs{O}^1$, and its class in the left hand side of (\ref{CongruenceQuotientPrimeDecomposition}) maps to $(x_1,\ldots ,x_n)$.
\end{proof}
Note that our proof also shows that the map
\begin{equation*}
\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{a})\to\prod_{j=1}^n\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{p}_j^{r_j})
\end{equation*}
is an isomorphism.
\begin{Corollary}\label{ChineseRemainderForPSL}
The canonical homomorphism
\begin{equation*}
\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{a})\to\prod_{j=1}^n\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{p}_j^{r_j})
\end{equation*}
is an epimorphism whose kernel is isomorphic to $(\mathbb{Z} /2\mathbb{Z} )^{d}$ for some $d<n$.
\end{Corollary}
\begin{proof}
The homomorphism $\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{p}_j^{r_j})\to\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{p}_j^{r_j})$ is always surjective, and it is injective precisely when $\mathfrak{p}_j^{r_j}$ divides $(2)$, otherwise it has kernel isomorphic to $\mathbb{Z} /2\mathbb{Z}$. Similarly the kernel of $\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{a})\to\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{a})$ is either trivial or $\mathbb{Z} /2\mathbb{Z}$. So the corollary follows from the remark preceding it.
\end{proof}
\begin{Corollary}\label{SurjectiveOnCoprime}
Let $\Delta\subseteq\mathrsfs{O}^1$ be a congruence subgroup, containing $\mathrsfs{O}^1(\mathfrak{m})$ for some ideal $\mathfrak{m}$ of $k$. Let $\mathfrak{a}$ be an ideal of $k$ which is coprime to $\mathfrak{m}$. Then the composition
$$\Delta\hookrightarrow\mathrsfs{O}^1\twoheadrightarrow\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{a})$$
is surjective.
\end{Corollary}
\begin{proof}
This is equivalent to the statement $\mathrsfs{O}^1(\mathfrak{m})\cdot\mathrsfs{O}^1(\mathfrak{a})=\mathrsfs{O}^1$, and this in turn follows from the isomorphism of finite groups
\begin{equation*}\mathrsfs{O}^1/(\mathrsfs{O}^1(\mathfrak{m})\cap\mathrsfs{O}^1(\mathfrak{a}))\to\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{m})\times\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{a}).\qedhere\end{equation*}
\end{proof}
\begin{proof}[Proof of Proposition \ref{CorollaryGammaLocallyCongruence}]
By Proposition \ref{StrongApproxSemiArithm} there exists some ideal $\mathfrak{m}$ of $k$ with $\mathrsfs{O}^1(\mathfrak{m})\subseteq\overline{\tilde{\Gamma}}$, where the latter denotes the closure of $\tilde{\Gamma }$ in $\widehat{\mathrsfs{O}}^1\subset G(\mathbb{A}^f)$. This does the job by Corollary \ref{SurjectiveOnCoprime}.
\end{proof}
\begin{Corollary}\label{CorChangingTheLevel}
Let $\mathfrak{a}$ and $\mathfrak{b}$ be two coprime ideals of $k$ which are both prime to $2$. Then the canonical homomorphism
\begin{equation*}
\mathrm{P}\mathrsfs{O}^1 (\mathfrak{a})/\mathrm{P}\mathrsfs{O}^1 (\mathfrak{ab})\to \mathrm{P}\mathrsfs{O}^1 / \mathrm{P}\mathrsfs{O}^1 (\mathfrak{b})
\end{equation*}
is an isomorphism.\hfill $\square$
\end{Corollary}
\section{Congruence Quotients of Semi-Arithmetic Groups}
\noindent Our next step is to determine the quotients on the right hand side of (\ref{CongruenceQuotientPrimeDecomposition}). This is done by distinguishing between the ramified and the unramified case. To simplify notation, let $K$ be a $p$-adic field with ring of integers $\mathfrak{o}_K$ and prime ideal $\mathfrak{p}=(\pi )$. Let $q=p^f$ be the cardinality of the residue class field $\kappa =\mathfrak{o}_K/\mathfrak{p}$. Let $B$ be an unramified quaternion algebra over $K$, and let $\mathrsfs{O}\subset B$ be a maximal order. We may assume that $B=\mathrm{M}(2,K)$ and $\mathrsfs{O}=\mathrm{M}(2,\mathfrak{o}_K)$; then $\mathrsfs{O}^1=\operatorname{SL} (2,\mathfrak{o}_K)$ and $\mathrsfs{O}^1(\mathfrak{p})$ is the kernel of the reduction map $\operatorname{SL} (2,\mathfrak{o}_K)\to\operatorname{SL} (2,\kappa )$.
\begin{Lemma}\label{OoneModOonepIsSLTwo}
Let $r\ge 1$. The reduction map $\operatorname{SL} (2,\mathfrak{o}_K)\to\operatorname{SL} (2,\mathfrak{o}_K/\mathfrak{p}^r)$ is surjective and thus induces an isomorphism $\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{p}^r)\to\operatorname{SL} (2,\mathfrak{o}_K/\mathfrak{p}^r)$. In particular $\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{p})$ is isomorphic to $\operatorname{SL} (2,q)$.
\end{Lemma}
\begin{proof}
Let
$$\overline{\gamma }=\begin{pmatrix}\overline{a} &\overline{b} \\ \overline{c} &\overline{d}\end{pmatrix}\in\operatorname{SL} (2,\mathfrak{o}_K/\mathfrak{p}^r)$$
and lift $\overline{\gamma }$ arbitrarily to a matrix
$$\gamma =\begin{pmatrix} a&b\\ c&d\end{pmatrix} \in\operatorname{GL} (2,\mathfrak{o}_K).$$
The determinant $\delta =\det\gamma$ is an element of $1+\mathfrak{p}^r$, hence so is its inverse $\frac{1}{\delta }$. Therefore
$$\gamma ' =\begin{pmatrix}\frac{a}{\delta }&\frac{b}{\delta }\\ c&d\end{pmatrix}\in\operatorname{SL} (2,\mathfrak{o}_K)$$
still reduces to $\overline{\gamma }$.
\end{proof}
\begin{Lemma}\label{HigherSubquotientsSolvable}
Let $r\ge 1$. Assumptions as before, the quotient $\mathrsfs{O}^1(\mathfrak{p}^r)/\mathrsfs{O}^1(\mathfrak{p}^{r+1})$ is isomorphic to $(\mathbb{Z} /p\mathbb{Z} )^{3f}$.
\end{Lemma}
\begin{proof}
We construct a map
\begin{equation*}
(\mathrsfs{O}/\mathfrak{p}\mathrsfs{O})_0\to \operatorname{SL} (2,\mathfrak{o}_K/\mathfrak{p}^{r+1}),\quad [A]\mapsto [1+\pi^rA].
\end{equation*}
Here the left hand side denotes the subgroup of those elements of $\mathrsfs{O}/\mathfrak{p}\mathrsfs{O}=M(2,\kappa )$ that have trace $\equiv 0\bmod\mathfrak{p}$. Note that $\det (1+\pi^rA)\equiv1+\pi^r\operatorname{tr} A\bmod\mathfrak{p}^{r+1}$, so the map is indeed well-defined. It is an injective group homomorphism, and its image is precisely the image of $\mathrsfs{O}^1(\mathfrak{p}^r)$ in $\operatorname{SL} (2,\mathfrak{o}_K/\mathfrak{p}^{r+1})$, which is isomorphic to $\mathrsfs{O}^1(\mathfrak{p}^r)/\mathrsfs{O}^1(\mathfrak{p}^{r+1})$.
\end{proof}
Now we turn to the ramified case. We use the explicit descritption of $B$ and $\mathrsfs{O}$ given in \cite[section 6.4]{MR1937957}. Let $L|K$ be the unique unramified quadratic extension, then $B$ is up to isomorphism given by
\begin{equation*}
B=\left\{\begin{pmatrix}a& b\\ \pi b' &a'\end{pmatrix}\middle\lvert a,b\in L\right\} ,
\end{equation*}
where $a\mapsto a'$ is the nontrivial element of $\operatorname{Gal}(L|K)$. This contains a unique maximal order,
\begin{equation*}
\mathrsfs{O}=\left\{\begin{pmatrix}a& b\\ \pi b' &a'\end{pmatrix}\middle\lvert a,b\in \mathfrak{o}_L\right\} ,
\end{equation*}
and $\mathrsfs{O}$ has a unique maximal two-sided ideal,
\begin{equation*}
\mathrsfs{M}=\begin{pmatrix}0&1\\ \pi & 0\end{pmatrix}\mathrsfs{O}=\left\{\begin{pmatrix}\pi a& b\\ \pi b' &\pi a'\end{pmatrix}\middle\lvert a,b\in\mathfrak{o}_L\right\} .
\end{equation*}
It satisfies $\mathrsfs{M}^2=\mathfrak{p}\mathrsfs{O}$. We define congruence subgroups $\mathrsfs{O}^1(\mathrsfs{M}^r)=\mathrsfs{O}^1\cap (1+\mathrsfs{M}^r)$, so that $\mathrsfs{O}^1(\mathfrak{p}^r)=\mathrsfs{O}^1(\mathrsfs{M}^{2r})$.
\begin{Lemma}
The quotient $\mathrsfs{O}^1/\mathrsfs{O}^1(\mathrsfs{M})$ is a cyclic group of order $q+1$.
\end{Lemma}
\begin{proof}
Since $L|K$ is unramified, the quotient $\lambda =\mathfrak{o}_L/\pi\mathfrak{o}_L$ is a finite field of order $q^2$. We construct a map
\begin{equation*}
\mathrsfs{O}^1/\mathrsfs{O}^1(\mathrsfs{M})\to\lambda^{\times },\quad \left[\begin{pmatrix} a&b\\ \pi b'& a'\end{pmatrix}\right] \mapsto a\bmod\pi .
\end{equation*}
This is easily seen to be an injective group homomorphism whose image is the kernel of the norm map $N_{\lambda\mid\kappa }$. That norm map is surjective to $\kappa^{\times }$, so its kernel has order $(q^2-1)/(q-1)=q+1$.
\end{proof}
\begin{Lemma}
Let $r\ge 1$. Then $\mathrsfs{O}^1(\mathrsfs{M}^r)/\mathrsfs{O}^1(\mathrsfs{M}^{r+1})$ is isomorphic to the additive group of $\kappa$.
\end{Lemma}
\begin{proof}
We construct injective group homomorphisms
\begin{equation*}
\mathrsfs{O}^1(\mathrsfs{M}^{2r})/\mathrsfs{O}^1(\mathrsfs{M}^{2r+1})\to\lambda ,\quad \left[\begin{pmatrix} a&b\\ \pi b'& a'\end{pmatrix}\right] \mapsto \frac{a-1}{\pi^r }\bmod\pi
\end{equation*}
and
\begin{equation*}
\mathrsfs{O}^1(\mathrsfs{M}^{2r-1})/\mathrsfs{O}^1(\mathrsfs{M}^{2r})\to\lambda ,\quad \left[\begin{pmatrix} a&b\\ \pi b'& a'\end{pmatrix}\right] \mapsto \frac{b}{\pi^{r-1}}\bmod\pi .
\end{equation*}
The image is in both cases the kernel of the trace map $\operatorname{tr}_{\lambda\mid\kappa }$.
\end{proof}
We summarise the results, reformulated for number fields:
\begin{Corollary}
Let $k$ be a number field and $B$ a quaternion algebra over $k$, unramified over at least one infinite place of $k$. Let $\mathrsfs{O}\subset B$ be a maximal order and let $\mathfrak{p}$ be a prime of $k$ of norm $q=p^f$. Let $r\ge 1$ and $H=\mathrsfs{O}^1/\mathrsfs{O}^1(\mathfrak{p}^r)$.
\begin{enumerate}
\item If $B$ is ramified at $\mathfrak{p}$, then $H$ is solvable; the prime numbers appearing as orders in its composition series are $p$ and the prime divisors of $q+1$.
\item If $B$ is unramified at $\mathfrak{p}$ and $\mathfrak{p}\nmid 6$, then $H$ is not solvable. Its composition factors are: once $\mathbb{Z} /2\mathbb{Z}$, once $\operatorname{PSL} (2,q)$ and $3f(r-1)$ times $\mathbb{Z} /p\mathbb{Z}$.
\end{enumerate}
\end{Corollary}
In case (ii) for $\mathfrak{p}\mid 6$ we have to replace $\operatorname{PSL} (2,q)$, which is not necessarily simple then, by its composition factors.
\section{Characters for Fuchsian Groups}
\noindent In this section we prove a criterion for two isomorphic lattices in $\operatorname{PSL} (2,\mathbb{R} )$ being conjugate:
\begin{Theorem}\label{CullerShalenForPSLTwoR}
Let $\Gamma$ be a group, and for $j=1,2$ let $\varrho_j\colon\Gamma\to\operatorname{PSL} (2,\mathbb{R} )$ be an injective group homomorphism such that $\varrho_j(\Gamma )$ is a lattice. Let $\Delta\subseteq\Gamma$ be a finite index subgroup, and assume that
\begin{equation}
\operatorname{tr}^2\varrho_1(\gamma )=\operatorname{tr}^2\varrho_2(\gamma )\text{ for all }\gamma\in\Delta .
\end{equation}
Then there exists a unique $a\in\operatorname{PGL} (2,\mathbb{R} )$ such that $\varrho _2(\gamma )=a\varrho_1(\gamma )a^{-1}$ for all $\gamma\in\Gamma $.
\end{Theorem}
The proof of Theorem \ref{CullerShalenForPSLTwoR} rests on the following result, see \cite[Proposition 1.5.2]{MR683804}, as well as on subsequent elementary lemmas.
\begin{Theorem}[Culler--Shalen]\label{CullerShalenOriginal}
Let $\varrho_1 ,\varrho_2\colon\Gamma\to\operatorname{SL} (2,\mathbb{C} )$ be two representations such that
\begin{equation}
\operatorname{tr}\varrho_1(\gamma )=\operatorname{tr}\varrho_2(\gamma )\text{ for every }\gamma\in\Gamma ,
\end{equation}
and assume that $\varrho_1$ is irreducible. Then there exists $a\in\operatorname{SL} (2,\mathbb{C} )$, unique up to sign, such that $\varrho_2(\gamma )=a\varrho_1(\gamma )a^{-1}$ for every $\gamma\in\Gamma$.
\end{Theorem}
\begin{Lemma}
Let $g\in\operatorname{PSL} (2,\mathbb{R} )$ and let $\Sigma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a group generated by two hyperbolic elements without common fixed points. Then there exists $s\in \Sigma$ with $sg$ hyperbolic.
\end{Lemma}
\begin{proof}
Lift $g$ to an element $G\in\operatorname{SL} (2,\mathbb{R} )$. First we will show that there exists some $S\in\tilde{\Sigma }$ with $\operatorname{tr} (SG)\neq 0$.
Assume, on the contrary, that $\operatorname{tr} (SG)=0$ for all $S\in\tilde{\Sigma }$. Choose two hyperbolic elements $S_1,S_2\in\tilde{\Sigma}$ without common fixed points; without loss of generality we may assume that
$$S_1=\begin{pmatrix}\lambda & 0\\ 0&\lambda^{-1}\end{pmatrix},\quad S_2=\begin{pmatrix}w&x\\ y&z\end{pmatrix},\quad G=\begin{pmatrix}a&b\\ c&d\end{pmatrix}$$
for some $\lambda >1$ and $xy\neq 0$. Then
$$\lambda a+\lambda^{-1}d=\operatorname{tr} (S_1G)=0=\operatorname{tr} (G)=a+d,$$
hence $a=d=0$ and
$$G=\begin{pmatrix}0 & b\\ c & 0\end{pmatrix},\quad bc=-\det (G)=-1,\text{ so }b,c\neq 0.$$
But then
$$cx+by=\operatorname{tr} (S_2G)=0=\operatorname{tr} (S_1S_2G)=\lambda cx+\lambda^{-1}by,$$
hence $cx=by=0$; but we know that $b,c,x,y\neq 0$, contradiction.
So there exists some $S\in\tilde{\Sigma }$ with $\operatorname{tr} (SG)\neq 0$; without loss of generality we assume that already $\operatorname{tr} G\neq 0$. Take some arbitrary hyperbolic $T\in\tilde{\Sigma}$; by the elementary equation
\begin{equation}\label{TraceRelationAB}
\operatorname{tr} (AB)+\operatorname{tr} (AB^{-1})=\operatorname{tr} (A)\cdot \operatorname{tr} (B)\text{ for all }A,B\in\operatorname{SL} (2,\mathbb{C} )
\end{equation}
then
$$\lvert\operatorname{tr} (T^NG)\rvert +\lvert\operatorname{tr} (T^{-N}G)\rvert\ge\lvert\operatorname{tr} (T^NG)+\operatorname{tr} (T^{-N}G)\rvert =\lvert\operatorname{tr} (T^N)\operatorname{tr} (G)\rvert .$$
But the right hand side goes to $\infty$ as $N\to\infty$, so for sufficiently large $N$, at least one of $\lvert\operatorname{tr} (T^NG)\rvert$ and $\lvert\operatorname{tr} (T^{-N}G)\rvert$ must be larger than $2$.
\end{proof}
\begin{Lemma}\label{FuchsiansAreGeneratedByHyberbolics}
Let $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a lattice. Then there exists a finite generating system of $\Gamma$ only consisting of hyperbolic elements.
\end{Lemma}
\begin{proof}
Assume that $\Gamma$ is generated by $g_1,\ldots ,g_n$. By \cite[Exercise 2.13]{MR1177168}, $\Gamma$ contains two hyperbolic elements $h_1,h_2$ without common fixed points; let them generate the group $S$. For each $1\le j\le n$ choose some $s_j\in S$ with $s_jg_j$ hyperbolic. Then $\Gamma$ is generated by the hyperbolic elements $h_1,h_2,s_1g_1,\ldots ,s_ng_n$.
\end{proof}
\begin{Lemma}\label{ReductionToRealCaseConjugation}
Let $a\in\operatorname{SL} (2,\mathbb{C} )$ and let $\Gamma\subset\operatorname{SL} (2,\mathbb{R} )$ be a lattice with $a\Gamma a^{-1}\subset\operatorname{SL} (2,\mathbb{R} )$. Then $a\in\mathbb{C}^{\times }\cdot\operatorname{GL} (2,\mathbb{R} )$.
\end{Lemma}
\begin{proof}
Since $\Gamma$ is Zariski-dense in $\operatorname{SL} (2,\mathbb{R} )$ we may deduce that $a\operatorname{SL} (2,\mathbb{R} )a^{-1}\subseteq\operatorname{SL} (2,\mathbb{R} )$. The sub-$\mathbb{R}$-vector space of $\mathrm{M}(2,\mathbb{C} )$ generated by $\operatorname{SL} (2,\mathbb{R} )$ is $\mathrm{M}(2,\mathbb{R} )$, so $a\mathrm{M}(2,\mathbb{R} )a^{-1}=\mathrm{M}(2,\mathbb{R} )$. By the Skolem--Noether Theorem, the automorphism $g\mapsto aga^{-1}$ of $\mathrm{M}(2,\mathbb{R} )$ has to be an inner automorphism, i.e.\ there exists $b\in\operatorname{GL} (2,\mathbb{R} )$ with $aga^{-1}=bgb^{-1}$ for all $g\in\mathrm{M}(2,\mathbb{R} )$ and hence, by linear extension, also for all $g\in\mathrm{M} (2,\mathbb{C} )$. But this means that $ba^{-1}$ is in the centre of $\mathrm{M}(2,\mathbb{C} )$ which is $\mathbb{C}^{\times }$.
\end{proof}
\begin{proof}[Proof of Theorem \ref{CullerShalenForPSLTwoR}]
Without loss of generality we may assume that $\Delta$ is torsion-free by Selberg's Lemma \cite[Lemma 8]{MR0130324}, hence it has a presentation
$$\Delta =\langle g_1,\ldots ,g_m\mid [g_1,g_{n+1}][g_2,g_{n+2}]\cdots [g_n,g_{2n}]=1\rangle \text{ with }m=2n$$
(in the cocompact case), or is free on some generators $g_1,\ldots ,g_m$ (otherwise).
By \cite[Theorem 4.1]{MR1124819} each $\varrho_j|_{\Delta}$ can be lifted to representations $\tilde{\varrho }_j\colon\Delta\to\operatorname{SL} (2,\mathbb{R} )$; furthermore again by that theorem we can arbitrarily prescribe the sign of each lift of $\varrho_j(g_i)$, so we may assume that
\begin{equation}\label{SameTracesForGenerators}
\operatorname{tr} \tilde{\varrho }_1(g_i)=\operatorname{tr}\tilde{\varrho }_2(g_i)\text{ for all }1\le i\le m.
\end{equation}
More generally,
$$\operatorname{tr} \tilde{\varrho }_1(\gamma )=\varepsilon (\gamma )\cdot\operatorname{tr} \tilde{\varrho }_2(\gamma )\text{ for all }\gamma\in\Delta ,$$
where $\varepsilon$ is some function $\Delta\to\{\pm 1\}$. Note that $\varepsilon$ is uniquely determined by this equation because the traces cannot be zero since elements of $\varrho_j(\Delta )$ are not elliptic. Furthermore $\varepsilon (g_i)=1$ for every generator $g_i$ by (\ref{SameTracesForGenerators}).
We now show that $\varepsilon$ is identically $1$. The crucial step is the following implication:
\begin{equation}\label{InductionStepForEpsilon}
\text{If }\varepsilon (\gamma )=\varepsilon (\delta )=1,\text{ then }\varepsilon (\gamma\delta )=\varepsilon (\gamma\delta^{-1} )=1.
\end{equation}
So assume that $\varepsilon (\gamma )=\varepsilon (\delta )=1$. We deduce from (\ref{TraceRelationAB}):
\begin{equation}\label{TraceEquationForXandY}
\begin{gathered}
\varepsilon (\gamma\delta )\operatorname{tr} \tilde{\varrho }_1(\gamma\delta ) +\varepsilon (\gamma\delta^{-1})\operatorname{tr} \tilde{\varrho }_1(\gamma\delta^{-1})=\operatorname{tr}\tilde{\varrho }_2(\gamma\delta )+\operatorname{tr}\tilde{\varrho }_2(\gamma\delta^{-1})\\
=(\operatorname{tr}\tilde{\varrho }_2(\gamma))\cdot (\operatorname{tr}\tilde{\varrho }_2(\delta ))=(\operatorname{tr}\tilde{\varrho }_1(\gamma))\cdot (\operatorname{tr}\tilde{\varrho }_1(\delta ))=\operatorname{tr}\tilde{\varrho }_1(\gamma\delta )+\operatorname{tr}\tilde{\varrho }_1(\gamma\delta^{-1}).
\end{gathered}
\end{equation}
If $\varepsilon (\gamma\delta )$ and $\varepsilon (\gamma\delta^{-1})$ were both negative, (\ref{TraceEquationForXandY}) would entail that $(\operatorname{tr}\tilde{\varrho }_2(\gamma ))\cdot (\operatorname{tr}\tilde{\varrho }_2(\delta ))=0$ which is absurd because $\Delta$ does not contain elliptic elements. If $\varepsilon (\gamma\delta )=1$ and $\varepsilon (\gamma\delta^{-1})=-1$, then $\operatorname{tr}\tilde{\varrho }_2(\gamma\delta^{-1})=0$ which is again absurd; the other mixed case is ruled out in an analogous way. This proves (\ref{InductionStepForEpsilon}).
Now we can prove that $\varepsilon (\gamma )=1$ for every $\gamma\in\Delta$ using induction on the word length $\ell (\gamma )$: this is the number of factors $g_j^{\pm 1}$ needed to obtain $\gamma$ as a product. If $\ell (\gamma )=1$ then $\gamma =g_j^{\pm 1}$; since $\varepsilon (\gamma )=\varepsilon (\gamma^{-1})$, this must be equal to $\varepsilon (g_j)=1$. If $\varepsilon (\gamma )=1$ for all $\gamma$ with $\ell (\gamma )\le n$ we may use (\ref{InductionStepForEpsilon}) and the trivial identity $\varepsilon (\gamma^{-1})=\varepsilon (\gamma )$ to show the statement for all $\gamma$ with $\ell (\gamma )\le n+1$. Therefore by induction, $\varepsilon$ is identically $1$, hence
\begin{equation*}
\operatorname{tr}\tilde{\varrho }_1(\gamma )=\operatorname{tr}\tilde{\varrho }_2(\gamma )\text{ for all }\gamma\in\Delta .
\end{equation*}
By Theorem \ref{CullerShalenOriginal} this means that $\tilde{\varrho }_1$ is conjugate to $\tilde{\varrho }_2$ within $\operatorname{SL} (2,\mathbb{C} )$, but since all images are real, the conjugation must be possible within $\operatorname{GL} (2,\mathbb{R} )$ by Lemma \ref{ReductionToRealCaseConjugation}. This in turn means that $\varrho_1|_{\Delta }$ and $\varrho_2|_{\Delta }$ are conjugate in $\operatorname{PGL} (2,\mathbb{R} )$.
We need to extend this to the entire group $\Gamma$. Without loss of generality we may assume that $\varrho_1|_{\Delta }=\varrho_2|_{\Delta }$. By Lemma \ref{FuchsiansAreGeneratedByHyberbolics} there exists a generating system $\gamma_1,\ldots ,\gamma_m$ of $\Gamma$, not necessarily related in any way to that of $\Delta$, such that all $\varrho_1(\gamma_j)$ are hyperbolic. But some power of each $\gamma_j$ is contained in $\Delta$, and hence $\varrho_1(\gamma_j)^N=\varrho_2(\gamma_j)^N$. Under the assumptions on $\gamma_j$ this entails $\varrho_1(\gamma_j)=\varrho_2(\gamma_j)$, i.e.\ $\varrho_1=\varrho_2$.
\end{proof}
\section{Modular Embeddings}\label{SectionModularEmbedding}
\noindent Let once again $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a semi-arithmetic lattice satisfying the trace field property, with trace field $k$, quaternion algebra $B$, maximal order $\mathrsfs{O}$ and algebraic group $G=\operatorname{Res}_{k|\mathbb{Q} }H$. As explained above, $\Gamma$ is a subgroup of the arithmetic group $\mathrm{P}\mathrsfs{O}^1$. Now that latter group naturally lives on the symmetric space of $G$, i.e.\ on $G(\mathbb{R} )/K$ for a maximal compact subgroup $K$. This space can be described explicitly as $\mathfrak{H}^r$ where $\mathfrak{H}$ is the upper half-plane and $r\le d=[k:\mathbb{Q} ]$. Let $\sigma_1,\ldots ,\sigma_d\colon k\to\mathbb{R}$ be the field embeddings, where $\sigma_1$ is the identity embedding. We also may assume that the quaternion algebra $B\otimes_{k,\sigma_i}\mathbb{R}$ is isomorphic to $\mathrm{M}(2,\mathbb{R} )$ for each $1\le i\le r$ and isomorphic to $\mathbb{H}$ for $r<i\le d$.
For each $1\le i\le r$ we choose an isomorphism $\alpha_i\colon B\otimes_{k,\sigma_i}\mathbb{R}\to\mathrm{M}(2,\mathbb{R} )$. We obtain an embedding
$$\alpha\colon\mathrsfs{O}^1\hookrightarrow\operatorname{SL} (2,\mathbb{R} )^r,\quad x \mapsto (\alpha_1(x),\ldots ,\alpha_r(x))$$
descending to an embedding $\alpha\colon\mathrm{P}\mathrsfs{O}^1\hookrightarrow\operatorname{PSL} (2,\mathbb{R} )^r$. We denote the image by $\Lambda =\alpha (\mathrm{P}\mathrsfs{O}^1 )$.
\begin{Theorem}
$\Lambda$ is an irreducible arithmetic lattice in $\operatorname{PSL} (2,\mathbb{R} )^r$.
\end{Theorem}
For the proof see e.g.\ \cite{MR0204426}.
Note that $\alpha (\Gamma )$ becomes a subgroup of $\Lambda$. It has finite index precisely if $\Gamma$ is already arithmetic; in every case $\alpha (\Gamma )$ is a Zariski-dense subgroup of $\Lambda$ by the proof of Proposition \ref{StrongApproxSemiArithm}. Zariski-dense subgroups of infinite index in arithmetic groups are called \emph{thin}, and so we have shown:
\begin{Corollary}\label{SemiArithmeticAreThin}
If $\Gamma$ is not arithmetic itself, the embedding $\alpha\colon\Gamma\to\Lambda$ realises $\Gamma$ as a thin group.
\end{Corollary}
Let $\operatorname{PSL} (2,\mathbb{R} )^r$ operate by component-wise M\"{o}bius transformations on $\mathfrak{H}^r$; the induced action of $\Lambda$ on $\mathfrak{H}^r$ is properly discontinuous and has a quotient of finite volume. This motivates the following definition:
\begin{Definition}
A \emph{modular embedding} of $\Gamma$ is a holomorphic embedding $F\colon\mathfrak{H}\to\mathfrak{H}^r$ such that
$$F(\gamma\tau )=\alpha (\gamma )F(\tau )$$
for every $\gamma\in\Gamma$ and every $\tau\in\mathfrak{H}$.
\end{Definition}
The following result which will be used later on is \cite[Corollary 5]{MR1745404}:
\begin{Proposition}\label{ModularEmbeddingEnablesToPinDownTrace}
Let $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a semi-arithmetic group which satisfies the trace field property and admits a modular embedding, and let $k=\mathbb{Q} (\operatorname{tr}\Gamma)$. Let $\gamma\in\tilde{\Gamma }$ be hyperbolic and let $\sigma\colon k\to\mathbb{R}$ be an embedding which is not the identity inclusion. Then $\lvert\sigma (\operatorname{tr}\gamma )\rvert <\lvert\operatorname{tr}\gamma\rvert$.
\end{Proposition}
Note that if $\Gamma$ is an arithmetic group then even $\lvert\sigma (\operatorname{tr}\gamma )\rvert <2$ by Proposition \ref{EquivalentCharacterisationsArithmetic}.
\section{Congruence Rigidity}\label{SectionCongruenceRigidity}
\noindent Let $\Gamma\subset\operatorname{PSL} (2,\mathbb{R} )$ be a semi-arithmetic lattice satisfying the trace field condition, with trace field $k=\mathbb{Q} (\operatorname{tr}\Gamma )$. Let $B=k[\tilde{\Gamma }]$ be the associated quaternion algebra and $G$ the algebraic group over $\mathbb{Q}$ with $G(\mathbb{Q} )=B^1$. Let $\mathrsfs{O}\subset B$ be a maximal order containing $\tilde{\Gamma }$, and let $\mathfrak{m}\subset\mathfrak{o}_k$ be such that a finite index subgroup of $\Gamma$ is ad\`{e}lically dense in $\mathrm{P}\mathrsfs{O}^1 (\mathfrak{m})$; in particular, $\mathfrak{m}$ satisfies the conclusion of Proposition \ref{CorollaryGammaLocallyCongruence}.
For the statement of the next proposition, let $\mathfrak{m}=\mathfrak{l}_1^{r_1}\cdots\mathfrak{l}_n^{r_n}$ be the prime factorisation of $\mathfrak{m}$. Let $\ell_j$ be the norm of the prime ideal $\mathfrak{l}_j$. Then $S(\mathfrak{m})$ is the finite set of all rational primes diving some $\lvert\operatorname{PSL} (2,\ell_j)\rvert$ (this includes the primes dividing $\ell_j$ or $\ell_j+1$). Note that if $\mathfrak{m}'$ is an ideal which has the same prime divisors as $\mathfrak{m}$ and if $\ell$ is a rational prime dividing the order of $\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{m}')$, then $\ell\in S(\mathfrak{m})$. Also $S(6)$ is the set consisting of $2,3$ and all prime divisors of orders of $\operatorname{PSL} (2,q)$ where $q$ is the norm of a prime ideal $\mathfrak{p}$ in $k$ with $\mathfrak{p}\mid 6$. Finally $S(\Gamma )$ is the union of $S(\mathfrak{m})\cup S(6)$, the primes lying over the ramification divisor of $B$ and the primes that ramify in $k$. Still, $S(\Gamma )$ is a finite set of rational primes.
\begin{Proposition}\label{CongruenceQuotientsGivePrimes}
Let $\Gamma$ as above, and let $q=p^f$ be an odd prime power which is prime to all primes in $S(\Gamma )$. Let $\Delta\subset\Gamma$ be a normal congruence subgroup such that $\Gamma /\Delta\simeq\operatorname{PSL} (2,q)$. Then there exists a unique prime $\mathfrak{p}$ of norm $q$ in $k$ such that $\Delta =\Gamma (\mathfrak{p})$.
\end{Proposition}
\begin{proof}
There exists an ideal $\mathfrak{n}$ such that $\Delta\supseteq\Gamma (\mathfrak{n})$ and a finite index subgroup of $\Delta$ is ad\`{e}lically dense in $\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n})$. We may assume that $\mathfrak{m}$ divides $\mathfrak{n}$. Write $\mathfrak{n}=\mathfrak{n}'\cdot\mathfrak{n}_{\mathfrak{m}}$ with $\mathfrak{n}'$ coprime to $\mathfrak{m}$ and $\mathfrak{n}_{\mathfrak{m}}$ having the same prime divisors as $\mathfrak{m}$; then $\Gamma$ also contains a subgroup which is ad\`{e}lically dense in $\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}_{\mathfrak{m}})$. By Proposition \ref{CorollaryGammaLocallyCongruence} this entails that $\Gamma$ surjects onto $\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}')$.
Denote the quotient map modulo $\Delta$ by
\begin{equation*}
\pi\colon\Gamma\to\operatorname{PSL} (2,q).
\end{equation*}
Note that $\pi$ is continuous in the ad\`{e}lic topology on $\Gamma$ since it vanishes on $\Gamma (\mathfrak{n})$.
Now $\Gamma (\mathfrak{n}')=\Gamma\cap\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}')$ is a normal subgroup of $\Gamma$, hence its image under $\pi$ is a normal subgroup of $\operatorname{PSL} (2,q)$. Since that group is simple, the image can only be $\operatorname{PSL} (2,q)$ or the trivial group. Assume it were the entire group, then in the sequence
\begin{equation*}
\operatorname{PSL} (2,q)\twoheadleftarrow \Gamma (\mathfrak{n}')/\Gamma (\mathfrak{n})\hookrightarrow\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}')/\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n})\simeq\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}_{\mathfrak{m}})
\end{equation*}
(where the isomorphism is by Corollary \ref{CorChangingTheLevel}) the order of the left hand side would divide the order of the right hand side. But the former is divisible by $p$, the latter only by primes in $S(\Gamma )$. A contradiction, hence the image of $\Gamma (\mathfrak{n}')$ under $\pi$ is the trivial group. In other words,
\begin{equation*}
\Delta\supseteq\Gamma (\mathfrak{n}').
\end{equation*}
This implies that $\pi$ descends to an epimorphism
\begin{equation*}
\pi\colon\Gamma /\Gamma (\mathfrak{n}')\twoheadrightarrow\operatorname{PSL} (2,q).
\end{equation*}
By Proposition \ref{CorollaryGammaLocallyCongruence} the inclusion $\Gamma\subseteq\mathrm{P}\mathrsfs{O}^1$ induces an isomorphism
\begin{equation*}
\alpha\colon\Gamma /\Gamma (\mathfrak{n}')\overset{\simeq}{\longrightarrow}\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}').
\end{equation*}
So by composition we obtain an epimorphism $\pi\circ\alpha^{-1}\colon\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}')\twoheadrightarrow\operatorname{PSL} (2,q)$. Let $\mathfrak{n}'=\mathfrak{p}_1^{r_1}\cdots\mathfrak{p}_n^{r_n}$ with distinct prime ideals $\mathfrak{p}_j$, and let $\operatorname{rad}(\mathfrak{n}')=\mathfrak{p}_1\cdots\mathfrak{p}_n$. Then $\mathrm{P}\mathrsfs{O}^1 (\operatorname{rad}(\mathfrak{n}'))/\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}')$ is a solvable normal subgroup of $\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}')$ by Lemma \ref{HigherSubquotientsSolvable}, so its image by $\pi\circ\alpha^{-1}$ has to be a solvable normal subgroup of $\operatorname{PSL} (2,q)$, i.e.\ trivial. Therefore $\pi\circ\alpha^{-1}$ factors through $\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\operatorname{rad}(\mathfrak{n}'))$; we summarise this in a diagram:
\begin{equation}\label{DiagramWithDashedEpi}
\xymatrix{
\Gamma /\Gamma (\mathfrak{n}') \ar[r]^{\simeq\hspace{0.6cm}}_{\alpha\hspace{0.6cm}} \ar@{->>}[rd]_{\pi } &
\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}') \ar@{->>}[r] \ar@{->>}[d] &
\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\operatorname{rad}(\mathfrak{n}')) \ar@{-->>}[ld]\\
& \operatorname{PSL} (2,q)
}
\end{equation}
Now the rightmost projects onto
\begin{equation}\label{ProductOfPOones}
\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{p}_1)\times\cdots\times\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{p}_n),
\end{equation}
and by Corollary \ref{ChineseRemainderForPSL} the kernel of this projection is an abelian normal subgroup which is therefore mapped to the identity element by the dashed arrow in (\ref{DiagramWithDashedEpi}). Hence that dashed arrow is defined on (\ref{ProductOfPOones}); by Lemma \ref{LemmaOnFiniteGroups} it actually has to factor through the projection onto one of them, composed with an isomorphism. We hence obtain
\begin{equation*}
\xymatrix{
\Gamma /\Gamma (\mathfrak{n}') \ar[r]^{\simeq\hspace{0.6cm}}_{\alpha\hspace{0.6cm}} \ar@{->>}[rd]_{\pi } &
\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{n}') \ar@{->>}[r] \ar@{->>}[d] &
\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{p}_j) \ar@{-->}[ld]^{\simeq }\\
& \operatorname{PSL} (2,q)
}
\end{equation*}
for some $1\le j\le n$. We may shorten this to
\begin{equation}\label{DiagramWithDashedIso}
\xymatrix{
\Gamma /\Gamma (\mathfrak{p}_j) \ar[rr]^{\simeq\hspace{0.5cm}}_{\alpha '\hspace{0.5cm}} \ar@{->>}[rd]_{\pi '} & &
\mathrm{P}\mathrsfs{O}^1 /\mathrm{P}\mathrsfs{O}^1 (\mathfrak{p}_j) \ar@{-->}[ld]^{\simeq }\\
& \operatorname{PSL} (2,q)
}
\end{equation}
with $\alpha '$ again induced by the inclusion $\Gamma\subseteq\mathrm{P}\mathrsfs{O}^1$. In this diagram $\pi '$ is obviously an isomorphism, therefore $\Delta =\ker\pi$ is equal to $\Gamma (\mathfrak{p}_j)$. The dashed isomorphism in (\ref{DiagramWithDashedIso}) shows that the norm of $\mathfrak{p}_j$ is $q$.
\end{proof}
\begin{Remark}\label{ReconstructionOfArithmeticSimilarityClass}
We note that this proposition enables us to reconstruct the splitting behaviour of almost all primes in $k$ from $\Gamma$ and its congruence subgroups: Let $p\notin S(\Gamma )$ be a rational prime in $\Gamma$. Then there exist only finitely many normal congruence subgroups $\Delta\triangleleft\Gamma$ such that $\Gamma /\Delta\simeq\operatorname{PSL} (2,q)$ for some power $q$ of $f$. Let these be $\Delta_1,\ldots ,\Delta_n$, and let the corresponding quotients be $\operatorname{PSL} (2,p^{f_1}),\ldots ,\operatorname{PSL} (2,p^{f_n})$.
On the other hand consider the prime decomposition $(p)=\mathfrak{p}_1\cdots\mathfrak{p}_m$ in $k$. Then $n=m$, and up to renumeration $\Delta_j=\Gamma (\mathfrak{p}_j)$ and $N(\mathfrak{p}_j)=p^{f_j}$. In particular we can reconstruct $[k\colon \mathbb{Q} ]=f_1+\ldots +f_n$ from the knowledge of $\Gamma$ and its congruence subgroups.
\end{Remark}
\begin{proof}[Proof of Theorem A] By Theorem \ref{CullerShalenForPSLTwoR} we may replace $\Gamma_j$ by finite index subgroups corresponding to each other under the isomorphism $f$. Hence we may assume that each $\Gamma_j$ is torsion-free and satisfies the trace field condition. Again by Theorem \ref{CullerShalenForPSLTwoR} it suffices to show that $\operatorname{tr}^2 f(\gamma )=\operatorname{tr}^2 \gamma\in\mathbb{R}$ for each $\gamma\in\Gamma_1$.
Denote the trace field of $\Gamma_j$ by $k_j$. Each number $a\in\mathfrak{o}_{k_j}$ has a \emph{characteristic polynomial} $\chi_a(x)\in\mathbb{Z} [x]$ which can be described as follows:
\begin{itemize}
\item it is the characteristic polynomial of the map $k_j\to k_j$, $v\mapsto av$ interpreted as a $\mathbb{Q}$-linear map;
\item it is equal to $\prod_{\sigma }(x-\sigma (a))$. Here $\sigma$ runs through a system of representatives of $\operatorname{Gal} (L_j|\mathbb{Q} )$ modulo $\operatorname{Gal} (L_j|k_j)$ where $L_j$ is the Galois closure of $k_j$.
\end{itemize}
Now let $p$ be a rational prime not in $S(\Gamma_1)\cup S(\Gamma_2)$. By Remark \ref{ReconstructionOfArithmeticSimilarityClass} we can decompose $p\mathfrak{o}_{k_j}$ into prime ideals
$$p\mathfrak{o}_{k_1}=\mathfrak{p}_1\cdots\mathfrak{p}_n,\quad p\mathfrak{o}_{k_2}=\mathfrak{q}_1\ldots\mathfrak{q}_n$$
in such a way that
\begin{equation}\label{HowfPermutesCongruenceSubgroups}
f(\Gamma_1(\mathfrak{p}_j))=\Gamma_2(\mathfrak{q}_j)\text{ and }\mathfrak{o}_{k_1}/\mathfrak{p}_j\simeq\mathfrak{o}_{k_2}/\mathfrak{q}_j.
\end{equation}
Then
\begin{equation}\label{ProductsPjQj}
\mathfrak{o}_{k_1}/p\mathfrak{o}_{k_1}\simeq\mathfrak{o}_{k_1}/\mathfrak{p}_1\times\cdots\times\mathfrak{o}_{k_1}/\mathfrak{p}_d
\end{equation}
is a finite-dimensional $\mathbb{F}_p$-algebra, and we may similarly define the characteristic polynomial $\chi_{\overline{b}}(x)\in\mathbb{F}_p[x]$ of an element $\overline{b}\in\mathfrak{o}_{k_1}/p\mathfrak{o}_{k_1}$ as the characteristic polynomial of the $\mathbb{F}_p$-linear endomorphism of $\mathfrak{o}_{k_1}/p\mathfrak{o}_{k_1}$ given by multiplication by $\overline{b}$. Then for $a\in\mathfrak{o}_{k_1}$ clearly
\begin{equation}\label{ComputeCharPolyModp}
\chi_a(x)\bmod p =\chi_{a\bmod p}(x)\in\mathbb{F}_p[x].
\end{equation}
We now claim that the characteristic polynomials of $\operatorname{tr}^2\gamma$ and $\operatorname{tr}^2f(\gamma )$ are congruent modulo $p$. To see this we use the abstract version of squared traces on finite groups introduced in section \ref{SectionFiniteGroups}. For each $1\le j\le n$, using (\ref{HowfPermutesCongruenceSubgroups}) we obtain an isomorphism of finite groups $\bar{f}\colon\Gamma_1/\Gamma_1(\mathfrak{p}_j)\to\Gamma_2/\Gamma_2(\mathfrak{q}_j)$. By the remark after Definition \ref{AbstractTraces}, $\operatorname{tr}^2\gamma\bmod\mathfrak{p}_j$ and $\operatorname{tr}^2f(\gamma )\bmod\mathfrak{q}_j$ are Galois-conjugate elements of the finite field $\mathbb{F}_q\simeq\mathfrak{o}_{k_1}/\mathfrak{p}_j\simeq\mathfrak{o}_{k_2}/\mathfrak{q}_j$. Hence there exists an isomorphism of $\mathbb{F}_p$-algebras
$$\alpha_j\colon\mathfrak{o}_{k_1}/\mathfrak{p}_j\overset{\simeq}{\longrightarrow}\mathfrak{o}_{k_2}/\mathfrak{q}_j$$
with $\alpha_j(\operatorname{tr}^2\gamma \bmod\mathfrak{p}_j)=\operatorname{tr}^2f(\gamma )\bmod\mathfrak{q}_j$. Gluing these together component-wise in (\ref{ProductsPjQj}) yields an isomorphism of $\mathbb{F}_p$-algebras $\alpha\colon\mathfrak{o}_{k_1}/p\mathfrak{o}_{k_1}\to\mathfrak{o}_{k_2}/p\mathfrak{o}_{k_2}$ with $\alpha (\operatorname{tr}^2\gamma\bmod p)=\operatorname{tr}^2f(\gamma )\bmod p$. Since characteristic polynomials are stable under algebra isomorphisms, we obtain
$$\chi_{\operatorname{tr}^2\gamma\bmod p}(x)=\chi_{\operatorname{tr}^2f(\gamma )\bmod p}(x)\in\mathbb{F}_p[x].$$
By (\ref{ComputeCharPolyModp}), this means
$$\chi_{\operatorname{tr}^2\gamma }(x)\equiv\chi_{\operatorname{tr}^2f(\gamma )}(x)\bmod p.$$
But this holds for infinitely many $p$, so
$$\chi_{\operatorname{tr}^2\gamma }(x)=\chi_{\operatorname{tr}^2f(\gamma )}(x)\in\mathbb{Z} [x].$$
Since we had assumed $\Gamma_1$ to be torsion-free, $\gamma$ cannot be elliptic. If it is parabolic, then $\operatorname{tr}^2\gamma =4$ and therefore $\chi_{\operatorname{tr}^2\gamma }(x)=(x-4)^d$. Hence also the characteristic polynomial of $f(\gamma )$ is $(x-4)^d$, and since $\operatorname{tr}^2f(\gamma )$ is a zero of this polynomial, $\operatorname{tr}^2f(\gamma )=4$, hence $f(\gamma )$ is parabolic as well.
Finally assume that $\gamma$ is hyperbolic. Then $f(\gamma )$ must also be hyperbolic because it cannot be parabolic (else $\gamma$ would be parabolic by the inverse of the previous argument). By Proposition \ref{ModularEmbeddingEnablesToPinDownTrace}, $\operatorname{tr}^2\gamma$ is the largest zero of $\chi_{\operatorname{tr}^2\gamma }(x)$, similarly for $\operatorname{tr}^2f(\gamma )$. Therefore $\operatorname{tr}^2(\gamma )=\operatorname{tr}^2f(\gamma )$.
\end{proof}
\section{An Example}
\noindent In our proof of Theorem A we did not use the full assumption that all congruence subgroups are mapped to congruence subgroups by the given isomorphism. We spell out in a concrete example how far an isomorphism between non-conjugate arithmetic groups can be from preserving congruence subgroups.
In \cite{MR702765} we find a complete list of all arithmetic groups of signature $(1;2)$, i.e.\ whose associated Riemann surfaces have genus one and which have one conjugacy class of elliptic elements, these elements being of order two. In particular all these groups are abstractly isomorphic, and we may just pick the first two of them:
$\Gamma_1'$ is generated by the two M\"{o}bius transformations
$$\alpha_1=\pm\begin{pmatrix}\frac{1+\sqrt{5}}{2} & 0\\ 0&\frac{-1+\sqrt{5}}{2}\end{pmatrix}\text{ and }\beta_1=\pm\begin{pmatrix}\sqrt{3} &\sqrt{2}\\ \sqrt{2} &\sqrt{3}\end{pmatrix}\! ,$$
$\Gamma_2'$ by the two M\"{o}bius transformations
$$\alpha_2=\pm\begin{pmatrix}\sqrt{2}+1 & 0\\ 0&\sqrt{2}-1\end{pmatrix}\text{ and }\beta_2=\pm\frac{1}{2}\begin{pmatrix}\sqrt{6} &\sqrt{2}\\ \sqrt{2} &\sqrt{6}\end{pmatrix}\! .$$
These are, respectively, generators satisfying the relation $(\alpha_j\beta_j\alpha_j^{-1}\beta_j^{-1})^2=1$. So there exists a group isomorphism $f\colon\Gamma_1'\to\Gamma_2'$ with $f(\alpha_1)=\alpha_2$ and $f(\beta_1)=\beta_2$. The $\Gamma_j'$ do not satisfy the trace field condition, but the $\Gamma_j=(\Gamma_j')^{(2)}$ (between whom $f$ also induces an isomorphism) do; in both cases the invariant trace field is $\mathbb{Q}$.
Then, with finitely many exceptions, $\Gamma_1/\Gamma_1(p)\simeq\operatorname{PSL} (2,p)\simeq\Gamma_2/\Gamma_2(p)$ for rational primes $p$; nevertheless, the proof of Theorem A shows that there can be only finitely many $p$ such that $f(\Gamma_1(p))$ is a congruence subgroup (and hence only finitely many $p$ with $f(\Gamma_1(p))=\Gamma_2(p)$).
\section{Concluding Remarks}
\begin{Remark}
The assumption that both groups admit a modular embedding is crucial although it only enters in the very last step of the proof. If $\Gamma$ is a semi-arithmetic lattice with invariant trace field $k$ and $\sigma\colon k\to\mathbb{R}$ a field embedding we obtain in a natural way a group $i_\sigma (\Gamma )\subset\operatorname{PSL} (2,\mathbb{R} )$, see \cite[Remark 4]{MR1745404}. There exist semi-arithmetic lattices $\Gamma$ with nontrivial Galois conjugates $i_\sigma (\Gamma )$ that are again lattices, and then the isomorphism $\Gamma\to i_\sigma (\Gamma )$ preserves congruence subgroups but not traces. For an explicit construction see e.g.\ \cite{AgolNew} referring to \cite[Proposition 4.11]{MR1643429}. But if $\Gamma$ admits a modular embedding, then none of the nontrivial Galois conjugates $i_\sigma (\Gamma )$ can be discrete by \cite[Theorem 3]{MR1745404}.
Note that the existence of a modular embedding enters the proof via Proposition \ref{ModularEmbeddingEnablesToPinDownTrace} which is its only genuinely non-algebraic ingredient: it is a consequence of the Schwarz Lemma.
One may still ask whether a weakened version of our main theorem holds in the general case: if $f\colon\Gamma_1\to\Gamma_2$ is an isomorphism between semi-arithmetic lattices in $\operatorname{PSL} (2,\mathbb{R} )$ respecting congruence subgroups, is it the composition of an inner automorphism of $\operatorname{PGL} (2,\mathbb{R} )$ with a Galois conjugation of the trace field?
\end{Remark}
\begin{Remark}
There exist arithmetic Fuchsian groups with different trace fields but whose congruence completions are isomorphic away from a finite set of primes. To see this, start with the polynomial in the remark after \cite[Theorem 5.1]{MR1800034}: the splitting field of this polynomial is a totally real Galois extension of $\mathbb{Q}$ with Galois group $\operatorname{PSL} (2,7)$. By the discussion in \cite[p. 358--359]{MR0447188} such a field contains two subfields $k_1$, $k_2$ which are not isomorphic but have the same Dedekind zeta function. Then there exists a finite set $S$ of rational primes such that $\mathbb{A}_{k_1}^S\simeq\mathbb{A}_{k_2}^S$. From this we can easily construct arithmetic Fuchsian groups over $k_1$ and $k_2$ with isomorphic prime-to-$S$ congruence completion.
There also exist non-isomorphic number fields with isomorphic finite ad\`{e}le rings (at all primes), see \cite{MR736723}. But no construction seems to be known where these fields are totally real.
\end{Remark}
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Bayer To Stop Selling Essure In USA | Ennis & Ennis, P.A.
Shouts of joy from tens of thousands of women injured by the Essure sterilization device were heard around the United States moments ago when Bayer announced it would no longer be selling the controversial device by the end of the year. This brings to an end a protracted battle waged by the grassroots movement, The Essure Problems Group, against the pharmaceutical giant, Bayer, a true David versus Goliath victory.
The United States is the last country in which Essure is being sold. Last September, "citing commercial reasons," Bayer announced it was ending sales outside of the United States. The Essure Problems Group helped accomplish this cessation of sales as well, with strong social media protests from Essure Problems Groups in Spain, France, Italy, The Netherlands, Finland and other European countries.
In February, Admins from the Essure Problems Group, Madris Tomes of Device Events and Essure attorney Holly Ennis, met with FDA Commissioner Scott Gottlieb and complained that many women were not being warned about the dangers of the device, despite the Black Box Warning. In April, the FDA imposed a unique restriction on the product by limiting sales to doctor's offices and medical practices who guaranteed to fully inform women about the products' risks. However, in a letter to FDA Commissioner just delivered yesterday, the Group advised Commissioner Gottlieb that none of the FDA's mandates were being followed by Bayer nor the implanting physicians.
According to the New York Times, Bayer said its decision was based on declining sales, and blamed "inaccurate and misleading publicity," as a key factor. The full article can be read at https://www.nytimes.com/2018/07/20/health/bayer-essure-birth-control.html However, it is believed that Bayer wanted to get out ahead of a powerful and damning documentary regarding Essure and the medical device industry, The Bleeding Edge, which will be released worldwide on Friday, July 27th. This coupled with the Essure Problems Group holding a rally and a screening of The Bleeding Edge outside of Bayer's New Jersey headquarters this week, may have hastened this announcement.
Whatever the reasons for the withdrawl of Essure from the market, tens and tens of thousands of women are rejoicing today and celebrating their victory in a long and hard-fought battle. Cheers to all the Essure Ladies. | {
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Homepage > CHAPTER XII Civil Remedies
CHAPTER XII Civil Remedies
Civil Remedies
54. Definition. -For the purposes of this Chapter, unless the context otherwise requires, the
expression "owner of copyright" shall include-
(a) an exclusive licensee;
(b) in the case of an anonymous or pseudonymous literary, dramatic, musical or artistic work, the
publisher of the work, until the identity of the author or, in the case of an anonymous work of joint
authorship, or a work of joint authorship published under names all of which are pseudonyms, the
identity of any of the authors, is disclosed publicly by the author and the publisher or is otherwise
established to the satisfaction of the Copyright Board by that author or his legal representatives.
55. Civil remedies for infringement of copyright. - (1) Where copyright in any work has been
infringed, the owner of the copyright shall, except as otherwise provided by this Act, be entitled to all
such remedies by way of injunction, damages, accounts and otherwise as are or may be conferred
by law for the infringement of a right :
Provided that if the defendant proves that at the date of the infringement he was not aware and had
no reasonable ground for believing that copyright subsisted in the work, the plaintiff shall not be
entitled to any remedy other than an injunction in respect of the infringement and a decree for the
whole or part of the profits made by the defendant by the sale of the infringing copies as the court
may in the circumstances deem reasonable.
(2) Where, in the case of a literary, dramatic, musical or artistic work, a name purporting to be that of
the author or the publisher, as the case may be, appears on copies of the work as published, or, in
the case of an artistic work, appeared on the work when it was made, the person whose name so
appears or appeared shall, in any proceeding in respect of infringement of copyright in such work, be
presumed, unless the contrary is proved, to be the author or the publisher of the work, as the case
may be.
(3) The costs of all parties in any proceedings in respect of the infringement of copyright shall be in
the discretion of the court.
56. Protection of separate rights. - Subject to the provisions of this Act, where the several rights
comprising the copyright in any work are owned by different persons, the owner of any such right
shall, to the extent of that right be entitled to the remedies provided by this Act and may individually
enforce such right by means of any suit, action or other proceeding without making the owner of any
other right a party to such suit, action or proceeding.
[Author's special rights. (1) Independently of the author's copyright and even after the
assignment either wholly or partially of the said copyright, the author of a work shall have the right-
(a) to claim authorship of the work; and
(b) to restrain or claim damages in respect of any distortion, mutilation, modification or other act in
relation to the said work which is done before the expiration of the term of copyright if such distortion,
mutilation, modification or other act would be prejudicial to his honour or reputation:
Provided that the author shall not have any right to restrain or claim damages in respect of any adaptation of a computer programme to which clause (aa) of sub-section (1) of section 52 applies.
Explanation.- Failure to display a work or to display it to the satisfaction of the author shall not be
deemed to be an infringement of the rights conferred by this section.]
(2) The right conferred upon an author of a work by sub-section (1), other than the right to claim
authorship of the work, may be exercised by the legal representatives of the author.
58. Rights of owner against persons possessing or dealing with infringing copies. - All
infringing copies of any work in which copyright subsists, and all plates used or intended to be used
for the production of such infringing copies, shall be deemed to be the property of the owner of the
copyright, who accordingly may take proceedings for the recovery of possession thereof or in respect
of the conversion thereof :
Provided that the owner of the copyright shall not be entitled to any remedy in respect of the
conversion of any infringing copies, if the opponent proves-
(a) that he was not aware and had no reasonable ground to believe that copyright subsisted in the
work of which such copies are alleged to be infringing copies; or
(b) that he had reasonable grounds for believing that such copies or plates do not -involve
infringement of the copyright in any work.
59. Restriction on remedies in the case of works of architecture. -(1) Notwithstanding anything
contained in
[the Specific Relief Act, 1963], where the construction of a building or other structure
which infringes or which, if completed, would infringe the copyright in some other work has been
commenced, the owner of the copyright shall not be entitled to obtain an injunction to restrain the
construction of such building or structure or to order its demolition.
(2) Nothing in section 58 shall apply in respect of the construction of a building or other structure
which infringes or which, if completed, would infringe the copyright in some other work.
60. Remedy in the case of groundless threat of legal proceedings. - Where any person claiming
to be the owner of copyright in any work, by circulars, advertisements or otherwise, threatens any
other person with any legal proceedings or liability in respect of an alleged infringement of the
copyright, any person aggrieved thereby may, notwithstanding anything contained
[in section 34 of
the Specific Relief Act, 1963] institute a declaratory suit that the alleged infringement to which the
threats related was not in fact an infringement of any legal rights of the person making such threats
and may in any such suit-
(a) obtain an injunction against the continuance of such threats; and
(b) recover such damages, if any, as he has sustained by reason of such threats.
Provided that this section shall not apply if the person making such threats, with due diligence,
commences and prosecutes an action for infringement of the copyright claimed by him.
61. Owners of copyright to be party to the proceeding. - (1) In every civil suit or other proceeding
regarding infringement of copyright instituted by an exclusive licensee, the owner of the copyright
shall, unless the court otherwise directs, be made a defendant and where such owner is made a
defendant, he shall have the right to dispute the claim of the exclusive licensee.
(2) Where any civil suit or other proceeding regarding infringement of copyright instituted by an
exclusive licensee is successful, no fresh suit or other proceeding in respect of the same cause of
action shall lie at the instance of the owner of the copyright. 62. Jurisdiction of court over matters arising under this Chapter. - (1) Every suit or other civil
proceeding arising under this Chapter in respect of the infringement of copyright in any work or the
infringement of any other right conferred by this Act shall be instituted in the district court having
jurisdiction.
(2) For the purpose of sub-section (1), and "district court having jurisdiction" shall, notwithstanding
anything contained in the Code of Civil Procedure, 1908, or any other law for the time being in force,
include a district court within the local limits of whose jurisdiction, at the time of the institution of the
suit or other proceeding, the person instituting the suit or other proceeding or, where there are more
than one such persons, any of them actually and voluntarily resides or carries on business or
personally works for gain.
122. Sub. by Act 38 of 1984, s. 57.
123. Subs. by Act 23 of 1983, s. 20, for "the Specific Relief Act, 1877" (w.e.f. 9-8-1984)
124. Subs. by s. 21, ibid., for "in section 42 of the Specific Relief Act, 1877" (w.e.f. 9;8-1984). INDIAN COPYRIGHT ACT, 1957
dec /2010 | {
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\chapter{Technical Details}
\vspace{3ex}
\vspace{3ex}
\textbf{Proof of Theorem \ref{theorem:1}.} To ease the notation, we drop the subscript ``$i$'' in the proof. Recall that $f(s^2|\sigma^2)$ and $\pi(\sigma^2)$ are the density function of $s^2|\sigma^2_i$ and the prior of $\sigma^2$ respectively. Define $m(s^2)$, $n(s^2)$ and $h(s^2)$ as
\begin{equation}\label{eqn:def:m}
m(s^2)=\int_0^\infty \,f(s^2|\sigma^2)\pi(\sigma^2)\,d\sigma^2,
\end{equation}
\begin{equation}\label{eqn:def:n}
n(s^2)=\int_0^\infty \sigma^2 \,f(s^2|\sigma^2)\pi(\sigma^2)\,d\sigma^2,
\end{equation}
and
\begin{equation}\label{eqn:def:h}
h(s^2)=\int_0^\infty (\sigma^2)^2 \,f(s^2|\sigma^2)\pi(\sigma^2)\,d\sigma^2.
\end{equation}
Note that $m(s^2)$ is the marginal distribution of $S^2$. Then
\begin{align*}
\hat\sigma_B^2=\frac{E\left[\,({\sigma^2})^2|S^2\,\right]}{E\left[\,{\sigma^2}|S^2\,\right]}
=\frac{\int_0^{\infty}(\sigma^2)^2 \pi(\sigma^2|s^2) \,d\sigma^2}{\int_0^{\infty}\sigma^2 \pi(\sigma^2|s^2) \,d\sigma^2}
=\frac{h(s^2)}{n(s^2)}.
\end{align*}
Take the derivatives of $n(s^2)(s^2)^{-(\frac{k}{2}-1)}$ with respect to $s^2$,
\begin{align}\label{eq:deriv_n}
\left[n(s^2)(s^2)^{-(\frac{k}{2}-1)}\right]'&=-\frac{k}{2}m(s^2)(s^2)^{-(\frac{k}{2}-1)}.
\end{align}
Consequently,
\begin{equation}\label{eq:nsc1}
{n(s^2)}{(s^2)^{-(\frac{k}{2}-1)}}=\int_0^{s^2} -\frac{k}{2} m(t) \,t^{-(\frac{k}{2}-1)} dt + C,
\end{equation}
for some constant $C$.
Note that the left hand side can be expressed as
\begin{align}\label{eq:nsc2}
n(s^2)(s^2)^{-(\frac{k}{2}-1)}
&=\int_0^\infty {(s^2)^{-(\frac{k}{2}-1)}\,\sigma^2f(s^2|\sigma^2)\pi(\sigma^2)\,d\sigma^2}\\ \nonumber
&=\int_0^\infty \frac{k\left(\frac{k}{\sigma^2}\right)^{\frac{k}{2}-1}e^{-\frac{ks^2}{2\sigma^2}}}{\Gamma\left(\frac{k}{2}\right)2^\frac{k}{2}} \cdot \,\pi(\sigma^2)\,d\sigma^2.
\end{align}
From (\ref{eq:nsc1}) and (\ref{eq:nsc2}), as $s^2$ approaches to zero,
\begin{align*}
C=\lim_{s^2 \rightarrow 0}n(s^2)(s^2)^{-(\frac{k}{2}-1)}=\frac{(k/2)^{k/2}}{\Gamma(k/2)}E\left(\frac{1}{\sigma^2}\right)^{k/2-1}=
\frac{k}{2}E\left(\frac{1}{S^2}\right)^{\frac{k}{2}-1}.
\end{align*}
Therefore,
\begin{align*}
{n(s^2)}{(s^2)^{-(\frac{k}{2}-1)}}
=\frac{k}{2} \int_{s^2}^\infty \,t^{-(\frac{k}{2}-1)} dM(t).
\end{align*}
Now, we consider the first and second order derivatives of $h(s^2)(s^2)^{-(\frac{k}{2}-1)}$ with respect to $s^2$,
\begin{equation}\label{eq:1}
\left[h(s^2)(s^2)^{-(\frac{k}{2}-1)}\right]'=-\frac{k}{2}n(s^2)(s^2)^{-(\frac{k}{2}-1)},
\end{equation}
\begin{equation}\label{eq:2nd:derivative}
\left[h(s^2)(s^2)^{-(\frac{k}{2}-1)}\right]''=\frac{k^2}{4}m(s^2)(s^2)^{-(\frac{k}{2}-1)}.
\end{equation}
Consequently,
\begin{align}\label{eq:3}
\left({h(s^2)}{(s^2)^{-(\frac{k}{2}-1)}}\right)'
&=\int_0^{s^2} \frac{k^2}{4} m(t)t^{-(\frac{k}{2}-1)} \,dt + C_1,
\end{align}
and
\begin{align}\label{eq:4}
{h(s^2)}{(s^2)^{-(\frac{k}{2}-1)}}
&=\int_0^{s^2}\int_0^{y} \frac{k^2}{4}m(t) \,t^{-(\frac{k}{2}-1)} \,dt\,dy + C_1 s^2 +C_2 \nonumber\\
&=\frac{k^2}{4}\int_0^{s^2} m(t)\,t^{-(\frac{k}{2}-1)}(s^2-t)\,dt + C_1 s^2 +C_2,
\end{align}
for some constants $C_1$ and $C_2$.
From (\ref{eq:1}) and (\ref{eq:3}), as $s^2$ approaches to zero, similar argument shows that
\begin{align*}
C_1=\lim_{s^2 \rightarrow 0} \left({h(s^2)}{(s^2)^{-(\frac{k}{2}-1)}}\right)'
=-\frac{k^2}{4}E\left(\frac{1}{S^2}\right)^{\frac{k}{2}-1}.
\end{align*}
Similarly, combine equations (\ref{eq:2nd:derivative}) and (\ref{eq:4}) and let $s^2$ approach to zero,
\begin{align*}
C_2=\lim_{s^2 \rightarrow 0} h(s^2)(s^2)^{-(\frac{k}{2}-1)} = \frac{k^2}{4}E\left(\frac{1}{S^2}\right)^{\frac{k}{2}-2}.
\end{align*}
Thus,
\begin{align*}
&\quad\,\, {h(s^2)}{(s^2)^{-(\frac{k}{2}-1)}}\\
&=\frac{k^2}{4}\int_0^{s^2} m(t)\,t^{-(\frac{k}{2}-1)}(s^2-t)\,dt
-\frac{k^2}{4}E\left(\frac{1}{S^2}\right)^{\frac{k}{2}-1}s^2 + \frac{k^2}{4}E\left(\frac{1}{S^2}\right)^{\frac{k}{2}-2}\nonumber\\
&=\frac{k^2}{4}\left[-\left(s^2\int_{s^2}^{\infty} m(t)\,t^{-\left(\frac{k}{2}-1\right)}\,dt\right)+ \left(\int_{s^2}^{\infty}m(t)\,t^{-(\frac{k}{2}-2)}\,dt\right) \right]\nonumber\\
&=\frac{k^2}{4}\int_{s^2}^{\infty}\,t^{-(\frac{k}{2}-1)}(t-s^2)\,dM(t). \nonumber
\end{align*}
Therefore,
\begin{align*}
\hat \sigma^2_B=\frac{h(s^2)}{n(s^2)
=\frac{k}{2}\left[ \frac{\int_{s^2}^{\infty}\,t^{-(\frac{k}{2}-2)}\,dM(t)} {\int_{s^2}^{\infty}\,t^{-(\frac{k}{2}-1)} \,dM(t)} - s^2 \right].
\end{align*}
\qed
\vspace{3ex}
\textbf{Proof of Theorem \ref{theorem:2}.} We introduce one of the momumental theorems in the empirical process, on which our proof is based, contributed by \citet{Blum:1955} and \citet{Dehardt:1971}.
\begin{theorem} (Blum-DeHardt)\label{Blum}
Let F be a class of measurable functions such that $ N_{[]}(\epsilon,\mathcal{F},L_1(P)) < \infty,\,\,$ for every $\epsilon>0$. Then $\mathcal{F}$ is P-Glivenko-Cantelli.
\end{theorem}
The bracket $[l,u]$ is the set of all the functions $f\in\mathcal{F}$ with $l\leq f\leq u$. An $\epsilon$-bracket is a bracket with $\Vert u-l \Vert\leq\epsilon$. The bracketing number $N_{[]}(\epsilon,\mathcal{F},L_1(P))$ is the minimum number of $\epsilon$-brackets with which $\mathcal{F}$ can be covered.
We only prove the part for the numerator and the denominator can be similarly done.
Let $\mathcal{F}=\left\{f : f(t,b)= t^{-(k/2-2)}\mathbb{I}( t>b),\,\, b >0\right\}$ and $P f(t,b) =\int_{b}^{\infty} {t}^{-(k/2-2)}\,dM(t).$ It suffices to show that $\mathcal{F}$ is a \textit{P-Glivenko-Cantelli} class of functions. Since $\int_{0}^\infty t^{-({k}/{2}-2)} \, dM(t) < \infty,\,\,$ for any $\,\,\epsilon>0,\,\,$ an infinite collection of real numbers $0=v_0<v_1<v_2<\cdots <v_m = \infty$ can be found such that
\begin{align*}
Pf(t,v_{j-1})-Pf(t,v_j)
&=\int_{v_{j-1}}^{\infty} {t}^{-(k/2-2)}\, dM(t) -\int_{v_j}^{\infty} {t}^{-(k/2-2)}\, dM(t)\\
&=\int_{v_{j-1}}^{v_j} {t}^{-(k/2-2)}\, dM(t)\\
&\leq \epsilon
\end{align*}
for all $1 \leq j \leq m$, with
\begin{equation*}
Pf(t,v_m^{-})=\lim_{v_m\uparrow {\infty}} Pf(t,v_m)=\lim_{v_m\uparrow {\infty}}\int_{v_m}^{\infty} {t}^{-(k/2-2)}\, dM(t)=0.
\end{equation*}
Consider the collection of brackets $\{[l_j,u_j],1 \leq j \leq m\}$, with $l_j(t) ={t}^{-(k/2-i)}\,1\{t \geq v_{j}\}$ and $u_j(t)={t}^{-(k/2-i)}\,1\{t>v_{j-1}\}$. Now each $f \in \mathcal{F}$ is in at least one bracket and $\vert u_j-l_j \vert_{P} = Pf(t,v_{j-1})-Pf(t,v_{j}^{-}) \leq \epsilon $ for all $1 \leq j \leq m$.
Thus, by Theorem \ref{Blum}, $\mathcal{F}$ is a \textit{P-Glivenco-Cantelli Class} of functions. \qed\\
\textbf{Proof of Theorem \ref{theorem:3}.} Let
\begin{equation*}
A_p(s_i^2)=\int_{s_i^2}^\infty t^{-\left(\frac{k}{2}-2\right)} \,dM_p(t),
A(s_i^2)=\int_{s_i^2}^\infty t^{-\left(\frac{k}{2}-2\right)}dM(t),
\end{equation*}
and
\begin{equation*}
B_p(s_i^2)=\int_{s_i^2}^\infty t^{-\left(\frac{k}{2}-1\right)} \,dM_p(t),
B(s_i^2)=\int_{s_i^2}^\infty t^{-\left(\frac{k}{2}-1\right)} \,dM(t).
\end{equation*}
According to the proof of Theorem \ref{theorem:2}, $\sup_{s_i^2\in R}|A_p(s_i^2)-A(s_i^2)|\to 0\,\,$ and $\sup_{s_i^2\in R}|B_p(s_i^2)-B(s_i^2)|\to 0\,\,a.s.$.
Let $L=\inf_{s_i^2\in D^\delta}\{ B(s_i^2)\}$. Then for any $\epsilon>0$, when $p$ is sufficiently large
\[
\inf_{s_i^2\in D^\delta}B_p(s_i^2) \ge L-\epsilon\,\,\,\,\, a.s.,
\]
and $ \sup_{s_i^2\in R}A_p(s_i^2) \le C,\,\,\, a.s.$ for some constant $C$.
Then
\begin{eqnarray*}
&&\sup_{s_i^2\in D^\delta}\left|\hat{\sigma}_{i,NEBV}^2 - \hat{\sigma}_{i,B}\right| \\
&=& \sup_{s_i^2\in D^\delta}\left|\,\frac{A_p(s_i^2)}{B_p(s_i^2)}-\frac{A(s_i^2)}{B(s_i^2)}\,\right|\\
&=&\sup_{s_i^2\in D^\delta} \left|\, \frac{A_p(s_i^2)(B(s_i^2)-B_p(s_i^2))}{B_p(s_i^2)B(s_i^2)}+ \frac{A_p(s_i^2)-A(s_i^2)}{B(s_i^2)}\,\right| \\
&\le & \frac{C}{L^2}\sup_{s_i^2\in D^\delta}\left|B(s_i^2)-B_p(s_i^2)\right| + \frac{1}{L} \sup_{s_i^2\in D^\delta}\left |A(s_i^2)-A_p(s_i^2)\right| \to 0, \,\,\,a.s..
\end{eqnarray*}
\qed
\vspace{3ex}
\subsection{Construction of Confidence Interval for Selected Parameter}
Note that the posterior distribution of $\theta_i$ is
\begin{equation*}
\,\,\,\theta_i \big|X_i, \sigma_i^2\,\,\,\sim \,\,\,\,N\left(\,\frac{\tau^2}{\tau^2+\sigma_i^2}X_i+\frac{\sigma_i^2}{\tau^2+\sigma_i^2}\mu,\,\,\, \frac{\tau^2 \sigma_i^2}{\tau^2+\sigma_i^2} \right).
\end{equation*}
When $\sigma_i^2$'s are known, the hyper-parameters $(\mu,\tau^2)$ can be estimated using the method of moments as
\begin{equation*}
\hat \mu =\bar X \,\textrm{ or }\, \sum_{i=1}^p\frac{X_i/\sigma_i^2}{\sum_{i=1}^p 1/\sigma_i^2}, \,\,\textrm{ and }\,\, \hat\tau^2=\max\left( \frac{1}{p}\sum_{i=1}^p(X_i-\hat\mu)^2-\frac{1}{p} \sum_{i=1}^p\sigma_i^2,\,\,\, \tau_0^2\right),
\end{equation*}
where $\tau_0^2$, known as the truncated value (\citet{Hwang:Qiu:Zhao:2009}), is defined as, with $\gamma^*\ge\Pr_{\tau^2}(\hat\tau^2=0)$,
\[
\tau_0^2=\frac{1}{p}\left(z_{\gamma^*}^2+z_{\gamma^*}\sqrt{z_{\gamma^*}^2+2\sum_{i=1}^p\sigma_i^2}\,\right).
\]
For unknown $\sigma_i^2$'s, we replace them by various estimates $\hat{\sigma}^2_{i}$ to get the following $100(1-\gamma)\%$ empirical Bayesian confidence interval
\begin{equation}\label{eq:CI}
\left(\hat \theta_i - z_{\gamma/2}\sqrt{\frac{\hat\sigma_{i}^2 \hat\tau^2}{\hat\sigma_{i}^2+\hat\tau^2}}\,,\,\,\,\hat \theta_i + z_{\gamma/2}\sqrt{\frac{\hat\sigma_{i}^2 \hat\tau^2}{\hat\sigma_{i}^2+\hat\tau^2}}\,\,\right),
\end{equation}
where
\begin{equation*}
\hat\theta_i =\frac{\hat\tau^2}{\hat\sigma_{i}^2+\hat\tau^2}X_i+ \frac{\hat\sigma_{i}^2}{\hat\sigma_{i}^2+\hat\tau^2}\hat\mu.
\end{equation*}
In many applications, we might be only interested in $\theta_{(p)}$ for which the corresponding $T$-statistic attains the maximum in magnitude among all the $T$-statistic, $T_i=\frac{X_i}{S_i}$. We then add the parentheses adjustment according to \citet{Hwang:Zhao:2013}.
In the comparison, we applied $\hat{\sigma}_{NEBV}^2$, $\hat{\sigma}_{ELJS}^2$ (\citet{Cui:Hwang:Qiu:Blades:Churchill:2005}) and $\hat{\sigma}_{TW}^2$ (\citet{Tong:Wang:2007}). We wanted to point out that these methods are not designed for estimating the variance post the selection. Actually, to the best of our knowledge, there is no methods designed for estimating the variances post the selection in the exising literature.
\subsection{Independent Case}
We generated $(X_i,S_i^2)$'s according to Model (\ref{eqn:model:mean}) with different choices of the prior for $\sigma_i^2$'s, including
inverse Gamma prior ($IG(\alpha,\beta)$), mixture of Gamma/inverse Gamma prior, and log-normal prior ($LN(\mu_v,\tau_v^2)$).
The dimension for the numerical study is 3,000.
After obtaining the statistic $(X_i,S_i^2)$, we made the inference for the parameters $(\theta_{(p)},\sigma_{(p)}^2)$ corresponding to the observation with the largest $t$-statistic in magnitude. These steps were replicated 1,000 times.
\begin{figure}
\begin{tabular}{c c}
\includegraphics[width=60mm]{Risk_p_2_a_723_b_246.pdf}&
\includegraphics[width=60mm]{Risk_p_2_a_805_b_472.pdf} \\
\includegraphics[width=60mm]{Risk_p_1_a_3000_b_1000.pdf} &
\includegraphics[width=60mm]{Risk_p_1_a_2444_b_722.pdf}
\end{tabular}
\caption{Plots of $\ln\textrm{(Risk)}$ for estimating $\sigma^2_{(i)}$ against $\frac{\tau^2}{\tau^2+E(\sigma^2_i)}$ under log-normal (the first row) and inverse gamma prior (the second row) for $\sigma^2_i$.}
\label{fig:indep_risk}
\end{figure}
\begin{figure}
\begin{tabular}{c c}
\includegraphics[width=60mm]{Risk_MixIG.pdf}&
\includegraphics[width=60mm]{Risk_MixGam.pdf}
\end{tabular}
\caption{Plots of $\ln\textrm{(Risk)}$ for estimating $\sigma^2_{(i)}$: $0.5*IG(6,1)+0.5*IG(6,4)$ for the left panel and $0.5*Gamma(4,1/16)+0.5*Gamma(6,1/8)$ for the right panel.}\label{fig:risk_mix}
\end{figure}
We first compared the risk of different estimators for estimating the variance $\sigma_{(p)}^2$. The logarithm of the risks based on the loss function (\ref{eq:lossselect}) are reported in Figure \ref{fig:indep_risk}. It is clearly seen that the proposed NEBV has the smallest risk for all the parameter settings.
Next, we considered the confidence interval for $\theta_{(p)}$. In addition to the three intervals by replacing $\sigma_i^2$ with one of the three variance estimators above, we included the second-order corrected (SOC) interval (\citet{Hwang:Zhao:2013}) and Bonferroni's corrected $T$-interval: $X_{(p)}\pm\, t_{k,\frac{\gamma}{2p}}\,S_{(p)}$. The SOC intervals are designed for the log-normal model where $\log S_i^2|\log \sigma_i^2\sim N(\log\sigma_i^2+m_k,\sigma_k^2)$ and $\log\sigma_i^2\sim N(\mu_v,\tau_v^2)$. We set the desired coverage probability as 95\%, namely $\gamma=0.05$.
\begin{figure}
\begin{tabular}{c c}
\includegraphics[width=60mm]{Coverage_p_2_a_723_b_246.pdf}&
\includegraphics[width=60mm]{Coverage_p_2_a_805_b_472.pdf} \\
\includegraphics[width=60mm]{Length_p_2_a_723_b_246.pdf}&
\includegraphics[width=60mm]{Length_p_2_a_805_b_472.pdf}
\end{tabular}
\caption{Plots of the coverage probabilities (the first row) and the average length ratios (the second row) of various intervals for $\theta_{(p)}$ against $\frac{\tau^2}{\tau^2+E(\sigma^2_i)}$ under log-normal prior with error bar: $0.95-1.96\sqrt{(0.95)(0.05)/1000}$.}
\label{fig:indep_lognormal}
\end{figure}
\begin{figure}
\begin{tabular}{c c}
\includegraphics[width=60mm]{Coverage_p_1_a_3000_b_1000.pdf} &
\includegraphics[width=60mm]{Coverage_p_1_a_2444_b_722.pdf}\\
\includegraphics[width=60mm]{Length_p_1_a_3000_b_1000.pdf} &
\includegraphics[width=60mm]{Length_p_1_a_2444_b_722.pdf}
\end{tabular}
\caption{Plots of the coverage probabilities (the first row) and the average length ratio (the second row) for various intervals of $\theta_{(p)}$ for the inverse Gamma prior
}
\label{fig:indep_gamma}
\end{figure}
We reported the simulated results corresponding to the log-normal prior in Figure \ref{fig:indep_lognormal}. The coverage probabilities were reported in the first row. It is seen that the intervals based on NEBV, the Bonferroni's corrected $t$-interval, and SOC intervals all guarantee good coverage probabilities for all the hyper-parameters. The intervals based on the other two estimators, ELJS and TW, have substantially low coverage probabilities. For instance, for the inverse Gamma prior with $\alpha=3$ and $\beta=1$, the coverage probability of intervals based on TW can be as low as 35\%. This is expected because these method are not designed for the setting post the selection. We also reported the average ratio of the length of all the confidence intervals to the length of $t$-interval based on the Bonferroni's correction in the second row of the figure. It is seen that among the three intervals which guarantee a desired coverage probability, the one based on NEBV is the shortest one.
In Figure \ref{fig:indep_gamma}, we reported the coverage probability and average length ratio of the various approaches for the inverse Gamma prior. The intervals based on NEBV and the Bonferroni's corrected $t$-interval still have good coverage probability. However, the coverage probability of SOC interval dropped below the nominal level. SOC intervals are designed to work well for the log-normal model and does not work well when this assumption does not hold.
\begin{figure}
\begin{tabular}{c c}
\includegraphics[width=60mm]{Coverage_MixIG.pdf} &
\includegraphics[width=60mm]{Coverage_MixGam.pdf} \\
\includegraphics[width=60mm]{Length_MixIG.pdf} &
\includegraphics[width=60mm]{Length_MixGam.pdf}
\end{tabular}
\caption{Plots of the coverage probabilities and the length ratio of confidence intervals for $\theta_{(p)}$ under Inverse Gamma and Gamma mixture prior for $\sigma^2_i$ : $0.5*IG(6,1)+0.5*IG(6,4)$ for left panels and $0.5*Gamma(4,1/16)+0.5*Gamma(6,1/8)$ for right panels.}
\label{fig:ind_mix}
\end{figure}
In Figure \ref{fig:ind_mix}, the variances $\sigma_i^2$'s were generated from a mixture Gamma/inverse Gamma distribution. Although SOC intervals can be shorter than the NEBV-based intervals, but the coverage probabilities of SOC intervals were much lower than 95\% for some parameter settings. The NEBV-based intervals are robust to the prior of $\sigma_i^2$'s and still work well. We have done extensive simulations and all of which demonstrated the patterns similar to the representative cases reported here.
\subsection{Dependent Case}\label{sec:dependent}
The previous estimators of the variances and the confidence intervals (\ref{eq:CI}) are based on the independence assumption. In this section, we compared their numerical performance when the independence assumption is violated. We generated the data from the multivariate normal distribution. Namely, for $i=1,2,\ldots, n$,
\begin{align}\label{eq:simulmodel2}
\begin{split}
\boldsymbol{X_{i,\cdot}}=(x_{i1},\ldots, x_{ip}) \,|\, \boldsymbol{\theta},\, \Sigma\,\,\,\, &\overset{}{\sim}\,\,\,\, N(\boldsymbol{\theta},\, \Sigma), \qquad \theta_i \,\,\,\, \overset{iid}{\sim}\,\,\,\, N(\mu, \tau^2).
\end{split}
\end{align}
Here, the variance-covariance matrix $\Sigma$ is given as $D^{1/2}RD^{1/2}$ where $D=diag(\sigma_1^2,\ldots,\sigma_p^2)$ with $\sigma_i^2\overset{iid}\sim IG(\alpha,\beta)$. Four types of correlation matrix $R$ were considered:
\begin{enumerate}
\item[(i)] Banded Correlation matrix ($\rho_{ij}=0$ when $|j-i|>d$ and $\rho_{ij}=\rho$ when $0<|j-i|\le d$),
\item[(ii)] AR Correlation matrix ($\rho_{ij}=\rho^{|i-j|}$),
\item[(iii)] Sparse Correlation matrix, and
\item[(iv)] Correlation matrix from real data.
\end{enumerate}
In the banded case, $(d, \rho)$ were set as $(5,0.1), (4,0.2), (3,0.3), (2,0.4)$, and $(1,0.5)$ respectively. For the AR case, $\rho$ was chosen as 0.5, 0.75, 0.9, 0.95, and 0.99 respectively. To get a sparse correlation matrix, we started with a $p\times p$ matrix $A$ by setting 1.5\% of randomly chosen entries as numbers from $uniform(a,b)$ and the rest as zero. Let $R=B^{-\frac{1}{2}}A'AB^{-\frac{1}{2}}$ where $B$ is a diagonal matrix with the diagonal-line elements being the diagonal line of $A'A$. The $R$ is a sparse correlation matrix and about 77\% of the entries are zero under this setting. We considered the following choices of $(a,b)$: $(-1,1),\,\,(0,1),\,\,(0.5,1),\,\,(0.9,1),\,\, $ and $(0.9,0.9)$.
\begin{figure}
\begin{tabular}{c c}
\includegraphics[width=60mm]{Coverage_AR_rho_75_df_2.pdf} &
\includegraphics[width=60mm]{Coverage_AR_rho_95_df_2.pdf}\\
\includegraphics[width=60mm]{Coverage_Banded_rho_30_df_2_k_3.pdf} &
\includegraphics[width=60mm]{Coverage_Banded_rho_40_df_2_k_2.pdf}\\
\includegraphics[width=60mm]{Coverage_Sparse_a_10_b_20_df_2_spar_77.pdf} &
\includegraphics[width=60mm]{Coverage_Sparse_a_5_b_5_df_2_spar_77.pdf}
\end{tabular}
\caption{Plots of the coverage probabilities of four intervlas with AR, Banded and Sparse correlation matrices.}\label{fig:dependent}
\end{figure}
\begin{figure}
\begin{tabular}{c c}
\includegraphics[width=60mm]{Length_AR_rho_75_df_2.pdf} &
\includegraphics[width=60mm]{Length_AR_rho_95_df_2.pdf}\\
\includegraphics[width=60mm]{Length_Banded_rho_30_df_2_k_3.pdf} &
\includegraphics[width=60mm]{Length_Banded_rho_40_df_2_k_2.pdf}\\
\includegraphics[width=60mm]{Length_Sparse_a_10_b_20_df_2_spar_77.pdf} &
\includegraphics[width=60mm]{Length_Sparse_a_5_b_5_df_2_spar_77.pdf}
\end{tabular}
\caption{Plots of the average length ratio of four intervlas with AR, Banded and Sparse correlation matrices.}\label{fig:dep:length}
\end{figure}
We have done extensive simulation studies and only reported representative results in Figure \ref{fig:dependent}. Under all these dependence cases, the coverage probability of the NEBV-based intervals for $\theta_{(p)}$ guarantee the desired coverage probability. On the other hand, the intervals based on ELJS and TW fail to achieve the satisfactory coverage probability.
In Figure \ref{fig:dep:length}, we reported the average length ratio of the confidence intervals.
\begin{figure}
\begin{tabular}{c c}
\includegraphics[width=60mm]{Coverage_Colon.pdf} &
\includegraphics[width=60mm]{Coverage_Leuk.pdf}\\
\includegraphics[width=60mm]{Length_Colon.pdf} &
\includegraphics[width=60mm]{Length_Leuk.pdf}\\
\end{tabular}
\caption{Plots of coverage probabilities, length ratio of confidence intervals for $\theta_{(p)}$ based on the Colon Cancer and Leukemia Data.}
\label{fig:covlength_Colon}
\end{figure}
In the last case, we considered a correlation matrix estimated from two microarray experiments : Leukemia (\citet{Golub:Slonim:Tamayo:1999}) and Colon Cancer (\citet{Alon:Barkai:Notterman:1999}). We downloaded the data from \url{http://www.bioconductor.org/packages/release/data/experiment/html/golubEsets.html} and \url{http://genomics-pubs.princeton.edu/oncology/affydata/index.html}. The leukemia data includes the expressions of genes extracted from patients with two types of leukemia($p=7129$): Acute Lymphoblastic Leukemia(ALL, 47 patients) and Acute Myeloid Leukemia (AML, 25 patients). The colon cancer data contains gene expressions of 2000 genes for 22 normal people and 40 patients. Since leukemia data and colon cancer data have 72 and 62 observations with 7128 and 2000 variables, respectively. We randomly selected 70 and 60 variables respectively from each dataset and calculated the sample covariance matrices which were treated as $\Sigma$ in the simulations.
The results of coverage probabilities, and length of the intervals for $\theta_{(p)}$ are shown in Figure \ref{fig:covlength_Colon}. What we have observed is similar to that for the other settings. The intervals based on NEBV guarantees a desired coverage probability; while the coverage probabilities of the intervals based on ELJS and TW could be much lower than the nominal level.
\begin{table}
\begin{tabular}{|ccc||ccc|}
\hline
Method & Mean &Median &Method & Mean & Median\\
\hline
\textit{Leukemia} & & & \textit{Colon} & & \\
$S^2$ & 0.211 & 0.209 & $S^2$& 0.238 & 0.232 \\
\textit{ELJS} & 0.166 & 0.164 & \textit{ELJS} & 0.176 & 0.170 \\
\textit{TW} & 0.169 & 0.167 & \textit{TW} & 0.178 & 0.172\\
\textit{NEBV} & 0.149 & 0.146 & \textit{NEBV}& 0.156 & 0.152 \\
\hline
\end{tabular}
\caption{Percentage of discordant genes for various intervals.}\label{tab:leukemia}
\end{table}
\section{Real data Analysis}\label{sec:realdata}
According to a 2016 poll of 1,500 scientists reported in the journal {\it Nature}, 70\% of them had failed to reproduce at least one other scientist's experiment (\citet{Baker:2016}). {\it Replication crisis}, which has long-standing roots, catches growing awareness in the last decades. A natural question is in what degree, the statistical conclusion of a certain method based on the data agrees with the conclusion when provided with different/new data set. In this section, we used the above two microarray data to examine the performance of various statistical methods.
For the Leukemia data set, we first randomly split the subjects into two subgroups such that both subgroups contain the similar numbers of subjects from ALL and AML groups. We then constructed confidence intervals based on one sub-group. We declared a gene to be significant if the corresponding interval does not enclose zero. We did the same for the other sub-group. We call a gene {\it discordant} if the interval based on the first subgroup does not enclose zero while the interval based on the second subgroup encloses zero. Namely, a gene is {\it discordant} implies that the conclusion that it is significant based on the first subgroup cannot be replicated based on the second one. We repeated these steps 1,000 times to calculate the average proportions of discordant genes. We did the same thing for the colon cancer data and reported the results in Table \ref{tab:leukemia} and Figure \ref{fig:boxplot}.
\begin{figure}
\begin{tabular}{|c|c|}\hline
\includegraphics[width=55mm,height=60mm]{HistLeuk.pdf} &
\includegraphics[width=55mm,height=60mm]{HistColon.pdf} \\
\hline
\end{tabular}
\caption{Boxplots of the percentage of discordant genes for leukemia and colon cancer data.}
\label{fig:boxplot}
\end{figure}
In Figure \ref{fig:boxplot}, we plotted the box-plot based on four interval constructions: intervals based on the sample variance, ELJS, TW, and NEBV. In Table \ref{tab:leukemia}, we summarized the summary statistic based on 1,000 replications. It is seen that the intervals based on NEBV commit the smallest number of {\it discordance} and the difference is statistically significant.
In summary, as shown in both simulations and real data analysis, the performance of the intervals based on NEBV is better than its competitors and is thus recommended.
\subsection{Loss Functions}
Let $\boldsymbol{\hat{\sigma}^2}=(\hat{\sigma}_1^2, \hat{\sigma}_2^2,\ldots, \hat{\sigma}_p^2)$ be an estimator of $\boldsymbol{\sigma^2}.$
Consider the following loss function:
\begin{equation}\label{eq:loss1}
L_1\left(\boldsymbol{{\sigma}^2},\boldsymbol{\hat\sigma^2}\right) =\sum_{i=1}^p\left(\frac{\sigma_i^2}{\hat \sigma_i^2}-1\right)^2.
\end{equation}
Other commonly used loss functions include
\begin{equation}
L_2\left(\boldsymbol{{\sigma}^2},\boldsymbol{\hat\sigma^2}\right) =\sum_{i=1}^p\left(\frac{\hat{\sigma}_i^2}{ \sigma_i^2}-1\right)^2,
\end{equation}
and
\begin{equation}
L_3\left(\boldsymbol{{\sigma}^2},\boldsymbol{\hat\sigma^2}\right) =\sum_{i=1}^p\left(\frac{\hat{\sigma}_i^2}{ \sigma_i^2}-\ln\frac{\hat{\sigma}_i^2}{\sigma_i^2}-1\right).
\end{equation}
The difference between $L_1$ and $L_2$ is the position of $\sigma_i^2$ and $\hat{\sigma}_i^2$ in the ratio.
The loss function $L_3$ is commonly known as the Stein's loss.
\begin{figure}[h!]
\includegraphics[width=130mm,height=100mm]{Loss_Function.pdf}
\caption{Loss Functions for $\hat\sigma^2$ (true value = 0.1)}\label{fig:loss}
\end{figure}
All these three loss functions are scale-invariant and equal zero when $\hat\sigma_i^2=\sigma_i^2$ for all $i=1,\ldots,p$. The loss increases when the ratio of $\hat{\sigma}_i^2$ to $\sigma_i^2$ moves away from one. Figure \ref{fig:loss} displays these loss functions when $p=1$ and $\sigma^2=0.1$. It is shown in the graph that, when the estimator of $\sigma^2$ is close to zero, the loss function $L_1$ and the Stein's loss function $L_3$ assign much larger penalty than the square loss function $L_2$. Estimating the variance by an even smaller number will result in a inflated probability of committing type I error which should be avoided. Therefore, one should put more penalty on the underestimation (P. 332 of \citet{Casella:Berger:2001}). The loss function $L_2$ fails to do so because there is a fixed upper limit for the penalty at the lower end. On the other hand, by using the loss function $L_1$, we can avoid such underestimation. Stein's loss function has also been used in literature (\citet{Stein:1977, Dey:Srinivasan:1985, Tong:Wang:2007}) and the penalty goes to $\infty$ when the estimation goes to zero. However, as Shown in Section \ref{sec:npeb}, the corresponding Bayes rule depends on the marginal density of the sample variances which is difficult to estimate.
In many applications, a practitioner is only interested in a certain set of parameters, denoted as $\mathcal{S}$, after applying a selection rule. For instance, in microarray analysis, a scientist can select a set of genes based on the magnitude of $T$-statistics and then zoom in on these parameters for further investigation. Upon selection, the loss function can be naturally modified as
\begin{equation}\label{eq:lossselect}
L_1^\mathcal{S}(\hat{\boldsymbol{\sigma}}^2, \boldsymbol{\sigma}^2) = \sum_{i\in\mathcal{S}}\left( \frac{\sigma_i^2}{\hat{\sigma_i}^2}-1\right)^2.
\end{equation}
\section{Introduction}\label{sec:intro}
\input{Intro.tex}
\section{Loss Functions and Risks}\label{sec:lossfunction}
\input{lossfunction.tex}
\section{Nonparametric Empirical Bayes Estimator for Variances}\label{sec:npeb}
\input{npeb.tex}
\section{Analytic Properties of NEBV}\label{sec:analytic}
\input{analytic.tex}
\section{Application to the Selected Intervals}\label{sec:application}
\input{application.tex}
\section{Conclusion}\label{sec:conclusion}
\input{conclusion.tex}
\newpage
\subsection{Model Assumption}
We consider the following non-parametric Bayesian hierarchical model
\begin{equation}
\begin{cases}\label{eqn:model}
\,\,\,S_i^2 \big|\sigma_i^2 &\overset{ind}{\sim} \,\,\,\,\sigma_i^2\frac{\chi_k^2}{k}, \\
\,\,\,\sigma_i^2 &\overset{iid}{\sim} \,\,\,\,\pi(\sigma_i^2),
\end{cases}
\end{equation}
where $\pi(\sigma_i^2)$ is an arbitrary prior of $\sigma_i^2$.
Under Model (\ref{eqn:model}), the marginal distribution of $S_i^2$ can be written as
\begin{equation*}\label{eqn:marginal}
m(s_i^2)=\int_0^\infty f(s_i^2|\sigma_i^2)\pi(\sigma_i^2)\,d\sigma_i^2,
\end{equation*}
and the posterior distribution of $\sigma_i^2|S_i^2$ can be written as
\begin{equation*}\label{eqn:posterior}
\pi(\sigma_i^2|s_i^2)=\frac{f(s_i^2|\sigma_i^2)\pi(\sigma_i^2)\,}{\int_0^\infty f(s_i^2|\sigma_i^2)\pi(\sigma_i^2)\,d\sigma_i^2}.
\end{equation*}
We will now derive the Bayes decision rule based on the loss function $L_1$ (\ref{eq:loss1}).
Given $\boldsymbol{S^2}=\left(S_1^2,\ldots,S_p^2\right)$, then
\begin{equation}\label{eqn:cond:loss:1}
E\left[\sum_{i=1}^p \left.\left(\frac{\sigma_i^2}{\hat \sigma_i^2}-1 \right)^2 \,\right| \boldsymbol{S^2} \right] = \sum_{i=1}^p\left[ \frac{1}{\hat{\sigma}_i^4}E\left((\sigma_i^2)^2|\boldsymbol{S^2}\right) -\frac{2}{\hat{\sigma}_i^2}E\left(\sigma_i^2|\boldsymbol{S^2}\right) +1\right].
\end{equation}
Therefore, the Bayes decision rule $\boldsymbol{\hat{\sigma}_{B}^2}=(\hat{\sigma}_{1,B}^2, \hat{\sigma}_{2,B}^2,\ldots, \hat{\sigma}_{p,B}^2)$ which minimizes the Bayes risk is
\begin{equation}\label{eqn:bayes:estimator}
\hat{\sigma}_{i,B}^{2} =\frac{E\left[\,(\sigma_i^2)^2|\boldsymbol{S^2}\right]}{E\left[\,{\sigma_i^2}|\boldsymbol{S^2}\right]}, \quad i=1,\ldots,p.
\end{equation}
\begin{theorem}\label{theorem:1}
Assume Model (\ref{eqn:model}). Let $m(s_i^2)$ be the marginal density of $S_i^2$ and $M(s_i^2)$ be the corresponding cumulative distribution function. Assume that both
\begin{equation*}
\int_{0}^{\infty}\,t^{-(\frac{k}{2}-2)}\,dM(t)\,\,\,\,\,
\textrm{and}\,\,\,\,\,
\int_{0}^{\infty}\,t^{-(\frac{k}{2}-1)} \,dM(t)
\end{equation*}
exist. Then, given $\boldsymbol{S^2}$, the Bayes decision rule of $\boldsymbol{\sigma}^2$ based on the loss function $L_1$ is
\begin{equation}\label{eqn:est:var}
\hat \sigma_{i,B}^{2}
=\frac{k}{2}\left[ \frac{\int_{s_i^2}^{\infty}\,t^{-(\frac{k}{2}-2)}\,dM(t)} {\int_{s_i^2}^{\infty}\,t^{-(\frac{k}{2}-1)} \,dM(t)} - s_i^2 \right].
\end{equation}
\end{theorem}
The Bayes decision rule (\ref{eqn:est:var}) relies on the marginal cumulative distribution function $M(t)$ which can be easily and reliably estimated using the empirical distribution function $M_p(t) =\frac{1}{p}\sum_i I( S_i^2\le t)$. When replacing $M(t)$ by $M_p(t)$, we have the following \textbf{N}on-parametric \textbf{E}mpirical \textbf{B}ayes estimator of the \textbf{V}ariances (NEBV).
\begin{align}\label{est:5}
\hat \sigma^2_{i,NEBV}
&=\frac{k}{2}\left[ \frac{\int_{s_i^2}^{\infty}\,t^{-(\frac{k}{2}-2)}\,dM_p(t)} {\int_{s_i^2}^{\infty}\,t^{-(\frac{k}{2}-1)} \,dM_p(t)} - s_i^2 \right] =\frac{k}{2}\left[\frac{\sum_{s_j^2\ge s_i^2}(s_j^2)^{-(\frac{k}{2}-2)}} {\sum_{s_j^2\ge s_i^2}(s_j^2)^{-(\frac{k}{2}-1)}} - s_i^2 \right].
\end{align}
Let
\begin{eqnarray*}
a_{ij} =\left\{ \begin{array}{ll} (s_j^2)^{-(\frac{k}{2}-1)}, & \textrm{if $s_j^2\ge s_i^2$}, \\
0,&\textrm{otherwise},
\end{array}
\right.
\end{eqnarray*}
$ A_i = \sum_j a_{ij}$, and $w_{ij}=\frac{a_{ij}}{A_i}$. The NEBV can be rewritten as
\begin{equation}\label{est:6}
\hat \sigma^2_{i,NEBV}=\frac{k}{2}\left( \sum_j w_{ij}s_j^2-s_i^2 \right).
\end{equation}
Note that $w_{ij}>0$ if and only if $s_j^2\ge s_i^2$, implying that when estimating $\sigma_i^2$, the estimator (\ref{est:6}) only relies on the data $s_j^2$'s which are greater than or equal to $s_i^2$. Second, $w_{ij}$ decreases with respect to $s_j^2$, implying that $\hat\sigma^2_{i,NEBV}$ puts less weight on those observations which are farther away from $s_i^2$.
For a given selection rule, let $S^2_{(i)}$ be the sample variance of the $i$-th selected data. Then the corresponding variance, $\sigma_{(i)}^2$, is estimated by
\begin{equation}\label{est:sel}
\hat \sigma^2_{(i),NEBV}=\frac{k}{2}\left( \sum_{j} w_{(i)j}s_j^2- s^2_{(i)} \right),
\end{equation}
where $w_{(i)j}$ is defined similar to $w_{ij}$ with $s_i^2$ being replaced by $s_{(i)}^2$.
We would like to point out that due to the nature of the NEBV, it suffers when estimating the parameters with the largest sample variances. When implementing this method, we estimate those parameters corresponding to the top $b$ (say $b=5$) largest sample variances by these sample variances.
When assuming Stein's loss function, basic calculation shows that
\[
\hat{\sigma}_{i,B}^{'2} = \frac{1}{E\left( \frac{1}{\sigma_i^2}\Big|S_i^2\right) } = \left( \frac{k-2}{kS_i^2} - \frac{2}{k}\cdot\frac{m'(S_i^2)}{m(S_i^2)}\right)^{-1}.
\]
The empirical Bayes version of this requires the estimation of the marginal density and its derivative. However, the estimation of the density function is a challenging problem itself and the performance of various techniques for density estimation further deteriorates at the tail. Additionally, choosing a tuning parameter optimally in kernel density estimation is a daunting task, not even to mention that the optimal tuning parameters for estimating the density and its derivative do not even agree.
On the contrary, the NEBV relies on the sample variances via its marginal cumulative distribution function, which can be easily estimated.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,891 |
Q: When would piping work - does application have to adhere to some standard format? What is stdin and stdout in Unix? I am using a program that allows me to do
echo "Something" | app outputilfe
But a similar program doesnt do that (and its a bash script that runs Java -jar internally).
Both works with
app input output
This leads to me this question . And why some programs do it and some don't ?
I am basically trying to understand in a larger sense how does programs inter-operate so fluently in *nix - The idea behind it- what is stdin and stdout in a simple layman terms and
A simple way of writing a program that takes an input file and writes an output file is:
Write a code in such a manor that the first 2 positional arguments get interpreted as input and output strings where input should a file that is available in the file system and output is a string that is where its going to write back the binary data .
But this is not how it is . It seems I can stream it . Thats a real paradigm shift for me. I believe its the File Descriptor abstraction that makes it possible? That is you normally write code to expect a FD as positional arguments and not the real file strings ? Which in turn means the output file gets opened and the fd is sent to the program once I execute the command in bash ?
It can read from Terminal and give the display to screen or a application . What makes this possible ? I think there is some concept of file descriptors that I am missing here ?
Does applications 'talk' in terms of File Descriptors and not file name as strings? - In Unix everything is a file and that means FD is used ?
Few other related reads :
http://en.wikipedia.org/wiki/Pipeline_(Unix)
What is a simple explanation for how pipes work in BASH?
confused about stdin, stdout and stderr?
A: Here's a very non-technical description of a relatively technical topic:
A file descriptor, in Unix parlance, is a small number that identifies a given file or file-like thingy. So let's talk about file-like-thingies in the Unix sense.
What's a Unix file-like-thingy? It's something that you can read from and/or write to. So standard files that live in a directory on your hard disk certainly can qualify as files. So can your terminal session – you can type into it, so it can be read, and you can read output printed on it. So can, for that matter, network sockets. So can (and we'll talk about this more) pipes.
In many cases, an application will read its data from one (or more) file descriptors, and write its results to one (or more) file descriptors. From the point of view of the core code of the application, it doesn't really care which file descriptors its using, or what they're "hooked up" to. (Caveat: Different file descriptors can be hooked up to file-like-thingies with different capabilities, like read-only-ness; I'm ignoring this deliberately for now.) So I might have a trivial program which looks like (ignoring error checking):
void zcrew_up_zpelling(int in_fd, int out_fd) {
char c;
ssize_t
while(read(in_fd, &c, 1)) {
if (c == 's') c = 'z';
write(out_fd, &c, 1));
}
}
Don't worry too much about what this code does (please!); instead, just notice that it's copying-and-modifying from one file descriptor to another.
So, what file descriptors are actually used here? Well, that's up to the code that calls zcrew_up_zpelling(). There are, however, some vague conventions. Many programs that need a single source of input default to using stdin as the file descriptor they'll read from; many programs that need a single source of output default to using stdout as the file descriptor they'll write to. Many of these programs provide ways to use a different file descriptor instead, often one hooked up to a named file.
Let's write a program like this:
int main(int argc, char **argv) {
int in_fd = 0; // Descriptor of standard input
int out_fd = 1; // Descriptor of standard output
if (argc >= 2) in_fd = open(argv[1], O_RDONLY);
if (argc >= 3) out_fd = open(argv[2], O_WRONLY);
zcrew_up_zpelling(in_fd, out_fd);
return 0;
}
So, let's run our program:
./our_program
Hmm, it's waiting for input. We didn't pass any arguments, so it's just using stdin and stdout. What if we type "Using stdin and stdout"?
Uzing ztdin and ztdout
Interesting. Let's try something different. First, we create a file containing "Hello worlds" named, let's say, hello.txt.
./our_program hello.txt
What do we get?
Hello worldz
And one more run:
./out_program hello.txt output.txt
Out program returns immediately, but creates a file called output.text containing... our output!
Deep breath. At this point, I'm hoping that I've successfully explained how a program is able to have behavior independent of the type of file-like-thingy hooked up to a file descriptor, and also to choose what file-like-thingy gets hooked up.
What about that pipe thing I mentioned? What about streaming? Why does it work when I say:
echo Tessting | ./our_program | grep -o z | wc -l
Well, each of these programs follows some form of the conventions above. our_program, as we know, by default reads from stdin and writes to stdout. grep does the same thing. wc by default reads from stdin, but by default writes to stdout -- it likes to live at the end of pipelines. And echo doesn't read from a file descriptor at all (it just reads arguments, like we did in main()), but writes to stdout, so likes to live at the front of streams.
How does this all work? Well, to get much deeper we have to talk about the shell. The shell is the program that starts other command line programs, and it gets to choose what file descriptors are already hooked up to when a program starts. Those magic numbers of 0 and 1 for stdin and stdout we used earlier? That's a Unix convention, and the shell hooks up a file-like-thingy to each of those file descriptors before starting your program. When the shell sees you asking for a pipeline by entering a command with | characters, it hooks the stdout of one program directly into the stdin of the next program, using a file-like-thingy called a pipe. A file-like-thingy pipe, just like a plumbing pipe, takes whatever is put in one end and puts it out the other.
So, we've combined three things:
*
*Code that deals with file descriptors, without worrying about what they're hooked to
*Conventions for default file descriptors to use for normal tasks
*The shell's ability to set up a program's file descriptors to "pipe" to other programs'
Together, these give us the ability to write programs that "play nice" with streaming and pipelines, without each program having to understand where it sits in the pipeline and what's happening around it.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,104 |
bool approximateVectorCompare(const std::vector<double>& lhs, const std::vector<double>& rhs) {
if(lhs.size() != rhs.size()) {
return false;
}
for(unsigned int a = 0; a < lhs.size(); a++) {
if(fabs(lhs[a] - rhs[a]) > 0.00001) {
return false;
}
}
return true;
}
// Constants set for testing, could be anything
const static int INPUTS(4);
const static int OUTPUTS(2);
const static int HIDDENS(3);
const static int NUM_IN_HIDDENS(6);
const static char * FILENAME = "temp/netfile.txt";
const static char * ACTIVATION_FUNCTION("sigmoid");
std::vector<double> input = {3, 5, 2, 5};
TEST_CASE( "Neural Network Contructor", "[network]" ) {
net::NeuralNet network = net::NeuralNet(INPUTS, OUTPUTS, HIDDENS, NUM_IN_HIDDENS, ACTIVATION_FUNCTION);
SECTION("Testing number of inputs") {
REQUIRE(network.numberOfInputs() == INPUTS);
}
SECTION("Testing number of outputs") {
REQUIRE(network.numberOfOutputs() == OUTPUTS);
}
SECTION("Testing number of hidden layers") {
REQUIRE(network.numberOfHiddenLayers() == HIDDENS);
}
SECTION("Testing for correct output actication function") {
REQUIRE(network.net[network.net.size() -1].getActivationFunctionName() == ACTIVATION_FUNCTION);
}
}
TEST_CASE("Neural Network Changing", "[network]") {
net::NeuralNet network = net::NeuralNet(INPUTS, OUTPUTS, HIDDENS, NUM_IN_HIDDENS, ACTIVATION_FUNCTION);
std::vector<double> oldWeights = network.getWeights();
std::vector< std::vector< std::vector<double> > > oldWeights3d = network.getWeights3D();
std::vector<double> oldOutput = network.getOutput(input);
SECTION("Randomizing weights") {
network.randomizeWeights();
REQUIRE(network.getWeights() != oldWeights);
REQUIRE(network.getWeights3D() != oldWeights3d);
REQUIRE(network.getOutput(input) != oldOutput);
}
}
TEST_CASE("Neural Network Storing", "[network]") {
net::NeuralNet network = net::NeuralNet(INPUTS, OUTPUTS, HIDDENS, NUM_IN_HIDDENS, ACTIVATION_FUNCTION);
std::vector<double> oldWeights = network.getWeights();
std::vector< std::vector< std::vector<double> > > oldWeights3d = network.getWeights3D();
std::vector<double> oldOutput = network.getOutput(input);
SECTION("Store into and load using streams") {
std::ofstream ostream;
ostream.open(FILENAME, std::ofstream::out | std::ofstream::trunc);
network.store(&ostream); // Store old
ostream.close();
std::ifstream istream;
istream.open(FILENAME, std::ifstream::in);
net::NeuralNet fileNet = net::NeuralNet(&istream); // load new
istream.close();
REQUIRE(approximateVectorCompare(fileNet.getWeights(), oldWeights));
REQUIRE(approximateVectorCompare(fileNet.getOutput(input), oldOutput));
std::vector< std::vector< std::vector<double> > > newWeights3d = fileNet.getWeights3D();
for(unsigned int a = 0; a < oldWeights3d.size(); a++) {
for(unsigned int b = 0; b < oldWeights3d[a].size(); b++) {
std::cout << "a: " << a << "; b: " << b << "\n";
REQUIRE(approximateVectorCompare(newWeights3d[a][b], oldWeights3d[a][b]));
}
}
}
}
TEST_CASE("Neural Network Copying", "[network]") {
net::NeuralNet network = net::NeuralNet(INPUTS, OUTPUTS, HIDDENS, NUM_IN_HIDDENS, ACTIVATION_FUNCTION);
std::vector<double> oldWeights = network.getWeights();
std::vector< std::vector< std::vector<double> > > oldWeights3d = network.getWeights3D();
std::vector<double> oldOutput = network.getOutput(input);
net::NeuralNet newNet = net::NeuralNet(network);
SECTION("Different weights") {
REQUIRE(approximateVectorCompare(newNet.getWeights(), oldWeights));
REQUIRE(approximateVectorCompare(newNet.getOutput(input), oldOutput));
std::vector< std::vector< std::vector<double> > > newWeights3d = network.getWeights3D();
for(unsigned int a = 0; a < oldWeights3d.size(); a++) {
for(unsigned int b = 0; b < oldWeights3d[a].size(); b++) {
REQUIRE(newWeights3d[a][b] == oldWeights3d[a][b]);
}
}
}
SECTION("Testing number of inputs") {
REQUIRE(newNet.numberOfInputs() == network.numberOfInputs());
}
SECTION("Testing number of outputs") {
REQUIRE(newNet.numberOfOutputs() == network.numberOfOutputs());
}
SECTION("Testing number of hidden layers") {
REQUIRE(newNet.numberOfHiddenLayers() == network.numberOfHiddenLayers());
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,374 |
{"url":"https:\/\/physics.stackexchange.com\/questions\/447157\/problem-with-loop-integral-hqet\/449199","text":"# Problem with loop Integral (HQET)\n\nI have come across the Integral:\n\n$$\\int_0^{\\infty}dx [x^2-ixa+c]^{n-\\frac{d}{2}}e^{-bx},$$\n\nwhere $$n = 1,2 ; a,b,c,d \\in \\mathbb{R}; b,d > 0$$. This integral should contain some divergences for $$d \\rightarrow 4$$ (for $$c=0$$). I guess one must be able to write it as some combination of Gamma functions.\n\n\u2022 Is $d$ a real number? \u2013\u00a0GiorgioP Dec 19 '18 at 6:31\n\u2022 Yes it is. Sorry. I fixed it in the question. \u2013\u00a0lomby Dec 19 '18 at 10:31\n\n\\begin{align} I&=\\int_0^\\infty (x-iax+c)^{n-\\frac{d}{2}} e^{-bx}\\,dx \\\\ &=\\int_0^\\infty \\left[\\left(x-\\frac{ia}{2}\\right)^2+\\frac{a^2+4c}{4}\\right]^{n-\\frac{d}{2}} e^{-bx}\\,dx \\\\ &=\\int_0^\\infty \\sum_{k=0}^{n-\\frac{d}{2}} {n-\\frac{d}{2}\\choose k} \\left(x-\\frac{ia}{2}\\right)^{2k} \\left(\\frac{a^2+4c}{4} \\right)^{n-\\frac{d}{2}-k} e^{-bx}\\,dx \\\\ &=\\int_0^\\infty \\sum_{k=0}^{n-\\frac{d}{2}}\\sum_{m=0}^{2k} {n-\\frac{d}{2}\\choose k} {2k \\choose m} \\left(\\frac{a^2+4c}{4} \\right)^{n-\\frac{d}{2}-k} \\left(-\\frac{ia}{2} \\right)^{2k-m} x^m e^{-bx}\\,dx \\\\ &= \\sum_{k=0}^{n-\\frac{d}{2}}\\sum_{m=0}^{2k} {n-\\frac{d}{2}\\choose k} {2k \\choose m} \\left(\\frac{a^2+4c}{4} \\right)^{n-\\frac{d}{2}-k} \\left(-\\frac{ia}{2} \\right)^{2k-m} \\int_0^\\infty x^m e^{-bx}\\,dx \\\\ &= \\sum_{k=0}^{n-\\frac{d}{2}}\\sum_{m=0}^{2k} {n-\\frac{d}{2}\\choose k} {2k \\choose m} \\left(\\frac{a^2+4c}{4} \\right)^{n-\\frac{d}{2}-k} \\left(-\\frac{ia}{2} \\right)^{2k-m}\\frac{m!}{b^{m+1}} \\\\ \\end{align} After using Wolfram Alpha to simplify the inner sum, we obtain \\begin{align} I&= e^{-iab\/2}\\sum_{k=0}^{n-\\frac{d}{2}} \\frac{\\Gamma\\left(2k+1, -\\frac{iab}{2}\\right)}{b^{2k+1}} {n-\\frac{d}{2}\\choose k} \\left(\\frac{a^2+4c}{4} \\right)^{n-\\frac{d}{2}-k} \\\\ \\end{align}\n\u2022 Thanks for you answer! I have a question though, because I forgot to mention explicitly that $d$ is in general not an integer. So in this formula the sum would be not defined, right? However this derivation should also work if you use the binomial series (see wiki)? \u2013\u00a0lomby Dec 19 '18 at 10:30\nI don't see why there should be any divergences at $$d=4$$ since (I assume that $$b>0$$) the expression $$x^2\u2212iax+c$$ is never zero on the real positive $$x$$ axis --- so there is no danger of dividing by zero anywhere in the integral. If we factor $$x^2-iax+c= (x-\\alpha)(x-\\beta)$$ then the integral will only misbehave if either of the the branch points at $$x=\\alpha$$ or $$x=\\beta$$ hit the endpoint at $$x=0$$, or if they become equal while at the same time pinching the contour.\n\u2022 Ah yes. I did enter the constant $c$ for generality. Actually I am looking for the Integral with $c=0$. Then it should be divergent at $d=4$. right? \u2013\u00a0lomby Dec 20 '18 at 12:54","date":"2019-09-17 08:44:41","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\": 14, \"wp-katex-eq\": 0, \"align\": 2, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 1.0000026226043701, \"perplexity\": 1266.5685028335456}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-39\/segments\/1568514573065.17\/warc\/CC-MAIN-20190917081137-20190917103137-00359.warc.gz\"}"} | null | null |
{"url":"https:\/\/walkingrandomly.com\/?m=201301","text":"## Explorations in overriding MATLAB functions\n\nJanuary 30th, 2013\n\nIn a recent blog post, I demonstrated how to use the MATLAB 2012a Symbolic Toolbox to perform Variable precision QR decomposition in MATLAB.\u00a0 The result was a function called vpa_qr which did the necessary work.\n\n>> a=vpa([2 1 3;-1 0 7; 0 -1 -1]);\n>> [Q R]=vpa_qr(a);\n\nI\u2019ve suppressed the output because it\u2019s so large but it definitely works. When I triumphantly presented this function to the user who requested it he was almost completely happy.\u00a0 What he really wanted, however, was for this to work:\n\n>> a=vpa([2 1 3;-1 0 7; 0 -1 -1]);\n>> [Q R]=qr(a);\n\nIn other words he wants to override the qr function such that it accepts variable precision types. MATLAB 2012a does not allow this:\n\n>> a=vpa([2 1 3;-1 0 7; 0 -1 -1]);\n>> [Q R]=qr(a)\nUndefined function 'qr' for input arguments of type 'sym'.\n\nI put something together that did the job for him but felt that it was unsatisfactory.\u00a0 So, I sent my code to The MathWorks and asked them if what I had done was sensible and if there were any better options.\u00a0 A MathWorks engineer called Hugo Carr sent me such a great, detailed reply that I asked if I could write it up as a blog post.\u00a0 Here is the result:\n\nApproach 1:\u00a0 Define a new qr function, with a different name (such as vpa_qr).\u00a0 This is probably the safest and simplest option and was the method I used in the original blog post.\n\n\u2022 Pros: The new function will not interfere with your MATLAB namespace\n\u2022 Cons: MATLAB will only use this function if you explicitly define that you wish to use it in a given function.\u00a0 You would have to find all prior references to the qr algorithm and make a decision about which to use.\n\nApproach 2: Define a new qr function and use the \u2018isa\u2019 function to catch instances of \u2018sym\u2019. This is the approach I took in the code I sent to The MathWorks.\n\nfunction varargout = qr( varargin )\n\nif nargin == 1 && isa( varargin{1}, 'sym' )\n[varargout{1:nargout}] = vpa_qr( varargin{:} );\nelse\n[varargout{1:nargout}] = builtin( 'qr', varargin{:} );\nend\n\u2022 Pros: qr will always select the correct code when executed on sym objects\n\u2022 Cons: This code only works for shadowing built-ins and will produce a warning reminding you of this fact. If you wish to extend this pattern for other class types, you\u2019ll require a switch statement (or nested if-then-else block), which could lead to a complex comparison each time qr is invoked (and subsequent performance hit). Note that switch statements in conjunction with calls to \u2018isa\u2019 are usually indicators that an object oriented approach is a better way forward.\n\nApproach 3: The MathWorks do not\u00a0recommend that you modify your MATLAB install. However for completeness, it is possible to add a new \u2018method\u2019 to the sym class by dropping your function into the sym class folder.\u00a0 For MATLAB 2012a on Windows, this folder is at\n\nC:\\Program Files\\MATLAB\\R2012a\\toolbox\\symbolic\\symbolic\\@sym\n\nFor the sake of illustration, here is a simplified implementation. Call it qr.m\n\nfunction result = qr( this )\nresult = feval(symengine,'linalg::factorQR', this);\nend\n\nPros: Functions saved to a class folder take precedence over built in functionality, which means that MATLAB will always use your qr method for sym objects.\n\nCons: If you share code which uses this functionality, it won\u2019t run on someone\u2019s computer unless they update their sym class folder with your qr code. Additionally, if a new method is added to a class it may shadow the behaviour of other MATLAB functionality and lead to unexpected behaviour in Symbolic Toolbox.\n\nApproach 4: For more of an object-oriented approach it is possible to sub-class the sym class, and add a new qr method.\n\nclassdef mySym < sym\n\nmethods\nfunction this = mySym(arg)\nthis = this@sym(arg);\nend\n\nfunction result = qr( this )\nresult = feval(symengine,'linalg::factorQR', this);\nend\nend\n\nend\n\nPros: Your change can be shipped with your code and it will work on a client\u2019s computer without having to change the sym class.\n\nCons: When calling superclass methods on your mySym objects (such as sin(mySym1)), the result will be returned as the superclass unless you explicitly redefine the method to return the subclass.\n\nN.B. There is a lot of literature which discusses why inheritance (subclassing) to augment a class\u2019s behaviour is a bad idea. For example, if Symbolic Toolbox developers decide to add their own qr method to the sym API, overriding that function with your own code could break the system. You would need to update your subclass every time the superclass is updated. This violates encapsulation, as the subclass implementation depends on the superclass. You can avoid problems like these by using composition instead of inheritance.\n\nApproach 5: You can create a new sym class by using composition, but it takes a little longer than the other approaches. Essentially, this involves creating a wrapper which provides the functionality of the original class, as well as any new functions you are interested in.\n\nclassdef mySymComp\n\nproperties\nSymProp\nend\n\nmethods\nfunction this = mySymComp(symInput)\nthis.SymProp = symInput;\nend\n\nfunction result = qr( this )\nresult = feval(symengine,'linalg::factorQR', this.SymProp);\nend\nend\n\nend\n\nNote that in this example we did not add any of the original sym functions to the mySymComp class, however this can be done for as many as you like. For example, I might like to use the sin method from the original sym class, so I can just delegate to the methods of the sym object that I passed in during construction:\n\nclassdef mySymComp\n\nproperties\nSymProp\nend\n\nmethods\nfunction this = mySymComp(symInput)\nthis.SymProp = symInput;\nend\n\nfunction result = qr( this )\nresult = feval(symengine,'linalg::factorQR', this.SymProp);\nend\n\nfunction G = sin(this)\nG = mySymComp(sin(this.SymProp));\nend\nend\n\nend\n\nPros: The change is totally encapsulated, and cannot be broken save for a significant change to the sym api (for example, the MathWorks adding a qr method to sym would not break your code).\n\nCons: The wrapper can be time consuming to write, and the resulting object is not a \u2018sym\u2019, meaning that if you pass a mySymComp object \u2018a\u2019 into the following code:\n\nisa(a, 'sym')\n\nMATLAB will return \u2018false\u2019 by default.\n\n## Fused Multiply Add (FMA) \u2013 One flop or two?\n\nJanuary 29th, 2013\n\nI am having a friendly argument with a colleague over how you calculate the peak number of floating operations per second (flops) for devices that support Fused Multiply Add (FMA).\u00a0 The FMA operation is d=a+b*c, an operation that can be done in one cycle on devices that support it.\n\nI say that an FMA operation is two flops, he says it\u2019s one.\u00a0 So, when I calculate the theoretical peak of a device I get twice the value he does.\u00a0 So, what do you think..is FMA one flop or two?\n\n## My \u2018Famous\u2019 StackOverflow question closed as not constructive.\n\nJanuary 22nd, 2013\n\nI like the StackOverflow range of question and answer sites and have hopped on and off them almost since the very beginning.\u00a0 When I logged in recently I was informed that one of my questions had been awarded the \u2018Famous Question\u2019 badge..i.e. it had been viewed over 10,000 times.\u00a0 The relevant question was Python blogs that you regularly follow? which was asked by me in the very early days of the site. Not only has it received 63 community up-votes and over 10,000 views but it\u2019s also been closed as \u2018Not constructive\u2019 by senior members of the Stack Overflow community.\n\nI find this contrast amusing!\n\n## How to cite MATLAB in research papers\n\nJanuary 14th, 2013\n\nIn a recent article, Citing software in research papers, I discussed how to cite various software packages.\u00a0 One of the commentators suggested that I should contact The Mathworks if I wanted to know how to cite MATLAB.\u00a0 I did this and asked for permission to blog the result.\u00a0 This is what they suggested:\n\nTo cite MATLAB (and in this case a toolbox) you can use this:\n\nMATLAB and Statistics Toolbox Release 2012b, The MathWorks, Inc., Natick, Massachusetts, United States.\n\nThis is the format prescribed by both the Chicago Manual of Style and the Microsoft Manual of Style. If you use a different style guide, you may apply a different format, but should observe the capitalization shown above, and include the appropriate release number. If the MathWorks release number (in the format YYYYa or YYYYb) is not readily available, you can use the point release numbers for the software, as in:\n\nMATLAB 8.0 and Statistics Toolbox 8.1, The MathWorks, Inc., Natick, Massachusetts, United States.\n\nThanks to The Mathworks for allowing me to reproduce this communication here at WalkingRandomly.\n\n## Citing software in research papers\n\nJanuary 10th, 2013\n\nR has a citation() command that recommends how to cite the use of R in your publications, information that is also included in R\u2019s Frequently Asked Questions document.\n\nTo cite R in publications use:\n\nR Core Team (2012). R: A language and environment for\nstatistical computing. R Foundation for Statistical\nComputing, Vienna, Austria. ISBN 3-900051-07-0, URL\nhttp:\/\/www.R-project.org\/.\n\nA BibTeX entry for LaTeX users is\n\n@Manual{,\ntitle = {R: A Language and Environment for Statistical Computing},\nauthor = {{R Core Team}},\norganization = {R Foundation for Statistical Computing},\nyear = {2012},\nnote = {{ISBN} 3-900051-07-0},\nurl = {http:\/\/www.R-project.org\/},\n}\n\nWe have invested a lot of time and effort in creating R, please\n\u2018citation(\"pkgname\")\u2019 for citing R packages\n\nThis led me to wonder how often people cite the software they use.\u00a0 For example, if you publish the results of a simulation written in MATLAB do you cite MATLAB in any way?\u00a0 How about if you used Origin or Excel to produce a curve fit, would you cite that?\u00a0 Would you cite your plotting software, numerical libraries or even compiler?\n\n## The NAG Fortran Compiler, Fortran Builder and a Fortran quiz\n\nJanuary 7th, 2013\n\nThe\u00a0Numerical Algorithms Group\u00a0(NAG) are\u00a0principally known for their numerical library but they also offer products such as a MATLAB toolbox and a Fortran compiler. \u00a0My employer, The University of Manchester, has \u00a0a full site license for most of NAG\u2019s stuff where it is heavily used by both our students and researchers.\n\nWhile at a recent software conference, I saw a talk by NAG\u2019s\u00a0David Sayers\u00a0where he demonstrated some of the features of the NAG Fortran Compiler. \u00a0During this talk he showed some examples of broken Fortran and asked us if we could spot how they were broken without compiler assistance. \u00a0I enjoyed the talk and so asked David if he would mind writing a guest blog post on the subject for WalkingRandomly. \u00a0He duly obliged.\n\nThis is a guest blog post by David Sayers of NAG.\n\nWhat do you want from your Fortran compiler? Some people ask for extra (non-standard) features, others require very fast execution speed. The very latest extensions to the Fortran language appeal to those who like to be up to date with their code.\n\nI suspect that very few would put enforcement of the Fortran standard at the top of their list, yet this essential if problems are to be avoided in the future. Code written specifically for one compiler is unlikely to work when computers change, or may contain errors that appear only intermittently. Without access to at least one good checking compiler, the developer or support desk will be lacking a valuable tool in the fight against faulty code.\n\nThe NAG Fortran compiler is such a tool. It is used extensively by NAG\u2019s own staff to validate their library code and to answer user-support queries involving user\u2019s Fortran programs. It is available on Windows, where it has its own IDE called Fortran Builder,\u00a0and on Unix platforms and Mac OS X.\n\nWindows users also have the benefit of some Fortran Tools bundled in to the IDE. Particularly nice is the Fortran polisher which tidies up the presentation of your source files according to user-specified preferences.\n\nThe compiler includes most Fortran 2003 features, very many Fortran 2008 features and the most commonly used features of OpenMP 3.0 are supported.\n\nThe principal developer of the compiler is Malcolm Cohen, co-author of the book, Modern Fortran Explained along with Michael Metcalf\u00a0and John Reid. Malcolm has been a member of the international working group on Fortran, ISO\/IEC JTC1\/SC22\/WG5, since 1988,\u00a0and the USA technical subcommittee on Fortran, J3, since 1994. He has been head of the J3 \/DATA subgroup since 1998 and was\u00a0responsible for the design and development of the object-oriented features in Fortran 2003. Since 2005 he has been Project\u00a0Editor for the ISO\/IEC Fortran standard, which has continued its evolution with the publication of the Fortran 2008 standard\u00a0in 2010.\n\nOf all people Malcolm Cohen should know Fortran and the way the standard should be enforced!\n\nHis compiler reflects that knowledge and is designed to assist the programmer to detect how programs might be faulty due to a departure from the Fortran standard or prone to trigger a run time error. In either case the diagnostics of produced by the compiler are clear and helpful and can save the developer many hours of laborious bug-tracing. Here are some particularly simple examples of faulty programs. See if you can spot the mistakes, and think how difficult these might be to detect in programs that may be thousands of times longer:\n\nExample 1\n\n Program test\nReal, Pointer :: x(:, :)\n\nCall make_dangle\nx(10, 10) = 0\nContains\nSubroutine make_dangle\nReal, Target :: y(100, 200)\n\nx => y\nEnd Subroutine make_dangle\nEnd Program test\n\nExample 2\n\nProgram dangle2\nReal,Pointer :: x(:),y(:)\nAllocate(x(100))\ny => x\nDeallocate(x)\ny = 3\nEnd\n\nExample 3\n\n program more\ninteger n, i\nreal r, s\nequivalence (n,r)\ni=3\nr=2.5\ni=n*n\nwrite(6,900) i, r\n900 format(' i = ', i5, ' r = ', f10.4)\nstop 'ok'\nend\n\nExample 4\n\n program trouble1\ninteger n\nparameter (n=11)\ninteger iarray(n)\ninteger i\ndo 10 i=1,10\niarray(i) = i\n10 continue\nwrite(6,900) iarray\n900 format(' iarray = ',11i5)\nstop 'ok'\nend\n\nAnd finally if this is all too easy \u2026\n\nExample 5\n\n! E04UCA Example Program Text\n! Mark 23 Release. NAG Copyright 2011.\n\nMODULE e04ucae_mod\n\n! E04UCA Example Program Module:\n! Parameters and User-defined Routines\n\n! .. Use Statements ..\nUSE nag_library, ONLY : nag_wp\n! .. Implicit None Statement ..\nIMPLICIT NONE\n! .. Parameters ..\nREAL (KIND=nag_wp), PARAMETER :: one = 1.0_nag_wp\nREAL (KIND=nag_wp), PARAMETER :: zero = 0.0_nag_wp\nINTEGER, PARAMETER :: inc1 = 1, lcwsav = 1, &\nliwsav = 610, llwsav = 120, &\nlrwsav = 475, nin = 5, nout = 6\nCONTAINS\nSUBROUTINE objfun(mode,n,x,objf,objgrd,nstate,iuser,ruser)\n! Routine to evaluate objective function and its 1st derivatives.\n\n! .. Implicit None Statement ..\nIMPLICIT NONE\n! .. Scalar Arguments ..\nREAL (KIND=nag_wp), INTENT (OUT) :: objf\nINTEGER, INTENT (INOUT) :: mode\nINTEGER, INTENT (IN) :: n, nstate\n! .. Array Arguments ..\nREAL (KIND=nag_wp), INTENT (INOUT) :: objgrd(n), ruser(*)\nREAL (KIND=nag_wp), INTENT (IN) :: x(n)\nINTEGER, INTENT (INOUT) :: iuser(*)\n! .. Executable Statements ..\nIF (mode==0 .OR. mode==2) THEN\nobjf = x(1)*x(4)*(x(1)+x(2)+x(3)) + x(3)\nEND IF\n\nIF (mode==1 .OR. mode==2) THEN\nobjgrd(1) = x(4)*(x(1)+x(1)+x(2)+x(3))\nobjgrd(2) = x(1)*x(4)\nobjgrd(3) = x(1)*x(4) + one\nobjgrd(4) = x(1)*(x(1)+x(2)+x(3))\nEND IF\n\nRETURN\n\nEND SUBROUTINE objfun\nSUBROUTINE confun(mode,ncnln,n,ldcj,needc,x,c,cjac,nstate,iuser,ruser)\n! Routine to evaluate the nonlinear constraints and their 1st\n! derivatives.\n\n! .. Implicit None Statement ..\nIMPLICIT NONE\n! .. Scalar Arguments ..\nINTEGER, INTENT (IN) :: ldcj, n, ncnln, nstate\nINTEGER, INTENT (INOUT) :: mode\n! .. Array Arguments ..\nREAL (KIND=nag_wp), INTENT (OUT) :: c(ncnln)\nREAL (KIND=nag_wp), INTENT (INOUT) :: cjac(ldcj,n), ruser(*)\nREAL (KIND=nag_wp), INTENT (IN) :: x(n)\nINTEGER, INTENT (INOUT) :: iuser(*)\nINTEGER, INTENT (IN) :: needc(ncnln)\n! .. Executable Statements ..\nIF (nstate==1) THEN\n\n! First call to CONFUN. Set all Jacobian elements to zero.\n! Note that this will only work when 'Derivative Level = 3'\n! (the default; see Section 11.2).\n\ncjac(1:ncnln,1:n) = zero\nEND IF\n\nIF (needc(1)>0) THEN\n\nIF (mode==0 .OR. mode==2) THEN\nc(1) = x(1)**2 + x(2)**2 + x(3)**2 + x(4)**2\nEND IF\n\nIF (mode==1 .OR. mode==2) THEN\ncjac(1,1) = x(1) + x(1)\ncjac(1,2) = x(2) + x(2)\ncjac(1,3) = x(3) + x(3)\ncjac(1,4) = x(4) + x(4)\nEND IF\n\nEND IF\n\nIF (needc(2)>0) THEN\n\nIF (mode==0 .OR. mode==2) THEN\nc(2) = x(1)*x(2)*x(3)*x(4)\nEND IF\n\nIF (mode==1 .OR. mode==2) THEN\ncjac(2,1) = x(2)*x(3)*x(4)\ncjac(2,2) = x(1)*x(3)*x(4)\ncjac(2,3) = x(1)*x(2)*x(4)\ncjac(2,4) = x(1)*x(2)*x(3)\nEND IF\n\nEND IF\n\nRETURN\n\nEND SUBROUTINE confun\nEND MODULE e04ucae_mod\nPROGRAM e04ucae\n\n! E04UCA Example Main Program\n\n! .. Use Statements ..\nUSE nag_library, ONLY : dgemv, e04uca, e04wbf, nag_wp\nUSE e04ucae_mod, ONLY : confun, inc1, lcwsav, liwsav, llwsav, lrwsav, &\nnin, nout, objfun, one, zero\n! .. Implicit None Statement ..\n! IMPLICIT NONE\n! .. Local Scalars ..\n! REAL (KIND=nag_wp) :: objf\nINTEGER :: i, ifail, iter, j, lda, ldcj, &\nldr, liwork, lwork, n, nclin, &\nncnln, sda, sdcjac\n! .. Local Arrays ..\nREAL (KIND=nag_wp), ALLOCATABLE :: a(:,:), bl(:), bu(:), c(:), &\ncjac(:,:), clamda(:), objgrd(:), &\nr(:,:), work(:), x(:)\nREAL (KIND=nag_wp) :: ruser(1), rwsav(lrwsav)\nINTEGER, ALLOCATABLE :: istate(:), iwork(:)\nINTEGER :: iuser(1), iwsav(liwsav)\nLOGICAL :: lwsav(llwsav)\nCHARACTER (80) :: cwsav(lcwsav)\n! .. Intrinsic Functions ..\nINTRINSIC max\n! .. Executable Statements ..\nWRITE (nout,*) 'E04UCA Example Program Results'\n\n! Skip heading in data file\n\nliwork = 3*n + nclin + 2*ncnln\nlda = max(1,nclin)\n\nIF (nclin>0) THEN\nsda = n\nELSE\nsda = 1\nEND IF\n\nldcj = max(1,ncnln)\n\nIF (ncnln>0) THEN\nsdcjac = n\nELSE\nsdcjac = 1\nEND IF\n\nldr = n\n\nIF (ncnln==0 .AND. nclin>0) THEN\nlwork = 2*n**2 + 20*n + 11*nclin\nELSE IF (ncnln>0 .AND. nclin>=0) THEN\nlwork = 2*n**2 + n*nclin + 2*n*ncnln + 20*n + 11*nclin + 21*ncnln\nELSE\nlwork = 20*n\nEND IF\n\nALLOCATE (istate(n+nclin+ncnln),iwork(liwork),a(lda,sda), &\nbl(n+nclin+ncnln),bu(n+nclin+ncnln),c(max(1, &\nncnln)),cjac(ldcj,sdcjac),clamda(n+nclin+ncnln),objgrd(n),r(ldr,n), &\nx(n),work(lwork))\n\nIF (nclin>0) THEN\nEND IF\n\n! Initialise E04UCA\n\nifail = 0\nCALL e04wbf('E04UCA',cwsav,lcwsav,lwsav,llwsav,iwsav,liwsav,rwsav, &\nlrwsav,ifail)\n\n! Solve the problem\n\nifail = -1\nCALL e04uca(n,nclin,ncnln,lda,ldcj,ldr,a,bl,bu,confun,objfun,iter, &\nistate,c,cjac,clamda,objf,objgrd,r,x,iwork,liwork,work,lwork,iuser, &\nruser,lwsav,iwsav,rwsav,ifail)\n\nSELECT CASE (ifail)\nCASE (0:6,8)\nWRITE (nout,*)\nWRITE (nout,99999)\nWRITE (nout,*)\n\nDO i = 1, n\nWRITE (nout,99998) i, istate(i), x(i), clamda(i)\nEND DO\n\nIF (nclin>0) THEN\n\n! A*x --> work.\n! The NAG name equivalent of dgemv is f06paf\nCALL dgemv('N',nclin,n,one,a,lda,x,inc1,zero,work,inc1)\n\nWRITE (nout,*)\nWRITE (nout,*)\nWRITE (nout,99997)\nWRITE (nout,*)\n\nDO i = n + 1, n + nclin\nj = i - n\nWRITE (nout,99996) j, istate(i), work(j), clamda(i)\nEND DO\n\nEND IF\n\nIF (ncnln>0) THEN\nWRITE (nout,*)\nWRITE (nout,*)\nWRITE (nout,99995)\nWRITE (nout,*)\n\nDO i = n + nclin + 1, n + nclin + ncnln\nj = i - n - nclin\nWRITE (nout,99994) j, istate(i), c(j), clamda(i)\nEND DO\n\nEND IF\n\nWRITE (nout,*)\nWRITE (nout,*)\nWRITE (nout,99993) objf\nEND SELECT\n\n99999 FORMAT (1X,'Varbl',2X,'Istate',3X,'Value',9X,'Lagr Mult')\n99998 FORMAT (1X,'V',2(1X,I3),4X,1P,G14.6,2X,1P,G12.4)\n99997 FORMAT (1X,'L Con',2X,'Istate',3X,'Value',9X,'Lagr Mult')\n99996 FORMAT (1X,'L',2(1X,I3),4X,1P,G14.6,2X,1P,G12.4)\n99995 FORMAT (1X,'N Con',2X,'Istate',3X,'Value',9X,'Lagr Mult')\n99994 FORMAT (1X,'N',2(1X,I3),4X,1P,G14.6,2X,1P,G12.4)\n99993 FORMAT (1X,'Final objective value = ',1P,G15.7)\nEND PROGRAM e04ucae\n\nAnswers to this particular New Year quiz will be posted in a future blog post.\n\n## A month of math software \u2013 December 2012\n\nJanuary 3rd, 2013\n\nWelcome to the last 2012 edition of A Month of Math Software..slightly delayed thanks to the December festivities.\u00a0 Thanks to everyone who\u2019s contributed news items over the last 2 years, please feel free to continue contacting me throughout 2013 and beyond.\n\nAccelerEyes sells the MATLAB Jacket to The Mathworks\n\n\u2022 AccelerEyes are the developers of GPU accelerated products such as Jacket for MATLAB and ArrayFire for C, C++, and Fortran.\u00a0 In a recent blog post, they announced that they have sold Jacket to The Mathworks.\u00a0 It will be interesting to see how The Mathworks integrate this technology into the Parallel Computing Toolbox (PCT) in the future.\u00a0 I sincerely hope that they don\u2019t split the PCT into two products, one for GPUs and the other for CPUs!\n\nFree computer algebra\n\nNumerical Libraries\n\n\u2022 Version 5.3 of the ACML linear algebra library for AMD-based systems was released in December.\n\u2022 Another of AMD\u2019s libraries was updated this month.\u00a0 The Accelerated Parallel Processing (APP) SDK hit version 2.8 and includes a preview of\u00a0AMD\u2019s new C++ template library, Codename \u201cBolt.\u201d.\u00a0 According to AMD, Bolt \u2018makes it easier for developers to utilize the inherent performance and power efficiency benefits of heterogeneous computing\u2019 The press release for this version of the APP SDK is available at\u00a0http:\/\/developer.amd.com\/wordpress\/media\/2012\/10\/APP-SDK-Bolt-CodeXL-Press-Release.pdf.\u00a0 Also, click here for more details concerning Bolt\n\u2022 Numeric Javascript saw two releases, v1.2.5 and v1.2.6\n\u2022 The HSL Software Library was updated this month adding three new routines to support Fredholm alternative for singular systems, efficient multiplication of the factors by a vector, and sparse forward solve.\n\u2022 amgcl is an accelerated algebraic multigrid for C++.\u00a0 According to the software\u2019s website \u2018You can use amgcl to solve large sparse system of linear equations in three simple steps: first, you have to select method components (this is a compile time decision); second, the AMG hierarchy has to be constructed from a system matrix; and third, the hierarchy is used to solve the equation system for a given right-hand side\u2019\n\nData Analysis and Visualisation\n\nMaple IDE\n\n\u2022 DigiArea have released an Eclipse based Integrated Development Environment (IDE) for Maple called, simply, Maple IDE.\u00a0 This commercial product is available for Linux, Windows and Mac OS X and seems to be a very similar concept to Wolfram\u2019s Workbench for Mathematica.","date":"2021-06-21 18:57:25","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.24093972146511078, \"perplexity\": 7421.311720464381}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623488289268.76\/warc\/CC-MAIN-20210621181810-20210621211810-00013.warc.gz\"}"} | null | null |
Encouraging results from South African TB vaccination trial
July 18th, 2018 Research Africa
An innovative clinical trial conducted by the University of Cape Town-based SA Tuberculosis Vaccine Initiative and the Desmond Tutu HIV Foundation provides encouraging new evidence that TB vaccines could prevent sustained infections in high-risk adolescents.
According to the World Health Organisation (WHO), about one-quarter of the world's population has latent TB infection, which means people have been infected by TB bacteria but are not ill with the disease and cannot transmit the disease. People infected with TB bacteria have a lifetime risk of falling ill with TB of 10%. In a prevention-of-infection phase 2 trial conducted in Worcester and Cape Town, South Africa, re-vaccination with the Bacille Calmette-Guerin (BCG) vaccine significantly reduced sustained TB infections in adolescents.
An experimental vaccine candidate, H4:IC31, also appeared to reduce sustained infections, although not at statistically significant levels. However, the trend observed for H4:IC31 is the first time a subunit vaccine has shown any indication of ability to protect against TB infection or disease in humans. TB infections that developed during the study were measured using a QuantiFERON®-TB Gold in Tube (QFT-GIT) test, a commercially available blood test that helps diagnose TB infections. In the trial, individuals who tested negative for QFT-GIT were considered to not have TB infection. The trial measured the rate by which individuals converted to QFT-GIT positive, interpreted as evidence of TB infection. Those individuals who tested QFT-GIT positive consecutively over 6 months were considered to have a sustained infection.
H4:IC31 is a sub-unit TB vaccine candidate being developed jointly by Aeras and Sanofi Pasteur and the Statens Serum Institute. BCG is the only licensed tuberculosis vaccine available globally.
The clinical trial was conducted at SATVI and at the Emavundleni Research Centre (part of the Desmond Tutu HIV Centre). The trial was funded by Sanofi Pasteur, the UK's department for international development, and Aeras. The study was approved by the Medicines Control Council of South Africa and the independent ethics committee of the University of Cape Town.
The study involved 990 HIV-negative, healthy adolescents (12 to 17 years of age) who had previously been vaccinated as infants with BCG. All participants were randomized evenly into three study arms: placebo, H4:IC31, or BCG revaccination. All participants were screened to ensure they were not infected with Mycobacterium tuberculosis (Mtb) prior to vaccination in the study.
The data showed that both vaccines appeared to be safe and produced an immune response in the adolescents studied. No vaccine-related serious adverse events were reported in the study, and the most common vaccine-related adverse event was injection site swelling in BCG revaccinated participants, typical for BCG vaccination.
For the primary efficacy outcome, 134 participants tested positive for an initial Mtb infection as measured by QFT-GIT conversion from negative to positive. When compared to the placebo, neither vaccine prevented initial Mtb infection (QFT-GIT conversion). For the secondary efficacy outcome, 82 participants exhibited a sustained QFT-GIT conversion which remained positive for at least 6 months.
In the BCG revaccination arm, the vaccine efficacy for preventing a sustained infection was 45.4% and was statistically significant. In the H4:IC31 arm, vaccine efficacy was 30.5%, but did not meet rigorous criteria for statistical significance.
This convincing BCG efficacy signal provides impetus for trials of BCG revaccination for prevention of TB disease in adolescents without Mtb infection, which would be needed to confirm direct clinical benefit of the prevention-of-infection approach. The modest efficacy effect of H4:IC31 encourages further testing of next generation subunit TB vaccines.
Dr Mark Hatherill, director of the SATVI and the study's principal investigator, said: "We are very pleased to publish the results of the first randomised, placebo-controlled prevention-of-infection trial for TB, which showed that vaccination may reduce the rate of sustained TB infection in a high-transmission setting. While neither vaccine proved to be statistically significant in preventing an initial TB infection, we are extremely encouraged by the efficacy findings against sustained TB infections. We believe the results from this novel trial design will provide significant scientific benefit to the field in understanding protection against TB infection, and based on this positive signal, we look forward to testing the potential of such vaccines to protect against TB disease among uninfected adolescents in a larger, more traditional prevention-of-disease clinical trial."
Dr Tom Scriba, deputy director immunology of SATVI, said "We are excited that this result provides an opportunity to identify the immune response that protects against sustained TB infection. This advance would accelerate rational development of new TB vaccines."
Dr Linda-Gail Bekker, a lead investigator for the trial, the COO at the Desmond Tutu HIV Foundation and president of the International AIDS Society, said: "We would like to thank all the study participants and their families for participating in this novel clinical trial. We believe the results are important and warrant further investigation into other subunit vaccines and a re-evaluation of BCG revaccination as a potential strategy to prevent TB in high-incidence countries. An effective TB vaccine remains an urgent global goal."
Dr Jacqueline Shea, CEO at Aeras, said: "These results highlight the importance of investing in new approaches to fighting the leading infectious disease killer and to evaluating new concepts in clinical trials. Further, the collaborative effort established between industry leaders, non-profits and clinical sites during this trial showed how powerful combining such forces can be for developing new interventions against a global health threat. The BCG results are important findings with significant public health implications, especially with the rise of drug-resistant strains, that could lead to saving millions of lives. Likewise, the novel prevention-of-infection trial design can be used to inform clinical development of new vaccine candidates before entry into large-scale prevention-of-disease efficacy trials. We are very grateful to the trial participants and our partners and funders who enabled the conduct of this trial."
Background: Recent Mycobacterium tuberculosis infection confers a predisposition to the development of tuberculosis disease, the leading killer among global infectious diseases. H4:IC31, a candidate subunit vaccine, has shown protection against tuberculosis disease in preclinical models, and observational studies have indicated that primary bacille Calmette–Guérin (BCG) vaccination may offer partial protection against infection.
Methods: In this phase 2 trial, we randomly assigned 990 adolescents in a high-risk setting who had undergone neonatal BCG vaccination to receive the H4:IC31 vaccine, BCG revaccination, or placebo. All the participants had negative results on testing for M. tuberculosis infection on the QuantiFERON-TB Gold In-tube assay (QFT) and for the human immunodeficiency virus. The primary outcomes were safety and acquisition of M. tuberculosis infection, as defined by initial conversion on QFT that was performed every 6 months during a 2-year period. Secondary outcomes were immunogenicity and sustained QFT conversion to a positive test without reversion to negative status at 3 months and 6 months after conversion. Estimates of vaccine efficacy are based on hazard ratios from Cox regression models and compare each vaccine with placebo.
Results: Both the BCG and H4:IC31 vaccines were immunogenic. QFT conversion occurred in 44 of 308 participants (14.3%) in the H4:IC31 group and in 41 of 312 participants (13.1%) in the BCG group, as compared with 49 of 310 participants (15.8%) in the placebo group; the rate of sustained conversion was 8.1% in the H4:IC31 group and 6.7% in the BCG group, as compared with 11.6% in the placebo group. Neither the H4:IC31 vaccine nor the BCG vaccine prevented initial QFT conversion, with efficacy point estimates of 9.4% (P=0.63) and 20.1% (P=0.29), respectively. However, the BCG vaccine reduced the rate of sustained QFT conversion, with an efficacy of 45.4% (P=0.03); the efficacy of the H4:IC31 vaccine was 30.5% (P=0.16). There were no clinically significant between-group differences in the rates of serious adverse events, although mild-to-moderate injection-site reactions were more common with BCG revaccination.
Conclusions: In this trial, the rate of sustained QFT conversion, which may reflect sustained M. tuberculosisinfection, was reduced by vaccination in a high-transmission setting. This finding may inform clinical development of new vaccine candidates.
Elisa Nemes, Hennie Geldenhuys, Virginie Rozot, Kathryn T. Rutkowski, Frances Ratangee, Nicole Bilek, Simbarashe Mabwe, Lebohang Makhethe, Mzwandile Erasmus, Asma Toefy, Humphrey Mulenga, Willem A Hanekom, Steven G Self, Linda-Gail Bekker, Robert Ryall, Sanjay Gurunathan, Carlos A DiazGranados, Peter Andersen, Ingrid Kromann, Thomas Evans, Ruth D Ellis, Bernard Landry, David A Hokey, Robert Hopkins, Ann M Ginsberg, Thomas J Scriba, Mark Hatherill
New England Journal of Medicine abstract
Aeras
Bacille Calmette-Guerin (BCG) vaccine
Desmond Tutu HIV Foundation
Emavundleni Research Centre
International AIDS Society
Medicines Control Council of South Africa
Sanofi Pasteur
South African Tuberculosis Vaccine Initiative (SATVI)
Statens Serum Institute
University of Cape Town
World Health Organisation (WHO)
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Do we need youth-friendly TB clinics? | {
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Q: bash overriding a single line in a text file with another while using variables Overview: I am trying to make a script that will take a list of machines and manually update their /etc/shadow files with a new root passwd. I know this isn't the best method but my boss wants this process automated. we are using a application called puppet for 90% of the update but some machines failed the update or can't have puppet installed, hence this dodgy fix.
(sorry for any stupid errors its only my 3rd week using any unix product, I have been a windows admin my whole life)
Issue:
I need to ssh into the PC's update the /etc/shadow file but only change the root user (not all systems have the same users and I don't want to remove any of those users in the process) I have gotten as far as being able to extract the current user in line 1 through ssh, then check if that user is indeed the root user but I am stuck on then updating the /etc/shadow file on the new machine as my boss has asked that the following standards happen.
I can't have any real user interaction in the script, so no manually typing the new passwd.
I am not allowed to have the new passwd displayed anywhere in clear text (inside the script or in another file)
Ok hopefully that's enough info onto the code.
root=user
unknown='unknown.txt'
filelines=`cat $unknown`
prod='new-shadow'
ohf='option-one-holding-file'
pel=prod-errorlog
for line in $filelines ; do
echo "Attempting to fix $line please wait"
ssh -oBatchMode=yes -l $user $line "awk '{if (NR==1) print \$0}' /etc/shadow" >> $ohf
if grep -q "root:" $ohf ; then
echo "root user located updating to produtcion password"
# ** This is the line that doesn't work **
ssh -oBatchMode=yes -l $user $line "sed -i '1s/.*/$prod/' /etc/shadow"
else
echo "unable to find root user this will require a manual fix this server will be listed in
the prod-errorlog file"
echo "$line" >> $pel
fi
done
The line in bold the sed line doesn't work I know why it doesn't work but I have no idea how to fix it at all, thank you to anyone who takes the time to look at this, I know the codes a bit of a mess, please forgive me.
A: To replace only the first line:
"echo '$prod' > /etc/shadow.new; tail -n +1 /etc/shadow >> /etc/shadow.new; mv -f /etc/shadow.new /etc/shadow"
Sorry for my previous wrong argument wrong: The '$prod' part in your script is correct, and is expanded OK. Yet $prod contains many reserved characters for regular expressions. Now this new version just create a new file (replacing the first line) and then move/overwrite on to the target one.
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{"url":"http:\/\/spdg.com.ar\/25tx9j\/e1fa90-measures-of-dispersion-questions-and-answers-pdf","text":"Higher value of co-efficient variation suggests greater degree of variation & lesser degree of stability. Learn interquartile range of deviation MCQs, \"Measures of Dispersion\" quiz questions and answers for admission and merit scholarships test. According to Prof. C.R. Answer: We have different measures of dispersion used in measuring the variation in a data set. vii) Compare the values of different measures for each crop. Find out central tendency of the series (mean or median) from which deviations are to be taken. Write down the features of mean deviation. $$\\overline { X }$$ = Mean value. Answer: Answer: NCERT Solution for Class 11 Statistics for chapter 6 Measures of Dispersion. 0000001591 00000 n Answer: Answer: are Rs. Median (M) $$=\\frac{N+1}{2}=\\frac{10+1}{2}=\\frac{11}{2}$$ Define quartile deviation. We take the following example for providing that the variance is uneffected by the choice of the assumed mean. What is the difference between Variance and standard deviation? Mean Deviation: Question 8. Define quartile deviation. x = mid value Total wages after increase in wages = 10000 + 1000 + Rs. Range is unduely uneffected by extreme range. Prove by an example that the Variance is uneffected by the choice of the assumed mean. It is not a well \u2013 defined measure since mean deviation from different, average (Mean, median & mode) will not be same. In equation, variance = $$(\\sigma)^{2}$$. trailer << \/Size 304 \/Info 268 0 R \/Root 282 0 R \/Prev 130891 \/ID[<5c38e2c274ce36de66f7fe195cd5b9b7><5c38e2c274ce36de66f7fe195cd5b9b7>] >> startxref 0 %%EOF 282 0 obj << \/Pages 278 0 R \/Type \/Catalog \/DefaultGray 279 0 R \/DefaultRGB 280 0 R \/AcroForm 283 0 R \/PageMode \/UseThumbs >> endobj 283 0 obj << \/Fields [ 188 0 R ] \/DR << \/Font << \/ZaDb 187 0 R \/Helv 186 0 R \/HeBo 288 0 R >> >> \/DA (\/Helv 0 Tf 0 g ) >> endobj 302 0 obj << \/S 370 \/T 491 \/V 567 \/Filter \/FlateDecode \/Length 303 0 R >> stream Variance is the square of standard deviation. The amount of Variation in income is shown by deviation from the central values. Deviation from the arithmetic . These short objective type questions with answers are very important for Board exams as well as competitive exams. Total Increase in wages = 50 \u00d7 20 = Rs. Range = 100 \u2013 20 = 80, Question 40. Question 33. The following table gives you the height of 100 person. b. compute and apply accurately the descriptive measures in statistics to data analysis and interpretation in solving problems related to research, business, education, technology, science, economics and others. 1. sures of dispersion. Name the measures based on the spread of values Measures of Dispersion Measures of Dispersion - Objective type Online Test Questions and Answers with Solution, Explanation, Solved Problems These measures give us an idea about the amount of dispersion in a set of observations. Other measure can be also dealt with analytically but derivation are harder. Mean deviation 3. When the observations are in kilograms, the absolute measure is also in kilograms. 0000001569 00000 n What is a Lorenz Curve? Symbolically variance = \u03c3\u00b2. Features of mean deviation. What do you mean by coefficient of variation? Treat all deviations as positive. We can assess how precise is the central tendency observations in the series. 44. H\ufffdc\"[V \ufffd\ufffd\ufffd\u01c0 |@6 \ufffd(\ufffd\ufffd\ufffdf2c}\/\ufffd\u0107Q\ufffd\ufffd!g\ufffd\u0245\ufffd\ufffdB? Answer: Calculate range from the following date: It is based on absolute deviation from central values. In the instance where all scores are exactly at the mean, there is no dispersion at all; dis-persion increases from zero as the spread of scores widens about the mean. Dispersion is a measure of the Variation of the items. What is Coefficient of Variation? It is used to compare unifromly, consistency and variability in two different series. Question 9. These solutions for Measures Of Dispersion are extremely popular among Class 11 Commerce students for Economics Measures Of Dispersion Solutions come handy for quickly completing your homework and preparing for exams. Answer: Mean deviation and standard deviation are the measure of dispersion from average. Average of the series refers to the central tendency of the series. $$\\mathrm{C.V}_{\\mathrm{w}}=\\frac{\\sigma}{\\mathrm{X}} \\times 100$$ Question 8. C.V = $$\\frac{\\sigma}{\\overline{\\mathrm{x}}}$$ \u00d7 100. 1. a. Answer: What is the main limitation of range? WHEAT Briefly explain the various measures calculated from standard deviation? %PDF-1.2 %\ufffd\ufffd\ufffd\ufffd $$\\sigma=\\sqrt{\\frac{\\sum \\mathrm{d}^{2}}{\\mathrm{n}} \\times \\mathrm{C}}$$. Answer: Mean or Median is used in calculating the mean deviation. Range and quatile deviation measure the dispersion by calculating the spread within which the values lie. = 172 = (-1)2 = 172 \u2013 (+1) = 172 \u2013 1 = 171. Question 20. Answer: 1. From the table use come to know that each family have average income of Rs. Question 25. It is calculated by dividing the standard deviation by arithmetic mean of data symbolically. a. demonstrate understanding of the key concepts of the different measures of tendency and measures of variability of a given data. 1. = 1.2 \u00d7 10 = 12 In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable. Average try to tell only one aspect of a distribution ie. x = deviation Answer: How do Range and Quartile deviation measure the dispersion? Consider the following two sets of data which have the same mean, 25, and the same range, 10, but obvious di erences in the pattern of variability: 2 021 23 4 526 7 8 \u2026 The harmonic mean H of the positive real numbers 1, 2, 3, . Based on all values: Not all measures of central tendency and not all measures of disper- 1. Variance = $$\\frac{\\sum X^{2}}{N}=\\frac{5750}{5}$$ = 1150 Runs Mean Deviation from A.M. = $$\\frac{\\sum \\mathrm{fd}}{\\sum \\mathrm{f}}=\\frac{998.4}{50}$$ = 19.96. Points to remember. Variance $$\\frac{\\sum x^{2}}{N}=\\frac{1710}{10}$$ = 171, b. = L \u2013 S = 72 \u2013 64 = 8 To check he quality of two breands of light bulbs, their lie in burning hours was estimated as under for 100 bulbs of each brand. 320,400,450,530,550,580,600,610,700.780,800. Since C.V. of bulbs of Brand B (27.34%) is less than that of Brand A (51.55), therefore the bulbs of brand B are more dependable. Question 2. Range and Quantile deviation based on the speread of values. This page contains short questions and answers about Measure of Dispersion which includes introduction to measure of Dispersion or variation, different types of dispersion such as range, standard deviation, variance, \u2026 On the other hand, a lower value of coefficient variation suggests lower degree of variability & higher degree of stability, uniformity, homogeneity \u2018and consistency. M.D. All questions and answers from the NCERT Book of Class 11 Commerce Economics Chapter 6 are provided here for you for free. Question 38. 2. Question 30. Steps involved in the calculation of mean deviation: Standard deviation is independent of origin as it is not affected by the Value of constant from which deviations are calculated. Only when we study dispersion along with average of series that we can have a comprehensive information about the nature and composition of a statistical series. In calculating standard deviation, algebraic signs are taken into account. Quartile deviation =, Question 5. Absolute measures of dispersion are expressed in terms of original unit of series. 18000. Simple interpretaion: Here Standard deviation = $$\\frac{\\sigma}{\\overline{\\mathrm{X}}}$$ \u00d7 100, 2. Coefficient of variation is a percentage expression of standard deviation. The range is defined as the difference between the largest and the smallest value of variable in the given set of value R = L \u2013 S. Question 22. 0000001845 00000 n Median Middle value of rank ordered data Value that separates the higher half of a data set from the lower half Given N-10, \u03a3 X = 10, \u03a3 X2 = 1090 Assumed mean = 45 Quartile deviation 4. representative size of values, to understand it better, we need to know the spread of values also. However, the mean deviation & standard deviation require a little more systematic calculation they, too are easy. Measures of Dispersion 40 Mean Deviation Example The weights of a sample of crates containing books for the bookstore are (in kgs.) Calculation of standard deviation from mean: Question 12. 0000004048 00000 n 0000003813 00000 n Range Quartile deviation, mean deviation and standard deviation arc the important measures of dispersion. Define mean deviation Answer: The arithmetic mean of \u2018x\u2019 The range and Quantile deviation do not depend on all values where as the mean deviation and standard deviation use all values of the variable the range is affected the most by extreme values. Answer: The choice is between X and Y on the basis of their five previous scores which are: Which batsman should be selected if we want, Coefficient of S.D. = Rs. 40 = Rs. 1. Calculate the absolute & relative values of dispersion. \u03a3 x = 440, $$\\overline{\\mathrm{X}}=\\frac{440}{10}$$ = 44 Answer: Merits: Question 10. It is quite satisfactory when only the middle half of the group is dealt with. Question 2. On the other hand, mean deviation & standard deviation calaculate the variation of value from a central value. Answer: Write down the merits of mean deviation? Co \u2013 efficient of variance. 200 Comparison of alternative measure of the dispersion has been discussed below. Each measure has its place in summarizing public health data. The mean deviation of the value \u2018x\u2019 about, Question 3. Question 31. Question 32. Coefficient of Variation is the percentage Variation in the mean, the standard being treated as the total Variation in the mean. The units of measurement of the mean deviation are the same as there of the variable. It is very simple & easy measure of dispersion. The range is the easiest one to calculate. Answer: Example: Calculate variance of 25, 60, 45, 30, 70, 42, 36, 48, 34 and 60 by actual mean assumed mean method. They give the answers in the same units as the units of the original observations. Define the range $$\\sigma=\\sqrt{\\frac{\\sum x^{2}}{n}-(\\bar{x})^{2}}$$, Question 17. The measure of central tendencies indicate the central tendency of a frequency distribution in form of an average. Question 10. It involves a harder calculation than the range & quantile deviation. Measures of Dispersion Chapter Exam Instructions. It depends on all the values of the variable. Take from central tendency ignoring signs (+, -) express it as | dx | Or (|dm|). Do you agree? Question 24. Answer: Answer: Question 4. The measurement of the scatter of the given data about the average is said to be a measure of dispersion or scatter. Calculate the range of the following observations : Greater value of dispersion implies lesser representativeness of the central tendency and vice versa. iii) Mean Deviation about mean Answer: Answer: Only mean is used in calculating the standard deviation. Why should we measure dispersion about some particular value? How is coefficient of quartile deviation calculated? The averages represent the series as a whole. , > 0 is defined to be = 1 Example: It ignores 50 percent of the extreme items. iv) Mean Deviation about Median 103, 97, 101, 106, 103. Answer: Question 11. =16, ii) Qusirtile Deviation (Q.D) It is closely Related to standard deviation. Exercise 8.1: Measures of Dispersion. Arithmetic mean. In statistics, the measures of dispersion help to interpret the variability of data i.e. average In this lesson, you will read about the following measures of dispersion : (a) Range (b) Mean deviation from mean (c) Variance 1. 0000014899 00000 n In Equation Variance = (SD)2. Measures of Dispersion \u2022Tell you how widely spread out the values are \u2022Most common are Range, Standard Deviation, and Variance Range \u2022The range of a data set is the difference between the maximum and minimum values in the set \u2022Example: >In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9. 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Curve which measures the extent of spread or dispersion of the variation of Rice is more reliable of of!","date":"2021-04-20 11:22:32","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7637577652931213, \"perplexity\": 1216.9014409521167}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-17\/segments\/1618039388763.75\/warc\/CC-MAIN-20210420091336-20210420121336-00421.warc.gz\"}"} | null | null |
and the Impact of Forest Management
Edge effects are changes to processes and species diversity along the edge into the forest. The edge has a large influence on tree and seedling mortality and somewhat lesser but still important effects on species richness and abundance. Forest management, particularly in the unique community of the roadside forest, may enhance the edge effects acting on plant communities.
In 8 of the Stormwise demonstration sites in CT a section of roadside forest was cut according to the Stormwise treatment and a section was left untouched (control). Within each section of forest, 3 transects were established running perpendicular to the road, 30m long, 30m from an edge (other than the road), and 10m from one another. Along the transects, each of the following were tracked throughout the growing season.
Woody plants (in 4m wide belts along the transects)
Herbaceous plants (in 1-sq-m plots along transects)
Light conditions (looked at with a ceptometer, as well as hemispherical photos along the transects)
Project Goals and Updates
The objectives of this study are to quantify the depth of road edge effects and environmental conditions in Stormwise treatment sites compared to control treatments throughout Connecticut. Specifically, between the management and control sites, we want to look at:
Differences in native versus invasive plant communities
Differences in the plant community structure and composition
Differences in light environments
➡ Depth-of-Edge Influence Analyses have been developed (Harper and MacDonald 2011) to test the significance of the magnitude of the edge influence at various distances from the edge, as compared to what would be expected in an interior forest plot.
➡ Preliminary results have shown us that the Stormwise treatments enhance the edge effects in the roadside forests, which was expected. Stormwise treatments are also promoting the growth of woody vegetation, both invasive and native, in the roadside forest. However, there is a lack of edge influence in control sites, indicating that the forests have had time to seal the edge following the establishment of the road.
➡ Phase 2 of the project, now underway, will involve a close look at the growth and development of native and invasive species growing in the Stormwise treatment sites as well as controls. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,284 |
\section{Introduction}
The physics of relativistic plasmas is a very general issue. High energy particles are expected to produce the hard emission of all high energy sources. These sources cover a large variety of scales and objects, such as X-ray binaries, AGN, or $\gamma$-ray bursts... Moreover, objects such as microquasars involve different states, with possibly several geometries. Different models have been proposed to account for the high-energy emitting medium, such as the two-temperature flows models, hot coronae, base of the jet, jet emitting disk... Despite this variety, the microphysics at work in the innermost regions of all these high energy sources is expected to be the same.
The physics of high energy plasmas is complex. It results from the combined effects of magnetic fields, the kinetic behaviour of particles and radiation processes. The evolution of such systems is highly non-linear and is described by intregro-differential equations rather than usual differential equations. The cross sections of most processes are quite complicated. And last, Coulomb collisions are often not efficient enough to keep the distributions thermal and to allow for the hydrodynamical or MHD approximations. This complexity makes analytical studies a real challenge and rather points towards the use of the numerical tool.
Numerical simulations of relativistic plasmas have been performed for more than 20 years now. Two main techniques have been used: the Monte Carlo method (hereafter MC, Pozdnyakov et al., 1980, Stern et al., 1995) and the kinetic approach. The Monte Carlo technique is very efficient in simulating steady state, 3D problems in a given geometry. However, whereas a precise description of geometrical effects can bring interesting constrains, the geometry of the sources is not known and MC simulations are very time consuming, limiting their use to a few long runs. When comparisons with observations, data fitting and exploration of a large parameter space is wanted, kinetic codes are more appropriate. These code can abandon the precise description of the geometry and focus on other features such as radiation processes. The first kinetic codes assumed pure thermal distributions (Fabian et al. 1986, Ghisellini 1988). Most recent simulations accounted for hybrid distributions of particles constituted of a low-energy, thermal component and a higher energy power-law tail (e.g. Lightman \& Zdziarski 1987, Coppi, 1992). However, they included only a limited number of processes, depending on the application they were dedicated to. Moreover such codes cannot address precisely issues such as thermalization mechanisms.
We have developed a new kinetic code that overcomes these limitations by including an exhaustive number of radiation and kinetic processes and by using arbitrary distributions of particles. In section 2, we present the code, its main properties and an illustration of the code capabilities about thermalization by synchrotron self-absorption. In section 3, we present preliminary results on the properties of acceleration mechanisms in X-ray binaries. This work is aimed to discriminate between the different acceleration processes proposed so far (collisions with hot protons, reconnection, shocks, turbulence...).
\section{The code}
\subsection{Basics}
The code developed is a one-zone code. It does not address the sources geometry explicitly. Instead, we assume an homogeneous sphere of fully magnetized plasma. The properties of this system are fully described by the particle and photon distributions inside this sphere. The exact radiation transfer is not solved throughout the sphere, but the emitted spectrum is computed using the usual {\it escape formalism}, where photons are assumed to have a given, uniform escape-probability. The exact escape probability is chosen to reproduce the steady state results of radiation transfer problems in spherical geometry (Lightman \& Zdziarski 1987, Coppi, 1992, Stern et al. 1995). Also, depending on the precise geometry of the source, the simulated plasma can be illuminated by a flux of external photons. The code accounts for such an illumination by injecting, in the entire sphere, photons of given temperature.
The code is time dependent. It evolves with time three distributions of species: the positron, electron, and photon distributions. Distributions are assumed to be isotropic, so that they only depend on one variable, namely the particle or photon energy. Equations on 1-dimension distributions are very rapid to solve and allow for an efficient code. In contrast to most previous works (see references here before), we do not assume thermal nor power-law particle distributions. The code allows for arbitrary energy distributions. In addition to the mentioned species, a thermal distribution of protons is described, the temperature of which can also be evolved with time.
Distributions are discretized in energy bins and the evolution equations are solved bin by bin. The numerical scheme is second order-accurate in space, and first order accurate in time. We use a semi-implicit scheme to overcome the Courant condition limitation. Because the equations are highly non-linear, iterations are made at each time step to converge towards the fully implicit solution. This numerical scheme enables rapid computing and
robust solutions.
In addition to a few numerical parameters, the code starts with given initial photon and particles distributions and uses the following set of physical parameters: the system size $R$, the magnetic field intensity $B$, and the luminosity $L_\nu$ and temperature $k_BT_\nu$ of illuminating soft photons. It solves the coupled kinetic equations for photons and particles and evolves their distribution according to the microphysics of relativistic plasmas described in the following section.
\subsection{Microphysics}
Have been included into the code the following processes: Compton scattering, cyclo-synchrotron emission and absorption, pair production and annihilation, lepton-proton bremsstrahlung emission and absorption, lepton-lepton and lepton-proton Coulomb collisions and various prescriptions for additional heating and particle acceleration. \\
$\bullet$ Compton scattering typically up scatters low energy photons by cooling high energy particles. It is described using the full isotropic Klein-Nishina cross section, without approximation (Jones 1968, Nagirner \& Poutanen 1994, Belmont 2008b). This cross section is integrated over the photon and particle distributions. For small-angle scattering, the energy variation in one single scattering event can become smaller than the grid resolution. To prevent severe accuracy issues, we use a Fokker-Planck approximation in this regime. \\
$\bullet$ The cyclo-synchrotron self-absorption is described by the synchrotron emissivity of one single electron in a given magnetic field and the related absorption coefficient. There is no exact formula valid in all regimes for these angle-integrated coefficients. We use a combination of asymptotic expressions for the sub- and ultra relativistic regimes (Ghisellini \& Svensson 1991, Katarzinsky 2006a). The resulting expressions are accurate in all regimes except for very low photon energies where a few harmonics start dominating the spectrum (Marcowith \& Malzac 2003). Synchrotron emissivity and absorption are used to build the coefficients of a Fokker-Planck equation on particles (Ghisellini et al. 1988, 1998). \\
$\bullet$ Pair production and annihilation are reproduced by using the full isotropic cross sections (Boettcher \& Schlickeiser 1997 and Svensson 1982 respectively), and integrated over the particle and photon distributions. Contrary to Compton scattering, this integration always remains accurate. \\
$\bullet$ Lepton-Proton bremstrahlung self-absorption produces additional soft photons and cools down high energy particles. It is described with the same formalism as synchrotron self-absorption. The full isotropic cross section is used (Heitler 1953, Jauch \& Rohrlich 1976), whose only approximation assumes sub-relativistic protons. For most applications to microquasars however, e-p bremstrahlung is not significant. Electron-electron and electron-positron bremsstrahlung have not been included in the code yet but their effect is though to be also negligible. \\
$\bullet$ Coulomb collisions tend to thermalize the particle distribution by cooling high energy particles and heating low energy ones. In addition, Coulomb interactions with hot protons can heat the lepton populations. Lepton-lepton and lepton-proton Coulomb collisions are also described with the Fokker-Planck formalism. The Fokker-Planck coefficients are derived from the cross section given in Nayaksin \& Melia 1998. \\
$\bullet$ The code also accounts for particle heating and acceleration. Namely, particles in the code can gain energy by a Coulomb-like heating mechanism; by stochastic acceleration, or by other non-thermal mechanisms (see section \ref{sec_acc}). When additional acceleration or heating is used, more parameters are required by the code: the heating rate, and some others depending on the included process.
More details on the numerical strategy and the included processes are given in Belmont et al. 2008a. The code developed reproduces most relevant processes of high energy plasmas such as the Comptonizing medium of microquasars. It uses general numerical schemes and cross sections accurate in all regimes. In particular, the photon distribution can span the entire electro-magnetic spectrum, from radio wavelengths (or lower energy), to TeV emission (or higher). The code can deal with particles from the sub-relativistic regime (with momentum $p>10^{-7} m_ec$) to the ultra-relativistic regime ($p<10^{-7} m_ec$). This makes the code very general and enables its use for many different astrophysical applications: X-ray binaries, AGN, $\gamma$-ray bursts...
\subsection{Example: the Synchrotron Boiler}
One of the new features of our code is the synchrotron self-absorption, which can play a crucial role in microqusars. For the first time this process is consistently taken into account in a global code, together with other radiation and kinetic processes. Here we present examples of runs made with our code to illustrate the {\it synchrotron boiler} mechanism (Ghisellini et al. 1988, 1998).
\begin{figure}[h!]
\includegraphics[width=.5\textwidth]{belmont_fig1.pdf} \includegraphics[width=.5\textwidth]{belmont_fig2.pdf}
\caption{Time evolution of the particle (left panel) and photon (right panel) distributions under effect of synchrotron self-absorption ($B=5.5\times 10^3$ G) and Compton scattering. Particle are injected at $\gamma=10$ with a constant rate ($ \dot{N}_{e-} = 10^7$ s$^{-1}$cm$^{-3}$) and escape in one dynamical time $R/c$. The Maxwell-Boltzmann distribution of same energy is over-plotted in dashed line.The size is here typical of AGN: $R=10^{13}$ cm. }
\label{sboiler}
\end{figure}
Fig. \ref{sboiler} shows the time evolution of the particle distribution and the emitted spectrum when only self-absorbed synchrotron radiation and Compton scattering are taken into account. Particles are continuously injected at high energy and are allowed to escape freely. The initial conditions correspond to an empty sphere. As time goes, the number of particles increases until it reaches a steady state, where losses equals the injection. The injected high energy particles start emitting soft synchrotron radiation. As a result, they cool down and form the low energy part of the distribution. When they reach very low energies, the particles start absorbing photons, which prevents them to cool further down. Simultaneously, high energy particles also up-scatter the soft synchrotron photons, producing the hard tail observed on the right panel.
In steady state, the particle distribution is quasi-Maxwellian, at least at low energy. A deviation is only observed at high energy, where particles are injected and cool down. This example illustrates the thermalization by synchrotron self-absorption. The efficiency of this mechanism depends on the parameter regime. It is very efficient for optically thin, magnetized sources with weak external illumination. For dense plasmas, Coulomb collisions become the dominant thermalization process, whereas strong Compton cooling prevents particles from being heated by absorption in strongly illuminated sources. In microquasars, thermalization by the synchrotron boiler mechanism can explain various properties of the state transition in X-ray binaries (Malzac \& Belmont 2008, and see also J. Malzac in these proceedings).
\section{Constraining acceleration processes in X-ray binaries}
\label{sec_acc}
Among others interesting issues, the code was used to address the heating problem of microquasars corona.
X-ray binaries exhibit two interesting canonical states: the low-hard state (LS hereafter), characterized by a rather low luminosity and a power-low spectrum extending to high energy with a cut-off at around 100 keV, and the high-soft state (HS), characterized by a higher luminosity and a spectrum composed by a soft excess at about a few keV and a steep high-energy tail extending to MeV energies, with no hint for a cut-off. Spectra in the LH state are well reproduced by thermal Comptonization models with plasma temperatures of about 100 keV, whereas spectra in the HS state are best reproduced by a black-body emission from the disk and its Comptonisation by high energy, non-thermal particles.
In all states, high energy particles must cool very quickly because of the various radiation cooling processes such a Compton scattering with soft photons. To keep a significant fraction of emitting high energy particle, power must be continuously injected into this hot medium. Various mechanisms have been proposed to account for this power supply, such as heating by hot protons, magnetic reconnection, turbulent heating, and shocks. However, the coupled effect of acceleration and all relevant radiation processes have not been studied in a consistent approach yet, and the mechanisms at work in microquasars remain poorly constrained. Moreover, the different particle distributions inferred in the different states (thermal in the LS state and non-thermal in the HS state) represent a real challenge to the modelling.
To investigate the various channels through which the power can be supplied to the Comptonizing medium, three prescriptions have been included in the code.
\subsection{Thermal heating}
Models such as two-temperature disks assume that protons and electrons are almost decoupled (Narayan \& Yi 1994). Protons are heated by a strong anomalous viscosity. Since they cannot radiate their energy and are only weakly coupled to electrons, they reach very high temperatures (typically 10-100 MeV). The coupling with leptons, although weak, allows to heat electrons, that then radiate this energy. This heating is by nature thermal and has been applied to reproduce X-ray binary spectra in the LH state (e.g. Esin et al. 1997).
To model such thermal heating, the code consistently describes the Coulomb collisions with a thermal population of protons. To bring more direct constraints, the heating rate, instead of the proton temperature, is set and the proton temperature responsible for this rate is computed consistently with the electron distribution.
Simulations with the code confirm that Coulomb heating produces thermal distributions and thermal spectra such as those observed in the LH state. Spectra of HS states can not be reproduced by such a pure thermal heating, nor can the non-thermal tails observed in some observations of microquasars in the LS state (McConnell et al. 2002).
\subsection{Non thermal acceleration}
Particles can also be accelerated by magnetic reconnection or shocks. Reconnection has been proposed to occur in an active corona overlying a turbulent, magnetized accretion disk (Galeev et al. 1979). Because of turbulence and buoyancy, field loops rise above the disk and reconnect into the corona, accelerating particles to the required energies. The detailed microphysics of reconnection and shocks is still uncertain and is out scope of this study. These processes are however thought to produce power-law distributions of particles.
Non-thermal particle acceleration is mimicked by injecting high energy particles with a power-law distribution. To conserve the total number of particles, leptons are physically removed from the system before they are re-injected as a power-law distribution. This injection is characterized by the minimal and maximal Lorentz factor of accelerated particles $\gamma_{\rm min}$ and $\gamma_{\rm max}$, the slope of the power-law $\Gamma$ and the injection rate.
Results of simulations with non-thermal acceleration are presented in theses proceedings by J. Malzac (see also, Malzac \& Belmont 2008). We just remind here the main results. Our simulations show that the non-thermal HS spectra are well reproduced by assuming non-thermal acceleration. They also show that the synchrotron self-absorption and Coulomb collisions in the LH state are efficient in thermalizing the distribution, and that models with pure non-thermal acceleration can also reproduce thermal spectra. As a result, models with one unique, non-thermal acceleration process can explain both LH and HS states of microquasars, the state transition resulting mostly from a change in the illumination from the cold accretion disk.
\subsection{Stochastic acceleration}
Last, in turbulent media, particles can also be accelerated by resonant interactions with plasma waves, such as Alf\'en or fast magnetosonic modes (Li \& Miller 1997, Katarsinsky et al. 2006b). Stochastic acceleration results in a diffusive process where some particles are accelerated and others are cooled down.
Stochastic acceleration is described by the 2nd order Fermi equations. To account for the fact that only particles above some energy are resonant with waves and thus accelerated, we added a threshold in the equations. The precise acceleration rate and threshold energy directly result from the details of the plasma turbulence, which is poorly constrained. Instead, these parameters are varied in the simulations in order to constrain the plasma properties.
\begin{figure}[h!]
\includegraphics[width=.5\textwidth]{belmont_fig3.pdf} \includegraphics[width=.5\textwidth]{belmont_fig4.pdf}
\caption{Steady state solutions for particle distributions (left panel) and photon spectra (right panel) for simulations with stochastic acceleration of different acceleration rate and no threshold. Only stochastic acceleration, self-absorbed synchrotron radiation and Compton scattering are switched on. The power injected into particles is $P= 1.8\times 10^{32}, 1.8\times10^{35}, 1.8\times10^{37}$, and $1.8\times10^{38}$ erg~s$^{-1}$, for the blue, green, orange, and red curves respectively. The other parameters are: $R=5\times10^{7}$ cm, $B= 7.9\times10^5$~G, $\tau=1$.}
\label{acc1}
\end{figure}
Simulations are completed including only Compton scattering, self-absorbed synchrotron radiation and stochastic acceleration. As no external illumination is added, all soft photons are produces by synchrotron emission.
Figure \ref{acc1} shows the steady state particle distributions and photon spectra when the acceleration rate in varied, with no threshold. As can be seen, the particle distributions are always quasi-thermal. Second order Fermi acceleration process is a diffusive process and it cannot produce hard tails of particles. The higher deviation from a Maxwellian distribution appears at high energy for very large acceleration rates. The corresponding spectra are typical of thermal Comptonization, as those observed in the LH state of X-ray binaries.
\begin{figure}[h1]
\includegraphics[width=.5\textwidth]{belmont_fig6.pdf} \includegraphics[width=.5\textwidth]{belmont_fig5.pdf}
\caption{Steady state solutions for particle distributions (left panel) and photon spectra (right panel) for simulations with stochastic acceleration of constant rate ($P=1.8\times10^{37}$~erg~s$^{-1}$) and different energy thresholds. Only stochastic acceleration, self-absorbed synchrotron radiation and Compton scattering are switched on. The threshold Lorentz factors are $\gamma_{\rm min}= 1, 1.4, 1.6, 2.2, 5$, and 10 for the blue, green, orange, and red curves respectively. Other parameters are: $R=5\times10^{7}$ cm, $B=7.9\times10^5$~G, $\tau=1$.}
\label{acc2}
\end{figure}
We also varied the threshold energy for acceleration at constant acceleration rate. Results are presented in Fig. \ref{acc2}. For low energy threshold, the distributions are thermal and so are the emitted spectra. However, these results show that when the threshold reaches relativistic energies ($\gamma_{\rm min} \ge 2$), the distributions strongly deviate from the Maxwell-Boltzmann distribution. Although the low energy part is always thermal, hard tails of particles are observed. The corresponding spectra are also strongly non-thermal.
These results show that stochastic acceleration is a potential candidate to explain the presence of high energy particles in X-ray binaries. Depending in the threshold energy, it can produce both thermal and non-thermal distributions. Although at this stage, the non-thermal spectra look more like blazar spectra than spectra of microquasars, only Compton scattering was included in these runs and the parameter space has not been investigated yet. Other regimes and other ingredients such as external illumination are expected to modify significantly the spectrum.
\section{Conclusion}
We presented a new one-zone, kinetic code developed to study the properties of the relativistic plasmas in high energy sources. For the first time, our code solved the coupled kinetic equationd for arbitrary distributions of particles and photons, including most relevant processes: Compton scattering, synchrotron and bremsstrahlung self-absorption, pair production/annihilation, Coulomb collisions and prescriptions for thermal, non-thermal and stochastic particle acceleration. This code is very general and can be used to model not only X-ray binaries, but also AGN and $\gamma$-ray bursts.
As a first example of the code capabilities, we presented some preliminary results on a recent work on acceleration processes in the Comptonizing medium of microquasars. We showed qualitatively that 1) thermal heating can account for the thermal spectra in the low-hard state of microquasar, 2) non-thermal acceleration can reproduce both the non-thermal high-soft state emisson and the thermal low hard state spectra, 3) stochastic acceleration usually produces thermal spectra but can also form non thermal tails for relativistic acceleration threshold. Wider exploration of the parameter space and real data fitting are required to give more reliable constraints.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 274 |
Wankdorf Stadium () is a football stadium in Bern, Switzerland. The second largest all-seater football stadium in Switzerland, it is the home ground of BSC Young Boys. It was also one of the venues for UEFA Euro 2008.
History
The present-day Stadion Wankdorf was built on the grounds of the former Wankdorf Stadium, which hosted the 1954 FIFA World Cup Final (The Miracle of Bern), and was then demolished in 2001. The new stadium has a capacity of 32,000 spectators, all seated. Integrated into the roof are solar panels with a yearly production of 1,200,000 kWh. The stadium was officially opened on 30 July 2005, although the first match in the new stadium had already taken place on 16 July 2005. Young Boys played against Olympique Marseille and lost 2–3 with 14,000 spectators watching. The match was considered an "infrastructure test", which is why no more than 14,000 tickets were sold.
The stadium was used by FC Thun for three Champions League home matches in 2005, and for one home match in the UEFA Cup round of 32 in 2006.
Fifteen years after the new stadium opened in 2005 (back then called Stade de Suisse), it was renamed Stadion Wankdorf in June 2020, in an effort to return to the stadium's roots.
Concerts
Bruce Springsteen performed at the stadium on 30 June 2009 as part of the Working on a Dream Tour in front of a sold-out crowd of 36,538 people.
AC/DC performed at the stadium on 8 June 2010 as part of their Black Ice World Tour and on 29 May 2016 during the Rock or Bust World Tour with Axl Rose as lead singer.
P!nk performed at the stadium on 10 July 2010 during The Funhouse Summer Carnival.
Muse performed a sold-out show at the stadium on 15 June 2013 as part of their The 2nd Law World Tour.
Bon Jovi performed at the stadium on 31 May 2006 during their Have a Nice Day Tour, in front of a sold-out crowd of 38,762 people. The band performed at the stadium for the second time on 30 June 2013 during their Because We Can, in front of a sold-out crowd of 28,868 people.
Depeche Mode performed at the stadium on 7 June 2013 during their Delta Machine Tour, in front of a sold-out crowd of 39,241 people.
One Direction performed at the stadium on 4 July 2014 during their Where We Are Tour.
On 15 July 2017, Celine Dion brought her Celine Dion Live 2017 tour to the stadium. She performed her sold-out show to 23,143 people, with a mixed set list of English and French.
On 5 June 2019 Rammstein performed in Bern during their Europe Stadium Tour 2019. The concert was sold out in several hours.
The Hot Seat
A peculiar feature of the Wankdorf Stadium is the presence of a single, red seat (the other seats are black and yellow). This was the first seat installed at the stadium, on 20 January 2005, and the honour of unveiling it was given to former Young Boys player and manager Walter Eich. There are no tickets available for this seat; every game the seat is occupied by a notable personality, often with ties to Young Boys.
Ice hockey attendance record
The Wankdorf Stadium with its artificial turf surface was an ideal candidate to provide Europe its first "new era" outdoor attendance record for ice hockey.
On 14 January 2007, the massive local rivalry of SC Bern and SC Langnau managed to fill the Stade de Suisse with 30,076 fans, an event which was sold out within 53 hours of tickets going on sale. These two rivals regularly fill SC Bern's home venue Bern Arena with over 17,000 spectators.
Matches
UEFA Euro 2008
The stadium was one of the venues for the UEFA Euro 2008. The Netherlands played all three games at the stadium during the tournament:
International matches
See also
List of football stadiums in Switzerland
References
External links
Stadion Wankdorf, bscyb.ch (in German)
Events, bscyb.ch (in German)
UEFA Euro 2008 stadiums in Switzerland
Football venues in the Canton of Bern
Switzerland
Outdoor ice hockey venues in Switzerland
Buildings and structures in Bern
Sports venues in the Canton of Bern
Sports venues completed in 2005
2005 establishments in Switzerland
21st-century architecture in Switzerland | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,147 |
The following is a chronicle of events during the year 1980 in ice hockey.
National Hockey League
Art Ross Trophy as the NHL's leading scorer during the regular season: Marcel Dionne, Los Angeles Kings
Hart Memorial Trophy: for the NHL's Most Valuable Player: Wayne Gretzky, Edmonton Oilers
Stanley Cup - New York Islanders defeat the Philadelphia Flyers 4 games to 2.
Canadian Hockey League
Ontario Hockey League: Peterborough Petes won J. Ross Robertson Cup.
Quebec Major Junior Hockey League: Cornwall Royals won President's Cup (QMJHL)
Western Hockey League: Regina Pats won President's Cup (WHL)
Memorial Cup: Cornwall Royals defeated Peterborough Petes
World Hockey Championship
Men's champion: Olympic year, no tournament
Junior Men's champion: Soviet Union defeated Finland
Winter Olympics
February - 1980 Winter Olympics: The United States men's hockey team wins the gold medal, defeating Finland in their last medal round game. Their extraordinary upset victory over the heavily favoured Soviet Union team in their previous medal round game became known as the "Miracle on Ice" in the US press.
Minor League hockey
American Hockey League: Hershey Bears Calder Cup
IHL: The Kalamazoo Wings capture the Turner Cup.
Season articles
References | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,381 |
/ Category / interview
Future Forward: Use a PERMIT System to Promote Safety on the Job Site
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Change Leader Interview: Success with an Unconventional, Decentralized Engineering Business
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,147 |
{"url":"https:\/\/geekhack.org\/index.php?PHPSESSID=o1f0vl3h3ndbgomuasuli04366e03ol2&action=printpage;topic=22780.0","text":"# geekhack\n\n## geekhack Projects => Making Stuff Together! => Topic started by: Dox on Mon, 10 October 2011, 16:06:53\n\nTitle: ErgoDox - Custom split ergo keyboard.\nPost by: Dox on Mon, 10 October 2011, 16:06:53\nI started designing a \"OTD class\" split ergo keyboard this weekend based on the key64 (http:\/\/www.key64.com) and I was thinking that maybe we could make it possible if there was some people interested.\n\nThe design is not final and there is still a lot of work to be done but here is where I am.\n[ATTACH=CONFIG]28310[\/ATTACH][ATTACH=CONFIG]28306[\/ATTACH][ATTACH=CONFIG]28307[\/ATTACH][ATTACH=CONFIG]28308[\/ATTACH][ATTACH=CONFIG]28309[\/ATTACH]\n\nCurrent design (based on feedback and comments) still not final:\n(http:\/\/geekhack.org\/attachment.php?attachmentid=28864&d=1318894674)\nTHE LAYOUT PRESENTED IS NOT FINAL. THE CONTROLLER WILL BE PROGRAMMABLE.\n\nThe price will be high \u00b1400$(highly depending on how many we are). What would be included: Full CNC anodized aluminium case and plate, PCB. What may be included or self-served: Switches, Keycaps, Diodes, Cable, Teensy, Assembly Leave your interest and comment below. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Mon, 10 October 2011, 16:43:44 Now available via Massdrop! https:\/\/www.massdrop.com\/buy\/ergodox (You will need to make an account with them) Updated with list: Interest collected via Geekhack: Code: [Select] 01. Dox...................2. (The creator himself!)02. DorkVader.............1. (Very likely)03. iWuzHere..............1p (under$150-200)04. demik.................1? (Looks Awesome, worried about soldering)05. Litster...............1. (Definitely interested)06. Sordna................1-2(Looks GREAT!) (will save 200 without case)07. RColinTaylor..........1p (if under $300)08. Mazora................1? (dependent on layout)09. Input Nirvana.........1? (Possible Interest)10. TheSoulHunter.........1p ($300 range)11. Christoffer.Braathen..1. (ALL IN!!!)12. Bretrex...............1. (Pcb only)13. Karacho...............1. (I want one)14. Quarzac...............1p (Interested, but worried about cost)15. REVENGE...............1. (Fantastic Project)(definitely want one now)16. Sleuth................1p (will see about cash)17. 18. Ascaii................1. (very interested; Heavy Metal only)19. Laffindude............1p (under $300) (still in this)20. Chef..................2. 21. eagleeye..............1P (under$300, depending on design)22. cyclonechuah..........1P (I'm interested if it's under $300.)23. Gilgam................124. 25. Gfresh404.............1P (maybe around$200)26. inaneframe............3+. (Currently looking to sell his car) (\"Dox, you're beautiful\")27. funkymeeba............1P (under $350 or so) (or more!)28. Hoggy.................1. (This is exactly what he needs!)29. mharrison.............1. (One if by trackpoint)30. wrtcedar..............1P (If under ~$300+)31. 32. fim...................1. (Does not want to solder)33. obra..................1. (interested in soldering service)34. bonega................1. (Soldered & ship to sweden, under 300)35. richie................1. (under $400& assembled)36. parak.................1? (Possible)37. Ironman31.............1. (If the keys come with it)38. mioytan...............1P (under 300)39. boli..................1-2($400)40. Icarium...............1P ($400)41. moogatronic...........1P (under$400)42. dzd...................1. (Wants one too!)43. itlnstln..............1. (would be in for one)44. heuristicist..........2P ($500 for all parts.$600 tops.)45. REVENGE...............1+ (Definately interested)46. Zanth.................1. (I would be in for one)47. Tafryn................1P (around $300)48. Thirdkind.............2. (definitely be in for 2)49. Sicyo.................1. (Would certainly be interested)50. pjpettis..............1? (I'm about 95% in for one.)51. ksweber...............1. (I am also interested in getting one)52. jedcred...............1. (Interested up to the shoulder with this design)53. gilgam................1. (\"i want one of this\" Who doesn't?)54. Salash................1. (Standard message of interest)55. minnus................1. (Please add me to the interest list as well)56. ekw808................1p (under 200)57. ic07..................4P*(2-4 pcb and 0-2 cases, depending on price)58. Laggy-gaga............1p (around 200)59. dirge.................2. (One put down [on] the list)60. ped...................1p (Not much over 400 :D )61. Kisakuku..............1. 62. seferphier............1p (200-250)63. Mycroftxxx............1p (depends on material)64. speedkills............1p (500, assembeld)65. molto.................1p (50, PCB only)66. Jesuswasazombie.......1p (Awesome if under 200)67. Inf3rn0_44............1p (Interested under 300)68. geekabit..............1p (Interested under 200)69. Necroleachate.........1p (Dreams will be fulfilled if under 200)70. jblack801.............1p (Definately in for$250)71. tradet................1p (Maybe under 200 tempts him)72. beguiledfoil..........1p (under 400 and blank)73. itunesacc.............1p (around 200)74. rburrows..............1p (around 400 soldered)75. tjweir................1p (interest at 300)76. OrangeJewce...........1-2(400 for all, assembled)77. Spharx................1p (miraculously 200)78. Sherryton.............1. (Dork put him down)79. bjarven...............1. (Interest Looks Great!)80. Whiterice.............1p (I'm in. 400.)81. Autolyze..............1. (totally interested)82. didjamatic............1-3(Depends on final price)83. merijn................1p (Starving Student Budget)84. mSSM..................1-2(well interested)85. effh..................2. (PCB for amazing firmware\/hacking ability)86. Salisen...............1p (interested in \"300\")87. Zifle.................1. (Timeline and Interest Check.)88. forcefollow...........2-3(hopes it will be produced soon)89. Surger................1-2(Most definately interested, what about f# keys?)90. Djuzuh................1p (might be interested, depending on price)91. ashleydev.............1. (Can I put in an order?)92. bisl..................3. (kinesis\/ergoDOX club)93. braaaiiins............1P (Pcb only if under 100)94. SubGothius............1P ($500 budget.)95. Hashbaz...............1. (Added to list.)96. localredhead..........1. (Count me in!)97. jochu.................1-2(Consider me interested)98. prdlm2009.............1. (may be interested)99. Tsangan...............1. (interested only after seeing the prototype working)100.Mkawa.................1. (in to help as usual)101.StaCT13...............1p (under$500 for everything, assembled)102.The_Beast.............1. (Always interested in a pcb)103.docomoz...............1. (\"I'm in. No matter what the cost\")104.kta...................1p ($500 range, at least noe set)105.bebuxe................1. (No matter what the cost!)106.gdaian................1. (Ergodox relieves frustration)Removed interest:31. Architect.............1-3. (one for sure. two more possible) From DT: Code: [Select] 01. Webwit................1. (I'm in for one if it comes to a group buy.)02. jakobcreutzfeldt......1. (Too \"mad\" to be marked yet)03. xbb...................1. (Thanks added to list)04. jcrouse...............1. (\"I want one list\")05. pingbat...............1. (utron dreams)06. forcefollow...........1. (one to replace his drool-damaged HHKB07. wiredPANDA............1. (Watches it develop)08. domoaligato...........1-2(from following this thread)09. PrinsValium...........3. (See #12 on GH. Needs a couple for \"Reference\")10. HzFaq.................1. (Really startnig to look awesome)11. bjarven...............1. (Waiting on this or kinesis12. yobfish...............1. (Joined the forum to be added!)13. nathanak21............1P (Without breaknig the bank)14. mintberryminuscrunch..1. (PCB Only)15. Findecanor............1. (all but case)16. DanGWanG..............1. (In for one!)17. AKIMbO................1. (Looks Amazing)18. ondast................1. (Interested in full version)19. justcallmecrash.......1-2(Again, depending on the costs. If it really is$30 ->2)20. regak.................1-2(Got his name down.)21. Possum................1. (Who wouldn't want one?)22. Damorgue..............1. 23. yobfish...............124. maxrunner.............1p (200-250)25. nodnerb...............1\u00a0 (In for one pair)26. Jim66.................1. (Moved From GH)(will be in for one)27. Kurrk.................1P (under the magic $300)28. WarlockD..............1. (Exactly what He's been looking for)29. maxrunner.............1. (he's interested in any way!)30. Aleksander............1. (He's on the list now, that's an excuse to get one)31. Fossala...............1. (on the list now)32. plaset36..............1. (interested in one)33. gilsoriano............1. (One whole)34. stevedreams...........1. (Has been counted)35. off...................1? (really starting tolook great)36. bill..................1. (case and PCB's)37. TheProfosist..........1. (somewhat interested)38. SubGothius............2. (two PCB's and more case ideas)39. mikelanding...........1. (Put me 1 in)40. Ian S.................1? (Subscribed)41. judascleric...........1? (ErgoDOX is an awesome project)42. sc3...................1. (In for 1 set of PCB's and maybe a case)43. lowkey144.............1. (added to this list)44. trygg.................1-2(if the price is right) 45. AloisiusFauxly........1. (At least PCB to dip in Canadian Syrup) I like to have a little thing about what the poster had to say about it, so I can better gauge interest and prices, feel free to tell me if you want it removed, or updated. Here is a list of people interested in receiving an assembled keyboard. Code: [Select] wiredPANDAHoggyFimObraDemik?bonegaRichieBoli (1-2)Icariumitlnstln (assembled up to the keycaps in cherry brown)Mazora ?Zanth (assembled up to the keycaps reds or browns)Thirdkind (natural Al, assembled, 'Otaku', Reds)Sicyo (natural Al assembled)speedkillsrburrows (would probably be okay with a kit)OrangeJewce (1-2)SurgerQuarzacyobfishdomoaligatogilsorianomikelandingjochuStaCT13 I am considering a soldering service: if someone else wants to do this, I'll add their info, but if no-one else wants to, I might do it. Anything to help the project! List of people offering some sort of soldering\/assembly service Code: [Select] The Profosist (USA)Dork Vader (USA)Geekabit (EU)Dirge (UK)localredhead (?)(I am sure there will be others when the time comes) If you're interested, PM me or post in this topic. Please also tell me if I missed you, or have any mistakes. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Mon, 10 October 2011, 16:56:18 It have a slope if you look at the side picture but it was easier to only model some flat spherical keycaps. Final keycap shape is not determined yet and my be left to the user. Yes the headers are for connecting the 2 halves. Title: [Interest Check] Custom split ergo keyboard. Post by: iWuzHere on Mon, 10 October 2011, 21:06:07 That looks pretty sweet, though price is quite high Title: [Interest Check] Custom split ergo keyboard. Post by: demik on Mon, 10 October 2011, 22:06:21 that looks awesome Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Mon, 10 October 2011, 22:37:57 I am interested definitely. How many do we need to get to the$400 range?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Mon, 10 October 2011, 23:02:33\nI was thinking something between 5 and 10 but the more the better.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Mon, 10 October 2011, 23:18:18\nThat's not a very high number to make. \u00a0We should be able to get at least 5. \u00a0Input Nirvana should be getting at least 2! \u00a0;) \u00a0More demand if we include the Korean community.\n\nWhat kind of keycaps would fit? \u00a0Geninue double shot Cherry keycaps? \u00a0Any suggestions on the default layout?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: demik on Mon, 10 October 2011, 23:26:21\nsince i dont know how to solder.. or actually build a keyboard.. would i be screwed in putting it together? im interested.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Mon, 10 October 2011, 23:30:52\nIt isn't very hard at all. \u00a0I just taught a 11-year-old to solder this last weekend. \u00a0There are a lot of youtube videos that teach you how to solder. \u00a0Take a look at them. \u00a0If you think you can do it, go to Radio Shack to buy a $10 kit to give it a try. If you can solder that kit, you should be able to solder switches and diodes onto the circuit board. Title: [Interest Check] Custom split ergo keyboard. Post by: demik on Mon, 10 October 2011, 23:33:06 i was actually going to try to solder this weekend lol. i want to make a switch box for a CST trackball, and i was going to try it on that since i figured it wouldn't be too expensive if i messed it up. Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Mon, 10 October 2011, 23:52:11 The hard part of soldering is not cooking components. The components on a KB are really quite heat tolerant. 80 some odd switches and just as many diodes would be plenty of training in order to not cook the controller. Since Dox is specifying a teensy you don't even solder the controller, just board to board connections. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 11 October 2011, 09:16:35 Quote from: litster;428699 That's not a very high number to make. We should be able to get at least 5. Input Nirvana should be getting at least 2! ;) More demand if we include the Korean community. What kind of keycaps would fit? Geninue double shot Cherry keycaps? Any suggestions on the default layout? Yeah I'll probably take 2 for myself too so we are already at 5! Genuine cherry keycaps will fit just fine except for the larger keys. For the layout I was going for something similar the original key64 but in qwerty. This will be completely re-programmable. [ATTACH=CONFIG]28376[\/ATTACH][ATTACH=CONFIG]28377[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: Findecanor on Tue, 11 October 2011, 10:24:58 Quote from: dorkvader;428524 Why flat? I could elaborate a bit on this, but I'll summarize: curved is hard. Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Tue, 11 October 2011, 10:26:40 And curved PCBs are friggin expensive. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Tue, 11 October 2011, 12:21:52 Looks GREAT ! Curving is a bit overrated, sometimes I think my kinesis is a bit too curved. What I really want is a split design so I could build cardboard bases and tilt the 2 sides anyway I want, all the way up to vertical, which I can't do with the fixed Kinesis, but I can definately do with what you are presenting here! It would be a nice improvement if you can do 4 thumbkeys per side instead of 2. (The Kinesis Advantage has 6, and even there I find myself wishing for more). Anyway, the extra thumbkeys will allow you to have an Fn key in each side, which will make it far easier to type things like ) and \". A trackpoint (http:\/\/geekhack.org\/showwiki.php?title=Island:4917) would be awesome too. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Tue, 11 October 2011, 13:15:45 Quote from: Dox Show Image (http:\/\/geekhack.org\/attachment.php?attachmentid=28310&d=1318280038) Show Image (http:\/\/geekhack.org\/attachment.php?attachmentid=28376&d=1318342570) Your keymaps don't match the keycap layout on the picture. On the picture, the left side, top row has one 2x width key on the left and six 1x width keys. The bottom row is also missing a 1x width key. Title: [Interest Check] Custom split ergo keyboard. Post by: Lanx on Tue, 11 October 2011, 13:55:10 looks great! an aluminum kinesis! i have comments if you want to hear them... they might sound negative tho, so i don't want to sound like i'm thread crapping. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 11 October 2011, 14:07:47 Thanks sordna, I'll look at what I can do to add some more thumb buttons. Quote from: litster;428993 Your keymaps don't match the keycap layout on the picture. On the picture, the left side, top row has one 2x width key on the left and six 1x width keys. The bottom row is also missing a 1x width key. I know, the layout pictures are from the key64. I need to work on the correct one for this iteration. Quote from: Lanx;429008 looks great! an aluminum kinesis! i have comments if you want to hear them... they might sound negative tho, so i don't want to sound like i'm thread crapping. I'm want to hear your comments. That's the purpose of this thread. Title: [Interest Check] Custom split ergo keyboard. Post by: Mazora on Tue, 11 October 2011, 14:41:16 Depending on the layout, I would be interested. By the way, it looks amazing. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Tue, 11 October 2011, 15:13:04 Quote from: Dox;429017 I know, the layout pictures are from the key64. I need to work on the correct one for this iteration. No problem, I will make one with my preference and post it here. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Tue, 11 October 2011, 15:22:13 Quote from: Dox;429017 Thanks sordna, I'll look at what I can do to add some more thumb buttons. Is it possible to make the two large outermost thumb keys into 2 separate keys each? Title: [Interest Check] Custom split ergo keyboard. Post by: Lanx on Tue, 11 October 2011, 15:49:22 Quote from: litster;429071 Is it possible to make the two large outermost thumb keys into 2 separate keys each? i wouldn't recommend it, as in 2 seperate buttons up and down? you kinda want a longer 1.25 key to (rest) your thumb on. i'd recommend something like this http:\/\/www.kinesis-ergo.com\/freestyle-vip-features.htm not all those features, but instead of how ppl put the feet\/tabs that make a keyboard slope on an incline, do that to the two boards and have 4 small feet\/tabs(2 per side) so that you can slope it inwards. like sordna, i'd recommend following kinesis thumb layout more than the c64, that is to have the 6 buttons on the thumb area, rather having extended buttons past towards the del\/tab\/numlk\/enter area. if you \"force\" yourself to learn to use enter\/backspace with the thumbs, these aren't needed. i've mocked the layout (since i actually had pcb's laying around) and for a 5 10' guy, the thumbs are really close, i think they need to be out more. imo and prolly sordna has more experience, the spherical keycaps on a kinesis homerow are awesome, while the rest of the keycaps are regular cylindrical. I believe this is the best arrangement because the spherical will allow you find \"home row\" easily while moving towards the other keys freely with a cylindrical shape. I guess f-keys are done by some keylock? Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Tue, 11 October 2011, 15:57:12 Here is my preferred layout. The Fn layer is not done yet. But for regular layout is very close to what i want given the fewer number of keys. I use the left Ctrl, Shift, ESC, and Tab all the time (but not Capslock), and I much prefer Tab, BackSpace, Enter, and right Shift at where they normally are. In general I prefer a layout that is as close to regular ANSI layout as possible. (http:\/\/geekhack.org\/attachment.php?attachmentid=28410&d=1318366895) Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Tue, 11 October 2011, 16:05:57 So litster... How do you get Win-L ? Only common combo I see getting blocked so far... Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Tue, 11 October 2011, 16:31:50 You mean the left Windows key? Ah, I see what you mean. You mean the Windows keys on the Fn layer. Yeah, they don't make any sense on the Fn layer. There is already a Windows key on the left side, so that should be good. Title: [Interest Check] Custom split ergo keyboard. Post by: Input Nirvana on Tue, 11 October 2011, 16:49:18 Hats off! Love it! I see the Key64 influence. My input: I would strongly suggest a serious consideration for an integrated pointing device. I've had my split Kinesis (see signature link) and I can tell you from over 6 months experience, that once you split, separate, incline, ergo layout, ergo key position, and macro, that moving your hand off the home row for cursor pointing becomes absolutely ridiculous. And that's the polite way of expressing the emotion. I have an Apple Mighty Mouse on the left and an IBM trackpoint on the right. I like touch pads and some trackballs, but again, leaving the home row becomes a cumbersome chore. As a matter of fact, the integrated pointing device really started the split Kinesis project. Regarding keywell curvature: I may not understand Sordnas view of the Kinesis wells being too curved, but then again, I rest my hands on the Kinesis palm pads. My hands are a mens large, so maybe that has something to do with it? I have a Kinesis Freestyle, and prefer the curved keywells, but the Freestyle is not a matrix layout nor does it have the columns height adjusted. I have not used anything like this particular configuration. I didn't notice, but is there any work on an awesome programmable controller? I have possible interest :) NOTE: I've recently had some extreme changes in my life that have dramatically shifted my time and priorities. I was about to administer the wood key cap buy, try and lead the custom controller project, and do some in-depth reviews with awesome pics of my Datahand, Alphagrip, Kinesis, and fully update and document the split Kinesis project. I wanted to build up these areas for Geekhack since GH has done so much for me. I apologize to anyone that has been waiting for me to perform on various topics, as I'm not certain when I will be able to continue. P.S. Wood key caps will probably go through WASD Keyboards soon. Title: [Interest Check] Custom split ergo keyboard. Post by: TheSoulhunter on Tue, 11 October 2011, 17:00:25 Id get one if its in the 300 USD range... Title: [Interest Check] Custom split ergo keyboard. Post by: cactux on Tue, 11 October 2011, 17:14:26 why not just taking baby steps first like. Reuse an ergonomic shell like the goldtouch board (not expensive) and add a custom PCB + internal logic + switches. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 11 October 2011, 17:16:12 Quote from: Lanx;429095 i wouldn't recommend it, as in 2 seperate buttons up and down? you kinda want a longer 1.25 key to (rest) your thumb on. i'd recommend something like this http:\/\/www.kinesis-ergo.com\/freestyle-vip-features.htm not all those features, but instead of how ppl put the feet\/tabs that make a keyboard slope on an incline, do that to the two boards and have 4 small feet\/tabs(2 per side) so that you can slope it inwards. like sordna, i'd recommend following kinesis thumb layout more than the c64, that is to have the 6 buttons on the thumb area, rather having extended buttons past towards the del\/tab\/numlk\/enter area. if you \"force\" yourself to learn to use enter\/backspace with the thumbs, these aren't needed. i've mocked the layout (since i actually had pcb's laying around) and for a 5 10' guy, the thumbs are really close, i think they need to be out more. imo and prolly sordna has more experience, the spherical keycaps on a kinesis homerow are awesome, while the rest of the keycaps are regular cylindrical. I believe this is the best arrangement because the spherical will allow you find \"home row\" easily while moving towards the other keys freely with a cylindrical shape. I guess f-keys are done by some keylock? Thanks for the input! I will try to work on the thumb area in general this week and post some new render when it's done. As for the keycaps, I really have no plan for this yet but I like the idea of the spherical home row only. Quote from: input nirvana;429130 Hats off! Love it! I see the Key64 influence. My input: I would strongly suggest a serious consideration for an integrated pointing device. I've had my split Kinesis (see signature link) and I can tell you from over 6 months experience, that once you split, separate, incline, ergo layout, ergo key position, and macro, that moving your hand off the home row for cursor pointing becomes absolutely ridiculous. And that's the polite way of expressing the emotion. I have an Apple Mighty Mouse on the left and an IBM trackpoint on the right. I like touch pads and some trackballs, but again, leaving the home row becomes a cumbersome chore. As a matter of fact, the integrated pointing device really started the split Kinesis project. Regarding keywell curvature: I may not understand Sordnas view of the Kinesis wells being too curved, but then again, I rest my hands on the Kinesis palm pads. My hands are a mens large, so maybe that has something to do with it? I have a Kinesis Freestyle, and prefer the curved keywells, but the Freestyle is not a matrix layout nor does it have the columns height adjusted. I have not used anything like this particular configuration. I didn't notice, but is there any work on an awesome programmable controller? I have possible interest :) NOTE: I've recently had some extreme changes in my life that have dramatically shifted my time and priorities. I was about to administer the wood key cap buy, try and lead the custom controller project, and do some in-depth reviews with awesome pics of my Datahand, Alphagrip, Kinesis, and fully update and document the split Kinesis project. I wanted to build up these areas for Geekhack since GH has done so much for me. I apologize to anyone that has been waiting for me to perform on various topics, as I'm not certain when I will be able to continue. P.S. Wood key caps will probably go through WASD Keyboards soon. Thanks input nirvana, I will seriously consider an integrated trackpoint in the design. I got to say that I spent a lot of time looking at that kinesis wiki. That's some good news for the wood keycaps! Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 11 October 2011, 17:21:23 Quote from: TheSoulhunter;429139 Id get one if its in the 300 USD range... Good to know, thanks! Quote from: cactux;429153 why not just taking baby steps first like. Reuse an ergonomic shell like the goldtouch board (not expensive) and add a custom PCB + internal logic + switches. Because I can, and the only way to get things the way I want them is to build it myself (my first and only cherry based boards are my doxkb). Title: [Interest Check] Custom split ergo keyboard. Post by: christoffer.braathen on Tue, 11 October 2011, 19:03:02 I'm ALL IN!!! Looks great, and the idea of splitting the two parts completely is great. Sing me up for one. Best Regards Christoffer Braathen Oslo, Norway Title: [Interest Check] Custom split ergo keyboard. Post by: Lanx on Tue, 11 October 2011, 19:18:28 Quote from: input nirvana;429130 Regarding keywell curvature: I may not understand Sordnas view of the Kinesis wells being too curved NOTE: Kinesis, and fully update and document the split Kinesis project. So far i'm in love with the depth and curve of the kinesis keywells (they could be angled\/sloped towards the middle more i think many of the kinesis users agree on this). yea there's zero kinesis hacking\/modding atm, imma try to fill the gap with that. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sat, 15 October 2011, 23:39:37 I reworked the thumb area a bit. Tell me what you think. [ATTACH=CONFIG]28744[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Sat, 15 October 2011, 23:42:41 That is nice! More placement options. Title: [Interest Check] Custom split ergo keyboard. Post by: bretrex on Sun, 16 October 2011, 00:12:24 I'd throw in for just the pcbs. It shouldn't be difficult to lay out the circuit board to be functional mirrored, allowing you to use the same board for both sides, helping cut the per-board cost. The full metal enclosure seems a bit rich for my blood, but would make an amazingly solid input device for those who can afford it. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sun, 16 October 2011, 00:28:42 Quote from: bretrex;432108 I'd throw in for just the pcbs. It shouldn't be difficult to lay out the circuit board to be functional mirrored, allowing you to use the same board for both sides, helping cut the per-board cost. The full metal enclosure seems a bit rich for my blood, but would make an amazingly solid input device for those who can afford it. The pcbs wont be symmetrical as the controller is on one half and the columns and rows of the other half have to be routed to the other side. The mounting plate will be symmetrical. Title: [Interest Check] Custom split ergo keyboard. Post by: calavera on Sun, 16 October 2011, 03:36:14 Do you have a plan view (top view) pic of the design? Title: [Interest Check] Custom split ergo keyboard. Post by: Findecanor on Sun, 16 October 2011, 03:50:51 Quote from: Dox;432084 I reworked the thumb area a bit. Tell me what you think. (Attachment) 28744[\/ATTACH] That looks like the thumb-key configuration that the Kinesis has. I find that on my Kinesis, I can not reach for the smaller thumb keys easily, and I wish that there was instead a key in-between the thumb keys and the main group. For me, the problem is mostly with the \"Alt\" keys, which is the topmost thumb key in each of the Kinesis' thumb groups. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sun, 16 October 2011, 09:45:32 Quote from: Dox;432116 The pcbs wont be symmetrical as the controller is on one half and the columns and rows of the other half have to be routed to the other side. The mounting plate will be symmetrical. You could just leave the controller area blank on one of the boards, but I don't think this will work because I don't think the cherry switch is symmetrical. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sun, 16 October 2011, 10:16:14 Quote from: calavera;432162 Do you have a plan view (top view) pic of the design? Here we go: [ATTACH=CONFIG]28763[\/ATTACH] Quote from: Findecanor;432166 That looks like the thumb-key configuration that the Kinesis has. I find that on my Kinesis, I can not reach for the smaller thumb keys easily, and I wish that there was instead a key in-between the thumb keys and the main group. For me, the problem is mostly with the \"Alt\" keys, which is the topmost thumb key in each of the Kinesis' thumb groups. Having them on the same level as the other keys will probably help with the reach and you still have 2 extra buttons at the \"interior\" of each hand. Quote from: dorkvader;432244 You could just leave the controller area blank on one of the boards, but I don't think this will work because I don't think the cherry switch is symmetrical. Not really, leaving the controller area empty on one side side and using a symmetrical pcb would simply route the signals of one half to the columns\/rows of the other one and not to the controller. And as you said, cherry switches aren't symmetrical. Title: [Interest Check] Custom split ergo keyboard. Post by: Karacho on Sun, 16 October 2011, 15:26:43 In my opinion and in result of my own tests, two buttons for the thumbs are best. Additional thumbbuttons are not good to reach. I want one to :) It should be reprogramable, right? Title: [Interest Check] Custom split ergo keyboard. Post by: Quarzac on Sun, 16 October 2011, 17:49:12 I won't pledge definite interest, but when would you be ordering all this? I like the idea, but I don't know if I could afford it. If it wasn't for a good long while, I'd have to start saving now, and maybe I could do it. It would be good if only to force me to type correctly. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sun, 16 October 2011, 17:51:57 I dont know, I still have a lot of work to do on the design and I'll have to save some cash too. I was thinking that maybe in 2-3 months would be good. Title: [Interest Check] Custom split ergo keyboard. Post by: Quarzac on Sun, 16 October 2011, 18:03:49 Hmm... If I get a job, that could work. I'll keep up with this, and closer to the trigger date I'll have a definitive answer. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Sun, 16 October 2011, 20:51:28 Quote from: Karacho;432439 In my opinion and in result of my own tests, two buttons for the thumbs are best. Additional thumbbuttons are not good to reach. Well, being a Kinesis user I appreciate the additional thumbkeys. Of course the smaller keys are a bit harder to reach than the larger ones, that is inevitable. But since this is programmable, you would put slightly less frequently used keys there. We do want the extra keys, however, definitely... I like to have 2 controls, 2 alts, 2 win keys, and 2 Fn (2nd layer keys) keys so I can always avoid one-hand combos which are bad for rsi\/carpal tunnel issues. The extra thumb keys allow doing 2-handed combos all the time; which is ergonomically superior. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sun, 16 October 2011, 20:54:16 Quote from: Dox;432485 I dont know, I still have a lot of work to do on the design and I'll have to save some cash too. I was thinking that maybe in 2-3 months would be good. I'll start saving now, too. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Sun, 16 October 2011, 21:39:31 With the new keys, I think I got everything on the first layer except F1-F12 and PrintScreen, Scroll Lock, And Pause\/Break. I keep most of the modifiers in the usual location as they are how I prefer :-). (http:\/\/geekhack.org\/attachment.php?attachmentid=28807&d=1318819026) Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Sun, 16 October 2011, 23:19:17 Fantastic project Dox! Hope you guys are able to put this into production! Title: [Interest Check] Custom split ergo keyboard. Post by: slueth on Mon, 17 October 2011, 01:28:15 I'm interested but we will see about cash lol.. Time to get a work working. Title: [Interest Check] Custom split ergo keyboard. Post by: calavera on Mon, 17 October 2011, 06:14:59 I was wondering if you could simplify the design. Here's what I was thinking. (http:\/\/i630.photobucket.com\/albums\/uu23\/calaveratf\/keyboards\/b.jpg) Or something more drastic and \"dynamic.\" (http:\/\/i630.photobucket.com\/albums\/uu23\/calaveratf\/keyboards\/a.jpg) Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Mon, 17 October 2011, 07:38:44 MM, that's a good point: Does that notch you take out in image #1 serve any non-aesthetic purpose? Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Mon, 17 October 2011, 09:10:37 Quote from: calavera;432675 I was wondering if you could simplify the design. Here's what I was thinking. Show Image (http:\/\/i630.photobucket.com\/albums\/uu23\/calaveratf\/keyboards\/b.jpg) Or something more drastic and \"dynamic.\" Show Image (http:\/\/i630.photobucket.com\/albums\/uu23\/calaveratf\/keyboards\/a.jpg) The first is possible and a good idea. The second one, I wont have enough place to fit the controller in there. Title: [Interest Check] Custom split ergo keyboard. Post by: calavera on Mon, 17 October 2011, 13:52:41 Where does the controller fit and how does the PCB look like? Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Mon, 17 October 2011, 14:08:16 The pcbs are not designed yet but the controller will be at the top right on the right hand. Something like that (old pic): [ATTACH=CONFIG]28848[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Mon, 17 October 2011, 17:43:33 Quote from: Dox;429159 (my first and only cherry based boards are my doxkb). Thought you said you had a WYSE around here somewhere? It seems like every day my interest in this project grows. If we can get this under$200: I'm in for sure, under $250: good chance, under$300: okay chance, depends on timing.\n\nGiven the interest garnered thus far, it sort of looks like we've a shot of getting 10+ made, which is pretty awesome.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Mon, 17 October 2011, 18:00:21\nThought you said you had a WYSE around here somewhere?\n\nIt seems like every day my interest in this project grows. If we can get this under $200: I'm in for sure, under$250: good chance, under $300: okay chance, depends on timing. Given the interest garnered thus far, it sort of looks like we've a shot of getting 10+ made, which is pretty awesome. I got a wyse on ebay for the keycaps and to try some different switches (black and getto red) for my doxkbs. Thanks for the interest, when this will be closer to completion I will post the prices for different quantity and hopefully that will bring in more people into it! Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Mon, 17 October 2011, 18:38:01 Quote from: calavera;432675 Show Image (http:\/\/i630.photobucket.com\/albums\/uu23\/calaveratf\/keyboards\/b.jpg) [ATTACH=CONFIG]28864[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Mon, 17 October 2011, 19:05:47 Looks good! Title: [Interest Check] Custom split ergo keyboard. Post by: Jim66 on Tue, 25 October 2011, 07:22:41 This looks very nice, I'm defo going to keep an eye on this thread. Title: [Interest Check] Custom split ergo keyboard. Post by: Lanx on Thu, 27 October 2011, 20:03:49 might wanna think about lining up the num-row with the fingers like kinesis\/maltron. It's actually easier for me now to touch type numbers on a matrix layout, than ever before, and i'm a numpad snob (of course i'll always num-type faster with num-pad, but matrix num-row is very good). Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Thu, 27 October 2011, 23:51:28 Quote from: Lanx;440816 might wanna think about lining up the num-row with the fingers like kinesis\/maltron. It's actually easier for me now to touch type numbers on a matrix layout, than ever before, and i'm a numpad snob (of course i'll always num-type faster with num-pad, but matrix num-row is very good). 100% agree. All split matrix keyboards are consistent, Kinesis, Maltron, Typematrix, and even the TrulyErgonomic as well as the Fingerworks Touchstream (my photo below). 1 is above Q, 5 is above T, 6 is above Y, 0 is above P (assuming qwerty layout). [ATTACH=CONFIG]30155[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: Lanx on Fri, 28 October 2011, 00:40:55 if we wanna go further with it, and i'm sure most kinesis guys think this way, if i have to type \"1\" i think \"use pinky\" if i have to type \"8\" i think use middle finger. i mean it's like going back to gradeschool and counting numbers with your fingers. If you guys are gonna do this, i think you should do it right, cuz no matter the layout qwerty,dvork or some weird customer layout... numrow 1through0 will always be the same. Title: [Interest Check] Custom split ergo keyboard. Post by: Ascaii on Fri, 28 October 2011, 05:41:47 Hot damn, color me interested. I will definitely need to save some cash up, but this might actually be worth it. Ill follow this thread, and check out layouts etc when im not at work^^. Tentatively put me down for 1. Title: [Interest Check] Custom split ergo keyboard. Post by: laffindude on Fri, 28 October 2011, 09:55:39 Semi interested if the cost is <300 for a kit without switches(I can source the switch myself). This Seems like an excellent candidate for 1 handed board, if the cable is on the left module. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Fri, 28 October 2011, 18:58:33 So I wanted to look at the number of people interested in this, so I added up everyone that looks like they may be in on one Dox is the only one who said they want 2. p means they are dependant on price, ? means they didn't specifically say they wanted one, but looked interested from their posts. Parenteses indicate notes I took from their posts. So I count ~6 or so who are interested regardless of anything. If the cost is acceptable the number grows significantly to ~12 The total of all people who look interested is 19 ( or actually 20 sets of boards, and 19 sets of cases.) So if we got 15-20 orders of this, what would the price look like? 'Cause if it means it'll be$250-$350, we'll get a LOT of interest. ErgoDox Interest check Compilation: ---- LIST MOVED TO SECOND POST: LOOK FOR IT THERE!!! ----- Hope this helps! --- Edit: Oh, and is \"ErgoDOX\" a good name? I read it somewhere, and liked it. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Fri, 28 October 2011, 19:36:48 Let's do it! I want to solder something! Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Fri, 28 October 2011, 20:00:16 Quote from: dorkvader;441469 Edit: Oh, and is \"ErgoDOX\" a good name? I read it somewhere, and liked it. You read it here: http:\/\/geekhack.org\/showthread.php?22412-Truly-Ergonomic-Communication-Sept-27-2011&p=431524&viewfull=1#post431524 I'm quite interested, especially if the keyboard comes with all the parts (including red MX switches), and preferably assembled and working :-) Title: [Interest Check] Custom split ergo keyboard. Post by: Lanx on Fri, 28 October 2011, 20:26:53 none for me, i'm just giving feedback from my experience modding a similar layout and using kinesis. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Fri, 28 October 2011, 20:30:19 Thanks Lanx, updated. Also, Sordna, I thought it was you, but I didn't check. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 28 October 2011, 23:00:28 Quote from: dorkvader;441469 So I wanted to look at the number of people interested in this, so I added up everyone that looks like they may be in on one Dox is the only one who said they want 2. p means they are dependant on price, ? means they didn't specifically say they wanted one, but looked interested from their posts. Parenteses indicate notes I took from their posts. So I count ~6 or so who are interested regardless of anything. If the cost is acceptable the number grows significantly to ~12 The total of all people who look interested is 19 ( or actually 20 sets of boards, and 19 sets of cases.) So if we got 15-20 orders of this, what would the price look like? 'Cause if it means it'll be$250-$350, we'll get a LOT of interest. ErgoDox Interest check Compilation: 01. Dox...................2 02. DorkVader.............1p (see above) 03. iWuzHere..............1p (Looks sweet) 04. demik.................1? (Looks Awesome, worried about soldering) 05. Lister................1 (Definately interested) 06. Sordna................1 (Looks GREAT!) 07. 08. Mazora................1? (dependant on layout) 09. Input Nirvana.........1? (\"Possable Interest\") 10. TheSoulHunter.........1p ($300 range)\n11. Christoffer.Braathen..1 (ALL IN!!!)\n12. Bretrex...............1 (Pcb only)\n13. Karacho...............1 (I want one)\n14. Quarzac...............1p (Interested, but worried about cost)\n15. REVENGE...............1? (Fantastic Project)\n16. Sleuth................1p (will see about cash)\n17. Jim66.................1? (Will keep eye on thread)\n18. Ascaii................1 (very interested)\n19. Laffindude............1p (if under $300) Hope this helps! --- Edit: Oh, and is \"ErgoDOX\" a good name? I read it somewhere, and liked it. Thanks for the compilation, with something like 15-20 keyboards we could probably reach a price closer to 300 than 400 but that is still very approximative. ErgoDox is the name I came up with before I did the renders for the OP. As everything else, it's not final but I think it's not bad at all. Quote from: litster;441489 Let's do it! I want to solder something! That's what I want to hear! Quote from: sordna;441506 You read it here: http:\/\/geekhack.org\/showthread.php?22412-Truly-Ergonomic-Communication-Sept-27-2011&p=431524&viewfull=1#post431524 I'm quite interested, especially if the keyboard comes with all the parts (including red MX switches), and preferably assembled and working :-) I don't have a source for red switches but I wouldn't mind doing the assembly\/firmware customization for people that doesn't have soldering equipment or experience. Quote from: Lanx;441531 none for me, i'm just giving feedback from my experience modding a similar layout and using kinesis. Your feedback is appreciated, thanks! Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Fri, 28 October 2011, 23:36:45 red switches are very hard to get. If you want red switches, you are better off buying and gutting a Poker or Leopold tenkeyless or some other cheaper red-switch keyboards. It might not be a bad idea as I think you can resell the Leopold keycaps, especially that \"special\" spacebar :-). Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 29 October 2011, 13:32:58 Quote from: litster;441613 red switches are very hard to get. If you want red switches, you are better off buying and gutting a Poker or Leopold tenkeyless or some other cheaper red-switch keyboards. It might not be a bad idea as I think you can resell the Leopold keycaps, especially that \"special\" spacebar :-). It's not that special after SP gets production up for the 6-post \"combined\" spacebars. Hmm, I count 64-72 Keys depending on thumb configuration, so that'd be 1500 or so keys for ~20 orders. You could maybe order from Cherry direct in quantities like that. Or$0.609\/key from mouser:\nhttp:\/\/www.mouser.com\/ProductDetail\/Cherry-Electrical\/MX1A-E1NW\/?qs=sGAEpiMZZMsqIr59i2oRcl0OtbIxCyKkAg8zsoDLHg0%3d\n\nIf it's any cheaper, I'd rather solder\/assemble it myself.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Lanx on Sun, 30 October 2011, 07:33:37\nwould these switches need those diodes? haven't ordered from mouser in a year, but i don't remember them offering or selling switches with diodes.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sun, 30 October 2011, 10:42:56\nI'd say since it is a DIY design, and diodes are so cheap, including them as part of the circuit is probably a good idea.\n\nLanx, some companies have the diodes on the board, and some put it in the switch. There is a spot for either an LED, or a normal diode on the cherry MX keyswitch.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Lanx on Mon, 31 October 2011, 03:53:22\noh yea i've seen it where they line up those retangular diodes vertically.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Jim66 on Mon, 31 October 2011, 04:06:33\nQuote from: sordna;440893\n100% agree. All split matrix keyboards are consistent, Kinesis, Maltron, Typematrix, and even the TrulyErgonomic as well as the Fingerworks Touchstream (my photo below).\n1 is above Q, 5 is above T, 6 is above Y, 0 is above P (assuming qwerty layout).\n\n(Attachment) 30155[\/ATTACH]\n\nYeah, the old 89 Maltrons have this layout, but the new 90 series have the 2 above Q.\n\n(http:\/\/www.maltron.com\/media\/hi-res\/3d_dual_89_90\/90_3d_tb_black1.jpg)\n\nI'm going to say that I'm going to agree with you too; I think that this board should follow the split matrix convention and have 1 above the Q.\n\nP.s., when we are talking 300-400; what currency is this? USD?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: gilgam on Mon, 31 October 2011, 13:38:44\nI woukd like one, fully functionnal, i never solder anything ..., but without keycaps as i use either b\u00e9po or azerty\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: RColinTaylor on Mon, 31 October 2011, 16:28:15\nInterested for under $300, capless. More or less curious about the final result as well. Title: [Interest Check] Custom split ergo keyboard. Post by: Chef on Thu, 10 November 2011, 22:06:07 This is really cool, please let me join this project. Title: [Interest Check] Custom split ergo keyboard. Post by: eagleeye on Sat, 12 November 2011, 15:23:35 I would *probably* be interested at$300 depending on the final design.\n\nPlease put me down on the list :)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sat, 12 November 2011, 21:30:56\nQuote from: eagleeye;450669\nI would *probably* be interested at $300 depending on the final design. Please put me down on the list :) I'll add you now. :) Also, putting list in my first post in this topic instead on random page in the middle --- Edit: added chef too. Sorry for missing you! 21 people so far and 22 or so potential interested. Title: [Interest Check] Custom split ergo keyboard. Post by: Input Nirvana on Fri, 02 December 2011, 13:36:50 Note on the thumb keys: Kinesis users will attest that the quantity of keys in the thumb cluster is a big plus. I have never heard of anyone unhappy with the quantity of thumb keys, and a couple wanted more. With my unscientific experiments, I have come to the conclusion that 2 additional keys per thumb could be added within the EXISTING 'range of thumb movement'. A 3rd key (low frequency) with a slight additional movement could be added. I may have a pic in my Kinesis Split Mod article... Note on case design: Being a Kinesis user I'm very in tune with this part....it seems to me that the case needs to be as minimal as possible where the butt of your palm would be -OR- larger with a palm rest \"built in\". Probably only Kinesis users will see this the way I do. I'd like to hear some feedback on this. Title: [Interest Check] Custom split ergo keyboard. Post by: cyclonechuah on Fri, 02 December 2011, 15:11:18 I'm interested if it's under$300.\n\nMore interested in lilster layout thou, prefer qwerty. looks like my ordered double shot from 7bit won't be as compatible as this awesome split type keyboard.\n\nFor cherry MX switch, i can supply you, if you're interested.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 02 December 2011, 15:39:08\nQuote from: input nirvana;462947\nNote on the thumb keys:\nKinesis users will attest that the quantity of keys in the thumb cluster is a big plus. I have never heard of anyone unhappy with the quantity of thumb keys, and a couple wanted more. With my unscientific experiments, I have come to the conclusion that 2 additional keys per thumb could be added within the EXISTING 'range of thumb movement'. A 3rd key (low frequency) with a slight additional movement could be added. I may have a pic in my Kinesis Split Mod article...\n\nNote on case design:\nBeing a Kinesis user I'm very in tune with this part....it seems to me that the case needs to be as minimal as possible where the butt of your palm would be -OR- larger with a palm rest \"built in\". Probably only Kinesis users will see this the way I do.\n\nI'd like to hear some feedback on this.\nCould you indicate the location of the keys that you would like to add on my render, this sounds interesting.\nI've been working a lot recently and I didn't had much time to put on this but I will continue as soon as I can. I want this to happen.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hashbaz on Fri, 02 December 2011, 22:48:00\nDo we have any notion of what the real price will be yet, or what the time frame for completion is? \u00a0Is $400 still a good estimate? And is that for just the case and PCB? Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Sat, 03 December 2011, 04:46:49 Wow! I want one. Please count me. As a kinesis user, I'd prefer the extra thumb buttons. Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Sat, 03 December 2011, 05:15:43 Would it be possible to add holes to screw in 'legs'? Saw a photo a long while back showing a metal keyboard that had holes to screw in some pegs (these had a threaded metal shaft and a rubber base). If there's two or three holes in line, then the user can choose the hole to control the tent. Just an idea, sadly it adds a bit to the cost. Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Sat, 03 December 2011, 05:34:53 Here's the link - http:\/\/geekhack.org\/showthread.php?22796-Aluminum-alloy-anodizing-shell-for-poker-pro-orders&highlight=poker+case Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Sat, 03 December 2011, 11:12:56 Quote from: hoggy;463281 Would it be possible to add holes to screw in 'legs'? Saw a photo a long while back showing a metal keyboard that had holes to screw in some pegs (these had a threaded metal shaft and a rubber base). If there's two or three holes in line, then the user can choose the hole to control the tent. Just an idea, sadly it adds a bit to the cost. Sounds easy enough to DIY. I didn't bother mentioning preferences about angling\/tenting because as long as the keyboard halves are compact and flat, you can easily prop and tent them any way you want by carving a piece or foam to use as a base, or cutting and gluing wine corks as pegs, or even building inclines from cardboard :-) But yes, it's a good idea to have holes in the case bottom, but that's easy enough to drill ourselves too if it ends up adding more cost. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 03 December 2011, 12:53:02 Quote from: cyclonechuah;462999 I'm interested if it's under$300.\n\nMore interested in lilster layout thou, prefer qwerty. looks like my ordered double shot from 7bit won't be as compatible as this awesome split type keyboard.\n\nFor cherry MX switch, i can supply you, if you're interested.\ninterest checked (and added to the list)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hoggy on Sat, 03 December 2011, 13:23:43\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Sat, 03 December 2011, 15:13:43\nIt is so awesome that we have so many keyboard projects going on here. \u00a0Really look forward to this one.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: gilgam on Sat, 03 December 2011, 15:50:04\nfor everything (the switches i may get them from the group buy).\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Skoobs on Sun, 04 December 2011, 03:09:29\nI would be interested, but it looks like the keyboard was designed without thought for the functionality. there isnt even enough keys for all of the standard keys on a keyboard. heres my thoughts: you need to have all of the standard keys exactly where you would expect to find them. i would put space on both sides on thumb keys, and the second thumb key could be CTRL on the left and ALT on the right. the row on the bottom needs another key (underneith the shift keys on both sides) so that the bottom row can be F1 through F12. the thick vertical keys (on the inside of the setup) should be split up to make sure you have enough keys for every standard key to be where it should be in a qewrty layout. i personally would ditch anything (besides numbers) that can be on a number pad, such as home, page up, page down, end, and the arrow keys. maybe the escape key should be split up to fit the tilde next to it. plus, it could then work with novelty escape keys. (or you could move the esc key up to where it says ergodox, and put ergodox next to the lights on the right hand pad. i think that would look cool.\n\nall in all, i love the idea, but i think it needs a major rework before i would commit money to the end product.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Sun, 04 December 2011, 03:33:16\nQuote from: Skoobs;463795\nI would be interested, but it looks like the keyboard was designed without thought for the functionality. there isnt even enough keys for all of the standard keys on a keyboard. heres my thoughts: you need to have all of the standard keys exactly where you would expect to find them. i would put space on both sides on thumb keys, and the second thumb key could be CTRL on the left and ALT on the right. the row on the bottom needs another key (underneith the shift keys on both sides) so that the bottom row can be F1 through F12. the thick vertical keys (on the inside of the setup) should be split up to make sure you have enough keys for every standard key to be where it should be in a qewrty layout. i personally would ditch anything (besides numbers) that can be on a number pad, such as home, page up, page down, end, and the arrow keys. maybe the escape key should be split up to fit the tilde next to it. plus, it could then work with novelty escape keys. (or you could move the esc key up to where it says ergodox, and put ergodox next to the lights on the right hand pad. i think that would look cool.\n\nall in all, i love the idea, but i think it needs a major rework before i would commit money to the end product.\nThen, you will have to make your own because I don't agree with the majority of your points. Thanks for your impressions.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Kurk on Sun, 04 December 2011, 06:07:24\nWow, how could I have overlooked thuis thread until now ? I am absolutely interested if the price doesnt exceed 300 usd by too much. It will be fully programmable, right?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: gilgam on Sun, 04 December 2011, 06:50:35\nIndeed :-)\n\nThe more specific you are the less orders you'll get...\nThe 68 keys layout is not my favorite, but such a small ergo keyboard is pure temptation.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Mon, 05 December 2011, 13:04:32\nQuote from: Kurrk;463825\nWow, how could I have overlooked thuis thread until now ? I am absolutely interested if the price doesnt exceed 300 usd by too much. It will be fully programmable, right?\n\nQuote from: gilgam;463558\nfor everything (the switches i may get them from the group buy).\n\nQuote from: ripster;463919\nFor the record I am not interested.\n\n----\nDox, any ideas what the cost would be if we had ~25 orders or so? I imagine the machining costs wolud be lower\/person than if there was only 5 or so.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Kindari on Sun, 11 December 2011, 17:34:57\nQuote from: litster;463533\nIt is so awesome that we have so many keyboard projects going on here. \u00a0Really look forward to this one.\n\nCan you mention some other custom projects on here? I found this one and the Phantom only.\n\nI'm interested in designing a custom ergonomic ANSI based board, and I'm looking for learning and\/or collaborators on the project before I really dive into it.\n\nThanks,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hashbaz on Sun, 11 December 2011, 17:56:38\nThere's also the Dox Keyboard (http:\/\/geekhack.org\/showwiki.php?title=Island:19227), which is like a custom Poker. \u00a0Lots of good advice in the wiki though for any homebrew keyboard project.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Gfresh404 on Sun, 11 December 2011, 21:40:31\nI'd definitely be down for one but not for $400. Maybe around$200 though\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Mon, 12 December 2011, 01:26:05\nQuote from: Gfresh404;468600\nI'd definitely be down for one but not for $400. Maybe around$200 though\n\nWow, we're getting a lot of interest!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Mon, 12 December 2011, 02:42:17\nI think a lot of us have passed the phase of buying new tenkeyless keyboards and used IBM Model Ms. \u00a0We are in the next phase, the phase which you build your own keyboards!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Mon, 12 December 2011, 03:05:18\nJust so we're clear, the standard will be Colemak with control to the LEFT of the A!?? \u00a0OMFG! \u00a0That's my layout! \u00a0This is MY keyboard! \u00a0So epic!\n\nI'm LITERALLY in keyboard nirvana right now!\n\nThe only thing I might want to change is get rid of the Alt-Gr, put the FN there and place the Enter key where the FN was.\n\nI am DOWN with this $300 or$400 whatever!\n\n. . . don't know whether I want to have browns or clears though. \u00a0I really need to try out some clears because I have no idea whether I'd like them or not.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hashbaz on Mon, 12 December 2011, 06:20:33\nQuote from: inaneframe;468726\n. . . don't know whether I want to have browns or clears though. \u00a0I really need to try out some clears because I have no idea whether I'd like them or not.\n\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Kindari on Mon, 12 December 2011, 08:02:11\n[ATTACH=CONFIG]34671[\/ATTACH]\nHey Dox-\n\nIs this attached image a possible alternative layout? I mean - would that work, or does something prevent that? Or is it possible to position the part above the keys vertically below them, thus creating a foot-bar type thing? I'm not really asking for this as much as trying to better understand the possibilities for keyboard designs.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Mon, 12 December 2011, 09:09:31\nThe only thing you need worry about is fitting all the required bits on the PCB. \u00a0So, on the right hand one the controller could live in that new location that has no keys without issue. \u00a0The question is whether the inter-board connections can fit in that tiny space left at the top.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Mon, 12 December 2011, 10:26:41\nQuote from: inaneframe;468726\nJust so we're clear, the standard will be Colemak with control to the LEFT of the A!?? \u00a0OMFG! \u00a0That's my layout! \u00a0This is MY keyboard! \u00a0So epic!\n\nI'm LITERALLY in keyboard nirvana right now!\n\nThe only thing I might want to change is get rid of the Alt-Gr, put the FN there and place the Enter key where the FN was.\n\nI am DOWN with this $300 or$400 whatever!\n\n. . . don't know whether I want to have browns or clears though. \u00a0I really need to try out some clears because I have no idea whether I'd like them or not.\nI would say the \"standard\" is 100% programmable for this one. You should be able to set yours up that way, yes. I plan to have a similar thing, but with Dvorak.\n\nAlso, keycaps would probably be up to you.\nI added you to the list!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Mon, 12 December 2011, 10:34:19\nWho's running this project, Dox or dorkvader? I'm confused.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: funkymeeba on Mon, 12 December 2011, 11:20:17\nYou know, I'm not sure why I didn't look at this sooner. It looks pretty sweet. Consider me game if the cost doesn't exceed $350 by much. If MX clears are an option that would be quite swell. If Colemak is the standard, it would be great if I could get caps to fit QWERTY, but I'm sure that's something that I can do even outside of this project. Title: [Interest Check] Custom split ergo keyboard. Post by: Input Nirvana on Mon, 12 December 2011, 12:21:07 Quote from: funkymeeba;468897 You know, I'm not sure why I didn't look at this sooner. It looks pretty sweet. Consider me game if the cost doesn't exceed$350 by much. If MX clears are an option that would be quite swell. If Colemak is the standard, it would be great if I could get caps to fit QWERTY, but I'm sure that's something that I can do even outside of this project.\n\nAn option:\nCustom key caps from WASD Keyboards :)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: funkymeeba on Mon, 12 December 2011, 12:27:40\nThat is a good thought, but I think that if I'm going to get a really fancy keyboard such as this, I might as well go the full nine with some PBT caps.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Mon, 12 December 2011, 17:20:47\nOh. . . oh. . . when can production start? \u00a0I'm thinking about this all the time. \u00a0Not good during finals week!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Mon, 12 December 2011, 17:42:55\nI still have a lot of work to do on this. I will probably have a few days between Christmas and the new year to complete the drawings. I'm currently learning a lot about electronics, I plan on using some multiplexer\/demultiplexer \u00a0between the 2 halves to have a reasonable amount of wire between the boards.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: funkymeeba on Mon, 12 December 2011, 17:57:03\nI'm definitely feeling no rush here. Heck, I have plenty of stuff I have to drop money on with the holiday rush and also moving into a new place. I'll definitely put some thought into what stuff I think might be neat for this in the next few days. I doubt there will be much, it already looks to be pretty slick.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Mon, 12 December 2011, 18:11:31\nIf I didn't have the money, I'd start a garage sale, EVERYTHING MUST GO!\n\nDox, you know you are the man, right?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: laffindude on Mon, 12 December 2011, 19:33:48\nQuote from: Kindari;468780\n(Attachment) 34671[\/ATTACH]\nHey Dox-\n\nIs this attached image a possible alternative layout? I mean - would that work, or does something prevent that? Or is it possible to position the part above the keys vertically below them, thus creating a foot-bar type thing? I'm not really asking for this as much as trying to better understand the possibilities for keyboard designs.\n\nI think a better idea is to tuck the controller above the thumb area, since it looks like Dox will add more thumb keys.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Mon, 12 December 2011, 22:52:58\nQuote from: sordna;468848\nWho's running this project, Dox or dorkvader? I'm confused.\n\nHeh, this is 100% Dox's game, I'm just trying to keep track of interest, so it's easier to figure out who's in when the time comes. I also plan to PM everyone on the list once some things are settled.\n\nDox: multiplexing would be great, that way we could keep it simple with the inter-board connectors. I'm only somewhat familiar with I2S, but I know there are other methods for chip-to-chip communication.\n\nThere's even a chance you could make the halves somewhat symmetrical, with a master\/slave chip, so you can plug in either half into the computer. The \"master\" would be the one attached to USB of course. Just an idea. There isn't really a benefit to this, but you would have the option to do away with the board connections, and just connect each half to the computer, or connect one half (either one) to the computer, and plug the slave board in, and go. I imagine this could be done with some sort of diode arrangement, or something. (you could just wire a diode to the power on one board, so that it goes hot if it's plugged in, if the pin is hot, automatically set controller to \"slave\" mode. I imagine this can also be done with some sort of multiplexing arrangement or whatever you'd have to get the chips talking to eachother.)\n\nFunkymeeba, I've added you to the \"unofficial list\".\n\nLaffindude: there were some mockups earlier on with more thumb buttons, did you get a look at them?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Mon, 12 December 2011, 23:00:34\nQuote from: Dox;463021\nCould you indicate the location of the keys that you would like to add on my render, this sounds interesting.\nI've been working a lot recently and I didn't had much time to put on this but I will continue as soon as I can. I want this to happen.\n\nFirst thing's first, I am very literally a disinterested party in terms of the thumb buttons myself. \u00a0That is to say I like the way it is now just perfectly fine. \u00a0If there were a couple extra buttons I would not mind but the way it is now is awesome as well, I don't need any additional ones as when I was trying out a kinesis recently, I never actually used the other keys, just the two long ones.\n\n[ATTACH=CONFIG]34825[\/ATTACH]\n\nOkay, so there is A and B, here's another point where I don't care and either would be fine with me.\n\nOn A, the thumb would rest on the second long key from the left. \u00a0As the thumb extends it has better dexterity, I have noticed, and when the thumb distends and is tucked in closer to the palm of the hand it has less dexterity. \u00a0With the two buttons further away, the thumb is better able to distinguish and select different keys.\n\nB is pretty self-explicative. \u00a0It is merely the way it is now with two buttons on the far end, looks a lot like the newer designs you did.\n\nAnyway, sorry for the crap gimping.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Tue, 13 December 2011, 16:35:20\nI will update the OP with the latest design to avoid confusion. Currently, it's like a kinesis.\n(http:\/\/geekhack.org\/attachment.php?attachmentid=28864&d=1318894674)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Tue, 13 December 2011, 17:10:17\nYeah, see, that is awesome! \u00a0I was just paying attention to what input nirvana was saying about having only two extra keys. \u00a0I only posted that picture because layout A in it was just about the only idea I had to share and offer up for criticism. \u00a0As it is, I'm probably going to up my stake in this to three keyboards.\n\nAll those buttons, hardly know what to do with myself!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Tue, 13 December 2011, 17:17:39\nDox, I like the new thumb keys, but I don't really like the number row. The proper alignment is: 5 over T and 6 over Y. Virtually all matrix keyboards are like this. You can easily achieve the proper alignment by moving -_ and =+ either in the two inner colums (where the 7 is in your new picture) or in the outer columns (as the longer sized keys). The latter approach is what Kinesis does since it doesn't have the extra inner columns you have (which I love by the way).\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Tue, 13 December 2011, 17:25:28\nThanks, I will change the lettering on my next renders. The controller will be programmable anyway so you could use any layout you want!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: CeeSA on Wed, 14 December 2011, 03:46:27\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Wed, 14 December 2011, 04:04:24\n+1 for trackpoint ... would be awesome, especially since the mini-guru isn't happening !\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Wed, 14 December 2011, 04:34:10\nOh and a soda fountain built-in! \u00a0Spikes! \u00a0We need spikes so that we can decimate our enemy if they ever attack us entrenched in our offices!\n\nOh, oh and you should build-in windshield wiper units so it can clean itself and your monitor. \u00a0Maybe a vacuum unit built into the bottom of it so it can keep a tidy desktop. . . better make it a wet\/dry vac to handle any wayward bodily fluids. . . speaking of which, have you considered attaching a robotic arm that it could like you know reach. . . umm nevermind :tape2:\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Wed, 14 December 2011, 09:48:35\nQuote from: inaneframe;470384\nOh and a soda fountain built-in! \u00a0Spikes! \u00a0We need spikes so that we can decimate our enemy if they ever attack us entrenched in our offices!\n\nOh, oh and you should build-in windshield wiper units so it can clean itself and your monitor. \u00a0Maybe a vacuum unit built into the bottom of it so it can keep a tidy desktop. . . better make it a wet\/dry vac to handle any wayward bodily fluids. . . speaking of which, have you considered attaching a robotic arm that it could like you know reach. . . umm nevermind :tape2:\nAlmost exactly the same thing happened in Plato's Republic\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: mharrison on Wed, 14 December 2011, 10:53:00\nTrackpoint would be lovely ;) As I type on an EnduraPro. My only other wish is Function keys, but I doubt that would happen. Depending on the price I might be up for this keyboard though. It's the only mechanical, matrix, split I can see....\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Thu, 15 December 2011, 09:15:36\nAs a design consideration: would there be a TP in the left? right? both? will there be one in a center module that both halves plug into? Is it still between the keys? I'm just not seeing how this works out.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: funkymeeba on Thu, 15 December 2011, 09:27:20\nIf it were up to me, I would put a trackpoint on the right. I end up using my left hand for modifiers almost all of the time, so it seems fair to keep using right for cursor stuff.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Thu, 15 December 2011, 09:57:05\nYup, on the right, between the YUHJ keys, per Input Nirvana's research (http:\/\/geekhack.org\/showwiki.php?title=Island:8110) on the topic ...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Thu, 15 December 2011, 10:57:37\nAlmost exactly the same thing happened in Plato's Republic\n\nI actually laughed out loud. . . polisci geek here. \u00a0Not to say the Republic isn't read by everyone because it is, it just takes a geek to literally laugh out loud at a lame joke about it.\n\nQuote from: sordna;471350\nYup, on the right, between the YUHJ keys, per Input Nirvana's research (http:\/\/geekhack.org\/showwiki.php?title=Island:8110) on the topic ...\n\nChemical release in my brain at this.\n\nI need to point out here that this will put the keyboard back up above 400.\n\nI think dox should just keep it simple:\n\nA) so it gets done\n\n&\n\nB) we don't lose half of the people who are interested now\n(25% from additional cost and 25% from those who do not like trackpoints)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Thu, 15 December 2011, 11:40:20\nAt least we should think about it as a future option, or make provisions in the case\/PCB or something for folks that want it. I honestly think a trackpoint will attract more folks that it will drive away. Those that don't like it can always remove the tip anyway. The non-launch of the trackpointed mini-guru (http:\/\/www.guru-board.com\/) was the top-voted disappointment (ping award) on deskthority... got twice more votes than the Truly Ergonomic delay.\nMy only concern about the trackpoint is that it could prove too difficult and derail the project. I'll leave the decision to Dox, we are just sharing some ideas\/suggestions here.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Ascaii on Thu, 15 December 2011, 12:07:51\nxnay on the trackpoint for me... I will be using a Filco touchpad between the halves, trackpoint would kill it for me.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Thu, 15 December 2011, 13:51:47\nYou could have space on the PCB\/firmware for that option, and the people who don't want a trackpoint can just not install it.\n\nInnerframe: Hah, I'm glad you got it! I read it in philosophy class. It also gets discussed frequently in philosophy club\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Thu, 15 December 2011, 18:15:56\nPosition placed on the PCB for soldering it in: \u00a0YES!! \u00a0I will install one this way if given the option!\n\nBuilt-in from get-go: \u00a0I'm not sure of the wisdom in this.\n\nIf we just have the position wired into the PCB for it then we could have the space for it on BOTH sides so it could accommodate both regs and southies.\n\nThis is a great idea if room can be made for it. \u00a0Thumb keys could be set up to act as mouse buttons etc.\n\nThen we will need to have four custom keys in that region made. \u00a0Another cost layer for the individuals who choose to have it.\n\nThis cost should not be put off on those who do not want trackpoints as it will lower the already minority appeal drastically. \u00a0It is already a niche piece and we can only do harm by too much personalization beyond what is already there.\n\nPut me down for 3!\n\nI will sell my 30\" monitor if I have to. \u00a0Or sell my car. . . whichever comes first. \u00a0:)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: funkymeeba on Thu, 15 December 2011, 19:36:50\nI don't think it would cost extra for getting the keys done. It seems like it would be an easy enough home mod. Frankly I don't really require a trackpoint, but I think it would be pretty neat. Making it optional is fine. I am fine either way.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Fri, 16 December 2011, 16:22:50\nQuote from: inaneframe;468726\nI'm LITERALLY in keyboard nirvana right now!\n\nInput nirvana????\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Fri, 16 December 2011, 17:22:33\nHey Dox, I have two items to nag you about:\n\n1)\nI've spent a tremendous amount of time contemplating\/using\/experimenting with Kinesis key placement\/add\/delete\/moves. I believe the most recent render is the best there can be WITHOUT moving fingers from the home row. This is almost the same as what I came up with. (my pic is pretty bad, and the added keys are covering some existing keys, but it's a mock up). It's perfectly ok to have keys that you need to move off home row to hit, but I decided I will not address that until I have made every effort to keep keys within the target range of fingers\/thumbs and staying on home row.\n\n[ATTACH=CONFIG]35228[\/ATTACH] [ATTACH=CONFIG]35229[\/ATTACH]\n\nThese are some of my thoughts on the right hand keywell (matching your right hand render):\n\n-The white key extreme lower right under the shift (pinky activated) was to possibly be a Fn key and is replicated on the left keywell. (I've added these 2 keys to my mod, it's quite excellent).\n-The white key under the arrow key, next to the right of the space key, if a little lower could be Sordnas palm activated shift key (maybe use a long key?).\n-The white key to the left lower side of thumb cluster, allows activation without leaving home row.\n-The long white keys to the left of \"HN\" and \"6Y\" I was undecided if they could be square (2 square keys to the left of \"Y\" and \"H\") or the long keys you see for easier touch-type targets.\n\nThe reasons I have been so hell-bent on increasing the number of keys, and keeping them within touch-type range, was to be able to provide dual modifiers (per Sordna, Architect). These adds allow 5 keys per side. With what I have here, Command\/Windows, CTRL, ALT\/OPT, shift, Fn, can be used by either hand, and still have the ability to have dual enters or whatever. And still have the option of a couple keys that take your fingers off home row, if you really want to do that :)\n\n2)\nRegarding the integrated trackpoint (or pointing device). I strongly suggest that you don't feel you can't move forward without it, but don't dare move forward unless you have made provisions for it. Again, I've spent so much time on this. Ask yourself this one question: Why am I making this? A: Ergonomics. What's more un-ergonomic than taking your hand off home row and off the keyboard?. Easy options for pointing devices are trackpoint, multi-direction scrollwheel, and thumb scrollball (see Alphagrip AG-5, I'm a huge fan of these things).\n\nRandom note. You know this design is screaming to be mounted on chair arms, or similar. What about a pointing device option then? What about tenting this keyboard...even worse, you'd have to \"un-tent\" your wrist to use a mouse or whatever, then \"re-tent\". How stone age and RSI prone is that?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Fri, 16 December 2011, 18:13:05\nQuote from: input nirvana;472390\nInput nirvana????\n\nI'm leaving your next post alone! \u00a0It's got some good ideas, that's all I will say.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 16 December 2011, 18:57:05\nQuote from: input nirvana;472442\nHey Dox, I have two items to nag you about:\n\n1)\nI've spent a tremendous amount of time contemplating\/using\/experimenting with Kinesis key placement\/add\/delete\/moves. I believe the most recent render is the best there can be WITHOUT moving fingers from the home row. This is almost the same as what I came up with. (my pic is pretty bad, and the added keys are covering some existing keys, but it's a mock up). It's perfectly ok to have keys that you need to move off home row to hit, but I decided I will not address that until I have made every effort to keep keys within the target range of fingers\/thumbs and staying on home row.\n\n(Attachment) 35228[\/ATTACH] (Attachment) 35229[\/ATTACH]\n\nThese are some of my thoughts on the right hand keywell (matching your right hand render):\n\n-The white key extreme lower right under the shift (pinky activated) was to possibly be a Fn key and is replicated on the left keywell. (I've added these 2 keys to my mod, it's quite excellent).\n-The white key under the arrow key, next to the right of the space key, if a little lower could be Sordnas palm activated shift key (maybe use a long key?).\nPalm key could be interesting.\n-The white key to the left lower side of thumb cluster, allows activation without leaving home row.\nI'll see what I can do for this but as a vim user, I got to say that there is already enough keys for my intended layout.\n-The long white keys to the left of \"HN\" and \"6Y\" I was undecided if they could be square (2 square keys to the left of \"Y\" and \"H\") or the long keys you see for easier touch-type targets.\nYeah I was thinking that those long keys being further inside could be easier to hit.\n\nThe reasons I have been so hell-bent on increasing the number of keys, and keeping them within touch-type range, was to be able to provide dual modifiers (per Sordna, Architect). These adds allow 5 keys per side. With what I have here, Command\/Windows, CTRL, ALT\/OPT, shift, Fn, can be used by either hand, and still have the ability to have dual enters or whatever. And still have the option of a couple keys that take your fingers off home row, if you really want to do that :)\nDual modifiers is possible in with the current render for me but I understand that some people may need some extra keys and I will consider it.\n\n2)\nRegarding the integrated trackpoint (or pointing device). I strongly suggest that you don't feel you can't move forward without it, but don't dare move forward unless you have made provisions for it. Again, I've spent so much time on this. Ask yourself this one question: Why am I making this? A: Ergonomics. What's more un-ergonomic than taking your hand off home row and off the keyboard?. Easy options for pointing devices are trackpoint, multi-direction scrollwheel, and thumb scrollball (see Alphagrip AG-5, I'm a huge fan of these things).\n\nI don't think I said it before but I would LOVE to have an integrated trackpoint. The only problem that I see is...... Where can you buy these things?? I think all the mods with trackpoint I've seen were from some hacked IBM rubber dome keyboards. I have to have something \"standard\" to be able to implement it correctly. I currently don't even own a trackpoint. If somebody have a source for these we need your help. Otherwise, the best I can do is the place a hole in the plate and PCB and put some traces on the PCB to connect one and leave the choice to the user. You will however always have the options to use mouse keys on a fn (or primary) layer.\n\nRandom note. You know this design is screaming to be mounted on chair arms, or similar. What about a pointing device option then? What about tenting this keyboard...even worse, you'd have to \"un-tent\" your wrist to use a mouse or whatever, then \"re-tent\". How stone age and RSI prone is that?\nI got a few mounting ideas that I want to try and chair mounted is one of them. I know... I know... integrated pointing device....\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Fri, 16 December 2011, 19:20:26\nHehe, I N at his finest. Just one note on the palm key: Where you have it on your mock up, it's actually an extra (and welcome!) thumb key.\nBy palm key, I mean a key that will be lower than the thumb cluster, like this:\n\n[ATTACH=CONFIG]35247[\/ATTACH]\n\nBut the location you put your key, is actually a welcome extra thumbcluster key, especially if you make it parallel with the thumb keys and align it so it lines up with the bottom edge of the space.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Fri, 16 December 2011, 23:40:30\nQuote from: sordna;472518\nHehe, I N at his finest. Just one note on the palm key: Where you have it on your mock up, it's actually an extra (and welcome!) thumb key.\nBy palm key, I mean a key that will be lower than the thumb cluster, like this:\n\n(Attachment) 35247[\/ATTACH]\n\nBut the location you put your key, is actually a welcome extra thumbcluster key, especially if you make it parallel with the thumb keys and align it so it lines up with the bottom edge of the space.\n\nThe pic is\/was from a group of photos with keys laid down 'just to visualize'. Others are shown in the Split Kinesis mod article. I took lots of crappy pics just to document and refer back to. I never had a formal 'Palm key' idea, although that one key has been in question a number of times for functionality and placement. If such a \"palm key\" were to exist, perhaps it's as easy as having it ride \"high\" so the palm doesn't have to lay completely flat and maybe should be a larger key cap? It may be a crazy idea, but the functionality could be awesome. Implementation is everything for something like this, and there may be no good way to incorporate it well, but it's certainly worth some effort. Anyones thoughts? If you have experience with a Kinesis that would help :)\n\nThis Aikon guys added thumb keys (3 per cluster)\n[ATTACH=CONFIG]35265[\/ATTACH]\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Sat, 17 December 2011, 11:29:12\nAs far as a trackpoint is concerned, I think it'd be a nightmare trying to get them via any other means aside from old hardware. Alps has something of an alternative (here (http:\/\/www.alps.com\/products\/WebObjects\/catalog.woa\/E\/PDF\/Switch\/MultiControl\/RKJXL\/RKJXL.PDF)), but at best it'd be only usable in the thumb location. I don't think this should be a showstopper regardless, unless you personally have it as a requirement of course :)\n\nHave you considered a resistive LCD? It could be used for reprogramming on the fly, or data interaction from the PC. They are relatively cheap nowadays, and I've been considering them for my own custom project for a while. They do tend to need a beefier controller with more pins, and obviously much more code.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Sat, 17 December 2011, 13:54:27\nA deal could easily be struck with Unicomp for trackpoints and relatively cheap too. \u00a0You could probably even email them and order one individually.\n\nIf an LCD gets added, I'm out.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Sat, 17 December 2011, 14:16:14\nI will send an email to unicomp to see what they can do. The trackpoint is not an absolute requirement but it would be a great feature.\nNo LCD.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Sat, 17 December 2011, 20:03:28\nQuote from: Dox;472850\nI will send an email to unicomp to see what they can do. The trackpoint is not an absolute requirement but it would be a great feature.\nNo LCD.\n\nI did not have luck with this. I spoke with Bob. Maybe you can do better.\nNo, the trackpoint is not an absolute requirement, but your exploring all avenues is. You have a great project with a lot of insight. Don't take a last minute short-cut, it's too valuable. Information is power. I'll help you if I can. You can always PM me.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Sun, 18 December 2011, 02:37:29\nQuote from: input nirvana;472983\nI did not have luck with this. I spoke with Bob. Maybe you can do better.\nNo, the trackpoint is not an absolute requirement, but your exploring all avenues is. You have a great project with a lot of insight. Don't take a last minute short-cut, it's too valuable. Information is power. I'll help you if I can. You can always PM me.\n\nSo that's a no on individual sales then?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Sun, 18 December 2011, 03:47:47\nI had originally called and spoke to Bob about using the trackpoint, and he said it probably couldn't be done. In retrospect, I think he misunderstood me, since the trackpoint that many of us have been robbing from KPD8923 keyboards is an unscrew-plug-n-play affair. I'm rusty on the exact discussion at this point (almost 2 years ago) as far as purchasing. I believe what needs to happen right now is contact should be made and info on what particular model of trackpoint to possibly be used needs to be fleshed out. Usability is a question, supplying is a question, pricing is a question.\n\nI can be very unhelpful if given the chance.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Sun, 18 December 2011, 13:00:40\nQuote from: input nirvana;473145\n\nI can be very unhelpful if given the chance.\n\nMaybe you could make some contact with Alps or Synaptic? \u00a0Compare pricing, etc.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sun, 18 December 2011, 16:26:14\n\nI repair a LOT of fujitsu laptops, which all use synaptics touchpads. Every time a top cover gets replaced, we throw the old one away (Fujitsu doesn't want it back) and each new one comes with a touchpad. I could start saving the old ones if we could use them for anything. They'd be used, but would work. The hard part is removing them without bending the PCB.\n\nMaybe not for this project, come to think of it. Does synaptics make touchpoints? I know ALPS makes touchpads, too.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Sun, 18 December 2011, 18:03:07\nSynaptics used to, I don't know about anymore though.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Sun, 18 December 2011, 18:26:41\nQuote from: inaneframe;473437\nSynaptics used to, I don't know about anymore though.\n\nI believe this was true a little over a year ago, but I'm not certain of exactly what and when. Re: Synaptic trackpoints\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Mon, 19 December 2011, 03:41:48\nQuote from: Dox;472505\nI got a few mounting ideas that I want to try and chair mounted is one of them.\n\nIf you saw the chair mount mechanics in the Split Kineisis mod article...I've looked at doing a lot of things, that one is the most simple, versatile, robust, and affordable.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Mon, 19 December 2011, 04:15:11\nQuote from: input nirvana;473639\nIf you saw the chair mount mechanics in the Split Kineisis mod article...I've looked at doing a lot of things, that one is the most simple, versatile, robust, and affordable.\n\nOh man, talk about some serious nirvana. \u00a0I'm so excited right now.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: mharrison on Mon, 19 December 2011, 15:08:00\nPut me down for one if the trackpoint is added :)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Wed, 21 December 2011, 05:26:43\nAny info on pointing sticks yet?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: wrtcedar on Wed, 21 December 2011, 17:11:23\nA split keyboard with mechanical switches is what I was looking for when I came to GH. So I'm interested. I'm not sure that I'm $400 worth of interested yet. I've still got some alternatives to think about. I'm pretty aggressively uninterested in an integrated trackpoint, by the way. I would be interested in support (screw holes?) for later securely attaching lifts to tent the board - something along the lines of what the Freestyle allows - along with a pad configuration on the bottom that would help keep it stable in that configuration. I get a bit concerned when look at the list of OS X incompatibilities that are showing up with the Truly Ergonomic keyboard. How difficult is it to program the firmware in a keyboard like this and how hard is it to address things like sleep\/wakeup problems? This is a very neat project! Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 21 December 2011, 21:05:48 Dox says he's looking into a system to chair-mount it, so I'm sure you'd be able to tent it pretty easily using the same system. Right now all I can imagine is those screw-holes they put on the backs of routers, powerstrips, and the like for wall mounting, though I really have no idea what it'll turn out to be in reality. I'm not sold on the trackpoint yet myself, but I imagine it'd probably be optional anyway. You'll have to check on the sleep\/wakeup, but the microcontroller (teensy?) is supposed to be very compatible with different systems (one of the reasons I'm interested in this project). It's also pretty easy to reprogram them. Want me to put you on the list as under$400?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: nesiax on Wed, 21 December 2011, 21:29:41\nQuote from: input nirvana;472983\nI did not have luck with this. I spoke with Bob. Maybe you can do better.\nNo, the trackpoint is not an absolute requirement, but your exploring all avenues is. You have a great project with a lot of insight. Don't take a last minute short-cut, it's too valuable. Information is power. I'll help you if I can. You can always PM me.\n\nHi Guys, i have been disconnected from geekhack since last months and then i found this project. What a nice surprise to found somebody who was developing a project with ideas coming from the key64 keyboard.\nI started designing the key64 at the begining of the year after the TE fiasco, none of their concepts are new i just borrow them from information i found at geekhack, deskthority and overclock.net and made references to them at the design page (http:\/\/www.key64.com\/keyboards) with the hope someday i will make it real.\nGeekhack is a wonderful place to anybody who find keyboards exciting, but is very addictive so i decided to stay away for a while, Dox: your keybord \"the dox keyboard\" is awesome, while i still prefer to be minimalistic in design, and follow the key64's motto \"No more keys you can type on\" i wish you make your design a reality, and share your experiences with us as you have one on the past with the staggered one.\nkeep up the good work !\np.d. Input Nirvana: i don't like the idea of a trackpoint inside a keyboard. I have a thinkpad and in my personal experience is so painful and is not as faster and as comfortable as a trackball, right now i use a logitech marble mouse, coming from a kensigton trackball.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Wed, 21 December 2011, 23:01:36\nWow, you did the Key64? I salute you sir!\n\nYou are an inspiration to us all.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Wed, 21 December 2011, 23:05:10\nQuote from: nesiax;475584\nHi Guys, i have been disconnected from geekhack since last months and then i found this project. What a nice surprise to found somebody who was developing a project with ideas coming from the key64 keyboard.\nI started designing the key64 at the begining of the year after the TE fiasco, none of their concepts are new i just borrow them from information i found at geekhack, deskthority and overclock.net and made references to them at the design page (http:\/\/www.key64.com\/keyboards) with the hope someday i will make it real.\nGeekhack is a wonderful place to anybody who find keyboards exciting, but is very addictive so i decided to stay away for a while, Dox: your keybord \"the dox keyboard\" is awesome, while i still prefer to be minimalistic in design, and follow the key64's motto \"No more keys you can type on\" i wish you make your design a reality, and share your experiences with us as you have one on the past with the staggered one.\nkeep up the good work !\np.d. Input Nirvana: i don't like the idea of a trackpoint inside a keyboard. I have a thinkpad and in my personal experience is so painful and is not as faster and as comfortable as a trackball, right now i use a logitech marble mouse, coming from a kensigton trackball.\n\nI'm not a trackpoint fan at all. Not. At. All. It's a means to an end. I have only got 4 options to have a pointing device built into the keyboard so you don't take your fingers off home row.\n1) Trackpoint. It exists.\n2) Scroll wheel. Custom. Narrower, with the side-to-side movement. This would have to be made, I have notes and intend to try it out next year, but I'm not very hopeful of a positive outcome.\n3) Apple scrollball from the Mighty Mouse or equal. I've seen these on some smartphones. The Apple scrollball does not move the cursor, but the screen, so I need to look into this more.\n4) Thumb scroll ball (ie: Alphagrip)\n\nLove the Key64, I reference it in the Split Kinesis Mod wiki.\nI need info on your firmware ability!\nP.S.-You never responded to my emails!!!!\n\nAlso about the chair mount. I am able to replicate the one that is shown, or modify a similar type of unit. If you want that to happen, PM me.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Wed, 21 December 2011, 23:54:34\nYup, trackpoint is a means to an end. I so much want to be on the home row, that I configured mouse keys on right side of my keyboard that work when I hold Caps Lock (mapped to AltGr). A trackpoint would be far far better than mouse keys, and of course I would still have a mouse or trackball next to the keyboard.\nBut for simple things like moving the mouse from one window to another a trackpoint on the keyboard is great.\n\nI mean sometimes you literally have to move your hand several inches and grab the mouse\/trackball, just to move the mouse pointer less than an inch, which is a terrible waste, and that's where mouse keys or a trackpoint come in.\n\nI also own a Fingerworks Touchstream, which has mousing on the keyboard itself, and that feature is so amazingly awesome that you can't believe.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Thu, 22 December 2011, 18:25:37\nDitto, I much prefer a mouse to a trackpoint but I would never buy a laptop that did not have one. . . more specifically, I do not buy laptops that have touchpads. \u00a0They are the third bane of my existence next to table booths at restaurants and those three specialty USB plugs you find on various digital cameras.\n\n[ATTACH=CONFIG]35720[\/ATTACH]\n\n[ATTACH=CONFIG]35721[\/ATTACH]\n\n[ATTACH=CONFIG]35723[\/ATTACH]\n\n[ATTACH=CONFIG]35724[\/ATTACH]\n\nThese are the things that I hate.\n\nAnyway, getting back to the topic at hand, I still think it shouldn't be standard but if it is going to come with the PCB ready, a standard type, size, and configuration has to be decided on and it has to be one that we could get without necessarily ripping open another keyboard (though I have a couple rubberdome IBM's with trackpoints just screaming for me to do it.)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: nesiax on Thu, 22 December 2011, 21:14:27\nQuote from: sordna;475632\nI also own a Fingerworks Touchstream, which has mousing on the keyboard itself, and that feature is so amazingly awesome that you can't believe.\n\nHi, while i don't like a trackpoint in a keyboard (just personal preference), the idea to have a mouse on a keyboard is a must have, specially when you have to work with CAD applications, that could sound strange, but when you have to position the mouse on a specific pixel then the keyboard is the perfect companion because their input is not as analog as the mouse tends to be.\nAnother useful aspect is when you have to scroll through a webpage for example, that would be nice for me.\nThat's my idea of a mouse just using keys, while pressing the Alt-Gr some keys become the mouse, others the roller up\/down, other the mouse clicks, and others will give you the mouse speed.\n(http:\/\/www.key64.com\/design\/alt-gr-pressed2.png\/image_large)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Thu, 22 December 2011, 21:42:26\nAnother idea would be to have this with the proposed function key with the locking mechanism available (speaking in QWERTY and Colemak placement):\n\nQuote\n\nqwert\nasdfg\nzxcvb\n\nQuote\n\nqwfpg\narstd\nzxcvb\n\nQuote\nKEY:\n\n> = Mouse Speed Increase\n< \u00a0= Mouse Speed Decrease\n\u21d6\u21d1\u21d7\u21d0\u21d2\u21d9\u21d3\u21d8 = Mouse Movements\n0 = Mouse 0 or Left Mouse Button\n\u01c0 = Mouse 1 or Middle Mouse Button\n\u01c1 = Mouse 2 or Right Mouse Button\n^ = Scroll Up\n\u2c7d = Scroll Down\n\nQuote\n\n^\u21d6 \u21d1 \u21d7 >\n\u01c0 \u21d0 \u00a00 \u21d2 \u01c1\n\u2c7d \u21d9 \u21d3 \u21d8 <\n\nOR\n\nQuote\n\n>\u21d6 \u21d1 \u21d7 ^\n0 \u21d0 \u00a0\u01c0 \u21d2 \u01c1\n<\u21d9 \u21d3 \u21d8 \u2c7d\n\nOR\n\nQuote\n\n>\u21d6 \u21d1 \u21d7 ^\n\u01c1 \u21d0 \u00a0\u01c0 \u21d2 0\n<\u21d9 \u21d3 \u21d8 \u2c7d\n\nOr some variation therein. \u00a0I like the third variation the most.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Thu, 22 December 2011, 22:53:09\nHere's my version of mouse keys, using it on an Ubuntu machine and KBC Poker keybard. Note that I use the us(altgr-intl) keyboard layout on all my machines, since I type Dvorak on the Kinesis but QWERTY on staggered keyboards such as the Poker.\n\nCode: [Select]\nxkbset m # enable mousekeysxkbset exp =m # avoid expiring mousekeys# Choose a keymap that has an extra layer (level 3),# add compose key (shift+ralt) and caps lock toggle by pressing both shifts:setxkbmap 'us(altgr-intl)' -option lv3:ralt_switch_multikey,shift:both_capslock# menu to grave\/tilde:xmodmap -e 'keycode 135 = grave asciitilde grave asciitilde'# rwin\/super to altgr:xmodmap -e 'remove mod4 = Super_R'xmodmap -e 'keycode 134 = ISO_Level3_Shift Multi_key'# caps to altgr (shift+caps locks it!):xmodmap -e 'remove Lock = Caps_Lock'xmodmap -e 'keycode 66 = ISO_Level3_Shift ISO_Level3_Lock'# numpad (just the keys needed for mouskeys)xmodmap -e 'keycode 30 = u U u U KP_7 KP_Home'xmodmap -e 'keycode 31 = i I i I KP_8 KP_Up'xmodmap -e 'keycode 32 = o O o O KP_9 KP_Prior'xmodmap -e 'keycode 44 = j J j J KP_4 KP_Left'xmodmap -e 'keycode 45 = k K k K KP_5 KP_Begin'xmodmap -e 'keycode 46 = l L l L KP_6 KP_Right'xmodmap -e 'keycode 58 = m M m M KP_1 KP_End'xmodmap -e 'keycode 59 = comma less comma less KP_2 KP_Down'xmodmap -e 'keycode 60 = period greater period greater KP_3 KP_Next'xmodmap -e 'keycode 19 = 0 parenright 0 parenright KP_0 KP_Insert'xmodmap -e 'keycode 47 = semicolon colon semicolon colon KP_Decimal KP_Delete'xmodmap -e 'keycode 20 = minus underscore minus underscore KP_Subtract KP_Subtract'xmodmap -e 'keycode 61 = slash question slash question KP_Divide KP_Divide'# that's all folks\n\nJust paste it into a script and it should work.\nI've been using mouskeys on the Kinesis as well, without need for any xmodmaps since it has the embedded numpad.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Architect on Fri, 23 December 2011, 03:09:38\nAnd curved is less stable. Sign me up for a few, if this goes to production.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Architect on Fri, 23 December 2011, 03:25:04\nIf it goes to production I'll buy three. One thing though - I really need a third key above the first double wide in the thumb block. Let's not just use the Kinesis design but improve on it. That extra key will allow for three modifier keys on both sides (Windows, Alt, Control or Command, Option, Control)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: wrtcedar on Fri, 23 December 2011, 04:21:56\nI'm not sold on the trackpoint yet myself, but I imagine it'd probably be optional anyway.\n\n...\n\nWant me to put you on the list as under $400? Like so many others, I'm confident that I'd want one at$300. I might have to think a bit about a cost that's significantly above that, but I like this idea enough that I can't rule it out. How's that for a mushy answer? I guess \"$300+\" works for now. I'm always surprised to hear ergonomic arguments in favor of the TrackPoint. I can't use them because they drive my tendonitis wild, so I view them as an RSI disaster. I used to work on projects with a group run by the inventor of the TrackPoint. This view wasn't very popular there. Title: [Interest Check] Custom split ergo keyboard. Post by: wrtcedar on Fri, 23 December 2011, 04:34:47 Quote from: Architect;476509 One thing though - I really need a third key above the first double wide in the thumb block. Let's not just use the Kinesis design but improve on it. That extra key will allow for three modifier keys on both sides (Windows, Alt, Control or Command, Option, Control) I like the idea of the three modifiers being available on both sides. What would that change do to the position of the thumb block relative to the rest of the keys? Or did I not follow what you were suggesting? Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Fri, 23 December 2011, 09:01:50 Quote from: wrtcedar;476530 I like the idea of the three modifiers being available on both sides. What would that change do to the position of the thumb block relative to the rest of the keys? Or did I not follow what you were suggesting? The blocks look like Kinesis copies, which is good, but they both have an empty spot above the first thumb double key. In other words, have three single keys along the top, and three (including the shared corner key) along the back side, half surrounding the two vertical double keys. Make sense? The three top keys could be the three modifiers, with the back two the navigation keys, as for the Kinesis. I really with Kinesis just added that one extra key. It would need to move out slightly from the other block. On the Kinesis an extra key should fit there, maybe if they moved the block out a millimeter or two. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Fri, 23 December 2011, 11:07:17 Architect, I don't think an extra key is needed, because this keyboard has extra keys in the middle that can be used as modifiers. Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Fri, 23 December 2011, 18:49:07 Quote from: sordna;476669 Architect, I don't think an extra key is needed, because this keyboard has extra keys in the middle that can be used as modifiers. Yeah that's possible, but the beauty and usability of the three modifier across the top, and the hole there just looks made for it. Well I'm game for a couple either way, but the three would be awesome if anybody else likes the idea. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Fri, 23 December 2011, 23:51:36 Quote from: Architect;476509 If it goes to production I'll buy three. Added! Quote from: wrtcedar;476527 Like so many others, I'm confident that I'd want one at$300. I might have to think a bit about a cost that's significantly above that, but I like this idea enough that I can't rule it out. How's that for a mushy answer? I guess \"$300+\" works for now. Changed! Quote from: Architect;476509 One thing though - I really need a third key above the first double wide in the thumb block. Let's not just use the Kinesis design but improve on it. That extra key will allow for three modifier keys on both sides (Windows, Alt, Control or Command, Option, Control) (emphasis mine) That's a good quote for the project. Improving on the kinesis would be pretty excellent. I've never seen one, so I really don't know for sure how that'd work out, but the cool part is: if you don't need any extra keys: you don't have to use them. Quote from: wrtcedar;476527 I'm always surprised to hear ergonomic arguments in favor of the TrackPoint. I can't use them because they drive my tendonitis wild, so I view them as an RSI disaster. I used to work on projects with a group run by the inventor of the TrackPoint. This view wasn't very popular there. Ugh, I used to have to put my wrists (and hands) in ice for 20 minutes, back when I was doing gymnastics. As a whole, Men's gymnastics is much worse on the wrists than women's, and pommel-horse especially so. Luckily, I don't seem to have any lasting issues. Anyway, I've not really been a fan of the TP, though I now prefer them to touchpads when working on customer's computers at work (I work at a warranty laptop repair center near college) because it's easier to use when the computer in question is up on shelf, so you can't see the touchpad. I'm still unsure about their use on keyboards, though. Anyway, I'm sure there will be an option to omit them from the final design. Also, I'm sure this is the only way to keep everyone happy about it, as it seems that half the people will only take one if it's concluded, and the other half don't want it if it's there. Having it as an option seems the only way to do, despite the added engineering difficulty. Quote from: Architect;476913 Yeah that's possible, but the beauty and usability of the three modifier across the top, and the hole there just looks made for it. Well I'm game for a couple either way, but the three would be awesome if anybody else likes the idea. I agree with you: it seems like a great idea to me, though as I said, I'm a little unsure about how it'll work out in practice, as I've not had any experience with using my thumbs on a keyboard like that. Title: [Interest Check] Custom split ergo keyboard. Post by: inaneframe on Sat, 24 December 2011, 02:33:54 Quote from: Architect;476913 the hole there just looks made for it. To what hole do you refer? Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 24 December 2011, 13:08:15 Architect: you prefer the maltron thumb area? http:\/\/www.maltron.com\/media\/hi-res\/3d_dual_89_90\/90_3d_tb_black1.jpg I don't see how we can add that, but a 1x key out between the 2x thumbkeys and the normal keyboard keys is surely possible. Maybe that's what we're after? edit: sort of hereabouts (in red). http:\/\/img856.imageshack.us\/img856\/8480\/topkbd.jpg Or adding it a bit lower and extending the case, we can have a \"palm key\" for shift or whatever. Hmm, adding jacks for extra switches\/footpedals might also be a good idea. Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Sun, 25 December 2011, 01:42:29 Quote Hmm, adding jacks for extra switches\/footpedals might also be a good idea. There's a whole world of accessibility switches out there - http:\/\/en.wikipedia.org\/wiki\/Switch_access They use a 3.5mm stereo jack. The vast majority are overpriced, but it looks quite easy to construct your own. Is that what you meant? I think it's a great idea, and I'm prepared to pay a bit more for it. I'm not too worried about the extra key, but I prefer your placement rather than shifting the block further out. Title: [Interest Check] Custom split ergo keyboard. Post by: fim on Sun, 25 December 2011, 06:09:28 I'd be interested in one provided that I can get it ready to be used (no soldering required) and you're willing to do international shipping (UK). Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sun, 25 December 2011, 11:24:23 I'll put you on the list, fim. Actually, if it's only a couple, and no-one else wants to do it, I'd be willing to solder people's together and quickly test them for just the cost of shipping if need be. I like through-hole soldering. Title: [Interest Check] Custom split ergo keyboard. Post by: obra on Mon, 26 December 2011, 19:43:03 I'd love one. Having a trackpoint would be amazing. I'd be willing to pay more for it to be fully assembled -- I know how not-handy I am with a soldering iron. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 27 December 2011, 01:06:20 I'll add you, obra. I may do a soldering service, unless someone else wants to cover that. Either way, I'm adding a section for people interested in receiving a fully assembled product. Title: [Interest Check] Custom split ergo keyboard. Post by: Pyrolistical on Tue, 27 December 2011, 04:03:20 First of all put me down for one with Cherry MX Blues But I have a few suggestions: 1. Make the keys a true matrix layout. You have lined up the keys vertically, but not horizontally. Kensis\/TypeMatrix is a true matrix keyboard. By doing this you'll also be able to save cost as the casting would be smaller. 2. Move the 6 key back to the right side. All the good split mechanical keyboards have the 6 on the right side. Pushing the +\/= key to the double size one is fine. 3. Use Kensis' layout of splitting the up\/down left\/right keys is probably the best thing to do. This way you can keep the {[]} keys together on the right side like Kensis 4. Investigate how much would it cost to also have anodized aluminium keycaps :D This way you can making it a selling feature that the entire keyboard is aluminium Title: [Interest Check] Custom split ergo keyboard. Post by: laffindude on Tue, 27 December 2011, 04:41:00 It is more ergonomic to have this layout since this board won't have the curvature of Kenesis. It'll be CNC machined, so you're paying for the billet anyways. 6 key... already explained many times in the thread. Anodized aluminum caps will cost more than the keyboard. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 27 December 2011, 12:14:15 Quote from: Pyrolistical;478264 First of all put me down for one with Cherry MX Blues But I have a few suggestions: 1. Make the keys a true matrix layout. You have lined up the keys vertically, but not horizontally. Kensis\/TypeMatrix is a true matrix keyboard. By doing this you'll also be able to save cost as the casting would be smaller. 2. Move the 6 key back to the right side. All the good split mechanical keyboards have the 6 on the right side. Pushing the +\/= key to the double size one is fine. 3. Use Kensis' layout of splitting the up\/down left\/right keys is probably the best thing to do. This way you can keep the {[]} keys together on the right side like Kensis 4. Investigate how much would it cost to also have anodized aluminium keycaps :D This way you can making it a selling feature that the entire keyboard is aluminium That one made me laugh this morning. You are ready to sacrifice an ergonomic aspect of the keyboard to save a few bucks but you are interested in cold feeling aluminum keycaps that would increase the cost A LOT. THE LAYOUT PRESENTED IS NOT FINAL. THE CONTROLLER WILL BE PROGRAMMABLE. (I hope this one will be clear enough) Title: [Interest Check] Custom split ergo keyboard. Post by: Pyrolistical on Tue, 27 December 2011, 17:46:48 Its more ergonomic according to who? If you are going to make a claim like that do you have a study to back up a vertically staggered layout is more ergonomic than a true matrix? Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 27 December 2011, 20:15:38 Right, so clearly any claims about a keyboard that doesn't yet exist are purely theoretical anyway. So the theory goes with this 'board, is that -like the kinesis- it's not staggered vertically, so your fingers will only have to move up and down between rows (not the little bit side to side they do now). The reason they're not completely symmetrical vertically is to accommodate for the greater length of the middle fingers: that way you'll be able to type with them all at the same extension\/inclination. A \"normal\" matrix 'board wouldn't allow you to do this. Now in practice: we won't really know until the keyboards are done, and even then we wouldn't know unless they got tested professionally, but that's how the theory goes. So: it's based on the fact that your fingers aren't all the same length vertically: it's meant to match up to your fingers, and as a result isn't \"true matrix\". If you don't have to move your fingers as much, or contort them very much to type, then it should be more ergonomic. I'd also argue that the kinesis isn't \"true matrix\" either, but I don't have one, and it's beside the point and \"splitting hairs\", but it's my opinion that this keyboard and the kinesis should be ergonomically superior to a \"normal\" matrix keyboard. Title: [Interest Check] Custom split ergo keyboard. Post by: Findecanor on Tue, 27 December 2011, 22:03:54 Quote from: dorkvader;478680 So the theory goes with this 'board, is that -like the kinesis- it's not staggered vertically, so your fingers will only have to move up and down between rows (not the little bit side to side they do now). I would say that the Kinesis Contoured is vertically staggered. Counting only on the home row, the offsets between index, middle and ring finger is very small, but the offset from the ring finger column to the little finger column is about 40% -- about as much as on flat vertically staggered keyboards. Title: [Interest Check] Custom split ergo keyboard. Post by: Pyrolistical on Tue, 27 December 2011, 22:07:57 I stand corrected on the Kinesis. It is not a true matrix. The only one currently in production seems to be TypeMatrix. You cannot compare the Kinesis to this keyboard. This keyboard is flat while the Kinesis has key wells. That might explain why Kinesis did not do a true matrix. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 28 December 2011, 00:49:44 Quote from: Findecanor;478744 I would say that the Kinesis Contoured is vertically staggered. Counting only on the home row, the offsets between index, middle and ring finger is very small, but the offset from the ring finger column to the little finger column is about 40% -- about as much as on flat vertically staggered keyboards. (http:\/\/www.ergocanada.com\/products\/keyboards\/advantage_images\/kinesis_orthogonal_keywell_609x390.jpg) (courtesy of ergo canada) It doesn't really look that way to me from the pictures, but I trust another user's first-hand testimony, especially when I still haven't seen one firsthand. Quote from: Pyrolistical;478745 I stand corrected on the Kinesis. It is not a true matrix. The only one currently in production seems to be TypeMatrix. You cannot compare the Kinesis to this keyboard. This keyboard is flat while the Kinesis has key wells. That might explain why Kinesis did not do a true matrix. Firstly: don't lose heart! There are lots of POS boards (from Access-is, tipro, and cherry) that are \"true-matrix\" that you may be interested in. Typematrix isn't the only one. Second: I can indeed compare the two. You raise a good point: the keyboards are different. Still, from what I can see, the Kinesis strives to take into account finger motion, and relative finger length by using keywells and a stagger situated to each finger. While we can contrast these keyboards in the keywell area, we can compare them in many other ways. In fact, now that I think of it, a large breadth of comparisons can be made. both are keyboards both will be programmible both use cherry MX keyswitches both use USB cables (is this true for the modern kinesis?) both are designed for ergonomics to some degree There are some important contrasts you bright up: the kinesis has keywells, this is \"flat\" the kinesis isn't splittable, this is split. While these clearly are differences, they do not solely define a keyboard. All similarities can be compared. If there were no contrasting remarks to be made, then it would follow that the two are indistinguishable. Like I said: I feel that the kinesis doesn't have a \"true matrix\" (good thing) because it tries to take into account the relative finger lengths. This one does, too (to some extent). Now, I haven't greatly studied ergonomics, but I feel like I'm at least on the right track here. Edit: cherry G80-1950 http:\/\/geekhack.org\/showthread.php?23642-eBay-US-Cherry-G80-1950-%28matrix-layout%29 http:\/\/www.ebay.com\/itm\/G80-1950PQAXB-CHERRY-COMPACT-MATRIX-KEYBOARD-BEIGE-\/180679116605?pt=PCA_Mice_Trackballs&hash=item2a1150873d 5 left at$79\/each\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Wed, 28 December 2011, 01:52:19\nboth use USB cables (is this true for the modern kinesis?)\n\nOf course, all Kinesis Advantage models are USB and even have an integrated USB hub for hooking up 2 more devices.\n\nQuote\nLike I said: I feel that the kinesis doesn't have a \"true matrix\" (good thing) because it tries to take into account the relative finger lengths. This one does, too (to some extent). Now, I haven't greatly studied ergonomics, but I feel like I'm at least on the right track here.\n\nYes, you are! But we need to be careful not to overdo it with the \"wave\" pattern. Subtle is key. Even on the Kinesis I'm not a huge fan of the keywells being so curved\/deep, I would prefer them to be a little flatter actually.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bonega on Wed, 28 December 2011, 10:31:54\nInterested, but need:\nSoldering and shipping to Sweden.\n\n300-\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: iWuzHere on Wed, 28 December 2011, 20:16:20\nDue to unfavourable financial circumstances, if this does not come to somewhere around $150-200, im afraid i cant really be part of it. Title: [Interest Check] Custom split ergo keyboard. Post by: inaneframe on Wed, 28 December 2011, 20:54:44 Dox, I think you should make it exactly how you have in mind. You have my 3 orders and all the other guys. I think that any suggestions such as drastic adjustments to key arrangement should just be ignored outright. I love how people come in and try to piss on the project and mark their territory after people have already shown interest in it as is and before it even gets off the ground. I can imagine the Wright Brothers almost having enough funds to get their plane built and some jagoff steps in and is all like \"hey, ya' know I might possibly consider putting in a couple bucks but I think the wings should be straighter since it would save money.\" You respond, \"well the wings are not perfectly straight for a reason, they have a bump in them, otherwise it wouldn't fly as well.\" Then him, \"do you have any proof that the wings aren't better off perfectly straight, huh? Mr. Wright? Huh?\" ANNOYING. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Wed, 28 December 2011, 21:27:20 Thanks inaneframe, I'm starting to think that I should do it like I did for my doxkb. Build one for myself to test the concept and design and give my drawings to those who want to build some. That way, they would have the possibility to tweak the design to their needs or try to organize a group buy to lower the cost. I really don't have the time to manage a group buy and I want to get it done. In the last 2 days, I tried to design a new case that would cost a lot less than the original I couldn't even afford one with the quote that I got. I'll post some pics soon. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Thu, 29 December 2011, 01:15:37 Quote from: bonega;478967 Interested, but need: Soldering and shipping to Sweden. 300- I'll add you Quote from: iWuzHere;479338 Due to unfavourable financial circumstances, if this does not come to somewhere around$150-200, im afraid i cant really be part of it.\n\nI'll update.\n\nCool, thanks DOX. One difference here is that it'd likely cost a lot less for 30 cases to be made than a one-off for you. I suspect it's a little more reasonable for people to print up PCB's for the Doxkb, and come up with a plate than it would be for this project. Ultimately, it's up to you, though.\n\nHave you considered getting someone else to handle distribution, etc of this GB (and just have you do the designwork)?\n\nI'll look forward to new pictures. Hopefully we can get this down to a price everyone can afford.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Thu, 29 December 2011, 02:00:50\nIf it helps, I don't care at all for an aluminum case. The main thing about this keyboard is the split and the ergonomics, not the case material. Plastic is fine by me. I don't even care about the color.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Thu, 29 December 2011, 03:03:34\nQuote from: sordna;479444\nIf it helps, I don't care at all for an aluminum case. The main thing about this keyboard is the split and the ergonomics, not the case material. Plastic is fine by me. I don't even care about the color.\n\nYou are such a non-elitest. I don't know if I can be seen around with you.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: slueth on Thu, 29 December 2011, 03:24:44\ncool dox hope to see this go forward.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Thu, 29 December 2011, 04:52:45\nI was non-elitist before it was cool.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Human on Thu, 29 December 2011, 10:08:42\nBetter made it 2 seperated boards(left hand and right hand), LOL...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Thu, 29 December 2011, 21:26:42\nOk, here is the new case. There is still no trackpoint.\n[ATTACH=CONFIG]36215[\/ATTACH][ATTACH=CONFIG]36214[\/ATTACH]\n\n2 set of 11 plates (including the mounting plate) per hand. The plates are symmetric for the second hand. I still need to do something to give it some angle\/mounting option.\n\nTo give you an idea, for 10 set of 11 plates (5 keyboards) not anodized, the cost would be around 110$per hand (plates only). Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Thu, 29 December 2011, 22:43:56 Looks nice! Should be pretty hefty in weight, which is good What parts are you using for screws? Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 30 December 2011, 06:59:09 Thanks lister, I got to say that I took a bit of inspiration from your cases. I will use some M3X12 countersunk cap screw like these. [ATTACH=CONFIG]36238[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: mharrison on Fri, 30 December 2011, 11:08:38 Not to rain on anyone's parade or efforts, but... add me as another for whom the aluminum case is the least interesting aspect of this keyboard. If I have to pay$400, more than half of that is for the case. I'd much rather pay $150-$250 with a wood or plastic case.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 30 December 2011, 11:30:02\nJust to clear a misconception about the case material. The same layered case in acrylic would cost around 20$more by hand than the current aluminium one. It's not the material that is expensive, it's the time to machine\/cut the plates that is the main part of the cost. If I was building hundreds or thousands of keyboards, I would get some injection moulds and a plastic case but for the low quantity, there is no magical trick around the cost. The case will cost more than half of the keyboard no matter the material. Nothing prevents you from designing your own keyboard if you think you can do this for 150$ (this is what I thought before I did my doxkb witch cost me around 400 each).\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hoggy on Fri, 30 December 2011, 12:18:21\nI think the effort on the case is worth while. \u00a0I hired a maltron a few years back. \u00a0The reactions people had went from positive (or weird) changed instantly to cheap rubbish if they picked it up. \u00a0Everyone who felt the weight assumed that if it's lightweight, then it's cheap and tat (as the maltron is much, much lighter than it looks).\n\nIf there's a choice between materials that cost roughly the same, I'd recommend the heavier option.\n\nI do have a weight limit on my keyboard shelf of 1.4kg...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: mharrison on Fri, 30 December 2011, 12:33:09\nQuote from: Dox;480288\nJust to clear a misconception about the case material. The same layered case in acrylic would cost around 20$more by hand than the current aluminium one. It's not the material that is expensive, it's the time to machine\/cut the plates that is the main part of the cost. Thank you for clearing up where the cost comes from. I wasn't implying that I could do better, I was assuming the cost was due to the aluminum. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Fri, 30 December 2011, 12:48:50 Dox is correct. Material is cheap. Cut time and design and the test runs to find problems of the design is the most expensive. Dox, besides screws, what nuts are you using? Thanks. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 30 December 2011, 12:52:54 No nuts! As the plates are aluminium, there will be screws on top and bottom and they will be threaded in the plates in the middle of the case. I'll post a cross section later. Title: [Interest Check] Custom split ergo keyboard. Post by: mharrison on Fri, 30 December 2011, 12:56:22 Have you thought about broadening the audience a bit? Throw it on Kickstarter and get 100 people to pay$300. It couldn't hurt.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Fri, 30 December 2011, 13:20:34\nSo... $220 for the plates\/case. If we are ordering the switches as a whole, we'll get super-discount pricing from mouser (like$0.79\/switch). What are we estimating on 25-50 PCB's: $50\/hand? we could do single layer, with using the cutoffs from the diodes to make jumpers if that'll acceptibly bring the price down. Finally: WOW dox: that layer case will look awesome. I'd buy two if I could afford it. Have you looked into CNC'ing a tool for a stamping press? We could get them all manufactured in 5 minutes if we did that. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Fri, 30 December 2011, 13:23:54 How about 3D printing the case? Heck, with a layered case, it can even be a DIY cardboard affair at minimal cost! Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Fri, 30 December 2011, 14:49:42 Quote from: sordna;480401 How about 3D printing the case? Heck, with a layered case, it can even be a DIY cardboard affair at minimal cost! [ATTACH=CONFIG]36282[\/ATTACH] Dox, one suggestion for your plates. If you can use thicker materials for the middle layers, then you don't have to cut as many plates, and that should lower the cost due to fewer layers to cut. You would likely still use thinner (1\/16\" or 1\/8\") plates for top and bottom layers. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 30 December 2011, 15:26:04 Quote from: mharrison;480375 Have you thought about broadening the audience a bit? Throw it on Kickstarter and get 100 people to pay$300. It couldn't hurt.\nI thought about it but with my current job, I don't have the time to manage something like this.\n\nSo... $220 for the plates\/case. If we are ordering the switches as a whole, we'll get super-discount pricing from mouser (like$0.79\/switch). What are we estimating on 25-50 PCB's: $50\/hand? we could do single layer, with using the cutoffs from the diodes to make jumpers if that'll acceptibly bring the price down. Finally: WOW dox: that layer case will look awesome. I'd buy two if I could afford it. Have you looked into CNC'ing a tool for a stamping press? We could get them all manufactured in 5 minutes if we did that. The PCB will be double sided. 50$ per hand is a good guess. I pretty sure that machining stamping tools would cost a lot more than the current laser cutting.\n\nQuote from: sordna;480401\nHow about 3D printing the case? Heck, with a layered case, it can even be a DIY cardboard affair at minimal cost!\nIt could be done but I'm not sure about the cost. I really don't think that it would reduce the price significantly. It can be done in cardboard as you said (and litster demonstrated) but I'm going with aluminium.\n\nQuote from: litster;480498\n(Attachment) 36282[\/ATTACH]\n\nDox, one suggestion for your plates. \u00a0If you can use thicker materials for the middle layers, then you don't have to cut as many plates, and that should lower the cost due to fewer layers to cut. \u00a0You would likely still use thinner (1\/16\" or 1\/8\") plates for top and bottom layers.\nI thought about it but the way the case is designed, there is not a lot of layer combination possible without having to machine the plates afterward (something I try to avoid to keep cost down).\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 30 December 2011, 15:52:55\nCross section:\n[ATTACH=CONFIG]36287[\/ATTACH]\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Pyrolistical on Fri, 30 December 2011, 16:16:55\nAre you using all the same keycaps for all the rows since its a flat keyboard?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Fri, 30 December 2011, 16:25:21\nQuote from: Pyrolistical;480551\nAre you using all the same keycaps for all the rows since its a flat keyboard?\n\nLet me answer this one: BECAUSE it's a flat keyboard, it should have normal keycaps (which have varying profiles) to give it a contour, just like 99% of the flat keyboards out there.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 30 December 2011, 16:27:11\nQuote from: sordna;480560\nLet me answer this one: BECAUSE it's a flat keyboard, it should have normal keycaps (which have varying profiles) to give it a contour, just like 99% of the flat keyboards out there.\nThis. But the keycap choice will be left to the users.\n\nEdit: I did a single height of spherical keycap for the renders because it's easier to model.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Fri, 30 December 2011, 16:38:27\nDox, what software do you use to render in 3D?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 30 December 2011, 16:40:32\nSolidWorks 2011\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: richie on Fri, 30 December 2011, 16:42:37\nJust read though the whole thread and I'm in if its less than $400 and ready constructed! How far can the 2 parts be separated because I'm thinking I can use this with a Wacom tablet in the centre? Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 30 December 2011, 16:47:17 Quote from: richie;480576 Just read though the whole thread and I'm in if its less than$400 and ready constructed!\nHow far can the 2 parts be separated because I'm thinking I can use this with a Wacom tablet in the centre?\nI ordered a few different connectors and cables a couple days ago to decide what is the best way to connect the 2 halves. I plan on having 2 short cables coming out from each halve that could be connected directly together or connected with an extra cable between them to give more separation.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Fri, 30 December 2011, 17:31:22\n@richcie, I'll put you on the lists.\n\nAbout connecting, and interconnecting, it's not a HUGE deal, but are you plannning on carrying the ground as well? Ideally, you'd have the connector connect to the aluminium case, and carry that \"ground\" to the other side. This would connect to the USB connector at the end. In an ideal world, it'd also be connected to the ground of the computer (earth) for proper grounding techniques, and it won't interfere with the operation, but it's something to consider as well.\n\nThe difference between neutral and ground is important, especially for analog electronics, and safety purposes. It's not analog, and the voltage\/current is too low to be a safety issue, but if we're designing it, we should do it right.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Ascaii on Sat, 31 December 2011, 02:10:14\nSo... $220 for the plates\/case. If we are ordering the switches as a whole, we'll get super-discount pricing from mouser (like$0.79\/switch). What are we estimating on 25-50 PCB's: $50\/hand? we could do single layer, with using the cutoffs from the diodes to make jumpers if that'll acceptibly bring the price down. Finally: WOW dox: that layer case will look awesome. I'd buy two if I could afford it. Have you looked into CNC'ing a tool for a stamping press? We could get them all manufactured in 5 minutes if we did that. As for switches, I highly recommend people joining the switch group buy over at DT. We currently have a price of 0.60$ per switch. That includes reds and clears! Im getting my switches for the dox there.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: fim on Sat, 31 December 2011, 04:39:39\nBtw, not sure if it's been mentioned or whether it's feasible but I was wondering if we could have a detachable usb cable instead of the built-in one (like the HHKB). That way, it'll be much easier to replace faulty cables and\/or use extensions.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sat, 31 December 2011, 10:21:02\nQuote from: Ascaii;480866\nAs for switches, I highly recommend people joining the switch group buy over at DT. We currently have a price of 0.60$per switch. That includes reds and clears! Im getting my switches for the dox there. Aw man, why come DT has to get all the good GB's? When's this gonna end? I want about a million of each. Thanks for the info Ascaii. Quote from: fim;480898 Btw, not sure if it's been mentioned or whether it's feasible but I was wondering if we could have a detachable usb cable instead of the built-in one (like the HHKB). That way, it'll be much easier to replace faulty cables and\/or use extensions. I think it should have a detachable one, though I'm not 100% sure on the internals layout and placement of the microcontroller. Title: [Interest Check] Custom split ergo keyboard. Post by: Inf3rn0_44 on Sat, 31 December 2011, 12:21:29 Sweet design, i'd buy if it was 200-300. Title: [Interest Check] Custom split ergo keyboard. Post by: inaneframe on Sat, 31 December 2011, 13:09:49 The teensy has a mini-b USB port on the shortest side of it anyway. If you wanted it hardwired, you'd have to mod it. Given the shape of the keyboard and the likely placement of the teensy board, it doesn't look like the port will be external to the device. This means the cable is easily replaceable by popping it open but not \"detachable\" on the fly. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 31 December 2011, 23:55:46 Quote from: Inf3rn0_44;481012 Sweet design, i'd buy if it was 200-300. Sure, I'll add you to the list. Quote from: inaneframe;481032 The teensy has a mini-b USB port on the shortest side of it anyway. If you wanted it hardwired, you'd have to mod it. Given the shape of the keyboard and the likely placement of the teensy board, it doesn't look like the port will be external to the device. This means the cable is easily replaceable by popping it open but not \"detachable\" on the fly. Yeah, I looked through the images, and that's what it looks like. I think on mine, I'd make (or buy) a mini-USB cable to plug into the teensy, and come out of the case, about a few inches (like in the concept art) then plug it into a normal extension cable for length. I want this to be portable. I'll also have to look up which pelican cases it'll fit in. Title: [Interest Check] Custom split ergo keyboard. Post by: inaneframe on Sun, 01 January 2012, 01:38:00 Here you go: http:\/\/www.usbfirewire.com\/uextendminib.html Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sun, 01 January 2012, 11:22:10 Wow, angled USB extensions: nice. Thanks for the link inaneframe Edit: Quote from: Ascaii;480866 As for switches, I highly recommend people joining the switch group buy over at DT. We currently have a price of 0.60$ per switch. That includes reds and clears! Im getting my switches for the dox there.\nHah! It's 7bit's phantom order, also on GH!\n\nOn the ergoDOX pricing:\n\nThere are 38 keys\/side at the moment, so I'm seeing ~$365 at the moment (110+50+ .60*38)*2 still not counting teensy, cables, connectors, keycaps, or shipping. I wonder if the cost of the plates will decrease for an order quantity of 60 (30 pairs). ---- I think I'm going to program mine so I can type one-handed like that frogpad, that way if I'm eating chips or something, I don't have to worry about getting my keyboard dirty. Title: [Interest Check] Custom split ergo keyboard. Post by: Kindari on Mon, 02 January 2012, 10:43:01 Dox, what kind of shop does this have to go through to get the plates cut? I have a few contacts in a couple different machine shops that might be able to get a deal on if that's the kind of service you need. I'd be happy to at least look into it for you, but I don't know what to tell them to get an accurate quote. Thanks. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Mon, 02 January 2012, 10:52:49 Quote from: Kindari;481832 Dox, what kind of shop does this have to go through to get the plates cut? I have a few contacts in a couple different machine shops that might be able to get a deal on if that's the kind of service you need. I'd be happy to at least look into it for you, but I don't know what to tell them to get an accurate quote. Thanks. The plates just need to be cut with a plasma cutter or something similar with high accuracy. I was planning to do the threading and the bolt countersunk myself to reduce the cost. I can send you a DWG file for the plates required for 1 hand later today. That way, you should be able to get an accurate quote. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Mon, 02 January 2012, 11:03:16 [ATTACH=CONFIG]36457[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Mon, 02 January 2012, 11:36:06 would water jet cutting work? That's what we use for the Phantom mounting plate. BiNiaRiS found a shop to do it for us. for the Phantom mounting plate, minimum order is$110, but it shouldj't be a problem for you since you have a lot of plates to cut for each case. \u00a0They should also have 1\/8\" aluminum. \u00a0the downside is I think you will need to paint it.\n\nFor a full keyboard, how many plates are there, and how many of the plates are exactly the same?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Mon, 02 January 2012, 11:59:31\nWater jet cutting can work too as long as it leaves clean edges. I need 11 1\/16 plates by hand so 22 by keyboard. I can't tell you yet how many plates are exactly the same but there wont be many. Maybe 2 pair of 2 plates by hand are exactly the same.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Mon, 02 January 2012, 12:37:24\nI looked at your case design again. \u00a0I see the differences between plates. \u00a0You maybe able to get more plates to be the same cut if you don't screw in from both the top and the bottom at different locations. \u00a0For example, have holes through and through from the top layer to the bottom layer. \u00a0You would need to use different screws and nuts though.\n\nAnother thing is, if you can make the holes and cable cut out symmetrical, then you could potentially have more plates be the same. \u00a0One of the sides have two holes for cable out, if they are lined up vertically at different height, then you could have the same plates for the cut out. \u00a0I am not sure if the PCB design could allow this though.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Mon, 02 January 2012, 13:22:39\nI want to keep my nut-less design (screw top and bottom) to keep a low minimum height.\nI cant place the holes for the USB and right\/left hand cable stacked vertically.\nWith a CAD drawing, the machine programming take only a few seconds (in modern machine shops) so I don't think I would save that much in having multiple similar plates as the major part of the cost is the cutting time itself.\nPost by: nesiax on Tue, 03 January 2012, 20:07:21\nHi , I come back to work on the key64 (http:\/\/www.key64.com\/), currently i am working on the first pcb prototype, i have made some changes regarding the initial design (http:\/\/www.key64.com\/design), one of the most important is the introduction of 64th key, which is a special key just for the purpose of programming the keyboard without the need for dip switches.\n\nFollowing excelent prinsvalium tutorial (http:\/\/geekhack.org\/showwiki.php?title=Design+your+own+Teensy+keyboard+in+KiCAD+how-to+guide), this is the 3d view of the left halve i got now:\n\n(http:\/\/www.key64.com\/news-1\/3dview.jpg\/image_large)\n\nAs soon as i finished it i will post the files at the key64 website for anyone who wants to adapt to their needs.\n\nAnother change: the keyboard will have 4 leds:\n\n\u2022 Num Lock\n\u2022 Caps Lock\n\u2022 Scroll Lock\n\u2022 Programming Led, a.k.a. 64 key led.\n\nI also made some changes regarding the placement of the keys, i am sure it varies according to the hands shape of each person, but here is the pdf (http:\/\/www.key64.com\/progress\/pcb-left.pdf) if somebody wants to test the footprint and check if that really follow your hand. \u00a0In particular i have changed the position of the thumbs and redesign the wave. \u00a0I would like to hear comments about it, i am not sure if that is too exagerated but that's what i got from my hands, or maybe we could make a \"standard\" wave.\n\nThis is the idea i have on how to join the two halves:\n(http:\/\/www.key64.com\/progress\/separation.jpg\/image_preview)\nis a cheaper retractable alternative that could be implemented in the ErgoDox.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Tue, 03 January 2012, 23:45:24\nHmm, some excellent ideas: are you an engineer?\n\n1. nice teensy location next to the thumb. I much prefer it that way, though I'm not sure if DOX would want to completely redesign his.\n\n2. The programming LED is great. Having a programming mode is cool, but having an LED so you know when you're in it is great. Hmm, Another idea is to have a row of LED's somewhere that light up if you're in another shifted layer (for example, hitting capslock shifts to all caps mode. Hitting fn+shift might move it to mousekeys mode, etc. Having lights available to the user to indicate this would be great. Like one lights up when fn is pressed (or if you have a way to \"lock\" the mode) and another would light up when altgraph is pressed, etc.\n\n3. So you'd join them with a rainbow cable? Wouldn't you be concerned that it'd break, or pull out? I imagine you'd have feet on the keyboard, so that the excess cable can go under the keyboard. \u00a0Hmm, you could use beefy connectors like the ones that were used in then (unrelated) project:\nhttp:\/\/www.amb.org\/forum\/a-delta1-hat-trick-of-sorts-t776.html\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Wed, 04 January 2012, 06:53:17\nI'll throw out some ideas for connecting two halves together that I researched for my own split project, generally from easiest to hardest, less awesome to more awesome, and obviously less time intensive to \"wtf this is taking forever\" :p\n\n\u2022 Use two controllers, that are separately programmed, with separate USB cables.\n\u2022 Use one controller, with one usb cable, and bring the matrix over from the other half via some cable (ideally commonly and cheaply available).\n\u2022 Use two controllers, that are separately programmed, with separate USB cables, and small cable (RJ11 or such) interconnect using SPI (or similar protocol) between the controllers. This allows for things like mod keys on one half affecting the keys on the other half like in 2, but with flexibility of using the halves individually if so desired.\n\u2022 Use two controllers, each of which picks up its key layout from a single shared memory location. Each half also has a USB2 hub; the controller interconnect is a USB3 cable going into the hub of the other half, with the SPI traffic of step 3 happening over the extra unused wires of the cable.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Wed, 04 January 2012, 09:12:13\nHmm, some excellent ideas: are you an engineer?\n\n1. nice teensy location next to the thumb. I much prefer it that way, though I'm not sure if DOX would want to completely redesign his.\n\n2. The programming LED is great. Having a programming mode is cool, but having an LED so you know when you're in it is great. Hmm, Another idea is to have a row of LED's somewhere that light up if you're in another shifted layer (for example, hitting capslock shifts to all caps mode. Hitting fn+shift might move it to mousekeys mode, etc. Having lights available to the user to indicate this would be great. Like one lights up when fn is pressed (or if you have a way to \"lock\" the mode) and another would light up when altgraph is pressed, etc.\n\n3. So you'd join them with a rainbow cable? Wouldn't you be concerned that it'd break, or pull out? I imagine you'd have feet on the keyboard, so that the excess cable can go under the keyboard. Hmm, you could use beefy connectors like the ones that were used in then (unrelated) project:\nhttp:\/\/www.amb.org\/forum\/a-delta1-hat-trick-of-sorts-t776.html\n1: I personally don't like this placement.\n2: Good idea but I can't implement this yet.\n3: There is no place for those beefy connectors and there is no place for a retractable cable in the case.\n\nQuote from: Parak;483034\nI'll throw out some ideas for connecting two halves together that I researched for my own split project, generally from easiest to hardest, less awesome to more awesome, and obviously less time intensive to \"wtf this is taking forever\" :p\n\u2022 Use two controllers, that are separately programmed, with separate USB cables.\n\u2022 Use one controller, with one usb cable, and bring the matrix over from the other half via some cable (ideally commonly and cheaply available).\n\u2022 Use two controllers, that are separately programmed, with separate USB cables, and small cable (RJ11 or such) interconnect using SPI (or similar protocol) between the controllers. This allows for things like mod keys on one half affecting the keys on the other half like in 2, but with flexibility of using the halves individually if so desired.\n\u2022 Use two controllers, each of which picks up its key layout from a single shared memory location. Each half also has a USB2 hub; the controller interconnect is a USB3 cable going into the hub of the other half, with the SPI traffic of step 3 happening over the extra unused wires of the cable.\n\n1: no.\n2: Yes\n3: no.\n4: no.\nI will use 1 controller only. Some other ideas are interesting.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: kps on Wed, 04 January 2012, 09:59:22\nQuote from: Parak;483034\nI'll throw out some ideas for connecting two halves together that I researched for my own split project, generally from easiest to hardest, less awesome to more awesome, and obviously less time intensive to \"wtf this is taking forever\" :p\n\nI'll add my thoughts from my own yet-another-split-project.\n\nQuote\n1. Use two controllers, that are separately programmed, with separate USB cables.\n\nDoesn't work on OS X, which treats separate keyboards as fully independent \u2014 a modifier on one doesn't affect others.\n\nQuote\n2. Use one controller, with one usb cable, and bring the matrix over from the other half via some cable (ideally commonly and cheaply available).\nNeeds a relatively large interconnect. (25-pin RS232 is the only common cable I can think of, other than plain ribbon.)\n\nQuote\n3. Use two controllers, that are separately programmed, with separate USB cables, and small cable (RJ11 or such) interconnect using SPI (or similar protocol) between the controllers. This allows for things like mod keys on one half affecting the keys on the other half like in 2, but with flexibility of using the halves individually if so desired.\n\nThis is similar to what I'm doing, with three (or more) controllers. Each key unit will have a small controller (ATmegax8, probably) to scan the matrix and report to the larger master controller (Teensy or similar), which will handle programmable remapping and USB to the host. The wire protocol between key units and master will be good ol' PS\/2 \u2014 it's proven in practice, has code libraries, and permits the parts to be tested independently: the key units with regular PS\/2-to-USB converters, and the master with existing PS\/2 keyboards. It also means that the master will, incidentally, itself be a reprogrammable multi-port PS\/2-to-USB converter.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Wed, 04 January 2012, 10:38:58\nQuote from: kps;483113\nNeeds a relatively large interconnect. (25-pin RS232 is the only common cable I can think of, other than plain ribbon.)\n\nIt's relatively simple enough to use a hardwired multiconductor cable, though depending on the conductors needed it might be hard to source in smaller quantities, and obviously inconvenient should the length need to be adjusted. One more possibility I could offer here, since we'd need around 13-15 wires, is an HDMI connector. They are cheap, small profile (even smaller as micro or mini), have cheap cables of any length, and carry 19 pins. The downside is that even regular HDMI connectors are SMD mounted - I could only find one that seems to have TH mounting and that's still very fine pitch, so soldering these in any case would be non-trivial.\n\nEdit: That's a pretty neat idea with PS\/2, BTW!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Wed, 04 January 2012, 10:48:00\nSingle fiber optic cable FTW !\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: kps on Wed, 04 January 2012, 11:07:39\nQuote from: sordna;483144\nSingle fiber optic cable FTW !\n\nI don't think there are any off-the-shelf parts that would let you power the remote unit over fiber.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: nesiax on Wed, 04 January 2012, 11:16:40\nThanks for the tip ! HDMI cable and connector will do ! at least for the key64 it fills the requirement for a 8x8 matrix \u00a0(16 lines), plus two leds and 1 ground = 19 lines which is exactly the same number of lines the hdmi cable offers !\n[ATTACH=CONFIG]36574[\/ATTACH]\n[ATTACH=CONFIG]36575[\/ATTACH]\nHowever i am thinking that this will be done on the key64 version 2, right now i just prefer to measure and latter i will optimize otherwise i will never finish the keyboard.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: nesiax on Wed, 04 January 2012, 12:33:29\nHmm, some excellent ideas: are you an engineer?\n\nWell, according to my university diploma , yes i am :)\n\n1. nice teensy location next to the thumb. I much prefer it that way, though I'm not sure if DOX would want to completely redesign his.\n\nThis is the unused space on the board i didn't find any other place to put besides the other halve at the same place.\n\nQuote\n2. The programming LED is great. Having a programming mode is cool, but having an LED so you know when you're in it is great. Hmm, Another idea is to have a row of LED's somewhere that light up if you're in another shifted layer (for example, hitting capslock shifts to all caps mode. Hitting fn+shift might move it to mousekeys mode, etc. Having lights available to the user to indicate this would be great. Like one lights up when fn is pressed (or if you have a way to \"lock\" the mode) and another would light up when altgraph is pressed, etc.\nThat's a good idea, however, if you do touch typing that's irrelevant, i just use them for \"debuging purposes\" and for backwards compatibility with PC 104 keys.\nI need to keep key64 minimalist in design, while i not pretend to start a discussion about how many keys a keyboard should have, just take a look at the apple remote control vs. direct tv remote control:\n[ATTACH=CONFIG]36576[\/ATTACH]\n[ATTACH=CONFIG]36577[\/ATTACH]\nI would bet Directv remote control was designed by engineers.\nWhile apple remote control was designed with people with usuability in mind (usually none of them engineers)\nThat's the way we need to think about keyboards, first focus on usability, then focus on engineering.\n\nQuote\n3. So you'd join them with a rainbow cable? Wouldn't you be concerned that it'd break, or pull out? I imagine you'd have feet on the keyboard, so that the excess cable can go under the keyboard. \u00a0Hmm, you could use beefy connectors like the ones that were used in then (unrelated) project:\nhttp:\/\/www.amb.org\/forum\/a-delta1-hat-trick-of-sorts-t776.html\n\nSome similar ones, i don't have the time to polish those keyboard details, i just want to follow the programming rule \"First measure, then optimize\", which implies i need it working ASAP, there is still a long way to go and optimizations could be done later.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Wed, 04 January 2012, 17:24:41\nI like the HDMI cable idea a lot! I will order a few connectors and check the possibilities.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Wed, 04 January 2012, 20:12:56\nQuote from: Dox;483408\nI like the HDMI cable idea a lot! I will order a few connectors and check the possibilities.\n\nHere (http:\/\/search.digikey.com\/us\/en\/products\/1746679-1\/A35075-ND\/1246897) is one of the few TH ones, but it's with a panel mount (meh). Haven't yet been able to find others (that are purchasable), so it's all SMD otherwise.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Kindari on Thu, 05 January 2012, 11:42:25\nQuote from: Parak;483480\nHere (http:\/\/search.digikey.com\/us\/en\/products\/1746679-1\/A35075-ND\/1246897) is one of the few TH ones, but it's with a panel mount (meh). Haven't yet been able to find others (that are purchasable), so it's all SMD otherwise.\n\nIf it's just a matter of pins, I think Dual Link DVI Cables have even more - something like 29 pins (24 on the normal array, + 5 by way of the little dash pin with 4 regular pins around it). I am NOT an engineer :) .\n\nEDIT: Also, what about wireless? Or am I just nuts. Like one receiver (USB) both halves connect to it. Or, the left half connects to the right half wireless, and the right half is USB to the computer.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Thu, 05 January 2012, 12:53:59\nTrue, DVI-I may have more pins, but it's huge in comparison to HDMI.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Thu, 05 January 2012, 15:42:57\nQuote from: Kindari;483872\nEDIT: Also, what about wireless? Or am I just nuts. Like one receiver (USB) both halves connect to it. Or, the left half connects to the right half wireless, and the right half is USB to the computer.\n\nWireless is way too difficult to implement, and is complete overkill in this scenario. There's just a simple need to bring over the matrix pins.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Thu, 05 January 2012, 20:41:35\nQuote from: Dox;483081\n3: There is no place for those beefy connectors and there is no place for a retractable cable in the case.\n\nI hate retractable cables too, but the beefy connectors are available at mouser. I'll get a part number soon.\n\nEdit: They're 3M products:\nThe 3000 and D3000 (right angle) series latech-eject headers: Here's the wibsite:\nhttp:\/\/solutions.3m.com\/wps\/portal\/3M\/en_US\/Interconnect\/Home\/Products\/ProductCatalog\/Catalog\/?PC_7_RJH9U5230O73D0ISNF9B3C3SI1000000_nid=D05Z5KX2YTit813Z8QWZB1glM0016ZP9KZbl\nhttp:\/\/solutions.3m.com\/wps\/portal\/3M\/en_US\/Interconnect\/Home\/Products\/ProductCatalog\/Catalog\/?PC_7_RJH9U5230O73D0ISNF9B3C3SI1000000_nid=PJBGTPPC88it813Z8QWZB1gl6W3K94MBQHbl\n\nAnd a link to other 3M solutions:\n\nReally, instead of improperly using an existing standard cable (HDMI) for a use it's not intended, we should be using standard connectors that are meant to do what we want. What will happen if I plug my TV up to this by mistake? Sure, I'd be stupid to do that, but what if a kid gets it? Mistakes can be made. I prefer .100 pin headers anyway, and everyone likes strain relief.\n\nPlus you can use rainbow cables to great effect (or black\/grey, if you want). These pin headers come in 10-64 positions, so we can get one exactly the right length. They're easy to terminate, and look awesome. You can't go wrong!\n---\nAnyway, that's what I think we should do. Misusing the HDMI spec (much as I dislike it) just irks me.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Architect on Sat, 07 January 2012, 21:11:39\nI'd recommend not using any cables other than USB for the connection. If you want one side to connect to the other hang a hub off the one with a port off the back for the other to plug into. Most controllers (all I've seen at least) stick a hub first thing in the chain anyhow. Anyhow non USB cables will come back to haunt us for sure (always did in my experience at least). About the VID\/PID don't try and get custom, ain't gonna happen. There are some generic blocks we can co-op I believe (been a while since I messed with this).\n\nEdit: Yeah, two controllers, one with a hub if you like (nice esthetic but I don't personally care) and input USB port or two (can hang the local mouse off the other if you like - Kinesis does this). No ribbons, that'll be messy - to solder and maintain. No other cables, needs emphasis, you'll be chasing down all sorts of nasty issues (reliability, specs, etc)\n\nEdit-Edit: Caught KPS's post. \"Doesn't work on OS X, which treats separate keyboards as fully independent \u2014 a modifier on one doesn't affect others.\" Right. Maybe USB-HOST? Darn, might have to rethink this, cables scare me (must be a bad childhood experience)\n\nMissed this comment earlier from dorkvadar \"Architect: you prefer the maltron thumb area?\nhttp:\/\/www.maltron.com\/media\/hi-res\/..._tb_black1.jpg\n\nI don't see how we can add that, but a 1x key out between the 2x thumbkeys and the normal keyboard keys is surely possible. Maybe that's what we're after?\"\n\nYeah I'm good. I never realized that about the Maltron - never tried one either. Anyhow I love the design now, don't change a thing, just be careful with the cables (and I'm good for three, yikes ...)\n\nPersonal commitment, I'm 1-2P (1 with 2 more pretty sure, didn't realize how much DIY is involved (too busy to DIY these days)). Put me down for having somebody do the soldering, thanks.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Sun, 08 January 2012, 19:59:25\nConnectors:\n[ATTACH=CONFIG]37015[\/ATTACH][ATTACH=CONFIG]37016[\/ATTACH]\n\n1: Ribbon connected on the PCB with an external connector\nPros: trough hole soldering, easy cable length modification, can use a verity of connector outside the case (DB15 in the example).\nCons: cable coming out of the case.\n\nI did some test, with the ribbon cable in shrink wrap, it wouldn't be too bad.\n[ATTACH=CONFIG]37017[\/ATTACH][ATTACH=CONFIG]37018[\/ATTACH]\n\n2: HDMI connector\nPros: Compact, detachable cable at the case, multiple cables available, less DIY.\nCons: Not the intended use, some people might plug it into a tv :der:, SMT soldering might be hard or impossible for some.\n\n3: Beefy 3M connector\nPros: Solid, detachable connection at the case.\nCons: Size (it fits in the case but I think it's overkill)\n\nThere is nothing like the prefect connector.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Barn on Sun, 08 January 2012, 20:26:21\nQuote from: vASILII;486266\nIt is not fair\n\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Sun, 08 January 2012, 20:54:54\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Barn on Sun, 08 January 2012, 20:56:16\nQuote from: sordna;486318\n\nI've reported too. :banplease: Wow... you guys have some strange smileys.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Sun, 08 January 2012, 21:44:48\n(http:\/\/geekhack.org\/attachment.php?attachmentid=37016&d=1326072984)\n\nDox, what is that cable connecting to the Teensy? \u00a0Do you have a link to where I can buy one? \u00a0I like it that it doesn't have the rubber arond the connector. \u00a0Thanks.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sun, 08 January 2012, 23:57:49\nQuote from: kps;483157\nI don't think there are any off-the-shelf parts that would let you power the remote unit over fiber.\n\nQuote from: litster;486365\n\nDox, what is that cable connecting to the Teensy? \u00a0Do you have a link to where I can buy one? \u00a0I like it that it doesn't have the rubber arond the connector. \u00a0Thanks.\nLooks to me like a normal USB, but with the rubber taken off (or just not put on). I'll check mouser.\n---\nForget mouser: here's some digikey:\nhttp:\/\/search.digikey.com\/us\/en\/products\/UX40A-MB-5P\/H2958-ND\/597534\nhttp:\/\/search.digikey.com\/us\/en\/products\/UX40-MB-5P\/H2955-ND\/597531\n---\n\nDox: I'm in favor of the massive 3M connector: It's great! but I also think option #1 will work just fine. Still, if it's available, why not go all out?\n\nAs I mentioned before, I don't think #2 HDMI is a good idea: too much con go wrong: not enough foolproofing. Maybe if we used an uncommon standard like 13W3, it'd work out.\n\nYou're right: finding the right corrector is hard, but if you can have it, it's amazing.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Mon, 09 January 2012, 00:14:09\nLooks to me like a normal USB, but with the rubber taken off (or just not put on). I'll check mouser.\n---\nForget mouser: here's some digikey:\nhttp:\/\/search.digikey.com\/us\/en\/products\/UX40A-MB-5P\/H2958-ND\/597534\nhttp:\/\/search.digikey.com\/us\/en\/products\/UX40-MB-5P\/H2955-ND\/597531\n\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Mon, 09 January 2012, 07:57:51\nIt's a shame they don't have 20 pin mini USB cables, seeing as how they have the connectors.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Mon, 09 January 2012, 10:29:17\nIf an IDC connector fits, that's great. Ribbon cables are ugly, and need to be crimped to length with an appropriate tool (or a hammer..), but can be sleeved during that process to look better-ish. Labor intensive, obviously.\n\nOf course, if something like a DB15 or DB25 fit height-wise, that makes it even more heavy-duty, as those cables are actually better for external applications unlike ribbon cables which are easier to damage. Height is about 0.5\" from the PCB for either connector. Cables are fairly common (http:\/\/www.monoprice.com\/products\/product.asp?c_id=102&cp_id=10215&cs_id=1021501&p_id=542&seq=1&format=2) for either one (http:\/\/www.monoprice.com\/products\/product.asp?c_id=102&cp_id=10212&cs_id=1021201&p_id=1583&seq=1&format=2).\n\nI won't get into a debate (which it isn't really as Dox has the last word) which one makes more sense in practical or theoretical terms, especially since I'm still on the fence about getting this board :p\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hoggy on Mon, 09 January 2012, 13:14:09\nQuote from: Parak;486604\nIf an IDC connector fits, that's great. Ribbon cables are ugly, and need to be crimped to length with an appropriate tool (or a hammer..), but can be sleeved during that process to look better-ish. Labor intensive, obviously.\n\nOf course, if something like a DB15 or DB25 fit height-wise, that makes it even more heavy-duty, as those cables are actually better for external applications unlike ribbon cables which are easier to damage. Height is about 0.5\" from the PCB for either connector. Cables are fairly common (http:\/\/www.monoprice.com\/products\/product.asp?c_id=102&cp_id=10215&cs_id=1021501&p_id=542&seq=1&format=2) for either one (http:\/\/www.monoprice.com\/products\/product.asp?c_id=102&cp_id=10212&cs_id=1021201&p_id=1583&seq=1&format=2).\n\nI won't get into a debate (which it isn't really as Dox has the last word) which one makes more sense in practical or theoretical terms, especially since I'm still on the fence about getting this board :p\n\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Mon, 09 January 2012, 13:21:24\nWow, 18 pages, 268 posts, this project is becoming the next mini-guru, hopefully with a positive outcome !\n\nBTW, I still think HDMI is worth a try, with cheap cables easily found in any length from 1.5ft and up, it's very attractive.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Mon, 09 January 2012, 19:09:42\nUnfortunately, a DB15 connector is too big to fit directly in the case.\n[ATTACH=CONFIG]37122[\/ATTACH]\n\nQuote from: sordna;486712\nWow, 18 pages, 268 posts, this project is becoming the next mini-guru, hopefully with a positive outcome !\n\nBTW, I still think HDMI is worth a try, with cheap cables easily found in any length from 1.5ft and up, it's very attractive.\n\nThanks, I still think HDMI is worth a try too. I'm still waiting for some connectors I ordered last week. I'm not a fan of ribbon cable either, especially in external applications.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Mon, 09 January 2012, 22:15:56\nQuote from: Parak;486604\nI won't get into a debate (which it isn't really as Dox has the last word) which one makes more sense in practical or theoretical terms, especially since I'm still on the fence about getting this board :p\n\nHmm, you're right about ribbon cables. I'll dig through the amphenol section of my mouser catalog and see what I may see. How many conductors were we after?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Tue, 10 January 2012, 06:40:38\n\nHmm, you're right about ribbon cables. I'll dig through the amphenol section of my mouser catalog and see what I may see. How many conductors were we after?\nSomething between 13 and 20\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Tue, 10 January 2012, 07:08:01\nMicro-D connectors would work great, except the connectors are $arm and cables are$leg :(\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Ascaii on Tue, 10 January 2012, 07:14:07\nsticking with HDMI would allow the use of MASSIVE BLING BLING monster cables...1000$cables, why not? xD Heres another idea: Though this might be a little complicated...we could just have two cat5 ports on each halves. It would require sleeving two cat5 cables together, but cat5 cables and connectors are even more readily available then HDMI. It would be possible to make a custom cable with a shrink wrapped ribbon cable that terminates in two cat5 plugs. Personally I like the idea of having the locking tab on the cat5...and with two heads we would have 16 conductors. Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Tue, 10 January 2012, 07:44:46 Wonder if there's a dual cat5 block that has the retention tabs on opposite sides. Easy single hand grip to remove would be nice. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 10 January 2012, 08:47:23 Quote from: Parak;487199 Micro-D connectors would work great, except the connectors are$arm and cables are $leg :( well put! Made me laugh. Quote from: alaricljs;487208 Wonder if there's a dual cat5 block that has the retention tabs on opposite sides. Easy single hand grip to remove would be nice. You mean like sideways? I've only seen upside up and upside down. Title: [Interest Check] Custom split ergo keyboard. Post by: Ascaii on Tue, 10 January 2012, 09:01:30 Id be happy even if its two single cat5 connectors, I love the damn things :P Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Tue, 10 January 2012, 09:52:34 Quote from: dorkvader;487236 You mean like sideways? I've only seen upside up and upside down. Doesn't particularly matter what the total block is oriented as, it just needs to fit the pcb\/case constraints. All I'm saying is that having the jacks oriented to each other so that the tabs are on opposite sides would make it easier to unplug the ganged connector. You could even epoxy the 2 together . Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Tue, 10 January 2012, 10:38:51 RJ45 jacks are even taller than DB15 connector, unfortunately, so I don't think they'd work. There's really not much out there that's readily accessible and meets our needs :\/ Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 10 January 2012, 11:25:25 Quote from: Parak;487330 RJ45 jacks are even taller than DB15 connector, unfortunately, so I don't think they'd work. There's really not much out there that's readily accessible and meets our needs :\/ Yeah, as you said, RJ45 are even taller than DB15 so there is no chance these will fit in the case. Look at all these HDMI cables (http:\/\/www.monoprice.com\/products\/subdepartment.asp?c_id=102&cp_id=10240). I think this option might be the best. Title: [Interest Check] Custom split ergo keyboard. Post by: Icarium on Tue, 10 January 2012, 13:20:22 Okay, this is my first post so hi everyone and sorry if this has been said already or is considered blasphemous. How about making it wireless? Title: [Interest Check] Custom split ergo keyboard. Post by: Icarium on Tue, 10 January 2012, 13:32:44 Okay, seriously, what's wrong with wireless? :) Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Tue, 10 January 2012, 13:40:52 Nothings wrong with wireless, except I think it's been mentioned and it's rather cost prohibitive since you'll need a total of at least 3 'units'. 1: the receiver on the PC end, 2: left hand board transmitter, 3: right hand board transmitter. And that's only if you can find a tech that enables you to use 2 transmitters on 1 receiver and process both signals at the same time. Maybe ZigBee or something similar, but other than names I don't know too much about it. Then of course you need a controller in each board to give the transmitter something to send, and then a controller on the receiver end to tell the PC what was sent. ouch, that's a lot of electronic gizmos. Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Tue, 10 January 2012, 13:43:51 Wireless is too complicated unless there's a volunteer that wants to design the entire controller pcb with wireless built in, and write all the associated (very non-trivial) firmware from scratch :p Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Tue, 10 January 2012, 15:18:48 Quote from: Icarium;487406 Okay, seriously, what's wrong with wireless? :) Quote from: alaricljs;487411 Nothings wrong with wireless, except I think it's been mentioned and it's rather cost prohibitive since you'll need a total of at least 3 'units'. 1: the receiver on the PC end, 2: left hand board transmitter, 3: right hand board transmitter. And that's only if you can find a tech that enables you to use 2 transmitters on 1 receiver and process both signals at the same time. Maybe ZigBee or something similar, but other than names I don't know too much about it. Then of course you need a controller in each board to give the transmitter something to send, and then a controller on the receiver end to tell the PC what was sent. ouch, that's a lot of electronic gizmos. I think Icarium is volunteering. Seriously. Title: [Interest Check] Custom split ergo keyboard. Post by: kps on Tue, 10 January 2012, 16:05:45 And, as the resident forum troll just unintentionally pointed out, wireless eats batteries, and you'll have your keyboard stop working when you're trying to snipe an auction or apologize to your girlfriend or something, sending you on a futile hunt for replacements, which are each bigger than the DB25 connector that was too bulky in the first place. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 10 January 2012, 16:14:05 Quote from: ripster;487498 Woohoo! Vote for me often. http:\/\/geekhack.org\/showthread.php?25737-The-OFFICIAL-2012-Troll-Poll! If you don't have anything constructive to add, I would ask you not to post here. Thanks in advance! Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 10 January 2012, 16:46:13 Quote from: Icarium;487406 Okay, seriously, what's wrong with wireless? :) Batteries. Hmm, just thought of something: we could carry power across two wires (very easy) and send the signals wirelessly. That is, if someone wants to come up with a workable solution that's not too expensive and will fit in the case. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 10 January 2012, 16:53:31 It will definitively not be wireless. I don't want to mess with batteries. Title: [Interest Check] Custom split ergo keyboard. Post by: Icarium on Tue, 10 January 2012, 17:18:50 Well, anyway, I'm interested. Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Tue, 10 January 2012, 18:55:48 Haven't read the entire thread, but I'm interested... as long as it comes with its own keys. I don't mind soldering on the switches though if that lowers the price. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 10 January 2012, 21:41:50 Quote from: ironman31;487605 Haven't read the entire thread, but I'm interested... as long as it comes with its own keys. I don't mind soldering on the switches though if that lowers the price. I'll add you, though getting keys for it should be pretty easy via WASD, and the A-Z keyboard area can be taken from any cherry MX. Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Tue, 10 January 2012, 21:51:52 Quote from: dorkvader;487679 I'll add you, though getting keys for it should be pretty easy via WASD, and the A-Z keyboard area can be taken from any cherry MX. Ok, I was just worried about finding keys that would fit the layout. Title: [Interest Check] Custom split ergo keyboard. Post by: inaneframe on Tue, 10 January 2012, 23:34:04 Quote from: Dox;487503 If you don't have anything constructive to add, I would ask you not to post here. Thanks in advance! First constructive post in ten pages, look what I found: http:\/\/www.sprintek.com\/products\/SK5100.aspx Might even be useful for colemak and dvorak conversions, etc. Title: [Interest Check] Custom split ergo keyboard. Post by: boli on Wed, 11 January 2012, 02:26:30 This keyboard looks very interesting, sort of like a splittable TrulyErgonomic (or split flat Maltron) with thumb keys similar to a Kinesis, sweet! As a Colemak and Kinesis user for about 4 years, and having tried a TrulyErgonomic and liking it but missing the thumb keys, this keyboard looks right up my alley. I could afford$400, would prefer no soldering, and would require international shipping. Reprogrammability in firmware is a must, as far as I can see this is a given (excellent, because I'd like to make a few adjustments: number row shifted one to the left, arrow keys and second Enter key on the left hand, and command\/option\/ctrl on the thumb(s), like my current layout (http:\/\/homepage.mac.com\/boli\/ars\/80329_kinesis_colemak_small.png)). It would have to work properly with OS X.\n\nIf I'd like it I'd soon need a second one, too, but I won't order 2 right off the bat without having tried it or someone I trust try and review one.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: mjoytan on Wed, 11 January 2012, 09:44:36\nHiya!\n\nTotally new here, and this caught my eye. \u00a0Cannot help but *covet* this lovely keyboard. \u00a0Nice work! \u00a0I've had the Kinesis Classic and Advantage for over 10 years now, and as much as I love it, this keyboard just looks a whole lot sexier! \u00a0Sign me up if you can make it for around $300! Thanks! Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 11 January 2012, 19:46:41 Quote from: inaneframe;487766 First constructive post in ten pages, look what I found: http:\/\/www.sprintek.com\/products\/SK5100.aspx Might even be useful for colemak and dvorak conversions, etc. Wow, that looks pretty good! I looked on their order page, and I only see evaluation boards. I don't know where we can get the chips, and the company might want us to order 1,000 of them. Quote from: boli;487822 This keyboard looks very interesting, sort of like a splittable TrulyErgonomic (or split flat Maltron) with thumb keys similar to a Kinesis, sweet! As a Colemak and Kinesis user for about 4 years, and having tried a TrulyErgonomic and liking it but missing the thumb keys, this keyboard looks right up my alley. I could afford$400, would prefer no soldering, and would require international shipping. Reprogrammability in firmware is a must, as far as I can see this is a given (excellent, because I'd like to make a few adjustments: number row shifted one to the left, arrow keys and second Enter key on the left hand, and command\/option\/ctrl on the thumb(s), like my current layout (http:\/\/homepage.mac.com\/boli\/ars\/80329_kinesis_colemak_small.png)). It would have to work properly with OS X.\n\nIf I'd like it I'd soon need a second one, too, but I won't order 2 right off the bat without having tried it or someone I trust try and review one.\nI don't know how distribution will go, you may have to order two as a \"leap of faith\", or there may be more available (like what ragnarock does with his keycaps). I'll put you down for 1-2 if that's okay.\n\nQuote from: mjoytan;487953\nHiya!\n\nTotally new here, and this caught my eye. \u00a0Cannot help but *covet* this lovely keyboard. \u00a0Nice work! \u00a0I've had the Kinesis Classic and Advantage for over 10 years now, and as much as I love it, this keyboard just looks a whole lot sexier! \u00a0Sign me up if you can make it for around $300! Thanks! I'll add you! Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Wed, 11 January 2012, 20:02:35 Quote from: inaneframe;487766 First constructive post in ten pages, look what I found: http:\/\/www.sprintek.com\/products\/SK5100.aspx Might even be useful for colemak and dvorak conversions, etc. This looks like AIKON. Interesting. Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Wed, 11 January 2012, 21:49:23 QFN *shudder*. I tried prototyping a usb hub based on a qfn chip - not fun to solder at all, even with a heat gun. Should have gone with a schmartboard or an assembly service in retrospect. Alas, most new chips of interest will come in QFN or at best QFP. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 11 January 2012, 23:08:17 Even QFP are daunting to me. DIP all the way (or SOIC at the very least) Title: [Interest Check] Custom split ergo keyboard. Post by: inaneframe on Wed, 11 January 2012, 23:49:02 Quote from: dorkvader;488278 Wow, that looks pretty good! I looked on their order page, and I only see evaluation boards. I don't know where we can get the chips, and the company might want us to order 1,000 of them. This is a negative? All I have to do is get an evaluation, play with it and get a little bit of investment. . . I could make it worth it. . . talking to the manufacturer now. Title: [Interest Check] Custom split ergo keyboard. Post by: Kurk on Thu, 12 January 2012, 03:36:00 You can order sample ICs at a hidden corner of their web page: http:\/\/www.sprintek.com\/order\/Orderics.aspx Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Thu, 12 January 2012, 06:37:03 Hmm, the SK7190 integrates a pointing stick controller too.. The chips look fairly low BOM, though I see no mention of key rollover\/diode support. Title: [Interest Check] Custom split ergo keyboard. Post by: Icarium on Thu, 12 January 2012, 08:05:51 I want to be on the list. 400$ would be okay if that includes everything. (Except assembly.)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Thu, 12 January 2012, 08:56:07\nThat controller or something similar is what the Chameleon controller is... lemme search\n\nAlso somewhere on Taobao.... \u00a0couldn't find them. \u00a0Imsto is the source.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Kurk on Thu, 12 January 2012, 08:57:15\nQuote from: Parak;488544\nHmm, the SK7190 integrates a pointing stick controller too.. The chips look fairly low BOM, though I see no mention of key rollover\/diode support.\n\nThe SK7190 is a pointing stick controller [del]only, no keyboard controller.[\/del] ...brain fart... ok, it's also a keyboard controller.\nBTW, N-key roll over support is explicitely mentioned with the SK5102 chip: http:\/\/www.sprintek.com\/products\/SK5102.aspx\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: kps on Thu, 12 January 2012, 09:02:49\nQuote from: Parak;488544\nHmm, the SK7190 integrates a pointing stick controller too.. The chips look fairly low BOM, though I see no mention of key rollover\/diode support.\n\nThe datasheet says it does ghost detection, which precludes n-key rollover. It may be that there are enough scan lines that this would not be a problem for a half-keyboard unit.\n\nThe nice thing about that chip from this project's point of view is that it can speak PS\/2 and has a downstream PS\/2 port, so it seems that the units could simply be daisy-chained.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Thu, 12 January 2012, 09:24:47\nQuote from: Icarium;488566\nI want to be on the list. 400 $would be okay if that includes everything. (Except assembly.) Are you interested in assembly, too? I'll add you after work. Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Thu, 12 January 2012, 09:32:49 Quote from: Kurrk;488599 The SK7190 is a pointing stick controller only, no keyboard controller. BTW, N-key roll over support is explicitely mentioned with the SK5102 chip: http:\/\/www.sprintek.com\/products\/SK5102.aspx Ah, missed the NKRO somehow. The SK7190 does specifically state that it has a keyboard controller though, unless I'm missing something again. Title: [Interest Check] Custom split ergo keyboard. Post by: Icarium on Thu, 12 January 2012, 10:16:12 Quote from: dorkvader;488629 Are you interested in assembly, too? I'll add you after work. Probably not, I think I have to screw it up at least once to know that I can't do it myself. :) Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Sat, 14 January 2012, 20:21:24 Sorry, I'm confused about the thumb keys in the latest design, at the front page I see two ideas. Are there two thumbers or six? If two then I have to regretfully bow out. Thanks - (and BTW, yes for sure no bluetooth! I've had too many problems with it, I want absolute connectivity in a keyboard) Title: [Interest Check] Custom split ergo keyboard. Post by: moogatronic on Sat, 14 January 2012, 21:39:19 I'm interested in this and would like to be added to the list. I've not assembled something like this before, but that part sounds almost as fun as having this design actualized! I suppose i'm conditional on the price being at or under 400. Time to start saving I guess! =) Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 14 January 2012, 22:47:25 Quote from: Architect;490770 Sorry, I'm confused about the thumb keys in the latest design, at the front page I see two ideas. Are there two thumbers or six? If two then I have to regretfully bow out. Thanks - (and BTW, yes for sure no bluetooth! I've had too many problems with it, I want absolute connectivity in a keyboard) As far as I know, the latest design has more than two thumbswitches. I believe the two-switch one was proposed at the beginning, and reworked into the kinesis-like grouping. Edit: page three http:\/\/geekhack.org\/showthread.php?22780-Interest-Check-Custom-split-ergo-keyboard&p=432084&viewfull=1#post432084 Quote from: moogatronic;490804 I'm interested in this and would like to be added to the list. I've not assembled something like this before, but that part sounds almost as fun as having this design actualized! I suppose i'm conditional on the price being at or under 400. Time to start saving I guess! =) Haha! That's the spirit, I'll add you presently. Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Sun, 15 January 2012, 04:14:17 Thanks dorkvader. Related question, again sorry if it's buried in there somewhere but I didn't find it, what are the dimensions of the keyboard\/each keypad? I'm concerned about the size, my Truly Ergonomic non split boards are really compact, and I've got a lot of controllers and such on my desk. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sun, 15 January 2012, 13:15:21 Hmm, you'll have to ask Dox. Often you can have that as part of your cad software. I don't remember exact sizing, but it'd be pretty easy to estimate. Each \"key\" is 0.75 inches wide. by that estimate, I'm getting less than 7.2 inches\/hand (at the maximum width). Ofcourse this will be less if you tent them. The bulk of the matrix (not counting the thumbs) is 7.5 keys wide, so it should be just over 5.6 inches wide. Since they are pretty positionable, I'm sure they won't take up that much space. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sun, 15 January 2012, 13:55:08 Dimensions: [ATTACH=CONFIG]37586[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Sun, 15 January 2012, 16:27:41 Hmm, as I look at it again, I think the \"wave\" is too much. Especially as you curve your fingers to type the lower row (ZXCVB) having to put the ring and middle finger more forward than the others feels unnatural. Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Sun, 15 January 2012, 16:53:49 Quote from: sordna;491200 Hmm, as I look at it again, I think the \"wave\" is too much. Especially as you curve your fingers to type the lower row (ZXCVB) having to put the ring and middle finger more forward than the others feels unnatural. Saw your post and answered it over there. The wave works for me, very natural, I'd vote to keep it. With split or curved designs like these the wave helps to auto-center the hands. The thing I'm working on is size, assuming about an inch between the hands in the picture above that makes for a bigger keyboard than I'd like, and I'm not sure the advantage of the split, ergonomically speaking. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Sun, 15 January 2012, 16:57:20 The split is essential, since people come in different sizes! As for the wave, I'm not against it, but I think it should be more subtle. Title: [Interest Check] Custom split ergo keyboard. Post by: dzd on Sun, 15 January 2012, 17:02:53 I want one too! This seems to be my \"ideal\" kb design. I was looking for a mix between Kinesis Advantage\/Maltron 2D, and Kinesis Countoured - this looks like it! I also think the Advantage\/Maltron 2D designs should have symmetrical 3-modifier key layout and would be EXCELLENT with a well-placed touchpad! I was going to put my next best hope in the Truly Ergonomic - but it's not even available! Your DOX looks even better. Hope it's available soon. One more thing - I thought it would be good to have an area below the keys to rest your palms. Don't know if that's been discussed here yet. Title: [Interest Check] Custom split ergo keyboard. Post by: Pyrolistical on Sun, 15 January 2012, 20:12:34 I have a Kinesis and my biggest complaint is the moved += button. I see you have moved it as well as other keys. I'll put my money where my mouth is and create my own \"ideal\" keyboard. Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Sun, 15 January 2012, 20:41:27 Quote from: sordna;491215 The split is essential, since people come in different sizes! As for the wave, I'm not against it, but I think it should be more subtle. Maybe, OTOH everybody's hands meet in the middle too, as they do for all primates. I'm trying to understand if the split is a ergonomic feature, and why people think so. Not saying it isn't, just looking for the evidence. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Sun, 15 January 2012, 20:47:42 Quote from: Architect;491331 Maybe, OTOH everybody's hands meet in the middle too, as they do for all primates. I'm trying to understand if the split is a ergonomic feature, and why people think so. Not saying it isn't, just looking for the evidence. They meet, but depending on the width of the shoulders the angle changes, so at minimum the 2 halves should be able to be rotated. Not to mention people's positioning *preferences* can be freely accomodated. Also, some folks like to mount their keyboard halves on chair arms, etc. For example, I plan to tent this keyboard, build some angled cardboard props and make it semi-vertical. I wouldn't be able to do that if it weren't split. The split is the most important feature in this keyboard, there are plenty non-split ergo keyboards in the market, Kinesis Advantage, Maltron, Truly Ergonomic, etc, it would be silly to create yet another. This will be the first ergonomic, columnar layout, truly split (movable halves) keyboard, that's the whole point of this project. Title: [Interest Check] Custom split ergo keyboard. Post by: moogatronic on Sun, 15 January 2012, 20:51:51 I think one important aspect of the split is the inherent ability to then adjust the keyboard halves to varying degrees of tilt, as well as vary the distance between hands. I do not necessarily agree that the split is necessary if the keys are placed at angles that would not force your wrists to strain while flexing, as the standard keyboard layout would require. Halved keyboards however, allow you to dynamically alter your ergonomic situation on a whim. (This is at least the ergonomic theory behind the smartfish keyboard, though, on that board, they seem to have copied the terrible staggered key structure from 'standard' boards, which seem to assume humans have two right hands) Quote from: Architect;491331 Maybe, OTOH everybody's hands meet in the middle too, as they do for all primates. I'm trying to understand if the split is a ergonomic feature, and why people think so. Not saying it isn't, just looking for the evidence. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Sun, 15 January 2012, 21:56:40 Here is what I mean \"more subtle\", look at the left half of the keyboard, I moved the 3 middle columns down a little. Sorry for the sloppy copy\/pasting but you get the point. EDIT: I just realized the innermost column was at same level as the one next to it. I think the innermost column should be a bit lower so that the index finger doesn't have to overstretch. So apart from lowering the 3 middle columns, I also lowered the innermost column too: [ATTACH=CONFIG]37629[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Mon, 16 January 2012, 01:23:39 Quote from: dzd;491218 I want one too! This seems to be my \"ideal\" kb design. I was looking for a mix between Kinesis Advantage\/Maltron 2D, and Kinesis Countoured - this looks like it! I also think the Advantage\/Maltron 2D designs should have symmetrical 3-modifier key layout and would be EXCELLENT with a well-placed touchpad! I was going to put my next best hope in the Truly Ergonomic - but it's not even available! Your DOX looks even better. Hope it's available soon. One more thing - I thought it would be good to have an area below the keys to rest your palms. Don't know if that's been discussed here yet. Added :) That's a good point: like the kinesis has the palmrests, etc. I still feel that the design should account for that ,but not have them inherent, that way one can make or add one's own to suit one's tastes. Quote from: Pyrolistical;491313 I have a Kinesis and my biggest complaint is the moved += button. I see you have moved it as well as other keys. I'll put my money where my mouth is and create my own \"ideal\" keyboard. So you are interested too? I'll add you anyway. Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Mon, 16 January 2012, 05:50:06 Quote from: dorkvader;491456 Added :) That's a good point: like the kinesis has the palmrests, etc. I still feel that the design should account for that ,but not have them inherent, that way one can make or add one's own to suit one's tastes. I think the present design is good. . If rests are desired then these (http:\/\/www.amazon.com\/3M-Leatherette-Antimicrobial-Protection-WR305LE\/dp\/B0016OV5MQ\/ref=sr_1_3?ie=UTF8&qid=1326714496&sr=8-3) should work fine, one on each hand tucked in right in front of the keyboard. Title: [Interest Check] Custom split ergo keyboard. Post by: Pyrolistical on Mon, 16 January 2012, 10:56:05 Quote from: dorkvader;491456 Added :) So you are interested too? I'll add you anyway. No. What I meant was I'll create my own kb Title: [Interest Check] Custom split ergo keyboard. Post by: dzd on Mon, 16 January 2012, 11:06:38 Quote from: Architect;491559 If rests are desired then these (http:\/\/www.amazon.com\/3M-Leatherette-Antimicrobial-Protection-WR305LE\/dp\/B0016OV5MQ\/ref=sr_1_3?ie=UTF8&qid=1326714496&sr=8-3) should work fine, one on each hand tucked in right in front of the keyboard. Yes - you can add your own off-the-shelf wrist rests. The cons are that you have too many individual parts on your desk (especially if you have several other input devices\/gadgets\/whatever on your desk, like you had mentioned you do - I do too). It'd be great if the DOX came with optional\/removable palm rests - like the Truly Ergonomic, for example (looks like they did a good job with that - but I've only seen pictures). But I know this might be asking too much from Dox. Quote from: moogatronic;491341 Halved keyboards however, allow you to dynamically alter your ergonomic situation on a whim. Exactly. I like split because I can change my position at my desk throughout the day. I'm often at my computer all through the day, with a sit\/stand desk. It's great getting to move the keyboard halves around on a \"whim\" to accommodate different positions. This really makes it feasible to be at your desk all day with a middle age body (heh) and not suffer (and in fact, enjoy it!). I tried a split keyboard that was good for changing positions through the day - that was great. But it was still missing other features I wanted (mechanical, and matrix layout). Another thing I like about the Dox is it looks like it doesn't have dedicated Function keys. I'd prefer Function keys on a separate, flat keypad\/keyboard. (But the drawback is one more separate, corded device on your desk). Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Mon, 16 January 2012, 20:32:15 Quote from: dzd;491720 Truly Ergonomic, for example (looks like they did a good job with that - but I've only seen pictures). But I know this might be asking too much from Dox. The TE wrist rest is fairly impressive. It has plastic smooth nubs or 'bolts that fit into corresponding sockets, plus the screws and form fitting shape. Acts like a part of the keyboard, it adds some size to the board and I'm surprised to find that I like it a lot. But I wouldn't recommend the EDox try to do this, too much risk\/work for little reward. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Mon, 16 January 2012, 22:08:04 I'm sort-of a fan of those wall-mount holes on routers and suchlike. Do you think they should be added to the bottom of the casing to ease in creating or adapting a tent or chair-mount setup? I sort-of feel that these things would be easier if there were something to grab onto. (http:\/\/www.cisco.com\/en\/US\/i\/200001-300000\/240001-250000\/242001-243000\/242657.jpg) Thanks to cisco http:\/\/www.cisco.com\/en\/US\/docs\/routers\/access\/1800\/1841\/hardware\/installation\/guide\/18inst.html#wp1053401 Title: [Interest Check] Custom split ergo keyboard. Post by: kps on Tue, 17 January 2012, 09:08:11 Quote from: dorkvader;492148 Do you think they should be added to the bottom of the casing to ease in creating or adapting a tent or chair-mount setup? For my own long-slow split project, I'm planning on using ball joints \u2014 specifically repurposed camera flash mounts, which are cheap and easy to get \u2014 at the back edge of the units. This wouldn't work as-is on the ErgoDox case (can't tap a hole in the layered edge) but something similar might. [ATTACH=CONFIG]37764[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: Icarium on Tue, 17 January 2012, 10:24:21 Quote from: kps;492406 For my own long-slow split project, I'm planning on using ball joints \u2014 specifically repurposed camera flash mounts, which are cheap and easy to get \u2014 at the back edge of the units. This wouldn't work as-is on the ErgoDox case (can't tap a hole in the layered edge) but something similar might. (Attachment) 37764[\/ATTACH] hm...shouldn't there be enough space to make a hole for screws somewhere? this is hard to discuss without sketches... I need a drawing board :p Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Tue, 17 January 2012, 11:44:44 Assuming the case is made out of something ferrous, one could build a ram mount using these (http:\/\/www.ram-mount.com\/CatalogResults\/PartDetails\/tabid\/63\/partid\/082065080045051051057085\/Default.aspx) as the attachment point to the keyboard half. Expensive, but looks to be quite reliable, and there's no need to make modifications to the case. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 17 January 2012, 20:40:28 Assuming the case is something ferrous, I have about 12 HD magnets that suddenly have a purpose. Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Tue, 17 January 2012, 20:42:51 No it's machined aluminum, as it should be. If you want to use magnets you can epoxy or glue a thin sheet of steel to the bottom. If you want a tripod mount it's easy enough to tap and thread just the way you want. I'm warming up to this, thinking of three again, update on the cabling? Title: [Interest Check] Custom split ergo keyboard. Post by: itlnstln on Thu, 19 January 2012, 12:08:54 I would be in for one with Cherry browns if it's completely assembled at least up to the caps. Title: [Interest Check] Custom split ergo keyboard. Post by: Mazora on Thu, 19 January 2012, 12:15:42 Me too ! Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Thu, 19 January 2012, 20:18:18 Quote from: itlnstln;494135 I would be in for one with Cherry browns if it's completely assembled at least up to the caps. Added Quote from: Mazora;494145 Me too ! I already have you (as #08), but were you also wanting the building service? I also found out that there's a topic on Deskthourity now, so I'm importing the interest from there. I've got all the post's up to Jan 04. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Thu, 19 January 2012, 20:30:19 You mean this thread? (http:\/\/deskthority.net\/viewtopic.php?f=7&t=1753) Hmm, you made a typo copying my comment ... Title: [Interest Check] Custom split ergo keyboard. Post by: heuristicist on Thu, 19 January 2012, 23:31:03 I'm new here but would be willing to buy this if I could get it for$300 or less (preferably CAD, but I guess USD is close enough) including tax and shipping. I can probably assemble it myself but I wouldn't want to buy anything else, so I would expect the 300 to include switches, caps, etc. As for soldering, I don't have an iron myself right now, but will probably want to buy one eventually... depending on when this keyboard is ready I might be able to help with that. Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Fri, 20 January 2012, 12:56:26 Definitely interested in one now, maybe more. I just need to learn how to solder surface mount stuff properly, that stuff always gets me. Title: [Interest Check] Custom split ergo keyboard. Post by: Zanth on Sat, 21 January 2012, 19:14:34 Quote from: itlnstln;494135 I would be in for one with Cherry browns if it's completely assembled at least up to the caps. I would be in for one, Reds or Browns, but I too would want it completely assembled at least up to the caps. Title: [Interest Check] Custom split ergo keyboard. Post by: thirdkind on Sun, 22 January 2012, 19:51:53 I'd definitely be in for 2 of these, but after reviewing my list of wants, it almost sounds *****y: - Assembled - Natural machined aluminum color with white keys - Otaku - Reds If I could get that (or at least a fully assembled base to which I could add appropriate keys), I'd take 2, definitely. I love my Filco Limited R, but a split keyboard with aligned keys is my dream. Title: [Interest Check] Custom split ergo keyboard. Post by: heuristicist on Mon, 23 January 2012, 02:12:59 BTW, now that I think of this, it would be nice if the bottom could have some notches (or something) to allow the keyboard to be tented\/angled, like the Freestyle Ascent. Obviously the design is up to you but just my0.02 on what would add flexibility :)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Tafryn on Mon, 23 January 2012, 12:26:08\nThis design is as close to my perfect keyboard as I'm ever likely to find. Count me in for one as long as it's around $300. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Mon, 23 January 2012, 12:50:22 I wonder if the case could have a palm rest... Or maybe I will just attach one to it. I do like the palm rest area on my Kinesis. Title: [Interest Check] Custom split ergo keyboard. Post by: sicyo on Wed, 25 January 2012, 11:56:40 I would certainly be interested but am with Thirdkind in that I would prefer natural aluminum and assembled as well. Subscribed! Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Fri, 27 January 2012, 02:24:41 You know, I have 50 people in the interest list, with 55 or so keyboards. I think we may be able to start getting into some real volume discounts here if we find the right place. Title: [Interest Check] Custom split ergo keyboard. Post by: KylJoy on Sat, 28 January 2012, 00:12:38 I'm on the verge... This thing looks awesome. With volume discount I'm about 95% in for one. Title: [Interest Check] Custom split ergo keyboard. Post by: bbbbqq on Sat, 28 January 2012, 00:46:14 Hey dox, can you tell me the measurement of the staggering ? ie: how much farther \"north\" is the W row is than the Q row, E row, etc Title: [Interest Check] Custom split ergo keyboard. Post by: ksweber on Sat, 28 January 2012, 14:17:56 Hi! I am also interested in getting one of this special designed keyboards. My preference would be: * assembled * natural machined aluminum color with blanc white keys * brown Cherry One question left to me: In many ergonomic guides a negative slope of the keyboard is propose to minimize wrist bending. Negative slope--meaning that the keyboard angles downward so that the side closest to your body is higher than the side away from your body. The side picture in the first post shows a positive slope. Please add me to the list. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Sat, 28 January 2012, 14:34:57 Quote from: ksweber;501686 In many ergonomic guides a negative slope of the keyboard is propose to minimize wrist bending. Negative slope--meaning that the keyboard angles downward so that the side closest to your body is higher than the side away from your body. The side picture in the first post shows a positive slope. I agree, the keyboard should lay flat and have a low height as possible, and it would be up to the user to attach legs\/supports and raise\/tilt it any way they wish. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 28 January 2012, 15:52:44 Quote from: bbbbqq;501340 Hey dox, can you tell me the measurement of the staggering ? ie: how much farther \"north\" is the W row is than the Q row, E row, etc I can't speak for Dox, but I imagine it'd be like other matrix boards: where the spacing left\/right is the same as up\/down. If this is the case, then it'd be 0.75 inches between keys, and would work with any 1x cherry mx compatible keycap (see, if it's less than that, the keycaps would hit eachother, and if it's more, you'd have to move your fingers a lot more) Title: [Interest Check] Custom split ergo keyboard. Post by: oneproduct on Sat, 28 January 2012, 21:10:11 He doesn't mean the space between keys in adjacent rows or within a given column, he means how it isn't a perfect grid and each column has a different y-offset to fit a hand, i.e. middle finger longer. :) Title: [Interest Check] Custom split ergo keyboard. Post by: Architect on Sun, 29 January 2012, 08:59:36 Remove my name from the list, thanks. Good luck with it, should be a great keyboard. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sun, 29 January 2012, 12:27:16 I will, but I don't think you should let people in the ergo subforum get the better of you, emotionally. I don't see how removing your interest from here will help anyone\/anything. Title: [Interest Check] Custom split ergo keyboard. Post by: jedcred on Tue, 31 January 2012, 12:09:45 I'm interested in this design (or at least, my shoulders are). I don't have a problem with assembly. Title: [Interest Check] Custom split ergo keyboard. Post by: gilgam on Tue, 31 January 2012, 16:56:57 hello i want one of this, but what about switches and diodes ? The group buy for the Phantom keyboard and switches is ending and i think i'll order some as the prices are nice. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Tue, 31 January 2012, 17:47:01 wasdkeyboards.com sells switches now, (http:\/\/www.wasdkeyboards.com\/index.php\/products\/keyboard-parts-1.html) I bought and used some already. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 31 January 2012, 17:50:08 Quote from: gilgam;504655 hello i want one of this, but what about switches and diodes ? The group buy for the Phantom keyboard and switches is ending and i think i'll order some as the prices are nice. Switched and diodes are the same as the Phantom ones. Standard cherry switches and 1n4148 diodes. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Tue, 31 January 2012, 17:56:56 Ah good to know about the diodes. Here, an amazon seller sells them for 1 cent each, so you can get 100 for$1 + $4.49 shipping =$5.49\nhttp:\/\/www.amazon.com\/Parts-Express-1N4148-Logic-Diode\/dp\/B0002KRC7C\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Tue, 31 January 2012, 18:02:44\nI ordered over 1000 of them for my doxKB. The cost was something around 0.0015$each. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Tue, 31 January 2012, 18:08:16 It would help if you mentioned where we can get them from at that price! Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 31 January 2012, 18:27:48 Oops I put one extra \"0\" in there, it was 0.015$ each, your amazon link is better!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Tue, 31 January 2012, 19:15:27\nQuote from: sordna;504699\nAh good to know about the diodes. Here, an amazon seller sells them for 1 cent each, so you can get 100 for $1 +$4.49 shipping = $5.49 http:\/\/www.amazon.com\/Parts-Express-1N4148-Logic-Diode\/dp\/B0002KRC7C lolwut @ Technical Details :D Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 31 January 2012, 23:07:25 Quote from: Parak;504756 lolwut @ Technical Details :D Quote Precision machined 6 cut RCA connector with split center pin Available in versions to fit three different ranges of TV sizes It IS parts express (sell expensive components for audio). I think they just accidentally pasted it in there. Jedcred and gilgam, I've added you interest. Title: [Interest Check] Custom split ergo keyboard. Post by: sicyo on Wed, 01 February 2012, 07:51:30 Where's this interest list being kept? I just want to make sure I'm on it. Thanks Title: [Interest Check] Custom split ergo keyboard. Post by: heuristicist on Wed, 01 February 2012, 13:29:54 Quote from: sicyo;505161 Where's this interest list being kept? I just want to make sure I'm on it. Thanks See the second post of this thread. Title: [Interest Check] Custom split ergo keyboard. Post by: sicyo on Wed, 01 February 2012, 14:30:40 Hah, thanks. Can't believe I missed that. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 01 February 2012, 18:57:59 Quote from: sicyo;505480 Hah, thanks. Can't believe I missed that. I had you down as #49 The reason I'm keeping it in post #2 is that I coincidentally was the first to post after DOX, and when I compiled the interest, I utilized the prime post real-estate. Title: [Interest Check] Custom split ergo keyboard. Post by: minnus on Tue, 07 February 2012, 20:40:58 It seems that the forum has rolled back a bit and my interest post was lost. I am still interested. Is there any way for people with interest to contribute in any way? Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 08 February 2012, 00:05:34 Quote from: minnus;508810 It seems that the forum has rolled back a bit and my interest post was lost. I am still interested. Is there any way for people with interest to contribute in any way? I have you and Salash down on the list. I'll update the second post. good thing I keep a backup on my laptop :p I dunno: I'm keeping track of interest, to help out with that detail. I know we're still looking for a decent connector between the halves (the bulky 3m Ribbon cable one I found looks good, but I'm thinking ribbon cables aren't ideal. HDMI has been suggested, but I really hate appropriating it to this use (It's \"wrong\", surface mount, dubious strain relief available, etc)), and other ideas have been proposed) If someone wants to browse mouser\/digikey for better exterior connectors that are low profile enough to work, that'd help. Also, I think scouting around for a shop that'll be able to cut the casings would be useful. Hmm, maybe we should publish a \"roadmap\" of all the work that's been done (design, etc) and that needs to be done (PCB, fab, etc), and people can search, and propose ideas. That said, The order would be like 100+ sets of those 11 or so \"plates\" that screw together, which I think is a fairly substantial order. Title: [Interest Check] Custom split ergo keyboard. Post by: mtl on Wed, 08 February 2012, 07:27:05 Quote from: dorkvader;508966 I know we're still looking for a decent connector between the halves (the bulky 3m Ribbon cable one I found looks good, but I'm thinking ribbon cables aren't ideal. HDMI has been suggested, but I really hate appropriating it to this use (It's \"wrong\", surface mount, dubious strain relief available, etc)), and other ideas have been proposed) You could make each half a stand-alone keyboard. One half could also contain a USB hub for linking up the pair, so you only need one USB cable going to the host (PC, etc.) Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 08 February 2012, 07:49:52 Quote from: mtl;509139 You could make each half a stand-alone keyboard. One half could also contain a USB hub for linking up the pair, so you only need one USB cable going to the host (PC, etc.) The possibility of digital communication has been discussed. I think it's the best idea if anyone can find\/write an implementation for it (Which is the hard part: that level of complexity adds a lot). USB would be a waste in this instance (It's not really means for inter-chip communications) maybe I2s would be better. Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Wed, 08 February 2012, 08:53:31 If you're going with a dual controller design you might be able to cram PS\/2 conversion into both halves and use PS\/2 between the halves and then USB to the PC. Halving conversion in both halves means being able to run the interconnect in either direction and USB from either side. Might need a dip switch or some other method to tell each side its role. This might even let you mirror image the PCB. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 08 February 2012, 20:25:48 Quote from: alaricljs;509164 This might even let you mirror image the PCB. No: there are some practical reasons we can't mirror it: first off the switches wouldn't fit. (they are asymmetrical). Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Wed, 08 February 2012, 20:28:04 You can still mirror it if you provision an extra solderable hole for each switch, which shouldn't increase the cost at all. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Wed, 08 February 2012, 20:29:14 Quote from: sordna;509687 You can still mirror it if you provision an extra solderable hole for each switch, which shouldn't increase the cost at all. That's what PrinsValium did to Phantom's PCB to support so many different layouts with just one PCB. Title: [Interest Check] Custom split ergo keyboard. Post by: sicyo on Thu, 09 February 2012, 07:51:31 I know a machine shop that might be able to do it, let me check with them. They also could handle tumbling and can out-source anodizing and nickel plating (one of the main reasons I'm interested) Also, as far as the connector we should pick something that is easily available and doesn't cause a hassle to be replaced. Couldn't a nice braided USB cable suffice? UPDATE: Got in touch with them and they can give us a quote if we provide a standard blue print showing dimensions and tolerances. CAD works too. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Thu, 09 February 2012, 18:04:06 Quote from: sicyo;510070 Also, as far as the connector we should pick something that is easily available and doesn't cause a hassle to be replaced. Couldn't a nice braided USB cable suffice? A USB cable only provides 4 contacts, we need something like 14-20. Now, this would work out well if we had some chip on the \"slave\" 'board convert the keypress to something digital, but the current idea is to just transfer the matrix over the cable. Edit: If anyone wants to implement this idea, I think a digital connection between boards is the best idea, but implementing it would be hard. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Thu, 09 February 2012, 18:06:36 My vote still goes for HDMI, due to enough conductors, small size, and very cheap & easy to find cables of varying lengths. Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Thu, 09 February 2012, 21:15:05 Quote from: sordna;510524 My vote still goes for HDMI, due to enough conductors, small size, and very cheap & easy to find cables of varying lengths. My only concern about HDMI is the flexibility of the cable. I purchased one of the thinner ones from monoprice and they still feel as if they would be too stiff to use as a connector. I have had many hdmi ports on various devices wear out due to stiff cables putting too much strain on them. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Thu, 09 February 2012, 23:12:13 I'm concerned about the surface mount (much less mechanically sound compared with through-hole) and the apparent lack of decent panel mount options for them. Not to mention the fact that it's the wrong protocol for the cable. We'd also (theoretically speaking ) owe the HDMI company money for each port on our device. Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Fri, 10 February 2012, 08:13:11 You'd only owe them a licensing fee if you implemented HDMI on the port. I'm wondering if some sadist wants to try implementing 1 half with shift registers and using serial over a small cable using RJ45s or the like. Title: [Interest Check] Custom split ergo keyboard. Post by: sicyo on Fri, 10 February 2012, 08:58:28 Dorkvader - you noted scouting around for a shop. I guess you don't have access to a CAD or exact dimensions\/tolerances? Or will I have to wait to hear from Dox? Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Fri, 10 February 2012, 09:19:10 Quote from: dorkvader;510769 I'm concerned about the surface mount (much less mechanically sound compared with through-hole) and the apparent lack of decent panel mount options for them. FWIW, a TH and panel mount connector is available here (http:\/\/search.digikey.com\/us\/en\/products\/1746679-1\/A35075-ND\/1246897). The panel mount part of it is definitely too high, though. Quote from: alaricljs;510938 You'd only owe them a licensing fee if you implemented HDMI on the port. I'm wondering if some sadist wants to try implementing 1 half with shift registers and using serial over a small cable using RJ45s or the like. SPI (4 wires) or I2C (2 wires) would only need an RJ11, but I think that even RJ11 is too high to fit. And yeah, implementing that type of protocol would be quite a substantial amount of work :( Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Fri, 10 February 2012, 09:22:09 Needs more than just 2 or 4 wires unless you want to have some form of MCU on the slave side. Clock, power, whatever else... hell, need power especially if you have an MCU. Title: [Interest Check] Custom split ergo keyboard. Post by: kps on Fri, 10 February 2012, 09:34:01 Quote from: Parak;510957 SPI (4 wires) or I2C (2 wires) would only need an RJ11, but I think that even RJ11 is too high to fit. And yeah, implementing that type of protocol would be quite a substantial amount of work :( SPI is pretty much trivial if you are using something like a USB AVR (e.g. Teensy) as the main controller. An I\/O expander like a 23S17 (http:\/\/search.digikey.com\/us\/en\/products\/MCP23S17-E%2FSP\/MCP23S17-E%2FSP-ND\/894276) would do everything the slave side needs. Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Fri, 10 February 2012, 10:08:35 Heh, how about VHDCI (http:\/\/www.molex.com\/molex\/products\/datasheet.jsp?part=active\/0714300008_IO_CONNECTORS.xml&channel=Products&Lang=en-US)? Complete overkill in terms of pins, rather expensive, but readily available and low profile. Or TDP Triad (http:\/\/www.molex.com\/molex\/products\/family?key=tdp_triad_differential_pair&channel=products&chanName=family&pageTitle=Introduction). Header (http:\/\/www.mouser.com\/ProductDetail\/Molex\/74960-3018\/?qs=sGAEpiMZZMvd2mIcYG7oaNDysQv32n8A3cY5Nb0GQvs%3d) + Cable (http:\/\/www.mouser.com\/ProductDetail\/Molex\/74576-0001\/?qs=QA2a3%252blgRt%252bCtR0ltQmc8Q%3d%3d). The downside is that the header is SMD. Title: [Interest Check] Custom split ergo keyboard. Post by: kps on Fri, 10 February 2012, 11:49:13 Or use an I\u00b2C I\/O expander (e.g. 23017 (http:\/\/search.digikey.com\/us\/en\/products\/MCP23017-E%2FSP\/MCP23017-E%2FSP-ND\/894272)) to get down to 4 conductors, and use 2.5mm audio (http:\/\/search.digikey.com\/ca\/en\/products\/SJ1-42515TS\/CP1-42515TS-ND\/659902) connectors. Cheap, compact, and through-hole. Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Fri, 10 February 2012, 12:10:21 Quote from: kps;511086 Or use an I\u00b2C I\/O expander (e.g. 23017 (http:\/\/search.digikey.com\/us\/en\/products\/MCP23017-E%2FSP\/MCP23017-E%2FSP-ND\/894272)) to get down to 4 conductors, and use 2.5mm audio (http:\/\/search.digikey.com\/ca\/en\/products\/SJ1-42515TS\/CP1-42515TS-ND\/659902) connectors. Cheap, compact, and through-hole. Hmm, that's a nice approach. SDA, SCL, Power, and Ground over the 4 conductors? Would still need a willing sap^H^H^H volunteer to create some sample code, and breadboard test it with a small matrix, I suppose. Title: [Interest Check] Custom split ergo keyboard. Post by: warzer0 on Fri, 10 February 2012, 22:23:01 Got any idea of a ballpack price for this thing? Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 11 February 2012, 10:48:54 Quote from: warzer0;511469 Got any idea of a ballpack price for this thing? I added it up once, based on Dox's quotes for 5 cases, and it was under$400 (something like $367) not counting keycaps or teensy. If we can get to 50 orders (up from 5), there's a chance the cases would be much cheaper, and the PCB's will probably be less than the$50\/hand I estimated. Shopping around may also prove useful.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ekw808 on Tue, 14 February 2012, 10:23:07\nThe most I could possibly pay for this board would be 200 O_O even though it looks pretty amazing\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: REVENGE on Wed, 15 February 2012, 00:58:38\nQuote from: ekw808;514166\nThe most I could possibly pay for this board would be 200 O_O even though it looks pretty amazing\nAssembled? I imaging that's doable at the current rate for self-assembly, labor would probably add $50 -$100.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: drojf on Thu, 16 February 2012, 01:22:35\nYou might find this diy keyboard build log relevant: The Humble Hacker Keyboard (http:\/\/geekhack.org\/showwiki.php?title=Island:6292)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Tue, 21 February 2012, 14:35:02\nI just saw the KeyPoard (http:\/\/geekhack.org\/showwiki.php?title=Island:26845) which looks really awesome, complete with phantom cut-outs on the switch mounting holes so that mounted switches can be opened up for servicing. I think we should add those cut-outs to ErgoDox as well.\n\n(http:\/\/geekhack.org\/attachment.php?attachmentid=41177&d=1329724607)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Wed, 22 February 2012, 20:43:56\n@dorkvader\/dox: If the price can stay below $400 for *everything* (except assembly), I'm definitely interested. If it can stay below$300, I'd like one. \u00a0If below $150-200, I think I might want two.. lol, or at least an extra case+PCB. Assuming it can get done in the next few months so I can get it together and get used to it before school, and of course that no future design decisions make it not work for me (which I don't expect to be the case). Created an account just so I could track this thread :) . A few of the things that matter to me: - The thumbs having a good amount of keys within easy reach (as in the current kinesis looking thumb group) - The cord between the two being cheap, easy to get, and *small* (as is being discussed). I've never tried, but it seems to me that anything thicker \/ less flexible than a typical usb cord would be a pain when the two halves of the keyboard were close together on a desk. And aesthetically, a ribbon cable connector or even an ethernet connector (or a pair of them), would ruin it IMO. 2x2.5mm audio connectors (like kps suggested) would be pretty cool, if there's nothing better in a single similarly sized and shaped cable. A few of the things that don't matter to me: - Assembly service. If it's going to be done by another member, and\/or going to cost more than maybe$20, I may as well take the opportunity to learn :)\n- Layout. \u00a0I'm planning to change it all anyway.\n- Whether the parts all come in the same box, or whether we have to get them from different places. \u00a0As long as they're not way too hard to find\/buy, and the total price can stay below my above limits.\n\nRandom preferences (if they make a difference here):\n- I'm leaning towards cherry browns, after a bunch of reading. \u00a0I haven't found a place to try them, but they sound like what I want.\n- Colored or clear keycaps. \u00a0I know these would be extra... but if they turn out not to be too much more, it'd be really cool.\n- O-rings (the soft ones), probably. \u00a0I assume these would be extra too.\n- For layout, I'll probably do something close to arensito, at least with the AltGr symbol layer.\n\nOther thoughts:\n- I'd prefer it not to be red. \u00a0Lol, though I guess I'd live if it were.\n- Once it gets closer to being done, if I'm not the only one here who's a noob at all things hardware, maybe someone could post links to save us searching around for all the parts we'll have to get ourselves, how to put it together (or at least common pitfalls), how to reprogram\/reflash the firmware for remapping (and other things?), and all that? \u00a0I understand it's DIY so I shan't complain, but it'd save me a bit of tangential effort.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Wed, 22 February 2012, 22:58:38\nQuote from: ic07;522476\n@dorkvader\/dox: If the price can stay below $400 for *everything* (except assembly), I'm definitely interested. If it can stay below$300, I'd like one. \u00a0If below $150-200, I think I might want two.. lol, or at least an extra case+PCB. Assuming it can get done in the next few months so I can get it together and get used to it before school, and of course that no future design decisions make it not work for me (which I don't expect to be the case). Created an account just so I could track this thread :) . A few of the things that matter to me: - The thumbs having a good amount of keys within easy reach (as in the current kinesis looking thumb group) - The cord between the two being cheap, easy to get, and *small* (as is being discussed). I've never tried, but it seems to me that anything thicker \/ less flexible than a typical usb cord would be a pain when the two halves of the keyboard were close together on a desk. And aesthetically, a ribbon cable connector or even an ethernet connector (or a pair of them), would ruin it IMO. 2x2.5mm audio connectors (like kps suggested) would be pretty cool, if there's nothing better in a single similarly sized and shaped cable. A few of the things that don't matter to me: - Assembly service. If it's going to be done by another member, and\/or going to cost more than maybe$20, I may as well take the opportunity to learn :)\n- Layout. \u00a0I'm planning to change it all anyway.\n- Whether the parts all come in the same box, or whether we have to get them from different places. \u00a0As long as they're not way too hard to find\/buy, and the total price can stay below my above limits.\n\nRandom preferences (if they make a difference here):\n- I'm leaning towards cherry browns, after a bunch of reading. \u00a0I haven't found a place to try them, but they sound like what I want.\n- Colored or clear keycaps. \u00a0I know these would be extra... but if they turn out not to be too much more, it'd be really cool.\n- O-rings (the soft ones), probably. \u00a0I assume these would be extra too.\n- For layout, I'll probably do something close to arensito, at least with the AltGr symbol layer.\n\nOther thoughts:\n- I'd prefer it not to be red. \u00a0Lol, though I guess I'd live if it were.\n- Once it gets closer to being done, if I'm not the only one here who's a noob at all things hardware, maybe someone could post links to save us searching around for all the parts we'll have to get ourselves, how to put it together (or at least common pitfalls), how to reprogram\/reflash the firmware for remapping (and other things?), and all that? \u00a0I understand it's DIY so I shan't complain, but it'd save me a bit of tangential effort.\n\nWow, welcome to Geekhack, that's a heck of a first post: Lots of good info here.\n\nFirstly, I don't want to take any credit away from Dox. He's the designer. I'm just keeping track of interest, and answering easy questions.\n\nGood point on the cable. Also note that very frequently, thinner cables will be able to suffer more bends before breaking: They have a longer service life in that respect, but are more fragile to tensile strain. I've seem some unwieldy USB cables before: One has full shielding with an aluminium wrap (I think it's from a LaCiE HDD)! Having TRRS connectors to carry power, Transmit signal, received signals, and ground would work, but at that point, we could totally use the ubiquitous USB connector. The hardest part is implementing a matrix to I2C or something, then having it decoded by a master teensy. Also note that it wolud have to be pretty high speed, or we wouldn't get NKRO on the slave half due to bandwidth limitations. At this point, the design of the cables also plays a large part, as crosstalk, and inductance degrade the highspeed signal. We would almost be better off at that point to go with a SMA connector (like for routers) or suchlike.\n\nHah, good point on the layout. One of the best features is the programmability of this: you can't just pick an arbitrary layout on just any keyboard, but with the Dox (or anything Teensy) you can.\n\nParts: I imagine there'll be a good BOM made up, where We'll distribute the plate\/case and PCB, then have a link to where you can buy the rest. You could conceivably have it ordered in a few minutes, Still, if we're distributing the plates\/case already, it might be a better idea to distribute the other components at the same time, for possible savings in bulk.\n\nKeycaps: I never imagined keycaps to come with the base kit. Many GH'ers have extra sets, and they're pretty easy to get (WASDkeyboards, anyone?) elsewhere. I also really want clear keycaps to go over my cherry greens in the mail.\n\nAs far as colour, we might be able to work something out with the Machine shop to get it anodized different colours. Ofcourse it would be pretty easy to paint it yourself.\n\nFinally: You should look at the phantom guide on the DT WIKI. This is almost the same project (only with the different physical aspect, integrated case, and possible complication of cables\/connectors) and there's a lot of good info there. I imagine when it comes time, We'll update it with some ergoDOX specifics. I've always wanted to write up a proper manual in LaTeX for download\/distribution.\nhttp:\/\/deskthority.net\/wiki\/Phantom_Instruction\n\nAnyway, I hope this helps. As always, it's up to DOX right now (as designer and de facto lead) but good ideas are always appreciated. It's good to get the problems sorted out before production.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Thu, 23 February 2012, 15:29:43\nThanks :)\n\nParts: I imagine there'll be a good BOM made up, where We'll distribute the plate\/case and PCB, then have a link to where you can buy the rest. You could conceivably have it ordered in a few minutes, Still, if we're distributing the plates\/case already, it might be a better idea to distribute the other components at the same time, for possible savings in bulk.\n\nSounds good to me. \u00a0Seems like this isn't the first time you guys have done this :)\n\nKeycaps: I never imagined keycaps to come with the base kit. Many GH'ers have extra sets, and they're pretty easy to get (WASDkeyboards, anyone?) elsewhere. I also really want clear keycaps to go over my cherry greens in the mail.\n\nOkay. \u00a0I do have to include keycaps in my price limit though, since I don't have any yet.. :\/ . \u00a0I did look around on WASD yesterday. \u00a0I'll have to shop around some more later.\n\nAs far as colour, we might be able to work something out with the Machine shop to get it anodized different colours. Ofcourse it would be pretty easy to paint it yourself.\n\nIt would be awesome if the machine shop could do different colors, or just natural colored (like thirdkind wants). \u00a0I looked up how to paint over anodized aluminum today, and it doesn't look fun (to me). \u00a0But again, it won't kill my interest, even though it's aesthetically important to me.\n\nFinally: You should look at the phantom guide on the DT WIKI. This is almost the same project (only with the different physical aspect, integrated case, and possible complication of cables\/connectors) and there's a lot of good info there. I imagine when it comes time, We'll update it with some ergoDOX specifics. I've always wanted to write up a proper manual in LaTeX for download\/distribution.\nhttp:\/\/deskthority.net\/wiki\/Phantom_Instruction\n\nThanks! \u00a0I've only glanced at it for now, but I'll read it more thoroughly when the ergoDOX gets closer to shipping.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Thu, 23 February 2012, 16:23:47\nQuote from: Parak;511104\nHmm, that's a nice approach. SDA, SCL, Power, and Ground over the 4 conductors?\n\nWould still need a willing sap^H^H^H volunteer to create some sample code, and breadboard test it with a small matrix, I suppose.\n\n@parak\/kps: You guys make it sound so hard. \u00a0The Teensy library documentation[1] makes it sound easy. \u00a0Which makes me feel naive, lol. \u00a0What am I missing? \u00a0The only problem (if it is one) that I can see is that this might only give us 6KRO without a lot of work.\n\n( Some relevant stuff i found, just to put it here. \u00a0Sorry if everyone already knows:\n- NKRO is possible with USB, but not common: geekhack.org\/showwiki.php?title=USB+versus+PS+2#Full+NKRO\n- Phantom firmware. \u00a0I thought it was NKRO, but the post says it's 6KRO, so I'd have to read\/learn more to figure it out: geekhack.org\/showwiki.php?title=Island:26742\n)\n\n[1] pjrc.com\/teensy\/td_keyboard.html (with something to handle I\u00b2C) in C, or pjrc.com\/teensy\/td_keyboard.html and pjrc.com\/teensy\/td_libs_Wire.html in what looks like C++\n\n((sorry for the links, i can't post real ones yet))\n\nEDIT:\nDon't mean to clog the thread with dev stuff. \u00a0Please let me know if there's another place I should put it.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Thu, 23 February 2012, 16:29:06\nPhantom's firmware is based off of Teensy's keyboard source. \u00a0It is 6KRO over USB right now. \u00a0When people get their hands on the Phantom hardware, hopefully it will turn into NKRO over USB.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Thu, 23 February 2012, 16:56:41\nI wish the ErgoDox will be 6KRO for maximum compatibility with any computer \/ OS. When I see NKRO over USB I run, run away from it; to me it's a useless feature and so I prefer the USB standard to avoid any possibility of issues with the various OSs I use. I lived with 2KRO just fine for years, and 6KRO is even better, and six plus modifiers is really more simultaneous keys than I will ever need.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Thu, 23 February 2012, 17:50:53\nQuote from: sordna;523515\nI wish the ErgoDox will be 6KRO for maximum compatibility with any computer \/ OS. When I see NKRO over USB I run, run away from it; to me it's a useless feature and so I prefer the USB standard to avoid any possibility of issues with the various OSs I use. I lived with 2KRO just fine for years, and 6KRO is even better, and six plus modifiers is really more simultaneous keys than I will ever need.\n\nThe interesting part about this is that the teensy NKRO I've seen is using USB standards and doing quite well at compatibility. \u00a0It's the mass-market usb-NKRO controllers that are introducing problems because of their poor implementation choices.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Thu, 23 February 2012, 23:27:23\nQuote from: ic07;523490\n@parak\/kps: You guys make it sound so hard. \u00a0The Teensy library documentation[1] makes it sound easy. \u00a0Which makes me feel naive, lol. \u00a0What am I missing? \u00a0The only problem (if it is one) that I can see is that this might only give us 6KRO without a lot of work.\n\n( Some relevant stuff i found, just to put it here. \u00a0Sorry if everyone already knows:\n- NKRO is possible with USB, but not common: geekhack.org\/showwiki.php?title=USB+versus+PS+2#Full+NKRO\n- Phantom firmware. \u00a0I thought it was NKRO, but the post says it's 6KRO, so I'd have to read\/learn more to figure it out: geekhack.org\/showwiki.php?title=Island:26742\n)\n\n[1] pjrc.com\/teensy\/td_keyboard.html (with something to handle I\u00b2C) in C, or pjrc.com\/teensy\/td_keyboard.html and pjrc.com\/teensy\/td_libs_Wire.html in what looks like C++\n\n((sorry for the links, i can't post real ones yet))\n\nEDIT:\nDon't mean to clog the thread with dev stuff. \u00a0Please let me know if there's another place I should put it.\n\nI'd say that any development ideas you have are okay is this thread. I certainly find them more interesting than checked interest :P\n\nSo there already exists I2C for Teensy? I should have known. Looks like almost everything's been done on ATmega.\n\nAbout #KRO: The Teensy supports NKRO logically, so it can recognize all the keystrokes, and keep them separate. As far as I know, the reason USB is usually 6KRO is due to bandwidth limitations, and it functioning on USB 1.1 for legacy (BIOS) purposes. There exists an implementation of NKRO over USB on the Teensy (see soarer), but I'm not 100% sure how it works out with the necessary bandwidth. My assumption has always been that it detects something from the computer and is only 6KRO (and slower) when it needs to be, then changes back to NKRO once it's into a full-OS, but I really have no idea.\n\nSee, I'm no EE, so I'm relatively new to this embedded system stuff. Also, I don't have a TEENSY, so I can't hardly breadboard an I2C solution.\n---\n\nShould I come up with a \"roadmap\" of stuff that needs to get done? I figure, if I do that, then people can tackle each bit, and we'd get more done faster. Like we could get the CAD files, and some people can talk to local machine shops. We can get someone working on implementing i2c as communication between the halves. We can get someone looking for solutions for the connector problem (either an easy cable for I2C or a larger one for passing the matrix) etc. Then we can have a list of design decisions to be made (fer example, number and placement of thumb keys, etc.)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Laggy-gaga on Fri, 24 February 2012, 09:07:15\nI will take one if around $200 bucks Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Fri, 24 February 2012, 17:47:55 Quote from: dorkvader;523936 Should I come up with a \"roadmap\" of stuff that needs to get done? I figure, if I do that, then people can tackle each bit, and we'd get more done faster. Like we could get the CAD files, and some people can talk to local machine shops. We can get someone working on implementing i2c as communication between the halves. We can get someone looking for solutions for the connector problem (either an easy cable for I2C or a larger one for passing the matrix) etc. Then we can have a list of design decisions to be made (fer example, number and placement of thumb keys, etc.) I think a roadmap, especially if it included a collection of relevant files, would be great :) . And since I've been thinking about it so much for the last few days, maybe I should just go ahead and volunteer to write and breadboard test the firmware (including i2c). I'm hoping two things though: 1) that if anybody more experienced than me wants to do it, somebody lets me know before I buy the chips, lol, and 2) that nobody minds if it's 6KRO for the moment, and written in C++ in the teensyduino environment. If that works out all right, I'll go from there. Also, I'm a comp. sci. undergrad, and I've never messed with firmware before, so I'm sure I'll need help with parts of it before I'm done (or at least a code review). If some of my basic assumptions turn out to be wrong (e.g. the teensyduino Keyboard or Wire libraries end up not working for us) I'll likely need a *lot* of help. If I do give it a shot, which Teensy and which I2C IO expander should I use? EDIT: There's a C implementation of TWI under the LGPL in the Arduino libraries (https:\/\/github.com\/arduino\/Arduino\/tree\/master\/libraries\/Wire\/utility). I still wouldn't mind trying it out, but if someone who knows what they're doing wants to just use this and the Teensy USB: keyboard (http:\/\/pjrc.com\/teensy\/usb_keyboard.zip) (and maybe the Phantom firmware (http:\/\/geekhack.org\/attachment.php?attachmentid=38982&d=1327895092)) code to put something together, that might be quicker. Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Fri, 24 February 2012, 19:09:46 Quote from: ic07;524691 If I do give it a shot, which Teensy and which I2C IO expander should I use? As kps mentioned earlier (http:\/\/geekhack.org\/showthread.php?22780-Interest-Check-Custom-split-ergo-keyboard&p=511086&viewfull=1#post511086), MCP23017 or MCP23018 should work here. I'm not at all sure what the difference between them is, even after looking at the datasheets, but 16 (outdated)\/17\/18 seem to have plenty of code samples floating around. Make sure to get the ones ending in SP, which indicates a DIP package. A regular teensy will be plenty due to the port expander being used. You can get the one with pins presoldered, too. I do wonder about the 2.5mm jack though. The datasheet (http:\/\/products.cui.com\/getPDF.aspx?fileID=7757) has a couple of types, both switched and unswitched. The consideration here is to make sure that insertion and removal of a plug while the teensy is on and providing voltage won't damage the I2C extender, though I'm probably overthinking it and the nonswitched one (CP1-42514-ND) will be fine. Title: [Interest Check] Custom split ergo keyboard. Post by: kps on Fri, 24 February 2012, 21:31:49 Quote from: Parak;524775 I do wonder about the 2.5mm jack though. The datasheet (http:\/\/products.cui.com\/getPDF.aspx?fileID=7757) has a couple of types, both switched and unswitched. The consideration here is to make sure that insertion and removal of a plug while the teensy is on and providing voltage won't damage the I2C extender, though I'm probably overthinking it and the nonswitched one (CP1-42514-ND) will be fine. Yeah, I'm not sure about that either, though I'm just a programmer with a screwdriver. Personally I would use a mini-DIN connector (with at least 5 pins, and SPI rather than I\u00b2C), but connector size seems to be a major concern here. Title: [Interest Check] Custom split ergo keyboard. Post by: molto on Mon, 27 February 2012, 21:21:21 I like the layout and would definitely would pay$50 for a PCB. \u00a0The case isn't worth hundreds of dollars to me. \u00a0I would rather just glue it down to a piece of plywood and save the money for the substantial amount that switches and keycaps will cost. \u00a0Is the plate necessary or will the PC hold the switches securely?\n\nTangential question, what do you-all think of splay (columns not parallel but farther apart at the top than the bottom)? \u00a0I think it is why I find the Microsoft Natural 4000 more comfortable than a GoldTouch but I'm not 100% sure.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Mon, 27 February 2012, 22:11:43\nHaving tried a Datadesk smartboard as well as a Kinesis Advantage (I also own a Goldtouch and a Microsoft natural0 I am firmly against any splay. Columns should be completely parallel and keys should be close together to minimize unnecessary hand\/finger movement.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: REVENGE on Mon, 27 February 2012, 22:46:22\nQuote from: sordna;528885\nHaving tried a Datadesk smartboard as well as a Kinesis Advantage (I also own a Goldtouch and a Microsoft natural0 I am firmly against any splay. Columns should be completely parallel and keys should be close together to minimize unnecessary hand\/finger movement.\nTrust the sordna!\n\nI need something to blow my money on, let's get this show on the road.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Tue, 28 February 2012, 00:10:30\nQuote from: molto;528809\nI like the layout and would definitely would pay $50 for a PCB. The case isn't worth hundreds of dollars to me. I would rather just glue it down to a piece of plywood and save the money for the substantial amount that switches and keycaps will cost. Is the plate necessary or will the PC hold the switches securely? I'll put you down for PCB interest. It seems you're going key64-style on the case? Not a bad decision. You can even DIY it in acrylic relatively cheaply, and easily enough to be worthwhile. Lucky for me, I will have enough switches to populate this, and with my purchasing habits, I don't really expect keycaps to be an issue. --- As far as the plate\/PCB, I think if we add plate-mount holes to the PCB, phantom-style, then you could go with either. IT makes he PCB more complicated, but is well worth it. Also, with the case design, we can have some extra plate-mounts made up for he people who will DIY their own cases. I wouldn't expect them to be too expensive, especially in the quantity we're after (And they are symmetric). Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Wed, 29 February 2012, 17:48:43 If this doesn't happen within 2 months then I'll be in if the price isn't much over$400, but for right now 7bit has made me bankrupt. :\/\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Wed, 29 February 2012, 18:45:15\nHI guys, I've been very busy with work during the last few weeks but things are slowing down a bit so I'll have more time to work on this.\nIf someone want to experiment with I2C or SPI go ahead because I will not. If someone can develop something functional with 1 controller, I will implement it to the PCB design.\n\nI have reworked the columns staggering as per sordna recommendation. Tell me what you guys think.\n[ATTACH=CONFIG]42238[\/ATTACH]\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Wed, 29 February 2012, 19:11:09\nHehe, subtle is nice. Hmm, I still think with just a 1-2mm adjustment we can fit another thumbkey:\n\n[ATTACH=CONFIG]42252[\/ATTACH]\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Thu, 01 March 2012, 12:59:16\nThanks for the update, it's looking nice :) .\n\nI ordered a Teensy 2.0 and some I2C chips the other day (along with some SPI ones just in case), so hopefully they'll come soon and I can make an attempt at the firmware. \u00a0I'm going to shoot for using the MCP23018 for now, which would allow us to use one 4-conductor 2.5mm jack (Vcc, GND, SCL, SDA), or two 2-conductor ones. \u00a0I'll let you guys know when I make some progress.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Thu, 01 March 2012, 13:59:12\nWhy 2.5mm? What's wrong with 3.5mm? It's more common, and I suspect there are even better\/more durable connectors to be had.\n\nStill, I thank you for all the works you're doing, This will be an elegant solution.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Thu, 01 March 2012, 14:17:45\nThe CUI 4 pin connectors have a difference of 1mm in height, 4mm for 2.5 vs 5mm for 3.5. As long as the 5mm one fits, then yeah, it'd be better as far as availability of cables goes. This doesn't matter for prototyping purposes though, except where it comes time to test live insertion\/removal of the connector.\n\n@ic07: Awesome, good luck!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Snarfangel on Thu, 01 March 2012, 14:20:27\nQuote from: sordna;531330\nHehe, subtle is nice. Hmm, I still think with just a 1-2mm adjustment we can fit another thumbkey:\n\n(Attachment) 42252[\/ATTACH]\n\nSo...Shift, Space, Enter on one side, and Shift, E, Backspace on the other? :)\n\nOf course, putting the E under the thumb isn't exactly QWERTY, but I do like how the blank keys are laid out..\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Thu, 01 March 2012, 15:12:13\nHeck, I might put L and S on the extra thumbs, so I can do \"ls\" in dvorak :-)\nIf you're not familiar with Dvorak, for \"ls\" you need to type \"P;\" (same pinky twice) on a QWERTY keyboard ...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Fri, 02 March 2012, 00:58:38\n@dorkvader: Sorry if that came out wrong - I don't have a real preference for 2.5mm vs 3.5mm, I just kind of picked one to mention in the post, lol. \u00a0Actually, now that I look at them again, I might prefer 3.5mm (for durability, if there's room for it), but I'm not really worried either way.\n\n@parak: Thanks!\nTitle: White, Strong & Flexible\nPost by: Dox on Sat, 03 March 2012, 11:58:49\nI've been impressed with the quality of prints I've seen from shapeways lately so I'm considering getting the case 3D printed in plastic instead of machined\/cut aluminium. I don't like the sharp edges and thicker border and screws of the layered aluminium plate design. Current volume for the case is 100.69cm^3 per hand so it would cost around 280$for both hands in their white, strong & flexible material (like the humblehacker (http:\/\/geekhack.org\/showwiki.php?title=Island:6292)). The case could also be ordered in different colors offered by shapeways (black, red, grey, indigo) or dyed\/painted afterward. Renders! [ATTACH=CONFIG]42548[\/ATTACH][ATTACH=CONFIG]42549[\/ATTACH][ATTACH=CONFIG]42550[\/ATTACH][ATTACH=CONFIG]42551[\/ATTACH][ATTACH=CONFIG]42552[\/ATTACH][ATTACH=CONFIG]42553[\/ATTACH] Tell me what you think! Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Sat, 03 March 2012, 12:13:22 280 seems kind of steep for just the plastic case. I dont mind the plastic, but only if its a good bit cheaper and the quality exceeds that of realforce boards Title: [Interest Check] Custom split ergo keyboard. Post by: dirge on Sat, 03 March 2012, 12:27:44 put me on the list for one please. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Sat, 03 March 2012, 13:38:51 Are those cutouts for costar stabilizers! I like it :-) Btw you may want to get some stabilizers from wasdkeyboards to determine the exact dimensions & placement: http:\/\/www.wasdkeyboards.com\/index.php\/products\/keyboard-parts-1\/cherry-mx-plate-mounted-stabilizer-clips-2pcs.html Hey don't forget to \"butterfly\" the switch cutouts, a-la phantom. Check this post from the KeyPoard thread, with dimensions: http:\/\/geekhack.org\/showwiki.php?title=Island:26845&p=530064&viewfull=1#post530064 Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Sat, 03 March 2012, 15:24:40 Quote from: Dox;533995 Tell me what you think!$280 for just the plastic case? That does seem to be a bit much. In general, I think people are willing to pay premium for metal cases that have been popping up recently because they represent something very different from the norm where most keyboards are made out of plastic.\n\nHave you done\/considered shopping around for CNC aluminum\/steel pricing? Sharp edges would not be a problem there. If it's possible to make the switch plate mirror-able, then it would save some money as well.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Sat, 03 March 2012, 15:30:54\nTo save cost I would be happy with a flat mounting plate\/electronics\/hardware, and a printout to help build a cardboard case.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: fim on Sat, 03 March 2012, 19:20:31\nI liked the initial idea of the aluminium case and 280$for a plastic case seems a bit high, so I'd say stick with metal \\m\/ Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Sat, 03 March 2012, 20:17:09 Metal case please. :D The$400ish price tag isn't an issue as far as I'm concerned, but only if it takes at least another 2 months or so. Dorkvader, could you put me on your interest list? I'll be in for one if it's not much more expensive than $400. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 03 March 2012, 21:36:04 Quote from: dirge;534015 put me on the list for one please. Quote from: ped;534320 Metal case please. :D The$400ish price tag isn't an issue as far as I'm concerned, but only if it takes at least another 2 months or so. Dorkvader, could you put me on your interest list? I'll be in for one if it's not much more expensive than $400. I'll add you both to the file and update later. Yeah, I'm willing to pay for a metal case, but I think$280 for plastic is just too much.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Sat, 03 March 2012, 23:33:07\nYeah, I'm willing to pay for a metal case, but I think $280 for plastic is just too much. I agree. Title: [Interest Check] Custom split ergo keyboard. Post by: sicyo on Sun, 04 March 2012, 09:08:17 I still like the shape but 280 is a bit much for plastic and one of my main interests here was getting the natural aluminum. Maybe we can find a newer machine shop with less of a steady business who would make it for cheaper. To relay to the rest of the interested people in this thread: the machine shop I know can't do it without stopping production on their business and even then it would still be really expensive. They did recommend laser cutting Dox's most recent Aluminum design though. Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Sun, 04 March 2012, 10:21:47 If a metal case is out of the question, then we should get one bad-ass type of plastic to use, and make it THICK. Title: [Interest Check] Custom split ergo keyboard. Post by: seferphier on Sun, 04 March 2012, 10:39:40 interested. willing to pay:$200-250\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Ascaii on Mon, 05 March 2012, 02:33:00\nOnly interested in heavy metal. I would also be against having both options because it will drive up the prices considerably.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: heuristicist on Mon, 05 March 2012, 04:30:59\nI seem to be the first going this way (unless I've missed a post) but I don't care regarding metal vs. plastic. I'm in it for the split ergo layout with mechanical switches! Go for whatever's cheapest!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Mycroftxxx on Thu, 08 March 2012, 11:03:53\nI would be interested in make a purchase depending on final price\/material.\nI'ld also be interented in helping out with the Firmware development and hardware selection. \u00a0Can anyone point me to the individual \"In Charge\" of this.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Thu, 08 March 2012, 11:24:27\nQuote from: Mycroftxxx;539103\nI would be interested in make a purchase depending on final price\/material.\nI'ld also be interented in helping out with the Firmware development and hardware selection. \u00a0Can anyone point me to the individual \"In Charge\" of this.\n\nDox\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Fri, 09 March 2012, 13:31:24\nQuote from: Mycroftxxx;539103\nI would be interested in make a purchase depending on final price\/material.\nI'ld also be interented in helping out with the Firmware development and hardware selection. \u00a0Can anyone point me to the individual \"In Charge\" of this.\n\nFirst, welcome to geekhack (haha, even though I'm new here myself).\n\nYup, Dox has the final say on everything, it's his project. \u00a0To some extent, hardware suggestions have been discussed in the thread.\n\nFor firmware, it's kind of me at the moment, since nobody else wanted to try writing one that used I2C to get the connector between the two halves down to 4 wires. \u00a0(Firmwares without that capability have already been written for other projects.) \u00a0That being said, I'm totally new to teensy development and figuring stuff out as I go, so I'm not really in a position to work with anyone... but you're quite free to write your own if you want. \u00a0If you do and it'd help, I'd be happy to open my forthcoming github account early and start posting my progress so we can share ideas.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sat, 10 March 2012, 00:24:53\nI think it'd be awesome if we got some collaboration going on this project.\n\nAfter thinking about it, I think metal is the way to go, and steel may well be better than aluminium. I'm thinking that the heavier metal will have a larger normal force on the desk, and therefore more friction and less slipping. Also, I really like items with heft!\n\nI'm thinking either a clearcoated or stainless steel, or matte black\/red would look the best, but that's all small stuff compared with firmware, etc.\n\nIf Y'all want to point me in the direction of some good firmware on teensy\/atmel hardware, I'd be interested in looking at your development. I've got no experievce, so it's dubious as to how much I could help out.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Sat, 10 March 2012, 02:21:06\nHere's the page of references I've been keeping as I figure stuff out: [ATTACH=CONFIG]43378[\/ATTACH]. \u00a0I'll start posting code when I have some :)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: speedkills on Sat, 10 March 2012, 03:45:57\nI'm in for one assembled under $500. How deep are the cases? If cabling is an issue could you use RJ45 cables on the bottom of the units and plug the cables in facing down? Two RJ45 flat cables are very flexible, flat, and are pretty small when laid on top of each other. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 10 March 2012, 17:00:16 Added, and updated. I think we determined that RJ45 (or 4P4C, etc.) are too tall to fit, though if it's close, we may be able to make it work out. Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Sun, 11 March 2012, 00:32:35 Quote from: dorkvader;540798 I think it'd be awesome if we got some collaboration going on this project. After thinking about it, I think metal is the way to go, and steel may well be better than aluminium. I'm thinking that the heavier metal will have a larger normal force on the desk, and therefore more friction and less slipping. Also, I really like items with heft! I'm thinking either a clearcoated or stainless steel, or matte black\/red would look the best, but that's all small stuff compared with firmware, etc. I agree, but I've got a stupid limit of 1.4kg on my keyboard tray at work. I'm sure I could manage 2kg, but that really would be it. The biggest surprise anyone gets with a maltron is it's very low weight. A lot of people associate low weight with cheapness - which I think is kind of normal behaviour, but it clashes with the price of titanium and carbon fibre... A good solid heft to the ergodox would be welcome. Title: [Interest Check] Custom split ergo keyboard. Post by: faffer on Sun, 11 March 2012, 04:38:59 Quote from: dorkvader;540798 I think it'd be awesome if we got some collaboration going on this project. After thinking about it, I think metal is the way to go, and steel may well be better than aluminium. I'm thinking that the heavier metal will have a larger normal force on the desk, and therefore more friction and less slipping. Also, I really like items with heft! Hot glue + lead fishing weights + whatever case material is cheapest. Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Sun, 11 March 2012, 07:43:46 Quote from: dorkvader;540798 I think it'd be awesome if we got some collaboration going on this project. After thinking about it, I think metal is the way to go, and steel may well be better than aluminium. I'm thinking that the heavier metal will have a larger normal force on the desk, and therefore more friction and less slipping. Also, I really like items with heft! I'm thinking either a clearcoated or stainless steel, or matte black\/red would look the best, but that's all small stuff compared with firmware, etc. If Y'all want to point me in the direction of some good firmware on teensy\/atmel hardware, I'd be interested in looking at your development. I've got no experievce, so it's dubious as to how much I could help out. I'd take a variation on that and get it done in aluminum and an optional brass plate insert for those that want extra weight, that way it would still be metal and people who have weight restrictions imposed by their keyboard trays can still use it. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sun, 11 March 2012, 11:38:44 What about galvanic corrosion? I suppose we could solve that with some thin plastic \"plate\" spacing it out. Bytheway, Dox says the volume is 100.69 cm^3\/hand. If that's the case (haha), and we go with steel (7.6 g\/cm^3) then the weight of the case is \"only\" 1.58 kg. So even with steel, we'd likely be able to get it under 2Kg, depending on the weight of the switches, PCB, etc. (an AL case is ~543 grams) Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Sun, 11 March 2012, 13:09:30 Maybe sandwiched acrylic ala litster? Just throwing another option out there as I don't care that much about the case material relatively speaking, as long as it's reasonably priced and isn't plain plastic. Title: [Interest Check] Custom split ergo keyboard. Post by: funkymeeba on Mon, 12 March 2012, 01:33:56 I'm not sure how much litster-style acrylic cases would cost, but I will say that those cases he made are very nice, and I certainly wouldn't mind a similar thing for these boards. Title: [Interest Check] Custom split ergo keyboard. Post by: Swede on Mon, 12 March 2012, 01:59:00 I would recommend to stay with aluminum. Price\/kg is about$5 and then ofc comes cutting and machining.\nI might be able to help with machining for free in return of one of these. But giving no guarantees.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Tue, 13 March 2012, 00:02:40\nI'm pretty sure the PMMA litster-style case would be about the same cost. Making these are pretty time\/labour intensive, and that's what we're really paying for, here.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ped on Tue, 13 March 2012, 06:54:24\nQuote from: Swede;543067\nI would recommend to stay with aluminum. Price\/kg is about $5 and then ofc comes cutting and machining. I might be able to help with machining for free in return of one of these. But giving no guarantees. Yes please! :D I was hoping you'd see this project and take interest in it. Title: [Interest Check] Custom split ergo keyboard. Post by: Swede on Tue, 13 March 2012, 08:42:19 Quote from: ped;544371 Yes please! :D I was hoping you'd see this project and take interest in it. I would be happy to provide any help with this. But again I will not guarantee anything. This all weighs on me having time to do the programming and getting approval from my school. And both are far from certain. Also shipping from Sweden is expensive as hell. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 13 March 2012, 11:23:01 Those who think 280$ is too much for a plastic case from shapeways.....\n\nI got a quote from http:\/\/www.firstcut.com\/\n[ATTACH=CONFIG]43936[\/ATTACH][ATTACH=CONFIG]43937[\/ATTACH][ATTACH=CONFIG]43938[\/ATTACH]\n\nMaybe Swede could do better.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Swede on Tue, 13 March 2012, 11:33:29\nQuote from: Dox;544540\nThose who think 280$is too much for a plastic case from shapeways..... I got a quote from http:\/\/www.firstcut.com\/ (Attachment) 43936[\/ATTACH] (Attachment) 43937[\/ATTACH] (Attachment) 43938[\/ATTACH] Maybe Swede could do better. Hahaha! HOLY ****! But I'm not that suprised :) Biggest cost for me will be the watercutter. If you can give me 2D drawings I can check if I can make these. Title: [Interest Check] Custom split ergo keyboard. Post by: Findecanor on Tue, 13 March 2012, 11:54:38 Bah! Because the keyboard is flat, the case\/plate does not need to be fancy. If you use PCB-mounted switches then the case would not have to be more complex than a box, basically. You don't even need stabilizers for the thumb keys -- the Kinesis does not have any and people never complain about that. You could also design the case so that only the top needs to be a remotely complex shape. Integrate the plate (if you really think that it is necessary) into that and bolt the PCB to it. Then the bottom could be a simple flat piece of sheet metal or plastic which you bolt on with the help of nylon spacers. Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Tue, 13 March 2012, 13:03:34 Quote from: Swede;544411 I would be happy to provide any help with this. But again I will not guarantee anything. This all weighs on me having time to do the programming and getting approval from my school. And both are far from certain. Also shipping from Sweden is expensive as hell. I live in Europe, shipping shouldn't be incredibly expensive to me. :P And if you can make it cheaper than Dox can please (with cherry on top) get permission from your school! :D I'll see if I can figure out a way to make time slow down so you have time to do the programming :P Title: [Interest Check] Custom split ergo keyboard. Post by: boli on Tue, 13 March 2012, 13:09:39 The case material doesn't matter much to me. Both my first and second favorite keyboards (Kinesis Advantage and TrulyErgonomic respectively) have plastic cases, and they work well. Of course an aluminum keyboard such as the Apple is sleek and good-looking, but function is more important IMO. As long as it's well made it's all good. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Tue, 13 March 2012, 14:48:06 I don't care about the case either. In fact I'll be happy getting this without a case if it will save me$200. I can always build a case with cardboard or InstaMorph.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: jwaz on Tue, 13 March 2012, 18:02:59\nDon't know how I missed this thread so long but... DOX these are awesoem! Count me intereseted... especially if under 200\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Tafryn on Tue, 13 March 2012, 18:41:30\nI have no preference for either a metal or a plastic case, but I think there should only be one case option to cut down on costs. If the chosen material doesn't meet everyone's needs, there's always the option of just grabbing the PCB and making a custom case out of stone, wood, sheep, or whatever material suits your fancy.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Icarium on Wed, 14 March 2012, 03:14:39\nMaybe I'm alone in this but from a scientific point of view a PCB mounted prototype without any case sounds entirely reasonable. Dox, would you mind sharing the layout? Maybe I can make a prototype at work. Don't worry I would still buy one. ;)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: seferphier on Wed, 14 March 2012, 04:28:03\ni think it might be cheaper just to buy a 3D printer and printing the cases in plastic.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Wed, 14 March 2012, 06:48:14\nSwitches would be harder to get if they were pcb mounted\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Wed, 14 March 2012, 16:40:13\nQuote from: ironman31;545598\nSwitches would be harder to get if they were pcb mounted\n\nIt's perfectly good to use plate mount switches, especially for a prototype.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Wed, 14 March 2012, 17:08:59\nQuote from: PrinsValium;546062\nIt's perfectly good to use plate mount switches, especially for a prototype.\n\n? I'm saying I am against pcb mounted switches.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Wed, 14 March 2012, 18:46:08\nThat is a bit of a YMMV. For example, all of my switch donor boards are PCB mounted POS boards, so it's far easier and cheaper for me to come up with PCB mount switches than plate mount. Note that both can be plate mounted, it'd just be up to the PCB board designer if they can account for the extra holes. Of course, the extra legs on PCB mount switches can be cut off, but that's not really an option for me as I need them to be reusable for my own projects :)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Wed, 14 March 2012, 20:08:03\nQuote from: Parak;546195\nThat is a bit of a YMMV. For example, all of my switch donor boards are PCB mounted POS boards, so it's far easier and cheaper for me to come up with PCB mount switches than plate mount. Note that both can be plate mounted, it'd just be up to the PCB board designer if they can account for the extra holes. Of course, the extra legs on PCB mount switches can be cut off, but that's not really an option for me as I need them to be reusable for my own projects :)\n\nIt's a little harder to find brand new pcb mx blues from donor boards, and a little less hard for browns. Not to mention, I'm not even sure they have pcb reds.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Wed, 14 March 2012, 20:20:57\nQuote from: ironman31;546263\nIt's a little harder to find brand new pcb mx blues from donor boards, and a little less hard for browns. Not to mention, I'm not even sure they have pcb reds.\n\nKinesis uses PCB reds with pins AND diodes (MX1A-L1DW) in their LF model. They sell a pack of 15 for $15. Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Wed, 14 March 2012, 20:50:18 Quote from: sordna;546270 Kinesis uses PCB reds with pins AND diodes (MX1A-L1DW) in their LF model. They sell a pack of 15 for$15.\n\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Wed, 14 March 2012, 20:56:20\nMaybe it's a good idea that the PCB (whether we go with a plate or not) has the holes to acommodate pins and diodes, even if PCB\/dioded switches are not necessarily used.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: inaneframe on Wed, 14 March 2012, 23:56:16\nJust to re-iterate, I'm still down for 3, possibly more.\n\nDox, you're beautiful.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Thu, 15 March 2012, 00:44:59\nQuote from: ironman31;546096\n? I'm saying I am against pcb mounted switches.\n\nOk, I should have expressed that more precisely.\n\nIt's perfectly fine to use plate mount switches where there is supposed to be PCB mounted ones, especially for a prototype.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Icarium on Thu, 15 March 2012, 04:25:21\nQuote from: PrinsValium;546465\nOk, I should have expressed that more precisely.\n\nIt's perfectly fine to use plate mount switches where there is supposed to be PCB mounted ones, especially for a prototype.\n\nI was just suggesting PCB mount because that seems easier to accomplish quickly.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Thu, 15 March 2012, 04:43:46\nThere is no big difference between PCB and plate mounted switches. The only thig is that there are two extra plastic pins to orient the PCB mounted switches better. This means that it is completely possible to use plate mounted switches instead where there is supposed to be PCB mounted ones. It only takes some more care to make sure the switches are soldered in straight.\n\nTo use PCB mount switches on a PCB that is not designed with the two extra alignment holes the extra plastic pins needs to be cut off. If there is room on the PCB it can be a good idea to include the extra alignment holes even if the PCB is intended to be used for plate mounting, since this makes it possible to use either plate or PCB mounted switches.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: geekabit on Thu, 15 March 2012, 08:42:48\nI'm interested, if under 200 EUR\/USD\/GBP\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: geekabit on Thu, 15 March 2012, 08:49:47\nI was wondering, why connect both halves together and only one hand to USB. Wouldn't it be more flexible to give both halves their own processor and USB cable? That way you could even decide to use only one half for single-handed typing. You could even incorporate a USB hub in the back, so you can daisy-chain the keyboard and plug in your mouse as well.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Thu, 15 March 2012, 09:59:41\nQuote from: PrinsValium;546572\nThere is no big difference between PCB and plate mounted switches. The only thig is that there are two extra plastic pins to orient the PCB mounted switches better. This means that it is completely possible to use plate mounted switches instead where there is supposed to be PCB mounted ones. It only takes some more care to make sure the switches are soldered in straight.\n\nThe plastic pins are not intended to help installation\/soldering, their main benefit is stability\/sturdiness. A regular MX switch with only 2 thin terminals to hold it, especially considering they are offset to one side of the switch, cannot withstand pulling keycaps. I've tried both types of switches in my kinesis mod (http:\/\/geekhack.org\/showwiki.php?title=Island:26579) and I know. A plate-mounted switch with diodes, has a better chance of surviving without pins, but a normal switch won't hold over time unless you never pull your keycaps.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Thu, 15 March 2012, 10:30:12\nI don't really think the switch modules were designed with keycap pulling in mind.. The pegs (I guess this is a less confusing word than pin in this case) could possibly contribute to mechanical stability under normal usage as well though. But I still think the main design goal is to make sure the switches are mounted straight. Using the specified diameter for the lead holes, there is quite enough rotational play to allow for messed up functionality.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Parak on Thu, 15 March 2012, 10:49:23\nQuote from: geekabit;546635\nI was wondering, why connect both halves together and only one hand to USB. Wouldn't it be more flexible to give both halves their own processor and USB cable? That way you could even decide to use only one half for single-handed typing.\n\nThis was discussed earlier in the thread, and is rather complicated to implement. For one, the two halves still need to connect to each other in some way because certain key functionality doesn't pass from one usb keyboard to another. In addition, there needs to be specific firmware logic that is then able to treat the two separate controllers and matrices as one in some way, considering the key map assignments in dual and standalone modes and such.\n\nQuote from: geekabit;546635\nYou could even incorporate a USB hub in the back, so you can daisy-chain the keyboard and plug in your mouse as well.\n\nMost likely there's no room for one, and if anything I'd think that it'd be a diy thing for individual people if they want to do that sort of thing. Maybe someday we'll have a free and open source controller\/firmware implementation with all these things built in, but one can only dream [of enough free time to focus on something like that].\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Thu, 15 March 2012, 13:00:33\nQuote from: PrinsValium;546688\nI don't really think the switch modules were designed with keycap pulling in mind.. The pegs (I guess this is a less confusing word than pin in this case) could possibly contribute to mechanical stability under normal usage as well though. But I still think the main design goal is to make sure the switches are mounted straight. Using the specified diameter for the lead holes, there is quite enough rotational play to allow for messed up functionality.\n\nAnyway, the pcb should have the holes, and folks are free to use whatever switches they like. For plate mounted switches without a plate, I would recommend hotgluing them on the PCB before soldering. Personally I love switches with pegs AND diodes, they are solid strong!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Necroleachate on Wed, 21 March 2012, 12:00:25\nI dream about a keyboard like this.\nOnly con is price.\nIf it gets below $200 I would consider buying it. Title: [Interest Check] Custom split ergo keyboard. Post by: jblack801 on Wed, 21 March 2012, 13:25:55 Quote from: Necroleachate;552569 I dream about a keyboard like this. Only con is price. If it gets below$ 200 I would consider buying it.\n\nI'm right there with you...\n\nConsidering if price reaches sub $200 range. Title: [Interest Check] Custom split ergo keyboard. Post by: Findecanor on Wed, 21 March 2012, 13:54:16 Quote from: Parak;546704 This was discussed earlier in the thread, and is rather complicated to implement. For one, the two halves still need to connect to each other in some way because certain key functionality doesn't pass from one usb keyboard to another. In addition, there needs to be specific firmware logic that is then able to treat the two separate controllers and matrices as one in some way, considering the key map assignments in dual and standalone modes and such. That depends on how the user wants to configure his keyboard. Not everyone needs a hardware layer. I think that the firmware should be one firmware downloaded individually to each keyboard via USB. On boot, each keyboard should auto-detect whether it is left or right (by a pin on the PCB), where it get its power from USB (Master or Stand-alone) or link-cable (Slave) and act accordingly. Each keyboard should store its own keymap. A special key combo to enter a Remap (like Kinesis Remap key) could be executed on either keyboard. When in Slave mode, the keyboard should handle keymap remapping commands from the Master through the link cable. That would mean that if you want to remap the keyboards or use a hardware layer, then you need the link cable. If you remap the keyboards and then reconnect both through USB then they should remember the keymaps. Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Wed, 21 March 2012, 15:06:34 If you're willing to consider them truly separate keyboards when connecting them separately, it might be practical. But DOX specifically said he'd use at most 1 Teensy and 1 I\/O expander. On the plus side, if DOX changes his mind, treating the 2nd Teensy as an I\/O expander until proper dual Teensy firmware could be written should be fairly trivial. Or if he doesn't, I suppose one could always buy another Teensy, put it inside an Altoids can with a few connectors (which I think looks really cool, lol), and use that as the right hand side to save desk space when they only want to use the left. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Wed, 21 March 2012, 17:46:34 Quote from: ic07;552763 If you're willing to consider them truly separate keyboards when connecting them separately, it might be practical. But DOX specifically said he'd use at most 1 Teensy and 1 I\/O expander. This. I got some HDMI connectors today to do some prototyping. Those pins tiny! 0.5mm pitch. Anyone know the best way to solder those with a standard soldering iron? [ATTACH=CONFIG]45211[\/ATTACH][ATTACH=CONFIG]45212[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: OPTiK on Wed, 21 March 2012, 20:15:37 Quote from: Dox;552911 This. I got some HDMI connectors today to do some prototyping. Those pins tiny! 0.5mm pitch. Anyone know the best way to solder those with a standard soldering iron? (Attachment) 45211[\/ATTACH] (Attachment) 45212[\/ATTACH] A really fine tip with fine guage wire lol. I could do that with my 12 watt soldering iron, doubt you can do it with a radio shack iron. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Wed, 21 March 2012, 20:34:35 I have done the right hand PCB layout. I'll add the option for PCB mounted switch as well as diodes inside the switch. [ATTACH=CONFIG]45248[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 21 March 2012, 20:49:19 Quote from: OPTiK;553025 A really fine tip with fine guage wire lol. I could do that with my 12 watt soldering iron, doubt you can do it with a radio shack iron. Alternatively, you can just flood over all the pins with a bunch of solder bridges, then suck off the excess with (normally) some copper braid. Those are surface mount, right? Will there be PCB support for if I want to -say- get some through-hole ones? Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Wed, 21 March 2012, 20:58:03 I'm getting excited Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Wed, 21 March 2012, 21:10:47 Quote from: dorkvader;553054 Alternatively, you can just flood over all the pins with a bunch of solder bridges, then suck off the excess with (normally) some copper braid. Those are surface mount, right? Will there be PCB support for if I want to -say- get some through-hole ones? Yes those are surface mount. I would need the datasheet of the connector to check if the holes would interfere. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Wed, 21 March 2012, 21:50:28 Quote from: Dox;553042 I have done the right hand PCB layout. I'll add the option for PCB mounted switch as well as diodes inside the switch. (Attachment) 45248[\/ATTACH] How about you make the PCB accommodate cherry switches that include the diodes? (and for folks not using switches with diodes, they can still surface-solder diodes at the same soldering points. Shouldn't be hard to make the PCB take DW switches (with pins, with diodes). Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Wed, 21 March 2012, 21:56:47 Quote from: sordna;553089 Quote from: Dox;553042 I have done the right hand PCB layout. I'll add the option for PCB mounted switch as well as diodes inside the switch. (Attachment) 45248[\/ATTACH] How about you make the PCB accommodate cherry switches that include the diodes? (and for folks not using switches with diodes, they can still surface-solder diodes at the same soldering points. Shouldn't be hard to make the PCB take DW switches (with pins, with diodes). .... Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Thu, 22 March 2012, 01:26:16 Quote from: Dox;552911 I got some HDMI connectors today to do some prototyping. [...] This doesn't mean I'm too late with the i2C firmware, does it? Couldn't say I'm close yet, but I'm making progress... Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Thu, 22 March 2012, 01:28:17 I plan to get red switches from Kinesis btw, they only sell pcb-mounted switches with pins and diodes, here's a couple I got a while back (photo is from my wiki. (http:\/\/geekhack.org\/showwiki.php?title=Island:26579) (http:\/\/geekhack.org\/attachment.php?attachmentid=39304&d=1328162640) Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Thu, 22 March 2012, 02:41:50 Dead set on using an HDMI connector? That's way beyond my soldering skill level! D: Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Thu, 22 March 2012, 09:11:13 ic07, you're not too late, I'm using HDMI until you get something working, but I want this to progress. sordna, switches with pins and diodes will be supported. Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Thu, 22 March 2012, 19:05:03 Quote from: dorkvader;553054 Alternatively, you can just flood over all the pins with a bunch of solder bridges, then suck off the excess with (normally) some copper braid. Those are surface mount, right? Will there be PCB support for if I want to -say- get some through-hole ones? After a few tries you get the amount of solder correct. After that it is a smooth experience (http:\/\/www.youtube.com\/watch?v=t06malVew40) =) Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Fri, 23 March 2012, 00:30:51 Yeah, but I'm still a little worried about all the relatively fine pitch chips I need to solder for a project I'm getting into. Title: [Interest Check] Custom split ergo keyboard. Post by: laffindude on Fri, 23 March 2012, 01:36:40 Hi. I am still in this even if I don't really check the thread. I see we're still stuck on the case. I am gonna fire off an email to a friend to see if he can help with the aluminum case. Title: [Interest Check] Custom split ergo keyboard. Post by: tradet on Sat, 24 March 2012, 18:26:11 Sounds tempting. Interested depending on the price.$200 maybe?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: jblack801 on Tue, 27 March 2012, 00:37:51\nQuote from: PrinsValium;554008\nAfter a few tries you get the amount of solder correct. After that it is a smooth experience (http:\/\/www.youtube.com\/watch?v=t06malVew40) =)\n\nI may be a bit of a soldering amateur, but damn that was awesome.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Tue, 27 March 2012, 00:47:00\nThis video is very impressive, such CLEAN soldering !!!\n\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Mon, 02 April 2012, 22:09:13\nGot I2C working the other day! \u00a0And spring break's coming up, so I'm hoping (God willing) to have at the very least some beta quality firmware done by the end of next week. \u00a0I'll post my documentation and code when I get it working. \u00a0Sorry it's taken so long, but thanks for being patient :) .\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Wed, 04 April 2012, 01:44:27\nThis is very good news, ic07! I am impressed with both your dedication and your results. We are patient here: Time is what is necessary for proper design.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Fri, 06 April 2012, 06:02:33\nG'damn these things are small. I ordered a bunch of 0402 components for using when reconstructing the Teensy directly on the main board. Time to do some practice I think, buying a finer tipped soldering iron, and finding someone willing to borrow me a stereo loupe perhaps...\n\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Fri, 06 April 2012, 07:59:30\nTin both pads, hold the 0402 down to the board with tweezers hit 1 pad with the soldering iron briefly. \u00a0Check to see if the other pad got sufficiently heated to be properly soldered. \u00a0Sometimes it happens. \u00a0Then finish it out.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dirge on Fri, 06 April 2012, 09:32:28\nkeep it up guys, in for at least one regardless of price.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: QuinRiva on Fri, 06 April 2012, 10:37:33\nI've been interested in making something along these lines for a while, and I've done a quick mock up based on Dox's design. \u00a0Mine will largely be sheetmetal based as that is the tools I have access to, so I'm looking at having the keys plate mounted and having the left and right keyboard mounted on a chair. \u00a0As far as curvature goes that isn't really much of a problem for me as I can do that pretty easily, but I've been having trouble trying to determine the best direction for curvature and the dimensions.\n\nAlso what have you used to draw the model and where have you sourced the switch models?\n\n[ATTACH=CONFIG]47545[\/ATTACH]\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 06 April 2012, 12:04:40\nQuote from: ic07;565242\nGot I2C working the other day! \u00a0And spring break's coming up, so I'm hoping (God willing) to have at the very least some beta quality firmware done by the end of next week. \u00a0I'll post my documentation and code when I get it working. \u00a0Sorry it's taken so long, but thanks for being patient :) .\nGreat! I'll wait for your documentation!\n\nQuote from: PrinsValium;568588\nG'damn these things are small. I ordered a bunch of 0402 components for using when reconstructing the Teensy directly on the main board. Time to do some practice I think, buying a finer tipped soldering iron, and finding someone willing to borrow me a stereo loupe perhaps...\n\nMan, thee things are sooo tiny, you should have gone with some 0603 or 0805.\n\nQuote from: QuinRiva;568863\nI've been interested in making something along these lines for a while, and I've done a quick mock up based on Dox's design. \u00a0Mine will largely be sheetmetal based as that is the tools I have access to, so I'm looking at having the keys plate mounted and having the left and right keyboard mounted on a chair. \u00a0As far as curvature goes that isn't really much of a problem for me as I can do that pretty easily, but I've been having trouble trying to determine the best direction for curvature and the dimensions.\n\nAlso what have you used to draw the model and where have you sourced the switch models?\n\n(Attachment) 47545[\/ATTACH]\nInteresting, are you going to use a curved PCB or just and wire it?\nI used SolidWorks for the model and I did the switch myself from the pictures and dimensions here (http:\/\/www.cherrycorp.com\/english\/switches\/key\/mx.htm).\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Fri, 06 April 2012, 16:47:26\nQuote from: alaricljs;568654\nTin both pads, hold the 0402 down to the board with tweezers hit 1 pad with the soldering iron briefly. \u00a0Check to see if the other pad got sufficiently heated to be properly soldered. \u00a0Sometimes it happens. \u00a0Then finish it out.\n\nYeah, the video pretty much shows how to do it, nothing new there either really. The thing is though, I could barely grab one of them with my \"pointy\" tip tweezers. Have to go needle tip with these suckers. I can probably fit ten or so of them on the tip of my soldering iron as well... Have to consider spacing on the layout as well to be able to get down to all solder pads.\n\nQuote from: Dox;568947\nMan, thee things are sooo tiny, you should have gone with some 0603 or 0805.\n\nI am going to seriously consider this.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Icarium on Fri, 06 April 2012, 17:36:05\nQuote from: alaricljs;568654\nTin both pads, hold the 0402 down to the board with tweezers hit 1 pad with the soldering iron briefly. \u00a0Check to see if the other pad got sufficiently heated to be properly soldered. \u00a0Sometimes it happens. \u00a0Then finish it out.\n\nDon't do that. If the tin on the other pad doesn't heat up properly the component will be raised above the pad. Tin one pad, place component and solder in place, then do the other pad.\n\nI have a stereo microscope and some very fine tips. It helps but it doesn't make the shaking go away. ;D\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Findecanor on Fri, 06 April 2012, 17:55:28\nQuote from: QuinRiva;568863\nAs far as curvature goes that isn't really much of a problem for me as I can do that pretty easily, but I've been having trouble trying to determine the best direction for curvature and the dimensions. (Attachment) 47545[\/ATTACH]\nIt is not that easy. The edges of each switch hole have to be straight and parallel or the switches will not fit properly.\nYou would have to separate the columns ...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: jblack801 on Fri, 06 April 2012, 17:57:46\nI hope it gets easier in the final product. I am comfortable with switch sized leads, but I don't own a microscope or steady hands for components this tiny. hehe\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: QuinRiva on Sat, 07 April 2012, 00:58:06\nDeflection is pretty small (0.3mm difference in height between the edge and the centre, and 0.2mm in the y-axis, but the later can be accounted for by bend deductions). \u00a0However I take your point, so I might try to knock something up with a transverse FR curve along the x-axis. \u00a0As far as precision goes, my pressbrake is rated at 0.002mm so that shouldn't be an issue:\n[ATTACH=CONFIG]47655[\/ATTACH]\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: QuinRiva on Sun, 08 April 2012, 02:53:20\nI've removed all curvature across the key-holes, and I'm working on the edges. \u00a0I've made the corners square for the moment, but I think that I've worked out a way around that, but it uses a crap load more metal.\n\nDox, is it possible to get a dimensional drawing of your design?\n\n[ATTACH=CONFIG]47771[\/ATTACH]\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sun, 08 April 2012, 15:00:26\nQuinRiva: that's a good looking keywell. If we could get kinesis-like keywells on this project, it would be amazing!\n\nCouple of manufactureing difficulties:\n1. it would be significantly harder to make. I imagine the only cost-effective way to get that shape would be to stamp it\n2. It raises the question on how to make a \"base\" for it. I wolud be fine with what is shown in your image, having an \"open\" keyboard like that, but if there needs to be some sort of case made, I imagine it would be difficult\n3. Making a PCB for that would be difficult, involving either multiple PCBs with connectors, or some sort of shaped\/curved\/flexible PCB\n\nNevertheless, the design is good, and all the issues aren't insurmountable. I imagine one could solder it point-to-point without too much difficulty. I don't know what it'd be to stamp them, though.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hoggy on Sun, 08 April 2012, 15:44:03\nMaltron keyboards are all signed by the person who makes them. \u00a0Any plans for the people involved in this project to do the same?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Input Nirvana on Sun, 08 April 2012, 16:03:26\n\nI like signing them too...how cool is that?????\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: QuinRiva on Mon, 09 April 2012, 03:17:52\nQuinRiva: that's a good looking keywell. If we could get kinesis-like keywells on this project, it would be amazing!\n\nCouple of manufactureing difficulties:\n1. it would be significantly harder to make. I imagine the only cost-effective way to get that shape would be to stamp it\n2. It raises the question on how to make a \"base\" for it. I wolud be fine with what is shown in your image, having an \"open\" keyboard like that, but if there needs to be some sort of case made, I imagine it would be difficult\n3. Making a PCB for that would be difficult, involving either multiple PCBs with connectors, or some sort of shaped\/curved\/flexible PCB\n\nNevertheless, the design is good, and all the issues aren't insurmountable. I imagine one could solder it point-to-point without too much difficulty. I don't know what it'd be to stamp them, though.\n\n1. \u00a0Not really, as I have stated I intend to use a laser and press-brake to manufacture. \u00a0Cost effectiveness is difficult to gauge as the large number of folds, most of which need to be accurate, demand a good-press brake and experienced operator. \u00a0I have access to a good pressbrake and my operator is an Astro robot. \u00a0However Dox's design could be manufactured on the cheap using sheet metal particularly if he squared the corners.\n2. \u00a0I've already designed the base (see pictures below); however I don't intend to have an enclosure that sits around the keys. \u00a0It wouldn't be too hard to make, I just don't think that it is necessary for plate mounted keyboards.\n3. \u00a0Not really, I intend to just use a flexible PCB (http:\/\/www.instructables.com\/id\/DIY-Flexible-Printed-Circuits\/). \u00a0They can be a bit tricky to solder on, so I think that the best option is to use a solid PCB for the core components, and then a flexible PCB for the keys.\n\nHope that makes some sense. \u00a0Keep up the suggestions though, as this is my first time at this sort of thing.\n\n[ATTACH=CONFIG]47882[\/ATTACH][ATTACH=CONFIG]47883[\/ATTACH][ATTACH=CONFIG]47884[\/ATTACH]\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Mon, 09 April 2012, 04:46:22\nI like the idea of the bend-to-create-a-case, but I don't like the curvature. First of all it's too exaggerated, the pinkies would likely suffer having to hit the edge columns at such an angle. Anyway, I would like this keyboard to be flat for the following reasons:\n\n1. It would make it much easier to type with one hand whenever you wanted to\n2. It would make it easier to type with 2-3 fingers on each hand (RSI battling technique)\n3. We don't need another Kinesis, whoever wants keywells can buy a pair from Kinesis with red or brown switches soldered in place and ready to go for just $90. Title: [Interest Check] Custom split ergo keyboard. Post by: Icarium on Mon, 09 April 2012, 15:16:26 Right, I was about to say the same thing as Sordna, just a little different. If you want keywells, buy Kinesis keywells and make the rest of the case. Kinesis keywells are plastic but that shouldn't be a problem because there are keys on top of it so you can't see it anyway. :) Apart from that I would say, if you're going for keywells make sure they're different from the Kinesis it would be much more interesting. Personally I am very much looking forward to the flat version as well. Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Mon, 09 April 2012, 16:03:18 Custom case for a pair of kinesis keywells sounds like a great spin off project for someone... Title: [Interest Check] Custom split ergo keyboard. Post by: Jim66 on Mon, 09 April 2012, 16:17:16 Quote from: Icarium;571685 Right, I was about to say the same thing as Sordna, just a little different. If you want keywells, buy Kinesis keywells and make the rest of the case. Kinesis keywells are plastic but that shouldn't be a problem because there are keys on top of it so you can't see it anyway. :) Apart from that I would say, if you're going for keywells make sure they're different from the Kinesis it would be much more interesting. Personally I am very much looking forward to the flat version as well. I agree with this too. I much prefer the idea of the original flat project. Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Mon, 09 April 2012, 18:08:12 Agreed. The curving keyboard is unappealing to my dollars. Title: [Interest Check] Custom split ergo keyboard. Post by: Findecanor on Mon, 09 April 2012, 19:13:14 I have made a 3D keyboard design that is a middle-ground between Dox's flat keyboard, Kinesis key wells and standard QWERTY. I made several physical models to try it out, both in clay and with key switches and test typed on them. I am still stumped on how to manufacture a small run and not cost a fortune. Anyway ... One conclusion that I came to is that I don't like the feeling when keys switches are angled too much. The ideal (for me) would actually be if all switches are pointing in the same direction but with curvature being from switches at different heights and with custom key caps. Slanted columns and traditional key caps may feel better than flat, but only if the curvature is very slight. Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Tue, 10 April 2012, 01:37:09 QuinRiva, what I forgot to say is that it looks like a really cool concept. If it ever goes ahead, please let me know. Please don't feel under appreciated. Title: [Interest Check] Custom split ergo keyboard. Post by: mbc on Tue, 10 April 2012, 05:30:26 About the cases. You could contact the guy that copied litster's case about producing your cases It would be a lot cheaper than aluminium Title: [Interest Check] Custom split ergo keyboard. Post by: QuinRiva on Wed, 11 April 2012, 03:41:02 I wasn't aware that the Kinesis Keywells were available separately, that would substantially simplify the manufacturing process. Does anyone know how I would go about buying the keywells (with Cherry Reds) and potentially the thumb area from Australia? Also does anyone know where I could get a dimensionalised drawing of the keywells? Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Wed, 11 April 2012, 10:50:26 Just go to http:\/\/kinesis-ergo.com\/ and you'll find contact info. Email them and ask, they sell parts and everything, including keywells with reds which they sell as an upgrade. Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Thu, 12 April 2012, 02:15:05 Beta firmware's ready :D . As far as I can tell from a little testing on my breadboard at least - it looks stable. The project is on github at https:\/\/github.com\/benblazak\/ergodox-firmware. The pertinent files at this point are probably: - The diagram of how i have it set up: [ATTACH=CONFIG]48135[\/ATTACH] (which is also here as an svg (https:\/\/raw.github.com\/benblazak\/ergodox-firmware\/master\/src\/keyboard\/ergodox\/_circuit-diagram.svg), but it looks like you'll have to download it to view it) - The text documentation for the Teensy 2.0 (https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/master\/src\/keyboard\/ergodox\/teensy-2-0.md) and MCP23018 (https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/master\/src\/keyboard\/ergodox\/mcp23018.md) code (which is less visually clear, but has lots more notes) - And the hex file (https:\/\/github.com\/downloads\/benblazak\/ergodox-firmware\/ergodox-firmware--20120411_2105.hex) of the current firmware build :) For notes on what it can do at the moment see the readme.md (on github) or the last commit message for the master branch. Let me know what you guys think :) . ::edit:: Wow, just realized I reversed the row pins for the MCP23018 in my diagram. It's correct in the .md file though. I'll have to fix the diagram later. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Thu, 12 April 2012, 11:24:41 Awesome job ic07! I'm going to order a few MCP23018 and modify my design accordingly. Now, what would be the best 4 wire connector\/cable. Title: [Interest Check] Custom split ergo keyboard. Post by: dirge on Thu, 12 April 2012, 11:34:10 This threads made me buy teensys and a breadboard.. I think I may be hooked... Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Thu, 12 April 2012, 12:07:44 4 pin Mini-DIN (http:\/\/en.wikipedia.org\/wiki\/Mini-DIN_connector#4-pin)? 4 conductor \"stereo\" 3.5mm TRRS (http:\/\/www.minute-man.com\/acatalog\/4_Conductor_3_5mm_Plugs_and_Jacks.html)? 2.5mm TRRS for silly smallness. RJ11 would be nice but I bet the jack is too big. Title: [Interest Check] Custom split ergo keyboard. Post by: uberben on Thu, 12 April 2012, 12:13:40 You could also go with a standard phone cable (http:\/\/en.wikipedia.org\/wiki\/4P4C#4P4C). Especially if this is going to be sold in volume, it would allow the end user to replace with whatever length and style (ie curly\/straight) they like by running over to the nearest dollar store. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Thu, 12 April 2012, 13:48:22 Curly phone cable would be ideal for this application! Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Thu, 12 April 2012, 17:18:02 A phone cable would be great but unfortunately the 4p4c socket is to high to fit in the case. The same goes for Mini-DIN. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Thu, 12 April 2012, 17:21:24 I'm sure there has to be low profile enough sockets... a lot of phones\/headsets seem to have pretty compact sockets on them. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Thu, 12 April 2012, 18:06:46 Quote from: sordna;574063 I'm sure there has to be low profile enough sockets... a lot of phones\/headsets seem to have pretty compact sockets on them. Sadly no. There is only 11.43mm from the top of the PCB to the top of the case so I would say that the maximum height for the connector is 8mm. The smallest 4p4c I found was about 15mm. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Thu, 12 April 2012, 18:17:17 Can't the PCB have a cutaway so that the socket has more room up and down? Of course the socket should be secured by the case, not by the PCB (you would need some flexible leads between socket and PCB). Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Thu, 12 April 2012, 18:36:25 Quote from: sordna;574103 Can't the PCB have a cutaway so that the socket has more room up and down? Of course the socket should be secured by the case, not by the PCB (you would need some flexible leads between socket and PCB). No, those sockets need to be soldered\/fixed on the PCB and even if I was doing that, the distance from the interior bottom to the top of the case is 16mm (13mm usable for a connector) it's still not enough. Let's find something else! Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Thu, 12 April 2012, 18:44:15 I still like the 3.5mm (or 2.5mm) TRRS best, especially aesthetically - as long as it's possible to make it safe from shorting Vcc and any of the other 3. It looks like the size limitations are going to keep things small enough for my taste whatever gets decided on though :) . If using 2 sockets is an option, have you looked at any of those small coaxial power connectors (http:\/\/en.wikipedia.org\/wiki\/Coaxial_power_connector)? Or something simple like a small 4 pin molex (http:\/\/en.wikipedia.org\/wiki\/Molex_connector)? (Actually, I used to think this connector would be too big and not very pretty, but now I'm starting to think it might look cool...) sordna: If you want a curly phone cable anyway, you could always cut the connectors off one and solder some others in their place. I've been sort of planning on making my own cable if I can, just to get the size and such just right. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Thu, 12 April 2012, 18:58:54 Quote from: ic07;574128 I still like the 3.5mm (or 2.5mm) TRRS best, especially aesthetically - as long as it's possible to make it safe from shorting Vcc and any of the other 3. It looks like the size limitations are going to keep things small enough for my taste whatever gets decided on though :) . If using 2 sockets is an option, have you looked at any of those small coaxial power connectors (http:\/\/en.wikipedia.org\/wiki\/Coaxial_power_connector)? Or something simple like a small 4 pin molex (http:\/\/en.wikipedia.org\/wiki\/Molex_connector)? (Actually, I used to think this connector would be too big and not very pretty, but now I'm starting to think it might look cool...) sordna: If you want a curly phone cable anyway, you could always cut the connectors off one and solder some others in their place. I've been sort of planning on making my own cable if I can, just to get the size and such just right. Yeah think that the TRRS option is the best for now. Avoiding to short the Vcc is easy, just put the power on the contact that is the furthest outside of the case. That way, there is no chance to short anything. I prefer to use cables\/connectors that are build for external use. That rules out the molex and ribbon cables. I can't seem to find a pcb mounted 4 contact TRRS 3.5 or 2.5mm. I have to continue searching. Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Thu, 12 April 2012, 19:47:40 Quote from: Dox;574136 I can't seem to find a pcb mounted 4 contact TRRS 3.5 or 2.5mm. I have to continue searching. http:\/\/search.digikey.com\/scripts\/DkSearch\/dksus.dll?x=0&y=0&lang=en&site=us&KeyWords=CP-43514-ND ? Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Thu, 12 April 2012, 19:50:19 Quote from: Dox;574136 I can't seem to find a pcb mounted 4 contact TRRS 3.5 or 2.5mm. I have to continue searching. Would this 2.5mm audio jack (http:\/\/www.digikey.ca\/product-detail\/en\/SJ1-42515TS\/CP1-42515TS-ND\/659902) work? Kps linked to it a while ago (I remembered because it was just just before I joined the forum and they were talking about I2C). Or maybe this 3.5mm audio jack (http:\/\/www.digikey.ca\/product-detail\/en\/SJ-43515TS\/CP-43515TS-ND\/368147) would be better - or maybe there's a different one on there that'd be preferable, I'm not really sure what some of the specs mean so I couldn't tell. :) Quote from: Dox;574136 Avoiding to short the Vcc is easy, just put the power on the contact that is the furthest outside of the case. What about things like if the connector gets plugged in to the right hand side first, and then shorts on the left hand side case (or some keys, or something)? Or am I just being paranoid now, lol. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Thu, 12 April 2012, 20:00:35 Thanks Parak, order placed! ic07, I prefer the 3.5mm as there is enough place for it and it will be more sturdy. No matter what side you plug first, with the power on the outside, I think there is no chance to short anything. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 13 April 2012, 15:53:31 ic07, I'm trying to compile your firmware but I get this error. Code: [Select] Compiling C: lib-other\/pjrc\/usb_keyboard\/usb_keyboard.cavr-gcc -c -mmcu=atmega32u4 -I. -gdwarf-2 -DF_CPU=16000000UL -Os -funsigned-char -funsigned-bitfields -ffunction-sections -fpack-struct -fshort-enums -Wall -Wstrict-prototypes -Wa,-adhlns=.\/lib-other\/pjrc\/usb_keyboard\/usb_keyboard.lst -I. -std=gnu99 -MMD -MP -MF .dep\/usb_keyboard.o.d lib-other\/pjrc\/usb_keyboard\/usb_keyboard.c -o lib-other\/pjrc\/usb_keyboard\/usb_keyboard.oLinking: firmware.elfavr-gcc -mmcu=atmega32u4 -I. -gdwarf-2 -DF_CPU=16000000UL -Os -funsigned-char -funsigned-bitfields -ffunction-sections -fpack-struct -fshort-enums -Wall -Wstrict-prototypes -Wa,-adhlns=lib-other\/pjrc\/usb_keyboard\/usb_keyboard.o -I. -std=gnu99 -MMD -MP -MF .dep\/firmware.elf.d lib-other\/pjrc\/usb_keyboard\/usb_keyboard.o --output firmware.elf -Wl,-Map=firmware.map,--cref -Wl,--relax -Wl,--gc-sections -lmc:\/winavr-20100110\/bin\/..\/lib\/gcc\/avr\/4.3.3\/..\/..\/..\/..\/avr\/lib\/avr5\/crtm32u4.o:(.init9+0x0): undefined reference to main'MAKE[1]: *** [firmware.elf] Error 1MAKE[1]: Leaving directory C:\/Users\/Dox\/GIT\/benblazak-ergodox-firmware-201e38c\/src'MAKE: *** [all] Error 2 I also tried your compiled .hex and nothing is happening. Any idea what's going on? Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Fri, 13 April 2012, 21:54:35 I think the compile error was from me using $(shell find ... '*.c') in the makefile (which in windows probably meant that no .c files were included in the build at all, lol). \u00a0Sorry, I forgot to think about that. \u00a0Hopefully it works now (using $(wildcard ... *.c)). As for the .hex, I just downloaded and retested it on my little setup, and it worked... What should happen is: - all the LEDs should go high for about 1 second (while USB initializes and we wait for drivers to load) - then all LEDs should go off unless one of the indicators is currently set (I have numlock on in the picture below) - it should wait for \"keypresses\" and generate them if they're detected Did I do the diagram wrong? I'll put an actual pic of my setup below just in case. breadboard setup: - note: row and column pins are disconnected; i don't have switches of any type at the moment, so i've been using temporary wires when i needed to test for keypresses [ATTACH=CONFIG]48226[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 13 April 2012, 23:26:45 Ok the hex file is working, I had my 2.2k resistors to the ground instead of vcc :doh:. I can now compile it too with the revised makefile. Thanks! Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sun, 15 April 2012, 11:44:15 I have tested the firmware on a breadboard and everything seem to work fine. I'm now modifying my 3d model with the 3.5mm TRRS and then the pcb. After 6 months, this is getting very close to the first prototype. Thanks to everyone who got involved in a way or an other until now! Title: [Interest Check] Custom split ergo keyboard. Post by: lorem3k on Sun, 15 April 2012, 22:04:52 You could probably use threaded 3.5mm connectors for extra connection strength. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 18 April 2012, 01:40:38 Quote from: lorem3k;575797 You could probably use threaded 3.5mm connectors for extra connection strength. Normally, I'm rather against those, but in this case, I think it's okay, as you can use non threaded connectors with most (All?) threaded jacks. I think the real issue now is finding threaded TRRS connectors. Bytheway, I would still prefer to have two 3.5mm jacks (one to send, and one to receive). It'd be much more flexible in terms of choice (there are a million TS and TRS jacks) and TS and TRS plugs are very durable, and easy to find. I grabbed 20 or so Neutrik (now REAN) NYS-231 TRS plugs. You can get them ~$.70 shipped in low quantities (.90 for the TRS version)\nhttp:\/\/www.daleproaudio.com\/p-4058-neutrik-nys226-35mm-ts-mono-connector-nickelsilver.aspx\n\nThese are easy to solder to, cheap and in practice have been more durable than the extremely beefy Canare F-16\n\nOne issue is that you'd be carrying mixed signals power\/data on the same connector.\n---\nI anticipate the largest issue with the TRRS connector is the fact that when it's plugged or unplugged, you will temporarily short each connector to ground as you unplug it or plug it in. This may not be a big issue for the data lines, but there should be some protection for when the power is temporarily shorted to ground.\n\nI will continue looking for a beefy enough low profile connector suitable for this task.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: rburrows on Mon, 23 April 2012, 23:09:32\nI love this design and I'm interested in one for ~400, possibly w\/ soldering service. I have a note\/suggestion (apologies if this is already covered upthread): Is it a deliberate design choice to have outer-bottom key normal-sized rather than wide like the 4 above it? From my own experience with the equivalent key as a modifier (alt) on the Truly Ergonomic board, having a wider key helps in two ways: As a single modifier: I tend to move my whole arm slightly out of home row alignment. This coarse motion stays accurate because of the wider key surface (Fitts' Law at work?). Similarly, I find swatting the wide hyphen\/minus on the top corner of the TE to be easier than on a traditional board. As a combo modifier with the key above: In this case, the pinky would actuate the bottom key and the ring finger the key above it. The pinky naturally wants to rest farther out than the ring finger, and in the current layout would tend to locate over the \"empty\" space that could be captured by a wider key. You're probably too far along on schematics and prototyping but I thought I'd put in my two cents. Keep up the great work! -Rob [ATTACH=CONFIG]48815[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: tjweir on Wed, 25 April 2012, 06:50:12 I'd like to register my interest at300 and offer a bit of inspiration:\nhttp:\/\/www.otd.kr\/bbs\/board.php?bo_table=album&wr_id=116384\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Wed, 25 April 2012, 10:04:11\nI have followed this thread closely for a month now, and have slowly built up enthusiasm for this project. Thus, I will throw my name in the hat as well, for anywhere between $300 and$400 (Edit: This would be fully assembled WITH keycaps). I very much look forward to seeing the first prototype!\n\nCheers,\n\nBen\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Jim66 on Thu, 26 April 2012, 04:16:37\nI'm not sure if any of you guys have seen this over at DT; it's a lovely split ergo 'home brew'.\n\nhttp:\/\/deskthority.net\/workshop-f7\/my-diy-keyboard-collection-or-how-i-became-a-kb-geek-t2534.html (http:\/\/deskthority.net\/workshop-f7\/my-diy-keyboard-collection-or-how-i-became-a-kb-geek-t2534.html)\n\n(http:\/\/deskthority.net\/resources\/bluecube-inside-view\/3109)\n(http:\/\/deskthority.net\/resources\/bluecube-laying-flat\/3108)\n(http:\/\/deskthority.net\/resources\/setup-with-mainly-standard-caps\/3112)\n(http:\/\/deskthority.net\/resources\/very-little-space-inside-but-just-enough\/3113)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Spharx on Thu, 26 April 2012, 07:57:47\nDamn this is gonna be expensive ;( and also I don't like the shapeways idea.\nDid you considered to make this projects more public so that you can find maybe company's who are willing to buy in larger scales or even sponsors?\nI would buy a metal version for up to 200$... but this would be a miracle if this could be happen. Pls update the first post if something changes in the design or the price since this is the first information that a uninformed person will get. Quote Last edited by Dox; 27 Dec 2011 at 17:15. Title: [Interest Check] Custom split ergo keyboard. Post by: jblack801 on Thu, 26 April 2012, 10:54:18 Quote from: Spharx;582682 Damn this is gonna be expensive ;( and also I don't like the shapeways idea. Did you considered to make this projects more public so that you can find maybe company's who are willing to buy in larger scales or even sponsors? I would buy a metal version for up to 200$ ... but this would be a miracle if this could be happen.\n\nPls update the first post if something changes in the design or the price since this is the first information that a informed person will get.\n\nOr even something like Kickstarter?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: suka on Thu, 26 April 2012, 11:21:50\nQuote from: Spharx;582682\nDamn this is gonna be expensive ;( and also I don't like the shapeways idea.\nAs I mentioned on deskthority the case parts of the blue split keyboard would cost around 50\u20ac \u00a0or even less if optimized for it. which I find rather cheap - but for that flat design a custom PCB would also work, true. \u00a0But then there would still be no case around it.\n\nThe idea of promoting it is tempting, but after that Desaster with the other great design on this forum (can't remember the name, programmable tenkeyless with tracking that was later copied in China) I am not anxious to put my work and money into something that would be too easy to copy anyways. \u00a0So open-sourcing the design documents and firmware as well as giving some help building it will allow anybody interested to recreate or better yet improve the design.\n\nGesendet von meinem MB525 mit Tapatalk 2\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hoggy on Thu, 26 April 2012, 14:02:20\nDo you mean Lowpoly's mini-guru? \u00a0Or Lilster's filco\/phantom case?\n\nThe danger of something more public like kickstarter is that you start to cross the line from a hobby to a job. \u00a0Hobbies are far more likely to be fun.\n\nThis is truly a boutique product. \u00a0Unless some company steals the idea, you may never get the chance again. \u00a0Grab it with both hands and get your wallet out.\n\nI'm sorry for the rant.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Thu, 26 April 2012, 14:07:22\nQuote from: hoggy;582978\nI'm sorry for the rant.\n\nIf that was a rant I think your blood sugar must be low, or perhaps you're on some depressant?\n\nAnyhow, while kickstarter is nifty there's a whole lot of work to put into making a project KS ready, and there's a whole lot of money that gets eaten by KS. \u00a0Also if you decide to go the KS route, you are deciding that if the KS funding falls through the project doesn't happen. \u00a0I don't know what sort of link you get to your funders, but here Dox gets the ability to say that he's going through with it one way or the other and the more people that are interested the lower the price is. \u00a0You can't vary pricing in KS based on funding and I'm sure they would crack down on someone trying to use KS as a communications platform to get the under-funded project going with different pricing by way of paypal.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Thu, 26 April 2012, 15:25:47\nSuka: Your project is awesome. \u00a0Jim66, thanks for the original post. \u00a0If I ever do a keyboard completely by myself, I'm gunna be digging out your link :) . \u00a0Also (in response to some comments on the deskauthority thread), for using a connector between the two halves, have you considered I2C or SPI I\/O expanders? \u00a0It looks like we'll stick with I2C for this project, but if you're willing to accept the extra wire (5 total instead of 4) SPI would be much faster (from experiment, a simple usage of I2C seems to limit the scan rate to ~167Hz IIRC). \u00a0We have a firmware (https:\/\/github.com\/benblazak\/ergodox-firmware) (that's not quite done, but should be stable enough) that'll handle I2C, if you didn't want to just add the capability to your own. \u00a0And if the Teensy has similar hardware support for SPI I doubt it'd be overly hard to add. \u00a0Anyway, thanks for the write up :) .\n\n[\/HR]\n\nRburrows, tjweir, OrangeJewce: I've been considering dorkvader kind of the official greeter all this time, but I wanted to welcome you too. \u00a0I'm glad to see people still posting to register interest!\n\n[\/HR]\n\nAnd Dox, I know I'm way late, but I never said how excited I was (am) that we're getting close to first prototype. :D\n\n[\/HR]\n\nDid we loose a few posts? \u00a0But anyway, the discussion made me think about it even more, and here's a few things I realized (I'll call the MCP23018 side the LH side, and the Teensy side the RH side, for the sake of brevity):\n\n\u2022 The LH side isn't connected to anything till we plug it in; so no matter how the contacts are arranged, only one side has power, and we're safe from direct Vcc\/GND shorts.\n\u2022 This makes me think it'd be better to put GND on the sleeve (and probably Vcc on the tip), like dorkvader was talking about. \u00a0He had better reasons - I just think it'd be more standard, and just as good.\n\u2022 I found one other project (http:\/\/www.seeedstudio.com\/wiki\/Electronic_Brick_-_OLED_128*64_Display) that was using TRRS for I2C. \u00a0He had it wired (tip to sleeve) SCL, SDA, Vcc, GND, with a resistor on Vcc it looks like (and I don't know if anything else).\n\n\u2022 The user will have a choice of which side to plug in first; so no matter how the contacts are arranged:\n\u2022 Either the LH Vcc pin will be brought low or the LH GND pin will be brought high; or both.\n\u2022 Would regular diodes on Vcc and GND be able to help us with this? \u00a0Or is the MCP23018 okay with that? \u00a0I wasn't able to find it in the datasheet (http:\/\/ww1.microchip.com\/downloads\/en\/DeviceDoc\/22103a.pdf).\n\n\u2022 Any RH pin will have a chance of touching any LH pin on each insert; so we need to make sure all the pins will be fine with that.\n\n\u2022 We also have to keep in mind that SCL and SDA will be oscillating between logic low and hi-Z with a 2.2k\u03a9 pull-up during insert (unless the RH side isn't plugged in to USB yet).\n\nAlso:\n\n\u2022 I still think we should at least put a current limiting diode (like this one) (http:\/\/www.mouser.com\/ProductDetail\/Semitec\/E-103\/?qs=wgO0AD0o1vtPvEuL9OtJxD39URT4QO5WtLCSYapIzZM%3d) on the RH Vcc. \u00a0If you want, it might be extra safe to put a 2mA one on the LH Vcc. \u00a0Or, since it looks like the MCP23018 can operate at full speed down to at least 2.7V, a current limiting resistor should also work.\n\n\u2022 Would it be good to have TVS diodes on all the pins, to protect from ESD? \u00a0I hadn't thought of that before, but it seems like a good idea to me, if there's room.\n\n[\/HR]\n\nI was wondering if anyone would care to design a QWERTY (and maybe Dvorak?) layout? \u00a0The current QWERTY layout is rather pathetic, but I just don't feel like putting that much time into it because I'm likely going to neglect both and give Arensito (http:\/\/www.pvv.org\/~hakonhal\/main.cgi\/keyboard) a serious shot. \u00a0What I'm thinking, if I can get decent QWERTY and\/or Dvorak layouts, is that I'll compile the firmware with all three layouts separately, and post 3 different .hex files for everyone's convenience. \u00a0If you'd like to take a look, please see the layout documentation file (https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/keyboard\/ergodox\/layout.md) on github (make sure you're on the 'dev' branch), and let me know if you have any questions.\n\nPartly implied in the above, I'm not currently planning to implement on-keyboard remapping. \u00a0I'm almost certain it wouldn't be technically hard (it might be almost trivial) with the current design, but I can't think of a good way to do it. \u00a0The thing is, if you're willing to learn the *smallest* bit about Make and C (or if you already know both; and I'll try to write a little howto before I consider the project done) you'll be able to remap to your heart's content *and* store keymaps much more easily than you could with on-keyboard remapping, and with no extra effort in the firmware. \u00a0If you're willing to learn a lot (or just a little extra, if you already know C), you'll be able to write new keypress\/release functions (all keypresses and releases are function calls) and do most anything you want, which wouldn't be possible at all with other methods. \u00a0If anyone has some good ideas about how on-keyboard remapping could work though, I'd be interested to hear them; if only because it's a problem I couldn't think of an elegant solution to.\n\nAlso, I'm currently working on NKRO. \u00a0I'd really like to make it work, but I'm not completely sure if I'll have the patience. \u00a0Is this very important to people?\n\nAnd if anyone has any other thoughts on the firmware I'd be interested to hear them, since the design is starting to finalize in my head. \u00a0Not sure what else I'll have the patience\/time to implement, but suggestions are always good.\n\nThanks :) . \u00a0Sorry this post is so long.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hoggy on Thu, 26 April 2012, 16:18:09\nNKRO is a great feature when buying - I think it's less important when actually using. \u00a0A good deal of members love Model Ms - and they have 2KRO.\n\nDid you mean 6KRO or full NKRO?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hoggy on Thu, 26 April 2012, 16:21:40\nQuote from: alaricljs;582989\nIf that was a rant I think your blood sugar must be low, or perhaps you're on some depressant?\n\nThere was a lot of editing...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Thu, 26 April 2012, 20:45:42\nQuote from: hoggy;583086\nDid you mean 6KRO or full NKRO?\n\nFull NKRO. \u00a0Right now we have 6KRO + 8 modifiers, since that's what the PJRC usb_keyboard example (which implements the usb keyboard boot mode) has.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hoggy on Fri, 27 April 2012, 00:33:08\nCool! 6 KRO + mods would be fine with me. \u00a0I don't type that fast and I use my fingers, not my fists.\n\nI'll take a look at the layouts over the weekend if that's okay.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hoggy on Fri, 27 April 2012, 01:11:26\nWould the controller be able to handle mouse movements? \u00a0My initial idea would be to have an embedded cursor key set in the right half (layer key in the left half) and the same on the left, but for the mouse. \u00a0The mouse click buttons would be on the thumb keys in the same layer.\n\nijkl - cursor keys\nedsf - mouse keys. \u00a0Mouse buttons on the two main thumb keys on the left half.\n\nAny thoughts?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Fri, 27 April 2012, 02:35:54\n:) \u00a0So it looks like I don't need to be sad if NKRO falls through then. \u00a0I *do* still want to try though, just because it'd be a shame for the USB spec to beat me like that...\n\nQuote from: hoggy;583601\nI'll take a look at the layouts over the weekend if that's okay.\n\nThanks!\n\n---\n\nAbout mouse movements, it's not possible in the firmware right now, but I think PJRC has some code that would work, so hopefully it won't be way too hard. \u00a0[EDIT: I tried it and it didn't work like I hoped - so it will be pretty hard, or at least pretty time consuming. \u00a0Oops. \u00a0But I'll see if I can do it anyway.] \u00a0Thanks for reminding me, by the way, I meant to support that at one point but then I forgot. \u00a0It's in my todo list now.\n\nAnd, sorry, no thoughts on mouse keys from me - lol, to be honest, between gvim and a real mouse, I don't see their purpose - but I think lots of other people here will be happy to have them around :) .\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: boli on Fri, 27 April 2012, 02:40:45\nQuote from: ic07;583044\nIf anyone has some good ideas about how on-keyboard remapping could work though, I'd be interested to hear them; if only because it's a problem I couldn't think of an elegant solution to.\n\nWhat do you think about the Kinesis way (http:\/\/www.kinesis-ergo.com\/tech_support\/remapping.htm)? The process is very simple:\n1. Enter remapping mode by pressing some key combination\n2. Press the key with the character you want to remap (source)\n3. Press key at the location you want the above characters to be at (target)\n4. Optionally repeat steps 2 and 3 for other keys\n5. Exit remapping mode by pressing some key combination\n\nWhile this is simple, there are some constraints: you always move all characters from a key, that is unshifted and shifted. That's mostly OK, but some people may want to move number row shifted symbols independently from the numbers themselves for example. Maybe advanced remappings such as this could require software, but basic remapping would not.\n\nImportant to note: In step 2 the current remapping does not matter, the \"source\" character is always from the default unremapped keyboard\n\nPersonally I like this approach a lot, it's very easy and requires no software. No matter which OS I boot into, I always have the layout I want.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sherryton on Fri, 27 April 2012, 15:09:48\nInterested. \u00a0Please put me down dork!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Fri, 27 April 2012, 15:56:44\nQuote from: boli;583673\nWhat do you think about the Kinesis way (http:\/\/www.kinesis-ergo.com\/tech_support\/remapping.htm)?\n\nI think it's good, within the limitations you mentioned. \u00a0Additionally, you cannot save or reload previous maps that you've made, so to me it'd seem that it was only good for quick remaps involving just a few keys. \u00a0Also, as you mentioned, the \"source\" character is always from the default unremapped keyboard - but with a DIY project there is no One True Default keyboard, as there is with a commercial product. \u00a0Actually, if things work out, there will be Three True Defaults, lol, along with the option to roll your own, which I was thinking would be rather confusing (and the Kinesis method of making everyone use the default QWERTY map to remap, even if their keycaps are Dvorak, seems unreasonable to me). \u00a0So that would increase the documentation burden a bit - and the burden on the keymap designers.\n\nStill, you're making me reconsider... \u00a0Are quick, small remaps common enough for it to be worth it? \u00a0Or, are Make and the avr-gcc toolchain (even with a nice howto written up) user unfriendly enough that the limitations of the Kinesis method are worth it for larger remaps? \u00a0I tend to forget that not everyone's perfectly at home with a terminal and a text editor, so I'm probably in need of some perspective here.\n\nQuote from: boli;583673\n[...] you always move all characters from a key, that is unshifted and shifted. [...]\n\nIn Kinesis defense, this is a (slightly annoying) consequence of how keyboards are designed. \u00a0That is, keys and shifted keys have the same keycode, and the host is responsible for registering different characters based on the presence of modifiers (which are either present for all the keys pressed, or none of them), so there's nothing the keyboard can do. \u00a0If you really wanted to move symbols around separately, it might be possible to implement shift as a layer key and use the standalone keycodes for symbols... but that'd be changing the meaning of things.\n\nWhich brings up another limitation of the Kinesis method: keycodes not present in the default layout aren't available at all.\n\nQuote from: boli;583673\nPersonally I like this approach a lot, it's very easy and requires no software. No matter which OS I boot into, I always have the layout I want.\n\nFor what it's worth, modding the keymap in the firmware source would be OS independent too - and the software required already works (with slightly different interfaces) on every major OS.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Fri, 27 April 2012, 20:05:30\nQuote from: hoggy;583634\nWould the controller be able to handle mouse movements?\n\nQuote from: ic07;583669\n[...] it's not possible in the firmware right now, but I think PJRC has some code that would work, so hopefully it won't be way too hard. \u00a0[...]\n\nSpoke too soon :\/ . \u00a0The PJRC keyboard and mouse code doesn't quite work together, so I have to go learn about device side USB before I can implement it, which might take a while. \u00a0Or I could use LUFA, but that looks just as hard. \u00a0Can't say when (or promise if) I'll have it done, but I'll work on it. \u00a0Sorry about that.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Fri, 27 April 2012, 20:10:53\nThere are other KB firmwares for the Teensy scattered about here, hasu has one w\/ mousekeys. \u00a0You might learn from those.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: suka on Sat, 28 April 2012, 02:19:40\nGive LUFA a try: it comes with several examples using both mouse and keyboard that serve as a good starting point.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sun, 29 April 2012, 01:00:25\nQuote from: sherryton;584107\nInterested. \u00a0Please put me down dork!\nUpdated the list!\n\nAll this talk of programming: I'm personally not that excited about it, especially given how easy it should be to program a new layout on these things. It might be a handy thing to have, but ultimately, I'd rather get the work done on that when we're waiting for them to ship. Same with full NKRO. It'd be amazing, but it's a \"want\" not a needed feature, and I feel it should be implemented once we are assured of the production and all critical features are taken care of.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Sun, 29 April 2012, 08:04:21\nAgreed\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: fossala on Sun, 29 April 2012, 08:08:25\nIs this still aiming at $400. What is included? Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sun, 29 April 2012, 14:19:31 Fossala: We're still trying to price things out. The last price update I remember was in december 2011: Quote from: Dox;479955 Ok, here is the new case. There is still no trackpoint. (Attachment) 36215[\/ATTACH] (Attachment) 36214[\/ATTACH] 2 set of 11 plates (including the mounting plate) per hand. The plates are symmetric for the second hand. I still need to do something to give it some angle\/mounting option. To give you an idea, for 10 set of 11 plates (5 keyboards) not anodized, the cost would be around 110$ per hand (plates only).\n\nNow, I imagine the cost will be somewhat lower, as the quantity will likely be an order of magnitude higher. From what I've read on machine shop prices, it might not be that much lower, though.\n\nSo if the case is $200 total, the PCB will likely come in under$100. Switches are ~$0.8*76=$60 (unless you're harvesting them from somewhere, or already bought them from 7bit), teensy is ~$18 (I think?). I don't know what the connecting cable, connectors and that signalling chip is, but I feel like it's under$30 all told.\n\nSo all in all, maybe about $400 without keycaps. The best savings will be in the PCB. Lots of PCB fabs will get you a much better deal in quantities of 50+, which we should have. No idea about getting the case cheaper, though. Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Sun, 29 April 2012, 18:34:10 sounds good. Title: [Interest Check] Custom split ergo keyboard. Post by: Autolyze on Sun, 29 April 2012, 18:51:47 I'm interested in one of these! I should have a bit of keyboard soldering experience under my belt by the time this gets produced. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Sun, 29 April 2012, 23:23:36 Quote from: dorkvader;585702 Fossala: We're still trying to price things out. The last price update I remember was in december 2011: Now, I imagine the cost will be somewhat lower, as the quantity will likely be an order of magnitude higher. From what I've read on machine shop prices, it might not be that much lower, though. So if the case is$200 total, the PCB will likely come in under $100. Switches are ~$0.8*76=$60 (unless you're harvesting them from somewhere, or already bought them from 7bit), teensy is ~$18 (I think?). I don't know what the connecting cable, connectors and that signalling chip is, but I feel like it's under $30 all told. So all in all, maybe about$400 without keycaps.\n\nThe best savings will be in the PCB. Lots of PCB fabs will get you a much better deal in quantities of 50+, which we should have. No idea about getting the case cheaper, though.\n\nThis seems very steep. Hopefully the target price will be reached which will also include keycaps. $400 for an assembled board sans-caps, IMO, might be out of reach for many of us. I suppose only time will tell. If you guys are looking for volunteers related to working with the Keyboard mapping software I suppose I would be down. Seems like it could be an interesting experience. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: boli on Mon, 30 April 2012, 03:09:40 Will the keyboard have F# keys? I just noticed there are none on the rendered pics: (http:\/\/geekhack.org\/attachment.php?attachmentid=36215) Title: [Interest Check] Custom split ergo keyboard. Post by: jblack801 on Mon, 30 April 2012, 19:08:01 Quote from: boli;586130 Will the keyboard have F# keys? I just noticed there are none on the rendered pics: I don't really see a need for dedicated f-keys. I'd prefer to have to do it similar to the poker where you hold FN+\"appropriate number\" to get your f-key. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 01 May 2012, 19:06:12 Quote from: Autolyze;585891 I'm interested in one of these! I should have a bit of keyboard soldering experience under my belt by the time this gets produced. I'll add you to the list! Quote from: OrangeJewce;586062 This seems very steep. Hopefully the target price will be reached which will also include keycaps.$400 for an assembled board sans-caps, IMO, might be out of reach for many of us. I suppose only time will tell. If you guys are looking for volunteers related to working with the Keyboard mapping software I suppose I would be down. Seems like it could be an interesting experience.\n\nCheers,\nI'm hoping we can get it down under $300, as a lot of people say they're committed up to that point. Quote from: boli;586130 Will the keyboard have F# keys? I just noticed there are none on the rendered pics: Show Image (http:\/\/geekhack.org\/attachment.php?attachmentid=36215) Well, since it's programmable, all the keys are dedicated F keys, if you want. I imagine though that there's not a huge amount of need, especially considering the prospect of layers. You can have a dedicated \"function\" key to turn all the regular number keys into function keys. I imagine if you use them a lot, you can even convert some of the modifiers on the side into function keys (as I imagine I'll have more modifiers near the thumb area. Title: [Interest Check] Custom split ergo keyboard. Post by: Parak on Wed, 02 May 2012, 00:04:20 If the pcb design can be exported in gerber, the costs from the chinese pcb shops would be pretty low in volume, likely under$50 per pair. Even less due to 2x volume scale if the design can be mirrored, though this would be a bit tricky. Cherry switches can be flipped around though, but there's also connectors and chips to consider..\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: boli on Wed, 02 May 2012, 02:41:47\nQuote from: jblack801;586795\nI don't really see a need for dedicated f-keys. I'd prefer to have to do it similar to the poker where you hold FN+\"appropriate number\" to get your f-key.\n\nHow do you press F12 on the Poker? (used to move optical media tray in\/out on Macs) :P\n\nWell, since it's programmable, all the keys are dedicated F keys, if you want. I imagine though that there's not a huge amount of need, especially considering the prospect of layers. You can have a dedicated \"function\" key to turn all the regular number keys into function keys. I imagine if you use them a lot, you can even convert some of the modifiers on the side into function keys (as I imagine I'll have more modifiers near the thumb area.\n\nF# keys are also nice to double as media keys and such, possibly when some sort of Fn is pressed (as e.g. on Apple keyboards). IMO Esc needs to be available on the top layer (without any modifiers) - that shouldn't be a problem with the extra keys around the main area.\n\nAs for the F# (and media) keys, I'm aware that 4 layers on the number row could partially do it (normal, shifted, function and media). There are not enough keys to spare for dedicated F#\/media keys... Compared to a Kinesis Advantage it as 5 fewer keys overall (8 more in the main area, 13 less in the function row).\n\nOn the Kinesis I use most F# keys as media keys (most importantly play\/pause and volume controls), and some of them as the real F# keys, namely those used for debugging in Eclipse. All of these are on the top layer, no modifier needed.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: mharrison on Wed, 02 May 2012, 10:35:29\nDon't mean to rain on the parade, but when I see the exploded view of the layers, I'm concerned with the bolt design. The size of the holes, especially with the tapering, that close to the edge seems way too big. I'm not convinced that the corners will hold up. It would be awesome if someone with experience in industrial design could comment.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Jim66 on Wed, 02 May 2012, 10:43:36\nI'm not sure if we are still going with this case design; not a lot has been said about the case recently.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: jblack801 on Wed, 02 May 2012, 17:54:33\nQuote from: boli;587911\nHow do you press F12 on the Poker? (used to move optical media tray in\/out on Macs) :P\nfn+\"=\/+\"\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: WhiteRice on Fri, 11 May 2012, 22:57:09\nIs this project still in flight? Is it Dox's project or a GH community endeavor?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Fri, 11 May 2012, 23:52:05\nQuote from: WhiteRice;590236\nIs this project still in flight? Is it Dox's project or a GH community endeavor?\n\nYup, it's nearing prototype :) . \u00a0And it's DOX's project - though there is a bit of community effort going on for interest tracking (dorkvader), and firmware (me), and a few people have said they might be able to make keymaps.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sat, 12 May 2012, 13:01:52\nI'm glad I have the interest list saved on my computer: Just reupdated the second post.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: WhiteRice on Sat, 12 May 2012, 16:16:21\nI'm in ~$400 Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Fri, 18 May 2012, 13:43:21 Update Bump! :bump2: Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 18 May 2012, 14:29:58 I've been working ~70h a week in the last few weeks so I didn't had much time to put on this. I have a 3 day weekend and I don't have anything planned so I want to finish the pcb layout and order it as soon as possible. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 19 May 2012, 00:35:49 Quote from: Dox;595464 I've been working ~70h a week in the last few weeks so I didn't had much time to put on this. I have a 3 day weekend and I don't have anything planned so I want to finish the pcb layout and order it as soon as possible. This is why we love you, Dox. You are super busy, and still dedicated. I mean, I only work 30 hours a week, and I'm not doing hardly anything to help. You are an inspiration to us all. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Mon, 21 May 2012, 17:56:46 PCB done! [ATTACH=CONFIG]50928[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Mon, 21 May 2012, 20:58:45 I have ordered some prototype PCBs. There is the option for PCB mounted switches, diode outside or inside the switch as well as SMD (http:\/\/ca.mouser.com\/ProductDetail\/Vishay-Semiconductors\/1N4148W-V-GS18\/?qs=9UrfSeCy%252bVa2LauxRB857Njw2wTz92Gf). Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 22 May 2012, 00:06:43 Wow, that's a good PCB, DOX! I especially like the profusion of mounting holes. We sholud have no trouble with flex. Are they one-sided PCB's with a lot of jumpers, or does the red denote traces on the second layer? Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Tue, 22 May 2012, 00:25:49 Nice one, Dox! My eyes started to follow the traces - it wasn't long before I got lost. Title: [Interest Check] Custom split ergo keyboard. Post by: dirge on Tue, 22 May 2012, 01:14:57 Can u buy me a PCB set please :) I can't wait for a final kit! Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Tue, 22 May 2012, 03:50:51 that's awesome, DOX! Title: [Interest Check] Custom split ergo keyboard. Post by: Netdewt on Tue, 22 May 2012, 11:34:53 Will the PCBs be available a la carte? Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Tue, 22 May 2012, 16:14:49 Nom, I'm with dirge on this! Can I buy a PCB? :D Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 22 May 2012, 17:33:26 Quote from: dorkvader;597347 Wow, that's a good PCB, DOX! I especially like the profusion of mounting holes. We sholud have no trouble with flex. Are they one-sided PCB's with a lot of jumpers, or does the red denote traces on the second layer? Thanks, these are 2 sided. The red traces are on the top layer of the PCB. Quote from: hoggy;597357 Nice one, Dox! My eyes started to follow the traces - it wasn't long before I got lost. Thanks, it's quite hard to follow from the picture, especially with the ground planes. Quote from: dirge;597369 Can u buy me a PCB set please :) I can't wait for a final kit! FYI, the prototype PCBs cost me ~300$ for 2 sets. Prices will be much lower with bigger quantity but I ordered the minimum qty just to test everything.\n\nQuote from: ic07;597396\nthat's awesome, DOX!\nThanks! Your firmware highly facilitate the tracing. I don't know if I have followed your intended matrix as I went for the simplest way to trace it with the assigned pins. There will probably be some remapping needed in the firmware. No big deal.\n\nQuote from: Netdewt;597612\nWill the PCBs be available a la carte?\nYes, when everything will be ready and tested!\n\nQuote from: ped;597829\nNom, I'm with dirge on this! Can I buy a PCB? :D\nI don't think a lot of people would want to pay 150$for a set of PCB that are not even tested yet. I should receive them next monday. Can't wait! Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Tue, 22 May 2012, 18:07:26 Looking good, DOX! Good to see all the diode placement options. I just recently soldered SMD diodes to my KMAC. It wasn't hard at all. Just need steady hands. Title: [Interest Check] Custom split ergo keyboard. Post by: Netdewt on Tue, 22 May 2012, 21:15:22 Quote from: Dox;597866 Yes, when everything will be ready and tested! That might interest me. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Tue, 22 May 2012, 21:32:38 Quote from: litster;597899 Looking good, DOX! Good to see all the diode placement options. I just recently soldered SMD diodes to my KMAC. It wasn't hard at all. Just need steady hands. Thanks lister! I decided to put the SMD as it wasn't much more work and it's good to have options. I'll probably go for the trough hole ones on the first prototype as I have a few hundreds of them but I may try the SMD on the final or the second prototype PCB. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Tue, 22 May 2012, 22:17:30 SMD diodes are a lot more expensive than through-hole diodes. And Mouser is cheaper than digikey. I ordered extra last time. because I it was only a couple more dollars to reach the next level of discount. Hehe, send me a set of PCBs and I can test for SMD diodes placement. :D I will pay for it, if you have extra. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 22 May 2012, 23:37:40 Great stuff Dox! Keep up the amazing work! Might even have to bump my order up! Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Thu, 24 May 2012, 01:38:37 Nice to see pcb-mount switches with pins and diodes supported! Those are the kinds of switches kinesis sells. Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Thu, 24 May 2012, 02:03:16 Kinesis sells individual switches? Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Thu, 24 May 2012, 04:37:53 Quote from: litster;598987 Kinesis sells individual switches? I think they sell the keywells and packs of 25 switches or something along those lines, but you have to email them about it as it's not listed anywhere. Title: [Interest Check] Custom split ergo keyboard. Post by: dirge on Thu, 24 May 2012, 07:58:18 Dox I'm loving this, get pics of those boards the moment they arrive! And I'm sure the boards would have been a bit cheaper if we'd thrown money at you for prototypes ;) Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Thu, 24 May 2012, 12:13:24 Quote from: dirge;599071 Dox I'm loving this, get pics of those boards the moment they arrive! And I'm sure the boards would have been a bit cheaper if we'd thrown money at you for prototypes ;) Makes sense though, if he overlooked something and it needs manual fixing then you'd think \"Damn, paid all that money for something 'broken'\". With that said, I'd have paid for one at that price. But yeah, exciting! :D Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Thu, 24 May 2012, 22:25:58 Quote from: litster;598987 Kinesis sells individual switches? They sell reds in 15 packs for sure (I got 2 such packs already), for larger quantities it will probably have to be a special order, but they're accomodating. All their switches are the style for their Kinesis Advantage (with pins for pcb mount, and with built-in diodes), so it would be MX1A-L1DW for their reds, and MX1A-G1DW for their browns. Boy is the Cherry Wiki (http:\/\/geekhack.org\/showwiki.php?title=Cherry+switches+and+boards) handy http:\/\/geekhack.org\/showwiki.php?title=Cherry+switches+and+boards Title: [Interest Check] Custom split ergo keyboard. Post by: litster on Fri, 25 May 2012, 02:31:57 sordna, do you know how much they charge for the switches? Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 25 May 2012, 09:07:28 Teaser... [ATTACH=CONFIG]51346[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: mkawa on Fri, 25 May 2012, 09:33:22 fascinating!! i don't think i'd be in for the casing, as I can never manage to type properly on split boards, but the boards are too intriguing to not build one up :) Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Fri, 25 May 2012, 09:40:34 Are those plated through-holes? Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Fri, 25 May 2012, 09:41:36 You have to jump through hoops to not get plated holes when you use kicad. Title: [Interest Check] Custom split ergo keyboard. Post by: WhiteRice on Fri, 25 May 2012, 10:39:11 Quote from: dorkvader;599810 Are those plated through-holes? I love it when you talk nerdy Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Fri, 25 May 2012, 10:56:52 So exciting Dox! Do you plan on posting pictures of you putting it all together? Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Fri, 25 May 2012, 14:41:10 Quote from: litster;599645 sordna, do you know how much they charge for the switches? Yes, a 15-pack of reds (MX1A-L1DW) goes for$15. So it's a dollar a switch. Kinesis part number for the 15-pack is KC009REP, they mainly sell these packs to people that are converting their Advantage keyboards to the LF version (you would buy a pair of red keywells for $90 I believe, and a 15-pack to swap the thumbswitches). However I bought 2 packs (30 switches for$30) without buying any keywells. They should be able to do a better price for larger quantity of switches, we should ask them how much they would charge for maybe a 90-pack.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: litster on Fri, 25 May 2012, 15:12:17\nyeah, I want these switches for ergo DOX as well as a custom keyboard I will be building that uses PCB mount switches with built in diodes. \u00a0But $1 each is too expensive. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Fri, 25 May 2012, 19:38:49 Pictures! [ATTACH=CONFIG]51436[\/ATTACH][ATTACH=CONFIG]51437[\/ATTACH][ATTACH=CONFIG]51434[\/ATTACH][ATTACH=CONFIG]51435[\/ATTACH][ATTACH=CONFIG]51432[\/ATTACH][ATTACH=CONFIG]51433[\/ATTACH] [ATTACH=CONFIG]51438[\/ATTACH] One small problem. I have installed the diodes the same way I have done for the DoxKB but the scanning in inverted in IC07 firmware so nothing registers for the moment. I tested with a jumper and everything seem to work fine otherwise. I'll try to invert the scanning in the firmware as the diodes are a PITA to desolder in the small plated The TRRS cable works like a charm! A HDMI cable would have been way too bulky. Title: [Interest Check] Custom split ergo keyboard. Post by: tadbitnerdy on Fri, 25 May 2012, 20:18:25 Interested! Amazing work! Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Fri, 25 May 2012, 22:20:19 Quote from: Dox;600266 Pictures! (Attachment) 51436[\/ATTACH] (Attachment) 51437[\/ATTACH] (Attachment) 51434[\/ATTACH] (Attachment) 51435[\/ATTACH] (Attachment) 51432[\/ATTACH] (Attachment) 51433[\/ATTACH] (Attachment) 51438[\/ATTACH] One small problem. I have installed the diodes the same way I have done for the DoxKB but the scanning in inverted in IC07 firmware so nothing registers for the moment. I tested with a jumper and everything seem to work fine otherwise. I'll try to invert the scanning in the firmware as the diodes are a PITA to desolder in the small plated The TRRS cable works like a charm! A HDMI cable would have been way too bulky. http:\/\/youtu.be\/p6RM6YE3EMI?t=25s Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Fri, 25 May 2012, 23:02:54 Does it have no soldermask? Wow, that picture of it loaded up with switches, with the LED's on looks amazing! I want to convert it to ascii-art, type it up on the typewriter (I have no printer at the moment) and put it on the wall! Now that you have the switches on a board, what do you think about the key placement? How does it feel? Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Fri, 25 May 2012, 23:09:04 So cool! Oh, can you please make sure the firmware is such that cherry switches with built-in diodes work? That's what should dictate the orientation... Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sat, 26 May 2012, 00:02:55 Quote from: dorkvader;600371 Does it have no soldermask? Wow, that picture of it loaded up with switches, with the LED's on looks amazing! I want to convert it to ascii-art, type it up on the typewriter (I have no printer at the moment) and put it on the wall! Now that you have the switches on a board, what do you think about the key placement? How does it feel? No soldermask as it's a \"prototype\". The final version will have a soldermask. I haven't played much with it yet but I think the key placement is pretty much spot on from my first impressions. Quote from: sordna;600373 So cool! Oh, can you please make sure the firmware is such that cherry switches with built-in diodes work? That's what should dictate the orientation... The way I placed the diodes on the PCB is the same orientation as the built-in diodes. So the firmware should be revised to follow this. Edit: [ATTACH=CONFIG]51456[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Sat, 26 May 2012, 00:39:27 Quote from: Dox;600395 The way I placed the diodes on the PCB is the same orientation as the built-in diodes. So the firmware should be revised to follow this. Oh grr, it should. I'll do that then. Might not be able to get to it for a few days though. Sorry to be busy now that things are getting so exciting, lol. I'll make time as soon as I can! So what we want (since the MCP23018 is open drain) is to have the columns hi-Z (off) \/ drive low (on), and the rows input with pull-up? Title: [Interest Check] Custom split ergo keyboard. Post by: dirge on Sat, 26 May 2012, 01:39:54 This feels so close now! Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Sat, 26 May 2012, 02:29:37 Dox, I don't know anything about electronics, but I noticed the right hand side has a diode per switch, but the left side hasn't... I'm curious - could you tell me why, please? PS - looks really sweet! Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Sat, 26 May 2012, 03:10:33 One minor gripe: I would've preferred the Teensy to be on the left side. That way, I could run just the left half for gaming. :evil: But nonetheless, that is just hot s***. Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Sat, 26 May 2012, 04:02:46 Quote from: ripster;600465 I quibble with your use of the word quip. QC'd. Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Sat, 26 May 2012, 05:21:35 Don't know if it's possible to fit the two options in the PCB, but if yes, could you allow for the 2x thumb keys be mountable POS style as an alternative? Title: [Interest Check] Custom split ergo keyboard. Post by: Nakkor on Sat, 26 May 2012, 08:04:40 Quote from: REVENGE;600456 One minor gripe: I would've preferred the Teensy to be on the left side. That way, I could run just the left half for gaming. :evil: But nonetheless, that is just hot s***. I agree with both statements. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sat, 26 May 2012, 10:56:44 Quote from: ic07;600409 Oh grr, it should. I'll do that then. Might not be able to get to it for a few days though. Sorry to be busy now that things are getting so exciting, lol. I'll make time as soon as I can! So what we want (since the MCP23018 is open drain) is to have the columns hi-Z (off) \/ drive low (on), and the rows input with pull-up? No problems, I'll wait for your revised firmware. Yes, we want the rows input with pull-up. Thanks again for doing this! Quote from: hoggy;600443 Dox, I don't know anything about electronics, but I noticed the right hand side has a diode per switch, but the left side hasn't... I'm curious - could you tell me why, please? PS - looks really sweet! There are diodes on both side for every switches. The left side diodes are just hidden behind the switches in the picture. Quote from: REVENGE;600456 One minor gripe: I would've preferred the Teensy to be on the left side. That way, I could run just the left half for gaming. :evil: But nonetheless, that is just hot s***. The good thing is that you can move the halves as you wish. Just place the right hand away and place the left hand beside your mouse. Quote from: ped;600490 Don't know if it's possible to fit the two options in the PCB, but if yes, could you allow for the 2x thumb keys be mountable POS style as an alternative? I don't know why you would want to do this. 2 switches for 1 key = double the activation force. Not something that I would want. And the keys that fits that placement are standard keys with centered stems and standard stabilizers. Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Sat, 26 May 2012, 11:28:36 Quote from: Dox;600619 I don't know why you would want to do this. 2 switches for 1 key = double the activation force. Not something that I would want. And the keys that fits that placement are standard keys with centered stems and standard stabilizers. Because it would allow for choosing to divide the keys into two 1x keys if desired. Never mind though, just a thought. Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sat, 26 May 2012, 11:42:36 ic07, could you add me (doxkb) as a collaborator on the project on github, I will update the layout and matrix file. Quote from: ped;600652 Because it would allow for choosing to divide the keys into two 1x keys if desired. Never mind though, just a thought. Yeah, It could be possible, I'll see what I can do but the case\/plate will only support the 2 unit keys. Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Sat, 26 May 2012, 11:52:59 Quote from: Dox;600661 Yeah, It could be possible, I'll see what I can do but the case\/plate will only support the 2 unit keys. Awesome, thanks! Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Sat, 26 May 2012, 23:42:57 This is the updated matrix. Code: [Select] # Documentation : Keyboard Matrix## Matrix [row##column] assignments* row and column numbers are in hex* coordinates without brackets are unused* left and right hands are mostly the same except that row += 6 for the left ....... rows x columns = positions; assigned, unassigned ....... ....... per hand: 6 x 7 = 42; 38, 4 ....... ....... total: 12 x 7 = 84; 76, 8 ....... ---------------------------------------------------------------------------- [B6][B5][B4][B3][B2][B1][B0] [50][51][52][53][54][55][56] [A6][A5][A4][A3][A2][A1][A0] [40][41][42][43][44][45][46] [96][95][94][93][92][91] 90 30 [31][32][33][34][35][36] [86][85][84][83][82][81][80] [20][21][22][23][24][25][26] [76][75][74][73][72] 71 70 10 11 [12][13][14][15][16] [64] 66 06 [04] [63] [60] [00] [03] [65][62][61] [01][02][05]-------------------------------------------------------------------------------Copyright © 2012 Ben Blazak <benblazak.dev@gmail.com> Released under The MIT License (MIT) (see "license.md") Project located at <https:\/\/github.com\/benblazak\/ergodox-firmware> Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Sun, 27 May 2012, 00:08:10 \u25d5 \u203f \u25d5 Title: [Interest Check] Custom split ergo keyboard. Post by: Jim66 on Sun, 27 May 2012, 18:32:26 Very excited about his. Great work Dox + everyone else that's been involved so far! Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Mon, 28 May 2012, 10:26:07 This really does feel like it's on the cusp! However we haven't seen anything on the case yet, so I would expect at least another month before final touches are made. Excellent, excellent work Dox! Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: dirge on Mon, 28 May 2012, 11:06:10 Cardboard case :) Title: [Interest Check] Custom split ergo keyboard. Post by: didjamatic on Mon, 28 May 2012, 11:39:49 Depending on final product I will take 1-3 of them. Can't commit 100% until I know the final product and price. Looks like a great keyboard. Title: [Interest Check] Custom split ergo keyboard. Post by: merijn on Mon, 28 May 2012, 12:09:27 If I can afford it as a student, I will buy one. It looks awesome, and I'd love to have one. Keep up the good work! Title: [Interest Check] Custom split ergo keyboard. Post by: mkawa on Mon, 28 May 2012, 12:19:33 Quote from: REVENGE;601092 \u25d5 \u203f \u25d5 DAT FACE! how much are the pcbs at medium quantity? i'd be interested in assembling a few pcbs for people over the next couple of months while case designs are finalized. imo i think it's a good idea to have some pcbs percolating and being beta tested for code development and as an opportunity to make changes to the pcb before a large quantity run btw, raw or plated pcbs can be just placed on top of soft surfaces to be used\/tested, or placed into prototyped cases of various materials ;) Title: [Interest Check] Custom split ergo keyboard. Post by: mSSM on Mon, 28 May 2012, 13:30:41 I am interested in one of these as well! Please with less Tab Keys though! :D Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Mon, 28 May 2012, 13:48:15 Quote from: ripster;601828 http:\/\/geekhack.org\/showthread.php?22780-Interest-Check-Custom-split-ergo-keyboard&p=428524&viewfull=1#post428524 I HATE being misquoted by a moderator! Dork, please fix. http:\/\/deskthority.net\/workshop-f7\/split-ergonomic-keyboard-project-t1753.html?hilit=Dox If you read through the first post, I lightheartedly misquoted (almost) everyone. Also, I wasn't a mod, when I \"quoted\" you. You have to be precise about this sort of thing. It's not a big deal for me to remove you from the list completely, or change your statement of interest. Just PM me or post here. Quote from: didjamatic;601971 Depending on final product I will take 1-3 of them. Can't commit 100% until I know the final product and price. Looks like a great keyboard. Quote from: merijn;601995 If I can afford it as a student, I will buy one. It looks awesome, and I'd love to have one. Keep up the good work! Quote from: mSSM;602036 I am interested in one of these as well! Please with less Tab Keys though! :D I'll add you all to the list presently. When I saw the tab keys I thought: How many cherry keyboards does DOX have? Edit: Keep in mind that a keyset is not planned (yet) so it's up to you DIYers to come up with keycaps. Nevertheless, I believe WASDkeyboards may be a good source if a GB ever occurs. I'd get a blank keyset for obvious reasons :p Title: [Interest Check] Custom split ergo keyboard. Post by: Dox on Mon, 28 May 2012, 18:12:03 Quote from: OrangeJewce;601903 This really does feel like it's on the cusp! However we haven't seen anything on the case yet, so I would expect at least another month before final touches are made. Excellent, excellent work Dox! Cheers, I'm working on the case right now. I will order a prototype from shapeways soon (1-2 week). Quote from: mkawa;601999 DAT FACE! how much are the pcbs at medium quantity? i'd be interested in assembling a few pcbs for people over the next couple of months while case designs are finalized. imo i think it's a good idea to have some pcbs percolating and being beta tested for code development and as an opportunity to make changes to the pcb before a large quantity run btw, raw or plated pcbs can be just placed on top of soft surfaces to be used\/tested, or placed into prototyped cases of various materials ;) For 10 PCB it's about 45$ each (90 for both).\n\nI placed some sticky insulation material in the corners to give a slope to the PCB. \u00a0I really like this placement so far for my\"ghost\" typing. Similar to the ms ergo 4000.\n[ATTACH=CONFIG]51680[\/ATTACH][ATTACH=CONFIG]51681[\/ATTACH][ATTACH=CONFIG]51682[\/ATTACH]\n\nI'll add you all to the list presently. When I saw the tab keys I thought: How many cherry keyboards does DOX have?\n\nEdit: Keep in mind that a keyset is not planned (yet) so it's up to you DIYers to come up with keycaps. Nevertheless, I believe WASDkeyboards may be a good source if a GB ever occurs. I'd get a blank keyset for obvious reasons :p\nHaha I don't even have 1 functional cherry keyboard except my DoxKBs. The tab keys are from the SP grab bag. I'm trying to figure what are the best profile for the vertical 1.5 keys. I think the tab is working quite well.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Mon, 28 May 2012, 18:33:01\nI think that the thumb keys are a bit too far out. The 3 furthest keys are hard to reach and my thumb is a bit too stretched in the standard (thumb on space) position.\nI will put them closer for the case prototype. I will cut the thumb from the PCB and hand wire it to test it.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dirge on Tue, 29 May 2012, 02:53:30\nGuess you never really know until you use it, love the work! \u00a0But needs more Dvorak ;)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Tue, 29 May 2012, 11:27:32\nAs an aside, I noticed the name on the PCBs was DoxErgo. I was kind of hoping it would be named the Dox64. I just love the sound of the latter, and since the design is based off of the Key64, I thought it was fitting. Regardless this looks great. I keep counting something like 38 keys a half, making a total of 76 keys. We might have to get a GB going just for a set of caps for this guy since it's so unique.\n\nCheers,\n\nP.S. If we can get the board for something like $250, I'd double my order. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 29 May 2012, 15:55:29 Do you mean$250 for PCB\/controller\/case or $250 for the PCB or what? Reason I ask is that some people are wanting to go \"up to\" a certain amount for a complete keyboard, and some are budgeting for other parts (because they have switches like me, or keycaps already, etc.) I'll update the list when I get home. --- As far as the Name: I though ErgoDOX was the accepted name for it (Sordna's work, if I recall correctly) That said. I think Dox76 would be good as well. I think it's really up to DOX, as he's really the project head here :p Also: DOX: are we going for shapeways\/plastic case n the final product, or just the prototype? I think we might be able to get just as good or a better price elsewhere for your metal plate case idea. Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Tue, 29 May 2012, 19:24:21 ErgoDox, not ErgeDox. BTW to keep the cost down for those that cannot afford the full monty, I would like to suggest that folks should be able to order this without case or plate. PCB mounted switches guarantee they will be solid, even without a plate, and as has been said, DIY cardboard case (or no case at all0 works for some folks. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 29 May 2012, 19:56:23 Dorkvader: YGPM As for the name: My bad, it does say ErgoDox. I don't mean to start a competition, and I hadn't re-read all 40+ pages of the thread to see if anyone had come up with a name previously, for forgive me if I had stepped on anyone's toes. Again I leave total veto power up to Dox, I only meant to prompt discussion (even if moot). I think we should wait and see what the costs are actually going to be. If it's going to be$300 without switches or caps then I suppose I'd agree with sordna. If we can keep it near or under $300 all included it might be better to just sell kits. I suspect that caps won't be expensive since most likely they would need to be blank. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: jblack801 on Wed, 30 May 2012, 12:44:14 man, seeing this project get moving... I think I'll have to revise my initial limit (not by much) Dorkvader, can you put me at a definitely if at$250?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Fri, 01 June 2012, 03:44:31\nDox:\nSorry it's taken so long... \u00a0I think I got it though :) . \u00a0Let me know if there's anything I missed. \u00a0Here's the updated hex file (http:\/\/'https:\/\/github.com\/downloads\/benblazak\/ergodox-firmware\/ergodox-firmware--20120601_0116.hex') (most recent post on the github downloads page (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/downloads')), compiled from the current github 'master' branch. \u00a0If you end up compiling yourself, please keep in mind that I changed the makefile a LOT since I last merged the branches - and I tried to keep it WinAVR compatible, but I may have missed something there too. \u00a0Hope not though.\n\nThanks a lot for posting the matrix update BTW. \u00a0I had just finished trying to follow the traces on the PCB when I saw it, but I completely missed the changes to the thumb groups. \u00a0And making a macro out of what you posted ended up being a better solution than my first idea anyway.\n\nHope that's it... \u00a0It's late and I'm really tired. \u00a0Let me know how it works!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 01 June 2012, 09:05:15\nThanks a lot ic07!! I will try it when I get home tonight and I will report back!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Fri, 01 June 2012, 10:01:37\nOne thing I've been thinking about, and it seems to be uniform across all of the other KB GB's that I've seen (specifically I'm thinking of the phantom since that's the last one in a while.), is that they allow ordering of switches along with the kit, as well as assembly (if one desires), and that way consolidate all of the ordering. I only mention this because it seems like it will be a huge headache for those of us wanting assembly to have to order switches separately and then ship it all to the assembler.\n\nMaybe I'm alone with that sentiment, and definitely putting cart before horse (since the prototyping isn't complete), but for whomever coordinates the inevitable GB it's food for thought.\n\nCheers,\n\nP.S.\nic07 you're the man. I have my fingers crossed that everything works great and that in the next couple of months (after the case prototype arrives) we can finally put up an order thread!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: REVENGE on Fri, 01 June 2012, 11:59:38\nHey sordna, any possibility for a big MX switch + diode group buy from Kinesis?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Fri, 01 June 2012, 13:09:33\nAs far as I know they don't sell diodes separately, they only have the MX switches that have built-in diodes, and only browns and reds.\nWhy don't you PM natas206 and invite him to this thread, as he works at Kinesis.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ped on Fri, 01 June 2012, 13:47:26\nWould be interesting to get a hold of some PCB mounted MX switch bottom housing with integrated diode. That's all I really want\/need since I've got plenty of switches on the way already. If a group buy would make them cheaper than buying small amounts as an individual direct from Kinesis, awesomesauce! Maybe we can get these from one of those electrical component websites too...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Fri, 01 June 2012, 14:19:55\nIf we end up including LED based switches, we might want to look into organizing a GB for caps that will make use of them... unless WASD sells appropriate caps. How do the bigger switches look on the Kinesis with the LEDs on?\n\nCheers,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Fri, 01 June 2012, 16:25:43\nQuote from: ped;605759\nWould be interesting to get a hold of some PCB mounted MX switch bottom housing with integrated diode. That's all I really want\/need since I've got plenty of switches on the way already.\n\nIf that's the case, what you want to do is simply get the diodes (1N4148). Most Cherry MX switches have a common housing; even if you're getting them without integrated diodes, the bottom housing has the holes\/marking for the diodes. You would need to open up the switches, bend the diode legs, insert the diode, close the switches.\nUnlike half cherry MX switch housings, diodes are actually obtainable, and very easily so:\nhttp:\/\/www.amazon.com\/gp\/product\/B0002KRC7C\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 01 June 2012, 16:42:04\nThe left hand is working perfectly! The right hand have some problems.\n\"Space\" = \"space\" + \"page down\"\n\"enter\" = \"enter\" + \"space\"\n\"page up\" = \"page up\" + \"enter\"\n\"left\" + \"down\" + \"up\" = \"left\" + \"down\" + \"up\" + \"right\"\nand a few others.\n\nI checked my PCB for shorts but I can't find one yet. I'll keep on searching.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Fri, 01 June 2012, 18:58:43\nI have double checked everything and nothing is grounded. The ghost keys change state when I place my hand under the pcb.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Fri, 01 June 2012, 23:28:32\nHmm :\/ . \u00a0I tested 'space', 'enter', and 'page up' just now on my breadboard setup, using a wire to short the row and column pins, and using both xev (a linux program for printing X events) and one of those pages for testing keyboard rollover (http:\/\/gadzikowski.com\/nkeyrollover.html) to see which keys registered, and they all worked properly. \u00a0Dunno what would be pulling the effected row pins (F0 and F1) low like that...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Sat, 02 June 2012, 00:29:11\nWhat kind is the chip on the left part? Those unconnected pins? What functions do they have. I've had all sorts of strange behavior with floating pins on ICs (the different result depending on which surface the setup has been sitting on in particular). At least on some sort of logics you really have to pull all pins either low or high for them to act right.\n\nEdit: I saw now that it is the right hand that is the problem. So my idea might not be worth much...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Sat, 02 June 2012, 00:48:16\nQuote from: alaricljs;599812\nYou have to jump through hoops to not get plated holes when you use kicad.\n\nActually, either they fixed this on one of the later versions, or I wrongly stated this earlier. There is a \"NTPH,Mechanical\"-setting for \"pads\" in my current version that does just this.\n\nHere is a guide (http:\/\/www.wayneandlayne.com\/blog\/2010\/12\/03\/how-to-build-kicad-on-ubuntu\/) on how to build the latest KiCAD on Ubuntu, probably works on other Linux version as well.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Sat, 02 June 2012, 01:42:25\nQuote from: PrinsValium;606055\nI've had all sorts of strange behavior with floating pins on ICs\n\nMmm *nods*, I read about that while I was learning stuff for this project. \u00a0Unless I mixed something up, internal pull-up is set on all unused pins. \u00a0Except D6 on the teensy side, since that's pulled low (IIRC) through an LED. \u00a0And the interrupt pins are floating I think on the left side (and there are some NC pins on that side as well..). \u00a0I can't think of any other exceptions off the top of my head.\n\nWe're using an MCP23018, and the Teensy 2.0 which has an ATMega23u4.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Sat, 02 June 2012, 01:56:56\nThe Teensy I am familiar with =) and I never had any of those problems using it. I would guess the IO-pins are pulled either way regardless if they are set as outputs or inputs (with pull-up), but it sure shouldn't hurt to turn on the pull-ups. Actually I think most of my problems have been with leaving RESET- or CLOCK-pins floating when playing\/learning logic ICs on a breadboard. When they start to flutter, very strange things tend to happen...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bebuxe on Sat, 02 June 2012, 05:03:12\nThis type of design on a keyboard is has always been what I wanted. Esp. when reclined Vertically. I wonder if we can add that, or just let the users do this. Also, would it not be easier to do the case in a type of hard acrylic (PMMA) by submersion into casts that are vertically assigned in some sort of silicon or rubber?\n\nI'll draw the idea in a few days, but basically it is a mold of the cases vertically aligned in a rubber\/silica\/foam cube with slits of these molds. Kinda like how cd cases are made. If you get it then I won't draw.\n\nAlso, the think I like about the size if the fact that we can abuse the Keyboard space to install an MCC or SD port to make it even boot. hehehe, we can even bootstrap a gumstix board to boot Linux with video, sound, wifi, and everything (http:\/\/gumstix.org\/software-development\/pre-built-images.html). God, How I love this era.\n\nFor now, lets concentrate on making this truly programmable KB. I wonder if we should do it from the keyboard, or flash the memory from an the computer? Still using the USB as power to flash the memory.\n\nTell me your Ideas, I know C, I can help in logic, but I do not know the advance stuff like Hex algorithms on the processor. I'd hate to use some proprietary with little documentation. I think I read this was going to be teensy, am I right? And really, I think we should not care about the BIOS compatibility. Everyone by now should have bought flashed ROMs with Phoenix Award BIOS or better yet coreboot. If you are a buyer, and say Nay, please do so.\n\nAlso, what encoding wille we use, UTF-8 or one of the latins?:\nhttp:\/\/en.wikipedia.org\/wiki\/Western_Latin_character_sets_(computing)\nI ask to see what I can do for output. I guess I need to read USB in a nutshell.\n\nAlso I work full time, so my contributions will be limited. I can offer a wiki if you like. Need to experiment with yawk.\n\nPS\nBehold this beauty:\nhttp:\/\/en.wikipedia.org\/wiki\/File:Lexus_LF-A_Crystallised_Wind.jpg\nAnd is functionality:\nhttp:\/\/en.wikipedia.org\/wiki\/File:Maylan-interior-design-neue-wiener-werkstaette-interlux-roehm-_evonik-_indeustries-contemporary-light-art-sedan-chair-seats-manfred-kielnhofer-illumination-auchtion.jpg\nSUSE Linux or The Attachmate Group was not part of this:\nhttp:\/\/en.wikipedia.org\/wiki\/File:Ted_Noten_Grandma's_Bag_Revisited_2009.jpg\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: REVENGE on Sat, 02 June 2012, 14:51:52\nQuote from: bebuxe;606110\nThis type of design on a keyboard is has always been what I wanted. Esp. when reclined Vertically. I wonder if we can add that, or just let the users do this. Also, would it not be easier to do the case in a type of hard acrylic (PMMA) by submersion into casts that are vertically assigned in some sort of silicon or rubber?\n\nI'll draw the idea in a few days, but basically it is a mold of the cases vertically aligned in a rubber\/silica\/foam cube with slits of these molds. Kinda like how cd cases are made. If you get it then I won't draw.\n\nAlso, the think I like about the size if the fact that we can abuse the Keyboard space to install an MCC or SD port to make it even boot. hehehe, we can even bootstrap a gumstix board to boot Linux with video, sound, wifi, and everything (http:\/\/gumstix.org\/software-development\/pre-built-images.html). God, How I love this era.\n\nFor now, lets concentrate on making this truly programmable KB. I wonder if we should do it from the keyboard, or flash the memory from an the computer? Still using the USB as power to flash the memory.\n\nTell me your Ideas, I know C, I can help in logic, but I do not know the advance stuff like Hex algorithms on the processor. I'd hate to use some proprietary with little documentation. I think I read this was going to be teensy, am I right? And really, I think we should not care about the BIOS compatibility. Everyone by now should have bought flashed ROMs with Phoenix Award BIOS or better yet coreboot. If you are a buyer, and say Nay, please do so.\n\nAlso, what encoding wille we use, UTF-8 or one of the latins?:\nhttp:\/\/en.wikipedia.org\/wiki\/Western_Latin_character_sets_(computing)\nI ask to see what I can do for output. I guess I need to read USB in a nutshell.\n\nAlso I work full time, so my contributions will be limited. I can offer a wiki if you like. Need to experiment with yawk.\n\nPS\nBehold this beauty:\nhttp:\/\/en.wikipedia.org\/wiki\/File:Lexus_LF-A_Crystallised_Wind.jpg\nAnd is functionality:\nhttp:\/\/en.wikipedia.org\/wiki\/File:Maylan-interior-design-neue-wiener-werkstaette-interlux-roehm-_evonik-_indeustries-contemporary-light-art-sedan-chair-seats-manfred-kielnhofer-illumination-auchtion.jpg\nSUSE Linux or The Attachmate Group was not part of this:\nhttp:\/\/en.wikipedia.org\/wiki\/File:Ted_Noten_Grandma's_Bag_Revisited_2009.jpg\nI think the sky and your wallet are the limits when it comes to case design and optional features.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Sat, 02 June 2012, 16:07:23\nI did some testing with the an adapted firmware from PrinsValium that I used for my doxkb at first and every key is registering correctly (no ghost keys).\nYou can download it here (http:\/\/www.lsdox.com\/ergodox\/ergodox_test.rar) if you want to take a look.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bebuxe on Sat, 02 June 2012, 16:21:20\n>REVENGE\nWell, it is a dream keyboard. One that I wanted to make, but nevertheless, do you not think it much cheaper to use PMMA for making the cases?\nI got a -1 of vertical alignment.\nHow it be programmed, OS level, or Hardware\/KB Level?\nSo it is the teensy, right? .\nIf so, what encoding do you all vote? UTF 8\u203d (I ask, cause there is a lot of symbols not needed in utf8\u2042 lots)\u203b\n\n\u203bIf you can't read these, it means you are not using UTF8, and probably do not need them.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: FedeQGMLY on Sat, 02 June 2012, 17:54:19\nHi guys, I'm new of GH, I found this thread looking for keyboards...and I think this project is awesome!\nI wasn't able to read 43 of the 46 pages of this thread (sorry), so I'm bluntly asking: do you have an idea about when you'll be able to actually sell\/ship this fantastic keyboard? And for which price approximately?\n\nAs someone previously pointed out, I also think keycaps are not mandatory...I mean, buying keycaps is not a problem as long as the keys are Cherry MX, am I wrong?\n\nFede\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Sat, 02 June 2012, 19:11:40\nQuote from: bebuxe;606333\nIf so, what encoding do you all vote? UTF 8\u203d (I ask, cause there is a lot of symbols not needed in utf8\u2042 lots)\u203b\n\n\u203bIf you can't read these, it means you are not using UTF8, and probably do not need them.\n\nYou keep asking about this encoding and I don't understand why. \u00a0Keyboards put out scancodes, they do not put out character set codes. \u00a0It is up to the OS to interpret the scancode and put the correct character on the screen (or alternately interpret it as the correct meta key).\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sat, 02 June 2012, 20:13:15\nQuote from: FedeQGMLY;606362\nHi guys, I'm new of GH, I found this thread looking for keyboards...and I think this project is awesome!\nI wasn't able to read 43 of the 46 pages of this thread (sorry), so I'm bluntly asking: do you have an idea about when you'll be able to actually sell\/ship this fantastic keyboard? And for which price approximately?\n\nAs someone previously pointed out, I also think keycaps are not mandatory...I mean, buying keycaps is not a problem as long as the keys are Cherry MX, am I wrong?\n\nFede\nHello and welcome to GH! I'll add you to the list. There's been a lot of pricing discussion, but nothing is set in stone yet. It all depends on what sort of volume pricing we can get. This is just a guess, but we should be able to get the PCB under $100, and the case maybe under$200. I haven't asked around for quotes yet, though.\n\nAs far as keyswitches and keycaps, some keyswitches are available at mouser.com, and there have been a number of group buys for them recently. Keycaps shouldn't be a huge issue, but you do have to realize that there are a large number of 1.5-width keys for the last row. You can see them as all the tabs and CTRL dox has in his picture, here:\nhttp:\/\/geekhack.org\/attachment.php?attachmentid=51456&d=1338008738\nThat's twelve 1.5 keys total, if I am seeing it right.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: hasu on Sat, 02 June 2012, 20:16:48\nDox and ic07, Great progress so far! and very inspired.\n\nAbout ghost key problem I have some words to say.\n\nIf you use port F you might want to check JTAGEN fuse bit and JTD bit of MCUCR. This JTAG configuration can prevent from operation of port F. Default fuse bit setting of Teensy makes JTAGEN fuse unprogrammed, so you won't have this program, though, I think you still should check this to make sure. See datasheet for detail.\nI'd like to recommend you try this code in init function:\nCode: [Select]\n \u00a0 \u00a0\/\/ JTAG disable for PORT F. write JTD bit twice within four cycles.\u00a0 \u00a0 MCUCR |= (1<<JTD);\u00a0 \u00a0 MCUCR |= (1<<JTD);\nAnd another one, you may want to add small delay between port setting and reading port while matrix scanning. I think you can have delay in _update_rows() in teensy-2-0.c. _delay_us(1 or 5) will be enough for this.\nIf you don't have this delay you might have a false reading of port.\nThough I'm not sure theory behind this :)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Sat, 02 June 2012, 20:30:08\nYes, my code contains those _delay_ms(1) after all changes to ports. I found erratic behavior without them. 1 us has been enough for me so far.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bebuxe on Sun, 03 June 2012, 05:20:10\n>alaricljs\nYes, but most of the scancodes are standardized HEX Interruption values that the OS decide in your favorite encoding. Most of the scan codes conform with the ISO\/IEC 9995 standard. That Is why ask if you like to have another to minimize\/optimize in the software overhead that UTF8 is.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: REVENGE on Sun, 03 June 2012, 15:21:33\nQuote from: bebuxe;606588\n>alaricljs\nYes, but most of the scancodes are standardized HEX Interruption values that the OS decide in your favorite encoding. Most of the scan codes conform with the ISO\/IEC 9995 standard. That Is why ask if you like to have another to minimize\/optimize in the software overhead that UTF8 is.\nStill unsure of what you're talking about. The scancode for each key is completely customizable at the hardware level by you, the end user.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Sun, 03 June 2012, 17:35:41\nQuote from: hasu;606415\nDox and ic07, Great progress so far! and very inspired.\n\nAbout ghost key problem I have some words to say.\n\nIf you use port F you might want to check JTAGEN fuse bit and JTD bit of MCUCR. This JTAG configuration can prevent from operation of port F. Default fuse bit setting of Teensy makes JTAGEN fuse unprogrammed, so you won't have this program, though, I think you still should check this to make sure. See datasheet for detail.\nI'd like to recommend you try this code in init function:\nCode: [Select]\n \u00a0 \u00a0\/\/ JTAG disable for PORT F. write JTD bit twice within four cycles.\u00a0 \u00a0 MCUCR |= (1<<JTD);\u00a0 \u00a0 MCUCR |= (1<<JTD);\nAnd another one, you may want to add small delay between port setting and reading port while matrix scanning. I think you can have delay in _update_rows() in teensy-2-0.c. _delay_us(1 or 5) will be enough for this.\nIf you don't have this delay you might have a false reading of port.\nThough I'm not sure theory behind this :)\n\nThanks a lot hasu!!! I have added a _delay_us(1) in the _update_rows() and everything register correctly now!\n\nCode: [Select]\nstatic inline void _update_rows( \u00a0 \u00a0 \u00a0 \u00a0bool matrix[KB_ROWS][KB_COLUMNS], uint8_t column ) {\u00a0 \u00a0 _delay_us(1);\u00a0 \u00a0 matrix[0][column] = ! teensypin_read(ROW_0);\u00a0 \u00a0 matrix[1][column] = ! teensypin_read(ROW_1);\u00a0 \u00a0 matrix[2][column] = ! teensypin_read(ROW_2);\u00a0 \u00a0 matrix[3][column] = ! teensypin_read(ROW_3);\u00a0 \u00a0 matrix[4][column] = ! teensypin_read(ROW_4);\u00a0 \u00a0 matrix[5][column] = ! teensypin_read(ROW_5);}\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Sun, 03 June 2012, 18:37:00\nic07, do you have a fn layer ready? I would need it to at least have F keys.\n\nedit: sent from the ergodox!\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Sun, 03 June 2012, 19:41:09\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Sun, 03 June 2012, 21:26:34\nSuper exciting! Can't wait for pictures of the case prototype to be shown!\n\nCheers,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Mon, 04 June 2012, 03:38:59\nThanks from me too hasu! \u00a0And PrinsValium. \u00a0And thanks DOX for trying it out and getting it working. \u00a0Changes now in the repo, and updated .hex on github (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/downloads') (and I deleted the bad one). \u00a0I put the _delay_us(1) at the end of the teensypin_write() macro.\n\nDOX:\nI also made a fn layer for you. \u00a0I feel like it's a mess (more than the current top layer), but it has the function keys, along with a few random symbols. \u00a0It's activated by holding down the lowermost of the 3 inside keys on either side of the board. \u00a0Here's a link to the layout file (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/keyboard\/ergodox\/layout\/qwerty.c') (it's only on the 'dev' branch for now) for convenience.\n\nAnd I'm excited that it's usable and in use now too!\n\nbebuxe:\nA USB keyboard in boot mode sends scancodes from the HID usage page 0x07 (which I made into a header file (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/lib\/usb\/usage-page\/keyboard.h'), if you'd like to see it), if I'm remembering my terms correctly. \u00a0There's also a usage page corresponding to UTF-8, but I'm not sure if it can be used by keyboards.\n\nAlso, remapping at this point is only possible by modifying the firmware, recompiling, and re-flashing. \u00a0Good news is, I don't think this will be too hard for anyone here, especially once I get around to writing a short howto. \u00a0On keyboard remapping is being considered (but only once everything else is done). \u00a0The rest is up to the OS.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Mon, 04 June 2012, 05:22:45\nQuote from: ic07;607097\nAlso, remapping at this point is only possible by modifying the firmware, recompiling, and re-flashing. \u00a0Good news is, I don't think this will be too hard for anyone here, especially once I get around to writing a short howto. \u00a0On keyboard remapping is being considered (but only once everything else is done). \u00a0The rest is up to the OS.\n\nI wonder how easy it would be to write up a quick frontend for changing layouts? Even if it just gave you a quick graphic of what you have, then output the proper source to flash the chip with, it'd be useful (to visual people like me)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dirge on Mon, 04 June 2012, 05:26:08\nI wonder how easy it would be to write up a quick frontend for changing layouts? Even if it just gave you a quick graphic of what you have, then output the proper source to flash the chip with, it'd be useful (to visual people like me)\n\nx2 I'm trying to get my head around the firmware and setup etc. \u00a0Finding it very difficult.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Mon, 04 June 2012, 07:58:13\nI wonder how easy it would be to write up a quick frontend for changing layouts? Even if it just gave you a quick graphic of what you have, then output the proper source to flash the chip with, it'd be useful (to visual people like me)\n\nFor the windows people, I have no problem drafting up a quick app that will allow adjustments of layouts. I will probably need some help interfacing it with the back end. If you want a Linux\/Unix GUI you might have to find another volunteer.\n\nI'll check out the firmware tonight, and see what I can do.\n\nCheers,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Mon, 04 June 2012, 08:04:09\nAlso,\n\nDOX, do you have a larger version of your avatar? I plan on using it for the About menu on the GUI, as well as making a .ico to use for the launcher. (Assuming you guys don't mind me writing up a front-end.)\n\nCheers,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: effh on Mon, 04 June 2012, 10:32:38\nHello All,\n\nI've been tracking this thread for a few days now, and this looks very interesting. I'm interested in 1 to 2 PCBs depending on final price. what with the need for key-switches as well, I can't afford to go in for the cases too.\n\nWith regards to simple remapping, I've just pulled down the code and winAVR [my duel boot box spends most of it's life in windows, go figure... : \u00a0( \u00a0 ] and it is possible to make gcc spit out a map-file, allowing us to locate the right symbol, and edit the hex file. Using this method it should be possible to distribute an \"official\" hex firmware and provide a utility that patches in changes to the keymap without requiring non-programmers to brave the world of C (and therefore from having to obtain and maintain tool-chains as well).\nI don't do user-interface programming but I can help with sorting out hex-file hacking.\n\nNotes[skip this section if you don't want the details.]: It will be necessary to make sure enough space is allocated for as many layers as is intended to be supported. It may also be necessary to clearly define which other symbols specify layer-shift keys.\n\nTo get the symbol map, add the following to LDFLAGS in the makefile: -Xlinker -Map=firmware.map\nAn example of the relevent section:\nCode: [Select]\n .progmem.data \u00a00x000000ac \u00a0 \u00a0 \u00a00x348 keyboard\/ergodox\/layout\/qwerty.o\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0x000002a4 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0_kb_layout_release\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0x00000154 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0_kb_layout_press\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0x000000ac \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0_kb_layoutFrom firmware.hex:\n:1000A0002EC200002CC200002AC20000E4E64B2849\nwe want 00ac, this starts at 00a0, so the relevent chunk of this line is E4 E6 4B 28, the first four keys in the map:\nKEY_RightControl; KEY_RightAlt; KEY_PageUp; KEY_ReturnEnter.\nmatrix.h specifies these as being { k00,k01,k02,k03, which ties up nicely with the right-hand thumb keys in the layer macro above and the matching qwerty keymap.\nNote that when replacing this lign in the hex-file, the first part needs to be written back unchanged and the last two chars are a checksum that will need updating for any changes.\n\nStill to determine: Does the teensy loader check any additional checksums? It isn't obvious from the map alone...\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Mon, 04 June 2012, 12:17:28\neffh,\n\nCan you give some details as to how you'd go from the modified hex file to re-flashing the firmware for the KB? It wouldn't be hard to have a separate \"user\" configuration hex file that could replace the default (with a restore option of course), what seems to be hard to do from the UI perspective is forcing the firmware to update. From a windows perspective, I wouldn't look forward to having to invoke a compile on the user's machines. Thoughts?\n\nCheers,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: effh on Mon, 04 June 2012, 12:40:28\nOrangeJewce,\n\nIt appears that there is a command-line version of the teensy loader here: http:\/\/pjrc.com\/teensy\/loader_cli.html\nThe point of directly modifying the hex file is that you don't have to do a compile, you've just \"hacked\" the result of the compile (the hex file) to have the keymap you want in it.\n\nI imagine that the utility would ship with the Teensy cli loader and a firmware version (.hex and .map or with the key details from the map hard-coded) which would then be used to either restore default or as the base to generate a custom firmware from.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Mon, 04 June 2012, 13:52:40\neffh,\n\nIt looks like you are right on all accounts. I'll make sure to package up the teensy CLI with the GUI. This will be on my TODO this evening after work. I am concerned there won't really be a way for me to test whether or not the process works without a controller handy but oh well. I'll have to rely on the Dox et al. to do the testing.\n\nCheers,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Mon, 04 June 2012, 14:21:32\nOrangeJewce, effh, you guys are awesome.\n\nModifying the hex is a good idea. \u00a0The only complication I can see is that layer switching is done by putting a different function for that key's location in the _kb_layout_press and _kb_layout_release matricies (see qwerty.c (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/keyboard\/ergodox\/layout\/qwerty.c') in 'dev' for an example).\n\nAllocating enough space for all the layers you want should only mean changing the value of KB_LAYERS in qwerty.h (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/keyboard\/ergodox\/layout\/qwerty.h') before compile. \u00a0Unused layers won't confuse anything.\n\nFor anyone trying to understand the layout, take a look at:\n\n- qwerty.h (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/keyboard\/ergodox\/layout\/qwerty.h') for the macro defining the number of layers, and the mapping from physical LED position to the meaning of the LEDs\n- qwerty.c (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/keyboard\/ergodox\/layout\/qwerty.c') for the keycodes, key press functions, and key release functions assigned to each physical key position\n- and usb\/usage-page\/keyboard--short-names.h (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/lib\/usb\/usage-page\/keyboard--short-names.h') for all availble keycodes (or usb\/usage-page\/keyboard.h (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/lib\/usb\/usage-page\/keyboard.h') for the actual hex codes)\n\nThose three files should contain everything you need. \u00a0If you want more information, you can look at:\n\n- matrix.h (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/keyboard\/ergodox\/matrix.h') for a more thorough description of the LAYER() macro used in 'qwerty.c', and what it's doing\n- and if you really want to get into it, key-functions.c (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/dev\/src\/lib\/key-functions.c') is where the functions called for each key(press|release) are defined; you might have to poke through the PJRC USB code (in src\/lib-other\/...) to understand parts though\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Mon, 04 June 2012, 15:01:26\nic07,\n\nMy thinking is that when you switch layers, the keyboard is using a different section of the compiled .hex to do the mapping. Therfore I would expect that we should still be able to directly hack our way through the compiled .hex to alter the key-mappings for each layer.\n\nGoing the GUI route would mean we might have to make some sacrifices if we choose not to recompile the firmware. My plan is to only offer the number of layers officially coded into the firmware source, so that would be 2 right now. However, if a user really wants more layers, then they can always edit the default.hex by replacing it with one of their own or by compiling the source.\n\neffh,\n\nI am concerned about the checksum issue. Are you sure that the teensy will refuse to accept updates if a modification is made to the .hex without generating new checksums? If that's the case we probably won't have any choice but to force a compile of the firmware source.\n\nCheers,\n\nOJ\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Dox on Mon, 04 June 2012, 17:41:36\nOrangeJewce and effh, good ideas for the remapping, keep it up!\n\nQuote from: OrangeJewce;607145\nAlso,\n\nDOX, do you have a larger version of your avatar? I plan on using it for the About menu on the GUI, as well as making a .ico to use for the launcher. (Assuming you guys don't mind me writing up a front-end.)\n\nCheers,\nPost 17 here (http:\/\/geekhack.org\/showthread.php?17374-My-keyboard-project). Thanks to calavera.\n\nic07, I think there is a bug with the fn layer. I used the prototype all day at work and sometimes, the fn layer becomes inaccessible after some use.\nOtherwise, everything went well. With the thumb keys a bit closer, it will be perfect! I already prefer it to the kinesis. With the flat shape, it gives me more freedom when I need it and the ability to place each hand in the optimal position is really great.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: effh on Mon, 04 June 2012, 18:59:33\nOrangeJewce,\n\nNo, I'm not that concerned about there being an aditional checksum, that would be an extra-work feature that would have required cooperation between teensy and winAVR or an extra added by ic07 (which hasn't been mentioned, so hasn't happened.) so it is a low probability.\nWith regards to switching sections of the compiled hex, all layers have been implemented as part of the same array and are contiguous.\n\nThe map I have here was built off of the dev tree and states that _kb_layout starts at 0x00ac, the next symbol being at 0x0154. that is 168 bytes.\nThe layer macro defines 84 bytes of data per layer, 168\/84 is 2. \u00a0Coincidentally, thats the number of layers currently in the dev-branch, so we've found all the keymap definitions. (though I've not fully explained to my satisfaction _kb_layout_press and _kb_layout_release. erg. Now I have. _kb_layout is of type uint8_t, the other two is of type kbfun_funptr_t (pointer to function). effective but fun to handle. Examination shows repetition at 16-bit intervals. But not of a sequence that ties up to the map's definition of the functions I was expecting. I'll do some more digging later when it isn't approching 0100.\nUpdate: The value stored in the press and release tables is the \"word address\" of the function in flash, while the map has the \"byte address\". the byte address from the map divided by 2 gives the value in the table. Note that the avr is a little endian device, so an address of 0x0b7e divided by two is 0x05bf and would appear in the .hex as bf05.\n\nSummary:\n#1: Don't worry about checksums, we'll cross that bridge if we meet it.\n#2: We also know now where all the keymapping is, even if we don't know the right values for the press and release functions yet.\n#3: Values of positions will change on each compile, so if we can work out how to extract the values programatically from the map, that would be best.\n\nic07,\n\nThe definition of the Layer macro is the fundamental mapping of what keys are where in the array, so that is going to be critical : \u00a0)\nSo far, so good.\n\nSorry about any typos, dyslexia and late nights don't mix.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Mon, 04 June 2012, 19:39:59\neffh,\n\nThanks for the clarification. I am working on the prototype GUI right now. I have all 76 buttons created, but have yet to implement the back end. Obviously that will take the longest to do, as I still don't really have a grasp as to how the firmware is going to work. For anyone interested I have forked off the git and made a UI branch. It is a WinForms project (It's just too easy for this kind of thing. Might upgrade to WPF later) in C#. I make a pull request later this evening. No ETA as of yet on how long this UI project will take, I presume there is at least a little time before we have a fully assembled prototype in Dox's Hands.\n\nCheers,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: effh on Mon, 04 June 2012, 20:32:07\nOrangeJewce,\n\nIf we can agree a simple (that means not xml) file interchange format, I can probably do a cut of code (c++ as for cross-platform usage and reduced writing time) that would modify the map in a hex-file\/map pair.\nI'm thinking something like:\nCode: [Select]\n:_kb_layout{lf}ababababababababababababababab{lf}:_kb_layout_press{lf}111111121111113111111411111{lf}:_kb_layout_release{lf}111111121111113111111411111{lf}where ab is a byte represented in ascii, 1 2 3 and 4 are press, release, layer increment and layer decrement and {lf} is a linefeed character (0x0a in the table)\nI can also set up options to allow getting the number of layers in the map from the map. (based on size of allocation.)\n\nThoughts?\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Mon, 04 June 2012, 20:45:41\neffh,\n\nThat sounds great!\n\nCheers,\n\nOJ\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Tue, 05 June 2012, 15:16:16\nQuote from: Dox;607456\nic07, I think there is a bug with the fn layer. I used the prototype all day at work and sometimes, the fn layer becomes inaccessible after some use.\n\nI looked at the logic again last night, and it still looks right to me... \u00a0Do you have any ideas? \u00a0Or at least, in laborious detail, what exactly's happening (maybe this calls for a PM) lol :) . \u00a0Sorry you have to help debugging stuff I wrote, but I can't think of a way to test it myself... :\/ . \u00a0If *any* keys are registering, those should be working too... \u00a0I suppose, worst case, I can try to start rewriting the thing next week.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Tue, 05 June 2012, 15:39:39\nQuote from: ic07;608033\nI looked at the logic again last night, and it still looks right to me... \u00a0Do you have any ideas? \u00a0Or at least, in laborious detail, what exactly's happening (maybe this calls for a PM) lol :) . \u00a0Sorry you have to help debugging stuff I wrote, but I can't think of a way to test it myself... :\/ . \u00a0If *any* keys are registering, those should be working too... \u00a0I suppose, worst case, I can try to start rewriting the thing next week.\n\nic07,\n\nIt would be helpful if we can keep changes to the backend to a minimum (outside of bug fixes like this), since effh & I will be relying on consistency there to create a usable GUI. Though we'll be hacking the compiled hex directly, it would be nice to be able to know that recompilation we do will give us consistent results. I am having a hard time following what's going on in main.c, in the innermost for loop. Where do you specify a switching between layers?\n\nCheers,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Tue, 05 June 2012, 15:47:12\nic07,\n\nfollow up: main.c is missing an include in the repo: . Can you add that?\n\nCheers,\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: bebuxe on Tue, 05 June 2012, 17:48:30\n>ic07\nThanks, that is exactly what I was talking about. Will make more \/layout\/ later, after I clean my apartment. I guess remapping will be the way to go here then at the OS level then.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Tue, 05 June 2012, 18:21:12\nYep, the possibility of HW remapping is one of the best features for me.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: effh on Wed, 06 June 2012, 01:28:09\nQuote from: OrangeJewce;608049\nic07,\n\nIt would be helpful if we can keep changes to the backend to a minimum (outside of bug fixes like this), since effh & I will be relying on consistency there to create a usable GUI. Though we'll be hacking the compiled hex directly, it would be nice to be able to know that recompilation we do will give us consistent results. I am having a hard time following what's going on in main.c, in the innermost for loop. Where do you specify a switching between layers?\n\nCheers,\n\nI'm going to have to counter that. For starters, I suspect a couple of changes will be necessary to support 3+ layers.\n\nic07, Make any changes you need\/want to make, just keep the layout in a nice sensible array\/set of arrays in \"progmem\". (I need to look up the details of that sometime : \u00a0)\n\nAt some point, it would make OrangeJewce's life easier if one of us could detail the order of keys in the array when expressed as flat memory, as that is the order I'll be needing the data in to in-fill the hex file.\n\nTo reiterate: so-long as _kb_layout, _kb_layout_press and _kb_layout_release don't change their definitions (and the functions used in _kb_layout_ don't change name and number), and that a map file has been built along with the hex file, what I have in mind should continue to work. Changes to those will require some degree of rework and thus notification of changes to them would be appreciated.\nGeneric Solutions for the win : \u00a0)\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Wed, 06 June 2012, 14:06:07\nQuote from: OrangeJewce;608049\nI am having a hard time following what's going on in main.c, in the innermost for loop. Where do you specify a switching between layers?\n\nThe innermost loop in main.c is *only* responsible for calling the appropriate function (assigned to each key in the layout matrices, and defined in lib\/key-functions.c), and then calling usb_keyboard_send() if necessary. \u00a0Everything else is done by the key function - so layer switching (changing the value of the current_layer variable at the top of the outer main() loop) is actually done in lib\/key-functions.c::kbfun_layer_inc() and lib\/key-functions.c::kbfun_layer_dec().\n\nQuote from: OrangeJewce;608058\nfollow up: main.c is missing an include in the repo: . Can you add that?\n\nis part of avr-libc. \u00a0And the #include is in main.c in every branch I checked (though, I did forget it a few commits ago, when I committed -> pushed without trying to compile first - which wasn't very smart of me, lol).\n\nQuote from: effh;608373\nic07, Make any changes you need\/want to make, just keep the layout in a nice sensible array\/set of arrays in \"progmem\". (I need to look up the details of that sometime : \u00a0)\n\n:) . \u00a0I don't anticipate changing how the _kb_layout* matrices are defined unless I really really (really) have to. \u00a0And the kbfun_*() functions used in _kb_layout_ shouldn't be changing much either (though, I'm not sure what you mean by \"name and number\"; but their names shouldn't change, and I won't remove any). \u00a0I'll do my best to let you guys know if I start messing with stuff that I think might affect you.\n\nAs a side note, having the layout matrices in PROGMEM is not guaranteed by the current design (it's the default, but it can be changed per layout). \u00a0I'm not planning to put any anywhere else though, since RAM only has enough space for ~2 layers IIRC, the EEPROM is even smaller, and the extra time\/code it takes to have stuff in PROGMEM appears to be inconsequential.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Wed, 06 June 2012, 17:38:01\nI'm interested in learning how to do some keymap-making or key layout changing. Is there some sort of documentation on how to do this:\n\nI'm interested in\nfunction layer (s)\nMouse buttons\nHitting both shifts activates capslock\n\nY'know, things like that. Are there any resources you can share?\n\nI might come up with some proposed keymaps for people.\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Wed, 06 June 2012, 18:22:53\nI'm interested in learning how to do some keymap-making or key layout changing. Is there some sort of documentation on how to do this:\n\nI'm interested in\nfunction layer (s)\nMouse buttons\nHitting both shifts activates capslock\n\nY'know, things like that. Are there any resources you can share?\n\nI might come up with some proposed keymaps for people.\n\nThe ultimate goal will be that when people get the keyboard, they will have access to our open source UI and firmware, which will allow them to use either the default QWerty \/ ic07 layout or any other layout of their choice (the software will automatically do any compiling and hardware flashing necessary). The UI will be Windows only, XP and above. If you're running linux, you'll have to manually edit the firmware, compile it, and flash the teensy 2.0 controller manually.\n\nMouse buttons won't be a part of the software as far as I know. I am not sure how the Teensy would handle this, seems to me it would almost have to register as two pieces of hardware to achieve. As far as we know, at the very least 2 layers will be available to the end users. A default and function layer. If you'd like to know what the default currently is, I point you to the source, or to sit tight until I can make a prototype UI available which will allow the designing of any custom layout of your choice. Let me know if you have any questions as I would be glad to help!\n\nCheers,\n\nOJ\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: Salisen on Thu, 07 June 2012, 18:16:23\nI'm definitely interested in getting one of these, ideally with a price lower than about $300. I know I'm very new around here, but I potentially could provide a soldering service for 2-3 Europe based people (sending to the UK and back from outside of Europe would cost a fortune in custom's fees). I'll be extremely busy around April to early June of 2013 due to the last exams of my degree, but I will otherwise have sufficient time. I noticed someone mentioned in the Phantom thread about needing PCB designers. On that note, electronics is a major hobby of mine: I have some experience with PCB design. For this reason I'd be interested in helping design the PCB, but preferably working with someone who can check things I'm working on occasionally, I'm not confident about avoiding mistakes (I'm a physics undergrad, not an electronics engineer!). I do have a bench supply, breadboard, etc though, so I can test layouts I design. Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Thu, 07 June 2012, 23:14:20 Quote from: dorkvader;608803 I'm interested in learning how to do some keymap-making or key layout changing. Is there some sort of documentation on how to do this: Not yet, unless you're comfortable with C and have time for a bit of reading. I can post links to the relevant files again if you like. But since OrangeJewce and effh are going to make a GUI, I'd recommend waiting for that. I'm sure it'll be more fun to use, in any case :) . - Function layers are being debugged. Once done, I'm sure the GUI will make them easy to work with. - Mouse buttons are in progress, but depend on my eventual comprehension of certain things about USB... I'm trying! - Hitting both shifts to activate capslock is a good idea. I'll see what I can do after layers work right. It \/shouldn't\/ be too hard. Quote from: OrangeJewce;608836 Mouse buttons won't be a part of the software as far as I know. I am not sure how the Teensy would handle this, seems to me it would almost have to register as two pieces of hardware to achieve. It will basically be pretending to be two devices, if I succeed in implementing it. It's not an uncommon thing though - IIRC, several custom firmwares around geekhack have this feature (hasu's included) - I just need to figure out how to do it myself. Quote from: OrangeJewce;608836 As far as we know, at the very least 2 layers will be available to the end users. A default and function layer. Would more be useful? I did the math just now, and I think there's room in flash for ~60 layers... lol. And having extra allocated won't hurt. How many do you think would be good? Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Thu, 07 June 2012, 23:33:17 An option you might want to look into is having layer lock key combos. This way you could hit Fn-1 (or something similar) and it would switch to the 'qwerty' layer as the default until another layer lock is used. This way a user could have several alternate layouts like dvorak and colemak at a simple key combo press. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Thu, 07 June 2012, 23:47:55 Quote from: ic07;609575 Not yet, unless you're comfortable with C and have time for a bit of reading. I can post links to the relevant files again if you like. But since OrangeJewce and effh are going to make a GUI, I'd recommend waiting for that. I'm sure it'll be more fun to use, in any case :) . - Function layers are being debugged. Once done, I'm sure the GUI will make them easy to work with. - Mouse buttons are in progress, but depend on my eventual comprehension of certain things about USB... I'm trying! - Hitting both shifts to activate capslock is a good idea. I'll see what I can do after layers work right. It \/shouldn't\/ be too hard. I would strongly suggest just waiting it out unless someone else wants to get adventurous with compiling firmware. I haven't heard from effh in a while regarding the UI backend, so I might begin implementing part of it myself over the weekend. We'll just have to see how much time I have, or if he gets back to me. :thumb: Quote from: ic07;609575 It will basically be pretending to be two devices, if I succeed in implementing it. It's not an uncommon thing though - IIRC, several custom firmwares around geekhack have this feature (hasu's included) - I just need to figure out how to do it myself. Alright so it would behave exactly as I thought. I didn't really think it was impossible, only that it couldn't be done with the controller registering itself as a single piece of hardware. There has been reports of by doing multiple registration, one loses correct functionality on a mac. This might need investigating if you manage to get mouse buttons implemented. I'm not sure how high up the ticket totem pole it is anyways. Quote from: ic07;609575 Would more be useful? I did the math just now, and I think there's room in flash for ~60 layers... lol. And having extra allocated won't hurt. How many do you think would be good? I think people would like at least 3, up to (I could imagine) 6, Qwerty+F'n Dvorak+F'n\/custom Colemak+F'n\/custom I guess people might want more than that, but really it'd be a stretch for phase 1. The great thing is that I plan on having an export feature (might not be on release but I'm going to try), which will allow the community to share their layouts, and it will be modular because the UI will be able to flash the controller with just the .hex file. Either way I'm still very excited about this project and look forward to delivering something at least usable by the community for creating, sharing, and distributing any layout they can possibly think of. Cheers, OJ Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Thu, 07 June 2012, 23:55:00 also ic07 YGPM Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Fri, 08 June 2012, 00:40:27 I'd say we should have support for 4 layers, to accommodate practitioners of NEO. I'd have: Dvorak QWERTY Function Special as my layers (special would be a testing layout, if I want to update Dvorak some, or overflow from function) I will want to have some combination of QWERTY and dvorak, so if the computer is expecting dvorak or qwerty, I can use a layer to match. Salisen, you're added to the list, but I haven't updated the OP yet. Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Fri, 08 June 2012, 01:19:21 One thing about layers that I am afraid many might be missing is that the harware \"layers\" is not the full story. The keyboard still only sends a combination of keys. There are no actual functions associated wit what the keys do in the OS. That is all up to the OS to decide. If i want for example my '1'-key to be the '&'-key on another layer that will not be the same as defining say 'SHIFT'+'1' as '&', it will not be the shift layer. That layer would be a shifted layer where the '7'-key on a layer with 'SHIFT' activated. Since it is the OS that usually handles layers it is a bit backwards to do it in the firmware. There are of course workarounds. On the Kinesis you can remap any key to do whatever any other key does. For example the switch the location of '1' and '&', and also program macro keys. The way I understand that they handle this is by defining every keypress as a keycode along with the modifier keys used for that particular key. That is every key is defined as a tuple of keycodes that are used simultaneously. If the '1'-key is set to be a '&'-key, the keyboard woll briefly send 'SHIFT'+'7' when the '1'-key is pressed. This works, but is a lot more tedious than I think everyone here is aware of =) This is not the full story either... say I want a layer on my keyboard where the 'A'-key is an '\u03b1'-key (alpha), Alpha is not even in the OS keymapping, no combination of keypresses will be able to produce it. All this may be possible to solve installing other drivers or something, but that I know nothing about, and also that wouldn't be very pretty at all... Title: [Interest Check] Custom split ergo keyboard. Post by: sordna on Fri, 08 June 2012, 01:32:55 Actually, the kinesis remaps entire keys. You can map 7 to 1 or 1 to 7 (dragging along the ! and & when shifted) but you cannot map 1 to & or 7 to ! or 1 to ! for that matter. Macros can contain any letters, modifiers, and symbols, but key remapping is for entire keys. Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Fri, 08 June 2012, 01:46:53 Ok, I didn't really know. I only remember seeing the Kinesis at work sending modified keys in a keyboard testing program where the keys light up, and the shift key was coming on and off a lot =) My own belief is that layers are best handled with custom character mappings on the OS side. This gives rise to the same portability issues as (potentially) having custom drivers. My Linux workaround when I get around to implement it would be to have a complete keyboard mapping typed out into a terminal by some keypress combo. Could just be a heap of \"xmodmap\"-commandos or an actual xkb-file with all the bells and whistles. Keyboard mapping is a complete mess in Linux in my opinion.. Other OSs I don't really know about. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Fri, 08 June 2012, 08:48:25 Quote from: PrinsValium;609612 One thing about layers that I am afraid many might be missing is that the harware \"layers\" is not the full story. The keyboard still only sends a combination of keys. There are no actual functions associated wit what the keys do in the OS. That is all up to the OS to decide. If i want for example my '1'-key to be the '&'-key on another layer that will not be the same as defining say 'SHIFT'+'1' as '&', it will not be the shift layer. That layer would be a shifted layer where the '7'-key on a layer with 'SHIFT' activated. Since it is the OS that usually handles layers it is a bit backwards to do it in the firmware. There are of course workarounds. We choose to alter the microcontroller because it's easier to do, and it works. Otherwise we'd need to craft OS specific drivers (not likely to happen). Quote from: PrinsValium;609612 On the Kinesis you can remap any key to do whatever any other key does. For example the switch the location of '1' and '&', and also program macro keys. The way I understand that they handle this is by defining every keypress as a keycode along with the modifier keys used for that particular key. That is every key is defined as a tuple of keycodes that are used simultaneously. If the '1'-key is set to be a '&'-key, the keyboard woll briefly send 'SHIFT'+'7' when the '1'-key is pressed. This works, but is a lot more tedious than I think everyone here is aware of =) This is not the full story either... say I want a layer on my keyboard where the 'A'-key is an '\u03b1'-key (alpha), Alpha is not even in the OS keymapping, no combination of keypresses will be able to produce it. All this may be possible to solve installing other drivers or something, but that I know nothing about, and also that wouldn't be very pretty at all... My understanding is the Kinesis allows on the fly hardware mapping outside of the OS. Afaik, has no handle in how the keymap is stored, altered, or saved with regards to the onboard memory of the Kinesis' microcontroller. My guess is its memory is addressable and maybe they use some form of pointer system (pure speculation), and so you can shift around the addressing of the keys directly. Unfortunately for us to implement a feature similar to this would most likely consume much of the available memory on our controller and severely limit the number of layers, with limited additional benefit over a UI. Also it may or may not take more development time than we currently have, but I defer to ic07 on this issue, since he's doing all the low level work. Title: [Interest Check] Custom split ergo keyboard. Post by: Salisen on Fri, 08 June 2012, 12:04:58 How are you looking to switch between layers? From the keyboard's point of view, I mean. My QPAD changes the backlighting brightness by holding fn and pressing one of two other keys. Could also use some sort of 3-4 way DIP switch on the PCB. Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Fri, 08 June 2012, 13:25:16 Quote from: OrangeJewce;609718 We choose to alter the microcontroller because it's easier to do, and it works. Otherwise we'd need to craft OS specific drivers (not likely to happen). My point still stands. There are more and less unsolvable layout issues working with the keyboard side alone. Quote from: OrangeJewce;609718 My understanding is the Kinesis allows on the fly hardware mapping outside of the OS. Afaik, has no handle in how the keymap is stored, altered, or saved with regards to the onboard memory of the Kinesis' microcontroller. My guess is its memory is addressable and maybe they use some form of pointer system (pure speculation), and so you can shift around the addressing of the keys directly. Unfortunately for us to implement a feature similar to this would most likely consume much of the available memory on our controller and severely limit the number of layers, with limited additional benefit over a UI. Also it may or may not take more development time than we currently have, but I defer to ic07 on this issue, since he's doing all the low level work. There is 1kB of EEPROM memory where the firmware can save settings from time to time. That is a lot of layouts.. Keycodes are only 1 byte, pointer probably the same. As Sordna said the Kinesis only supports swapping keys, not really remapping individual \"characters\". A key swapping function should be fairly straight forward to implement... No need to have the firmware \"finished\" before the physical product is finalized. The prototype is a perfectly well functioning keyboard (ok there may possibly be some bugs). The Teensy is infinitely re-programmable, and this is easily done as well. You will have forever to improve upon the firmware. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Fri, 08 June 2012, 14:07:33 Quote from: PrinsValium;609822 My point still stands. There are more and less unsolvable layout issues working with the keyboard side alone. I guess I don't understand then exactly what your point is, so I apologize. The design decision was made to work from the keyboard end to ensure compatibility with any OS, because that would mean doing a single implementation as opposed to many. There are always going to be pros and cons to any design decision. There really isn't such a thing as \"Finished\" in programming, as one can always improve it. However, the firmware should be stable and have some basic features that are cornerstones of why we are undergoing this project. Remapping is one of those features. However, we shouldn't get into an argument about coding methodology here, I don't feel this is the right place. If you would like to draft up drivers for Windows or any of the other OSes we'd be more than happy to see what it is you come up with. The more the merrier :thumb:. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: effh on Fri, 08 June 2012, 15:50:03 For those wishing to play with the windows side of keyboard-layouts, I found this utility belonging to microsoft. http:\/\/msdn.microsoft.com\/en-us\/goglobal\/bb964665.aspx I've not done more than download it yet, but I'm looking to cure my caps-lock problem..... : ) Update: Okay, so that is the next best thing to useless - for some reason, some specific keys can not be changed... like caps-lock. I note that this utility does allow you to specify alternate shift mappings, so combined with changing the actual keyboard firmware may form part of a complete solution. Title: [Interest Check] Custom split ergo keyboard. Post by: mSSM on Fri, 08 June 2012, 18:47:13 What do you guys think - can this be a good replacement for a Kinesis? And is there an ETA for the \"final\" prototype (including the case)? I am deliberating getting either the Ergo Dox or the Kinesis; I can't afford both. :( Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 09 June 2012, 01:04:28 Quote from: mSSM;610027 What do you guys think - can this be a good replacement for a Kinesis? And is there an ETA for the \"final\" prototype (including the case)? I am deliberating getting either the Ergo Dox or the Kinesis; I can't afford both. :( I've not tried a TE, but I see this as a better version of that. Also keep in mind that whatever you get, you can probably resell it for most of the value in the classifieds once you're done. Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Sat, 09 June 2012, 02:18:50 The resale value of the ergodox is likely to be close to the final price. If you buy the Kinesis first, you will probably miss out on the ergodox. If you buy the ergodox, you'll have the option of the Kinesis later. Title: [Interest Check] Custom split ergo keyboard. Post by: mSSM on Sat, 09 June 2012, 08:29:10 Quote from: hoggy;610193 The resale value of the ergodox is likely to be close to the final price. If you buy the Kinesis first, you will probably miss out on the ergodox. If you buy the ergodox, you'll have the option of the Kinesis later. Good point; my impression was that the resale price of the Kinesis is reaaaally bad. Neither here nor on deskthority are people particulary interested in those. And eBay is even worse. Last Kinesis went for 25% of its original price. :( Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Sat, 09 June 2012, 10:36:07 Quote from: mSSM;610275 Good point; my impression was that the resale price of the Kinesis is reaaaally bad. Neither here nor on deskthority are people particulary interested in those. And eBay is even worse. Last Kinesis went for 25% of its original price. :( The ErgoDox will be a really unique, and most likely will be a rare piece of hardware. For that reason alone you can expect it to retain value well. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Sat, 09 June 2012, 11:06:50 Quote from: OrangeJewce;609869 I guess I don't understand then exactly what your point is, so I apologize. The design decision was made to work from the keyboard end to ensure compatibility with any OS, because that would mean doing a single implementation as opposed to many. There are always going to be pros and cons to any design decision. I've explained as well as I think I am able to. I'm only trying to warn you to not try to solve an unsolvable problem. The limitations that come with working from the keyboard side alone may or may not apply to your needs. I'm just saying that everything cannot be done that way. Quote from: OrangeJewce;609869 If you would like to draft up drivers for Windows or any of the other OSes we'd be more than happy to see what it is you come up with. The more the merrier :thumb:. Cheers, If I had any idea how to do it, I probably wouldn't be that crazy. My point is that keymappings on the OS side solves all but the portability issues. It would have been easier if keyboards were designed to send unicode characters or something similar, and the OS would handle only the conversion if another map than the physical one on the keyboard was required. There are of course good reasons to why it is the way it is as well. I know how to do keyboard mappings in Ubuntu (sort of). It is insanely messy for such a simple thing but it works and it solves most problems much more nicely. Edit: Ok, most problems might be an exaggeration, but there are a lot more options altering the OS key mapping. And I also wanted to add that there already is layer support in the firmware if I understand correctly. It might just not be completely bug free. Title: [Interest Check] Custom split ergo keyboard. Post by: Icarium on Sat, 09 June 2012, 14:15:00 I thought on the windows side people were pretty happy with what Autohotkey can do? Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Sat, 09 June 2012, 15:26:23 Quote from: Icarium;610387 I thought on the windows side people were pretty happy with what Autohotkey can do? It's not ideal: not easily portable, does not work with certain programs. Title: [Interest Check] Custom split ergo keyboard. Post by: Salisen on Sat, 09 June 2012, 17:48:31 Quote from: REVENGE;610414 It's not ideal: not easily portable, does not work with certain programs. I think it can be flagged up by anti-cheating software in games as well. Not really worth the risk. Title: [Interest Check] Custom split ergo keyboard. Post by: hoggy on Sun, 10 June 2012, 02:29:54 Quote from: mSSM;610275 Good point; my impression was that the resale price of the Kinesis is reaaaally bad. Neither here nor on deskthority are people particulary interested in those. And eBay is even worse. Last Kinesis went for 25% of its original price. :( There you go then. Get the Kinesis board from here or ebay and then get the ergodox in this group buy. The Kinesis is a great board, if you think you need one, get one! Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Sun, 10 June 2012, 21:40:08 Quote from: alaricljs;609580 An option you might want to look into is having layer lock key combos. This way you could hit Fn-1 (or something similar) and it would switch to the 'qwerty' layer as the default until another layer lock is used. This way a user could have several alternate layouts like dvorak and colemak at a simple key combo press. Layer lock key combos are a good idea, and would be easy to put on a key in a function layer. I'll plan to add that capability in a bit. Thanks! Quote from: OrangeJewce;609584 I think people would like at least 3, up to (I could imagine) 6 Quote from: dorkvader;609602 I'd say we should have support for 4 layers, to accommodate practitioners of NEO. Mmkay. Thanks :) . I think I'll allocate 10 then, by default, just to have a nice round number. Having extra shall not hurt. Quote from: OrangeJewce;609718 My understanding is the Kinesis allows on the fly hardware mapping outside of the OS. ... Also it may or may not take more development time than we currently have, but I defer to ic07 on this issue, since he's doing all the low level work. Quote from: PrinsValium;609822 There is 1kB of EEPROM memory where the firmware can save settings from time to time. That is a lot of layouts.. Keycodes are only 1 byte, pointer probably the same. As Sordna said the Kinesis only supports swapping keys, not really remapping individual \"characters\". A key swapping function should be fairly straight forward to implement... It would be possible to implement Kinesis like remapping, but it involves tradeoffs that, the more I think about them, the less I want to make them. A complete layer (keycode + two function pointers for a 12x7 matrix, function pointers being 16 bit) is 420 bytes, which means the EEPROM could actually only hold two. We could limit special functions from maps with that capability, and store only the keycodes in the EEPROM, or I could devise a method for only storing changed layout info there; or we could limit the number of layers to two. But I don't really like the idea of doing any of that for such an (IMO) limited gain in functionality. I'm open to reconsider though, if I find that there's really enough interest. Quote from: Salisen;609782 How are you looking to switch between layers? From the keyboard's point of view, I mean. My QPAD changes the backlighting brightness by holding fn and pressing one of two other keys. Could also use some sort of 3-4 way DIP switch on the PCB. We're switching layers using keypresses (fn\/layer keys). Layer lock key combos are planned (thanks to alaricljs for the suggestion). If anyone wants to change the keyboard's default\/startup layer though, they'll have to reflash the controller (but that should be easy enough, especially on Windows once OrangeJewce and effh are done with their UI). Quote from: PrinsValium;610342 My point is that keymappings on the OS side solves all but the portability issues. It doesn't though. Remapping any of the 'lock' keys, for instance, is hard to do OS side. But I understand what you're saying about limitations. Personally, I'm going to use both methods (OS remapping for Greek characters and OS functions, firmware for everything else). Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Mon, 11 June 2012, 02:44:12 Quote from: ic07;610998 It would be possible to implement Kinesis like remapping, but it involves tradeoffs that, the more I think about them, the less I want to make them. A complete layer (keycode + two function pointers for a 12x7 matrix, function pointers being 16 bit) is 420 bytes, which means the EEPROM could actually only hold two. We could limit special functions from maps with that capability, and store only the keycodes in the EEPROM, or I could devise a method for only storing changed layout info there; or we could limit the number of layers to two. But I don't really like the idea of doing any of that for such an (IMO) limited gain in functionality. I'm open to reconsider though, if I find that there's really enough interest. Store a backup of the \"standard\" 12x7 layout array, after that there should be room for perhaps 11 more copies of this that can be modified any way required. The base array could be stored in flash memory as well. That would give room for another one as well as protect it from corruption =) I don't know if on the fly remappings like on the Kinesis is very useful when you can program the keyboard anyway you like anyhow. Storing macros in the EEPROM sounds more interesting to me. I envision those as linked lists of (key, modifiers, next pointer)-triplets. Each list item would take 4 bytes if pointers are 2 bytes. Quote from: ic07;610998 It doesn't though. Remapping any of the 'lock' keys, for instance, is hard to do OS side. But I understand what you're saying about limitations. Personally, I'm going to use both methods (OS remapping for Greek characters and OS functions, firmware for everything else). Of course you are correct. Things the OS doesn't need to know about is best kept in the dark =) I should have said that \"character mapping\" problems are best solved on the OS side. Once again macros might be the solution I'm actually looking for. Do I want to type '\u03bb' or really just \"\\lambda\"? =D There is also a micro SD-card adapter (http:\/\/pjrc.com\/store\/sd_adaptor.html) for the Teensys. Imagine GBs of data... I had plans to use one as a keylogger on my own keyboard. I haven't been experimenting any with it, but there are adapters in my home built boards. Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Mon, 11 June 2012, 06:12:55 Quote from: PrinsValium;611101 Storing macros in the EEPROM sounds more interesting to me. I envision those as linked lists of (key, modifiers, next pointer)-triplets. Each list item would take 4 bytes if pointers are 2 bytes. Hmm, I hadn't been thinking about macros; and I would think those were easier to do in the OS (or.. I use gvim, so that's where mine are). Still interesting though, maybe I'll think about them again sometime when I'm not so tired :) . Would you prefer them in firmware? If so, why? [\/HR] DOX: Updated firmware in 'dev'! And new .hex posted. Hopefully those layer switching problems are gone now... please let me know if you test it. It seemed to be working properly in my cursory little breadboard test. OJ, effh: I touched lib\/key-functions* a bit, but I didn't change any function names (or get around to adding any yet). Most of the layer logic that changed was in main(), and I can't recall doing anything that would effect you guys. And I think that's it. I'm tired, coz it's really late o_o , but I wanted to get the modified layer code out as soon as I could, in case DOX was waiting for it. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Mon, 11 June 2012, 09:19:08 Quote from: PrinsValium;611101 There is also a micro SD-card adapter (http:\/\/pjrc.com\/store\/sd_adaptor.html) for the Teensys. Imagine GBs of data... I had plans to use one as a keylogger on my own keyboard. I haven't been experimenting any with it, but there are adapters in my home built boards. Hmm, interesting! This would also guarantee I'd never be able to take it into work and use it, though. In a similar vein, are there any good programs (linux or windows) that track how many keystrokes you've done? Sort of a mouse odometer for the keyboard. Peel free to PM me so as not to get too far off topic if you must. Also< I'd lay that macro-functionality would probably be pretty useful. I can imagine using it for a number of things. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Mon, 11 June 2012, 09:59:53 Quote from: PrinsValium;611101 ...Of course you are correct. Things the OS doesn't need to know about is best kept in the dark =) I should have said that \"character mapping\" problems are best solved on the OS side. Once again macros might be the solution I'm actually looking for. Do I want to type '\u03bb' or really just \"\\lambda\"? =D... Quote from: ic07;611126 Hmm, I hadn't been thinking about macros; and I would think those were easier to do in the OS (or.. I use gvim, so that's where mine are). Still interesting though, maybe I'll think about them again sometime when I'm not so tired :) . Would you prefer them in firmware? If so, why?... Quote from: dorkvader;611178 Hmm, interesting! This would also guarantee I'd never be able to take it into work and use it, though. In a similar vein, are there any good programs (linux or windows) that track how many keystrokes you've done? Sort of a mouse odometer for the keyboard. Peel free to PM me so as not to get too far off topic if you must. Also< I'd lay that macro-functionality would probably be pretty useful. I can imagine using it for a number of things. I have to agree with the above, Dork, the OS is much better suited for macro handling than the firmware. I still disagree with Prins' assertion that the OS is better for handling character mappings than the KB when you're working with a non-standard layout, but it's a dead horse at this point. But hey, if macros make it into the firmware at some point (maybe after initial release?) that would be fantastic. No updates yet on the GUI, I plan on putting in some hours this week to see if I can get a \"Shell\" of it working by the weekend. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Mon, 11 June 2012, 14:29:30 A friend who has both a Kinesis and one of my Teensy keyboards wrote his own basic macro functionality for the latter. I know he uses it for some things, but not really exactly what. I know I myself often do repetetive things on the keyboard. I should probably do them in smarter ways to start with. But some basic macro functionality is a good start to not learn to do things right =) Putting the macro functionality on the OS side once again screws up portability.. My vim-fu is very faint. I guess emacs does macros too, I just haven't learned. But they could be useful in other contexts as well. The same friend as above also use a keylogger (in the OS though) to collect statistics of keypresses. He says it never seizes to be disturbing to see his passwords in clear text =D There should be plenty of keylogger available from fishy corners of the net. Search for key logging and take the plunge... Quote from: OrangeJewce;611203 I still disagree with Prins' assertion that the OS is better for handling character mappings than the KB when you're working with a non-standard layout, but it's a dead horse at this point. I'm not going to argue too much about this. But there are limitations you just can't get around. Getting characters that are not in the map the OS is set to for one is next to impossible (macro alt-codes might solve that though...). Moving characters between layers of different \"shift-depth\" will get pretty messy and involve sending shift\/alt-combos even when they could be unwanted. But hey, I don't really care =) Edit: Function keys and an embedded numpad would be things best handled as layers in firmware. But that much I think we all agree about. Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Mon, 11 June 2012, 17:33:01 About macros, now that I've slept, I can see there being times where i'd like to have them in firmware. How to implement, and whether or not I feel they're justified (personally), I'm not sure yet. I've opened an issue (http:\/\/'https:\/\/github.com\/benblazak\/ergodox-firmware\/issues\/10') on github, if anyone's concerned... :) or discussion can continue here of course. Title: [Interest Check] Custom split ergo keyboard. Post by: Netdewt on Mon, 11 June 2012, 20:53:24 I wish I had something intelligent to contribute to this thread. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Mon, 11 June 2012, 23:00:16 Quote from: Netdewt;611679 I wish I had something intelligent to contribute to this thread. Registering your interest counts as an intelligent contribution. Very intelligent, in this case. Title: [Interest Check] Custom split ergo keyboard. Post by: Zifle on Tue, 12 June 2012, 01:48:09 Quote from: dorkvader;611743 Registering your interest counts as an intelligent contribution. Very intelligent, in this case. In that case, I would like to register my interest as well! Speaking of, which time frame are we looking at at this point? A couple of months, a year ... ? I wouldn't be able to afford in the next two or three months, but later in the year, I'd most likely have the finances to cover it. I've been thinking, not sure whether this has been discussed previously, as I haven't followed the thread the whole way through, will we be able to use either side of the board independently of the other? I could see myself \/ others wanting to use it as a gaming pad, without having to necessarily have both sides on the desk. Title: [Interest Check] Custom split ergo keyboard. Post by: ped on Tue, 12 June 2012, 03:24:57 No. Only the right side may be used independently of the other, or at least that is the way it is being designed right now. For the left side to be active, it must be connected to the right side via TRRS cable. The reason for this is that it was decided early on by Dox, I think, that only one controller would be used, which means that one of the halves had to be chosen as the 'host' half, so to speak. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 12 June 2012, 07:06:31 Quote from: Zifle;611832 In that case, I would like to register my interest as well! Speaking of, which time frame are we looking at at this point? A couple of months, a year ... ? I wouldn't be able to afford in the next two or three months, but later in the year, I'd most likely have the finances to cover it. I've been thinking, not sure whether this has been discussed previously, as I haven't followed the thread the whole way through, will we be able to use either side of the board independently of the other? I could see myself \/ others wanting to use it as a gaming pad, without having to necessarily have both sides on the desk. Dox had suggested that the case prototype should be arriving shortly. I am not sure if there will be a second round of PCB prototypes (move thumb keys), after that there isn't really a huge amount of work left from the hardware side. I would say it is looking like it will be in the next 2-3 months as opposed to 6-8. Maybe Dox can chime in here. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: Zifle on Tue, 12 June 2012, 15:01:45 Quote from: ped;611868 No. Only the right side may be used independently of the other, or at least that is the way it is being designed right now. For the left side to be active, it must be connected to the right side via TRRS cable. The reason for this is that it was decided early on by Dox, I think, that only one controller would be used, which means that one of the halves had to be chosen as the 'host' half, so to speak. That makes sense, although I'm slightly sad to hear the outcome, given my previous reasoning. Regardless, that alone should not be a reason to pass on something like this ^^ Quote from: OrangeJewce;611923 Dox had suggested that the case prototype should be arriving shortly. I am not sure if there will be a second round of PCB prototypes (move thumb keys), after that there isn't really a huge amount of work left from the hardware side. I would say it is looking like it will be in the next 2-3 months as opposed to 6-8. Maybe Dox can chime in here. Cheers, Sounds good, looking forward to seeing upcoming pics of a more finished device! Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Tue, 12 June 2012, 15:06:54 Don't forget that with sufficient desk space and a properly sized cable you just put the left half where you want it and tuck the right half out of the way (or vice versa). If you choose to do your own case you could even devise a scheme to stand that half on edge so even less desk space is needed. Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Tue, 12 June 2012, 15:17:38 I think would be possible to make both halves identical using the same PCB for both the left and right half. It looks to me like there would be enough room to fit both the Teensy as well as the other IC there on top. If the PCB was done this way it would be possible to choose to use any or both halves, and also which half the USB cable would be running to. The controller parts from the Teensy can be bought elsewhere and surface mounted, this saves some space. The ATmega chips can be run on their internal 8MHz oscillator as well, cutting the number of required components down. I've been experimenting successfully with this today =) This requires reprogramming some fuse bits though, which in turn requires reloading the bootloader, both which requires a programmer unit... And the stock bootloader as well as the LUFA one are both 4kB. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 12 June 2012, 15:59:13 Quote from: PrinsValium;612147 I think would be possible to make both halves identical using the same PCB for both the left and right half. It looks to me like there would be enough room to fit both the Teensy as well as the other IC there on top. If the PCB was done this way it would be possible to choose to use any or both halves, and also which half the USB cable would be running to. The controller parts from the Teensy can be bought elsewhere and surface mounted, this saves some space. The ATmega chips can be run on their internal 8MHz oscillator as well, cutting the number of required components down. I've been experimenting successfully with this today =) This requires reprogramming some fuse bits though, which in turn requires reloading the bootloader, both which requires a programmer unit... And the stock bootloader as well as the LUFA one are both 4kB. This topic was discussed a long time ago and it was determined that only one controller was going to be used. But everyone is more than welcome to customize their Dox however they Feel! (I think your mod would be sick, if you ever undertake it as a project :thumb:) Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Tue, 12 June 2012, 16:31:44 This would really not change anything (other than the PCB layout). There could be separate USB controllers on either side, or one controller and a slave side (either side being the slave\/master), or a single PCB could be used as a one handed keyboard of left or right hand type. This would also double the number of same design PCBs which may or may not have an impact on price. If there are huge amounts already this doesn't make too big a difference. The main problem is the possible need to use a serial programmer to set up the controller chips. This would likely have to be done by someone from here in bulk before shipping them out to people. I'm of course more than willing to help out with what I know about chip programming, bootloaders, PCB design and all. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 12 June 2012, 22:15:30 Quote from: PrinsValium;612175 This would really not change anything (other than the PCB layout). There could be separate USB controllers on either side, or one controller and a slave side (either side being the slave\/master), or a single PCB could be used as a one handed keyboard of left or right hand type. This would also double the number of same design PCBs which may or may not have an impact on price. If there are huge amounts already this doesn't make too big a difference. The main problem is the possible need to use a serial programmer to set up the controller chips. This would likely have to be done by someone from here in bulk before shipping them out to people. I'm of course more than willing to help out with what I know about chip programming, bootloaders, PCB design and all. I may have brought up having identical PCB's. The issue is that it still has to work with it \"flipped\". You could maybe do this with a lot of settable jumpers (like: Set to \"A\" for LH and \"B\" for RH). Also, Trace routing becomes difficult, and the cherry keyswitches are not symmetrical, so you'd need an extra hole per switch. Then, having the possibility of chosen controller per side was discussed. This idea had much more going for it, as it's actually somewhat feasible. I don't think anyone came up with a decent plan to implement this (I think HW implementation is the best, so the controller doesn't \"know\" any better. Having a \"master and slave\" controller setup was rejected as well (Is it even possible with teensy?) Anyway, if you come up with a good implementation for this, I don't see any reason to not include the capability. --- So other than ugly shapeways plastic, has anyone come up with a good place to make the case? Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Tue, 12 June 2012, 23:28:36 I don't think you need to do almost anything at all to get it to work flipped. But I just woke up and may not have thought this through all the way. Just mount the USB controller on one side and let the slave IC location be empty, And vise versa on the other side. The switch is unidirectional by construction. They would be the only components needing to switch side. Through hole diodes are of course \"flip symmetric\" as as well (Internal diodes could still be used if they are mounted \"backwards\"). The flippable footprint should be no problem. Internal diode and LED holes also line up when it is flipped. [ATTACH=CONFIG]52840[\/ATTACH] Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Wed, 13 June 2012, 00:12:36 Having the ability to build either side as the \"main\" board would be fantastic. Title: [Interest Check] Custom split ergo keyboard. Post by: uberben on Wed, 13 June 2012, 01:36:10 Quote from: PrinsValium;612439 I don't think you need to do almost anything at all to get it to work flipped. But I just woke up and may not have thought this through all the way. Just mount the USB controller on one side and let the slave IC location be empty, And vise versa on the other side. The switch is unidirectional by construction. They would be the only components needing to switch side. Through hole diodes are of course \"flip symmetric\" as as well (Internal diodes could still be used if they are mounted \"backwards\"). The flippable footprint should be no problem. Internal diode and LED holes also line up when it is flipped. (Attachment) 52840[\/ATTACH] This sounds doable to me. It has a lot of advantages, but will require much more careful layout. Title: [Interest Check] Custom split ergo keyboard. Post by: Salisen on Wed, 13 June 2012, 07:23:51 You could have a 10x10 matrix for the switches, perhaps, and seperate it into two 5x10 halves. Divert one of the matrices through the connector (would have to be 16 way) to the other side. From each switch on the board, have traces running to the IC, and to the connector, total of 4 traces for each. For each pin on the connector, have one trace running to the IC, and one running to the switches through an array of jumpers (you'd need 16 total, I think). For the slave board, the jumpers would be present and an IC would not, so all IC connections would be redundant, leaving only the traces to the connector. For the master, the jumpers would be left empty, traces would run from the IC to the set of switches on that board, and from the IC to the connector. I don't think you'd have the option of putting the IC on either board though. On one of the two it would have to be underneath as opposed to on top, or the pins would be the wrong. The Teensy is quite tall, so you'd make the keypad unnecessarily thick. Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Wed, 13 June 2012, 07:32:39 I was thinking of using SMT components to rebuild the \"Teensy\". And I am pretty confident the slave IC comes in a smaller SMT package as well.. I know DOX wrote the part number somewhere but I can't seem to find it again =P You would only need to do a regular key matrix and trace rows and columns to both the serial slave IC as well as the USB controller. Then choose which side to solder the controller\/slave IC to. The traces to the other would only end up unconnected. It will look funny that the traces from the slave IC will lead to the connector, and from there down to the controller again =D There should be no need for jumpers anywhere, I think when trying to figure this out in my head... Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Wed, 13 June 2012, 07:44:59 While I think the discussion about multi-controller and symmetrical PCBs is fantastic, and these ideas sound awesome, short of Dox completely renegging on this major design decision all of these proposals are going to stay in the realm of vaporware. I just don't see him having invested in several PCB prototypes just to do an overhaul on the PCB design, and because work has begun on the case prototype, it wouldn't make sense to push the project back further. TBH I really want to see the final product (pics!), not to mention have it in my hands in 3 months as opposed to another year for a redesign. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Wed, 13 June 2012, 07:57:08 Quit being so negative.. geesh, and by the way Quote from: Dox;607456 Otherwise, everything went well. With the thumb keys a bit closer, it will be perfect! Looks like there may be a PCB redesign whether you like it or not.. It is pretty quick by the way. And I do think DOX had meant to do more work on the PCB as it was. Those prototypes don't look like a finished product at all... Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Wed, 13 June 2012, 09:30:50 Quote from: PrinsValium;612585 Quit being so negative.. geesh, and by the way Looks like there may be a PCB redesign whether you like it or not.. It is pretty quick by the way. And I do think DOX had meant to do more work on the PCB as it was. Those prototypes don't look like a finished product at all... Firstly, let's not make this personal. I wasn't attacking you, or your ideas. I was simply stating that the decision regarding these most recent proposals had already been made a long time ago, and that bringing them back from the dead had very little chance to change anything. I'm not going to argue about what Dox may or may not do in the future, because I am not him, nor can I control what he does. That being said and based on what I read earlier, when Dox makes a decision he tends to stand by it. You're welcome to critique me as much as you want, but in this case I feel pretty confident in saying that neither multiple controllers, in any configuration, nor flippable PCBs are going to make it into the feature set of the ErgoDox hardware. Secondly, shortening some traces on a PCB does not count as a total redesign. In fact, Dox was going to do the mod himself on the PCBs by simply cutting the thumb section and doing a little bit of hand-wiring... Quote from: Dox;602337 I think that the thumb keys are a bit too far out. The 3 furthest keys are hard to reach and my thumb is a bit too stretched in the standard (thumb on space) position. I will put them closer for the case prototype. I will cut the thumb from the PCB and hand wire it to test it. I implore you to start seeing what is there, as opposed to what your mind wants you to see. Until the man himself intervenes here, I'm done discussing hardware. Firmware and UI, I'm all ears, because very few decisions have been made. ic07 and I have expressed that we are open to new ideas and features for it, and thus encourage discussion along those lines. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Wed, 13 June 2012, 09:46:04 Could be some excellent ideas for the ergoDOX V2 With the flippable PCB, how does it work out what with that extra chip? Also, one could have two locations for the Teensy, depending on what hand\/side you have, you could use different holes across the top. Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Wed, 13 June 2012, 10:19:06 I PMed DOX to ask if I could have a look at the schematics. I'll wait and see what he says. I don't want to interfere with his work if he doesn't want me to. But really, I think a flippable PCB is quite simple to put together. That being said without me having given it a decent try. The Teensy can be mounted on either side really. Since it is through hole it only needs to be mounted upside down if changing side. The only slight annoyance this comes with is reaching the reset button on it. That is easily solved with a hole in the PCB. This I have done before =) Bending the legs backwards on that other IC is probably not a good idea though... Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Wed, 13 June 2012, 14:48:29 Quote from: alaricljs;612141 Don't forget that with sufficient desk space and a properly sized cable you just put the left half where you want it and tuck the right half out of the way (or vice versa). If you choose to do your own case you could even devise a scheme to stand that half on edge so even less desk space is needed. Or for an extra ~$25 and a little work, you could put a Teensy and a TRRS connector in an altoids can, and use that for the right hand side :) .\nTitle: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Wed, 13 June 2012, 20:11:36\nQuote from: ic07;612818\nOr for an extra ~$25 and a little work, you could put a Teensy and a TRRS connector in an altoids can, and use that for the right hand side :) . Whoah, that's brilliant, I hadn't considered that. Now I want like 5 more of those teensy's. Title: [Interest Check] Custom split ergo keyboard. Post by: mSSM on Sat, 16 June 2012, 16:28:28 As regards the switches: 7bit is currently doing a group buy of cherry switches (both plate and PCB mounted) over at deskthority: http:\/\/deskthority.net\/marketplace-f11\/cherry-mx-taking-pre-orders-t2760.html Just thought it's worth mentioning. Of course getting in on that group buy depends on the time frame we are looking at as regards the final production of the dox. :-) How many keys we are actually going to have? EDIT: Silly me, he has a thread here at Geekhack as well, in the group buys section. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Sat, 16 June 2012, 22:22:08 I count 36 keyswitches per hand from the images DOX posted here: http:\/\/geekhack.org\/showthread.php?22780-Interest-Check-Custom-split-ergo-keyboard&p=602321&viewfull=1#post602321 So that's 72 total, right? Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Sun, 17 June 2012, 01:17:05 Quote from: dorkvader;615204 I count 36 keyswitches per hand from the images DOX posted here: http:\/\/geekhack.org\/showthread.php?22780-Interest-Check-Custom-split-ergo-keyboard&p=602321&viewfull=1#post602321 So that's 72 total, right? Pretty sure it's 38 per hand = 76 total. (I cheated a little though, since I looked at how many were mapped in the firmware before I looked at the picture again to make sure). :) Title: [Interest Check] Custom split ergo keyboard. Post by: mSSM on Sun, 17 June 2012, 07:14:24 Well, now I am certainly tempted to justs join that group buy. Which switches do you think would fit the ErgoDox best? I am thinking either linear MX Reds, or alternatively clicky MX Blues or MX Whites (I like their sound better). Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Sun, 17 June 2012, 07:20:45 Quote from: mSSM;615421 Well, not I am certainly tempted to justs join that group buy. Which switches do you think would fit the ErgoDox best? I am thinking either linear MX Reds, or alternatively clicky MX Blues or MX Whites (I like their sound better). Answer: Get two! One with reds and one with whites! Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Sun, 17 June 2012, 11:14:49 If it doesn't end up being too much, I might get two sets of PCBs and one case to just change them out with different switches. Title: [Interest Check] Custom split ergo keyboard. Post by: Surger on Tue, 19 June 2012, 07:29:27 I've just scanned this thread and am most definitely interested in the keyboard that is being developed. Glad to see all the knowhow on geekhack is being put into practice! Add me to the list. I've been on a quest for a better keyboard for many years and have tried *all* the usual suspects and failures, only to get more dissapointed. I'm currently compromising on a Kinesis Freestyle and concluded that separation is more important to me than angling\/tenting, etc. If only it had better quality keys... While I tried to grasp as much of the current status\/development as I could, I may have missed some info, since obviously I couldn't read every single message in this thread. So forgive me if one of my comments has already been dealt with. Maybe it would be an idea to add some more FAQs on the website? First, I agree with most of the development decisions, layout, functionality, etc. Congrats on your efforts of merging the best aspects of all current mediocre keyboards ;-) Costs: I consider 300 dollars or more perfectly acceptable. I'm at the keyboard over 10 hours a day. I pay top money for the best ergonomic chair I can find and use high quality monitors. Why save on what I consider the most important aspect of computing: a comfortable input device. Honestly, I'd pay a lot more for any keyboard that met my needs. Quality, durability, flexibility outweigh costs. Build: Can't really figure out how this will work. Are we supposed to order certain parts ourselves and finish the keyboard? Or will certain community members do this? My technical\/engineering knowhow is too limited to do this. I can imagine this will be a mayor obstacle for people who are interested in the final product. Functionality: While I understand the choice for compactness and minimalistic design, I find the lack of Function keys a serious flaw. Before you jump on me, let me explain. To me, a keyboard geared at heavy PC users should focus on being ergonomic in all aspects, including minimizing the usage of a mouse or pointing device. I use Alt+ Control + Function key combination hundreds of time a day in all sorts of programs and can't imagine using a keyboard that doesn't have these. It would drastically slow me down. (Does everybody seriously use a mouse to close a program when Alt+F4 is within reach?) Adding these to a different layer or reassigning them doesn't really solve the problem: If I have to switch layers, use a combination, switch back, I'm doubling the amount of keys I have to use. If I'd assign them to the number keys, other shortcuts (such as Control+1 through 4) in Outlook are gone. I fully understand that this contradicts some of your initial design\/functionality choices, but still wanted to share my thoughts, mostly because I'm surprised this hasn't been discussed in more detail. ;-) Maybe adding a X-keys device (key stick, XK-24) for Function keys... ? Still interested in the keyboard though.... Hell, I'd buy a few just to keep you guys motivated! Title: [Interest Check] Custom split ergo keyboard. Post by: mSSM on Tue, 19 June 2012, 07:41:04 Quote from: Surger;616929 Functionality: While I understand the choice for compactness and minimalistic design, I find the lack of Function keys a serious flaw. Before you jump on me, let me explain. To me, a keyboard geared at heavy PC users should focus on being ergonomic in all aspects, including minimizing the usage of a mouse or pointing device. I use Alt+ Control + Function key combination hundreds of time a day in all sorts of programs and can't imagine using a keyboard that doesn't have these. It would drastically slow me down. (Does everybody seriously use a mouse to close a program when Alt+F4 is within reach?) Something like that heavily depends on the operating system you are using, does it not? For my day to day tasks I mainly use mutt and vim in a terminal multiplexer (tmux), Firefox with the Pentadactyl plugin, and PDF readers such as llpp or mupdf, where all of the mentioned programs have vim-like keybindings. My window manager (Xmonad) also has vim-like keybindings. I _never_ use the mouse, and I do not even rely heavily on Alt, Control or function keys (CTRL is my most heavily used key). While I certainly understand your need to cut back on using the mouse, your operating system (Windows of some flavour, I figure), is not really meant for that kind of work. But even so, if you use appropriate programs, you have don't have to have special functions keys. I don't really understand what more keys you need on that keyboard. What's missing? Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Tue, 19 June 2012, 07:51:56 Quote from: mSSM;616931 While I certainly understand your need to cut back on using the mouse, your operating system (Windows of some flavour, I figure), is not really meant for that kind of work. But even so, if you use appropriate programs, you have don't have to have special functions keys. I don't really understand what more keys you need on that keyboard. What's missing? So you're saying change his entire workflow and the programs he uses in order to suit the keyboard? That's a bit silly. I'm interested in this project because of the engineering involved, so my opinion is not one coming from a potential user... That said, I wouldn't buy a keyboard without F-keys. I've been pondering designing my own board and am sorely tempted to include a 2x5 set on the left (ala Sun type-5) to have more keys. This way I can have all the f-key combos for the programs I use and then all my own combos for other uses. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 19 June 2012, 08:07:46 Quote from: alaricljs;616934 So you're saying change his entire workflow and the programs he uses in order to suit the keyboard? That's a bit silly. I'm interested in this project because of the engineering involved, so my opinion is not one coming from a potential user... That said, I wouldn't buy a keyboard without F-keys. I've been pondering designing my own board and am sorely tempted to include a 2x5 set on the left (ala Sun type-5) to have more keys. This way I can have all the f-key combos for the programs I use and then all my own combos for other uses. Even as a Windows user and developer, I never use the F'n keys. Maybe I'm just not pro enough for that kind of thing, but if I really needed a certain set, I don't think it's unruly to add a few keystrokes to switch to a different layer which, say, has remapped the numrow to f'n keys, and then when finished jump back to the base layer. I understand your hesitance about not having the F'n keys, and while custom layers may not be the perfect solution, it's a heck of a lot better than nothing. This board, tbh, is probably not the most ideal for a Windows user, but it can definitely work. Still getting 2 if I can! ic07, YGPM. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: Djuzuh on Tue, 19 June 2012, 08:11:29 Depending on the price, I might be interested too. I'll see :s. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 19 June 2012, 08:19:50 Quote from: Djuzuh;616942 Depending on the price, I might be interested too. I'll see :s. Save for a while! It's going to be an amazing board, and there may never be another run of them again! ;) Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: Djuzuh on Tue, 19 June 2012, 08:23:14 Quote from: OrangeJewce;616949 Save for a while! It's going to be an amazing board, and there may never be another run of them again! ;) Cheers, But\u2026 But\u2026 All those other amazing GBs and boards?*:( Title: [Interest Check] Custom split ergo keyboard. Post by: Surger on Tue, 19 June 2012, 09:09:46 Quote from: mSSM;616931 While I certainly understand your need to cut back on using the mouse, your operating system (Windows of some flavour, I figure), is not really meant for that kind of work. Windows, which is perfectly suited for cutting back on using the mouse. You'll find that you can operate practically all commonly used Window functions and programs with a huge number of shortcuts (and many of these use the Function keys). The majority of casual PC users doesn't know this and doesn't use them, but I believe many professionals in text entry\/editing related jobs DO use these. By excluding Function keys, these potentials buyers are - maybe - lost. Quote from: OrangeJewce;616941 ...I don't think it's unruly to add a few keystrokes to switch to a different layer which, say, has remapped the numrow to f'n keys, and then when finished jump back to the base layer. I understand your hesitance about not having the F'n keys, and while custom layers may not be the perfect solution, it's a heck of a lot better than nothing. This board, tbh, is probably not the most ideal for a Windows user, but it can definitely work. Yes, obviously it can work, which is why I'm definitely interested, but - like I said - it will decrease efficiency. Are there any numbers on which OS people who are interested are using? While I appreciate this keyboard may be intended\/designed more for other OS, if (at any point) this project would turn more commercial, considering the needs of Window users may make the difference between success and failure. Just by sheer numbers of potential buyers. Ah well, I'm guessing there's no chance in hell adding Function keys will be considered at this point... and I certainly don't want to sidetrack this initiative, so moving on! Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 19 June 2012, 09:16:07 Quote from: Surger;616971 Windows, which is perfectly suited for cutting back on using the mouse. You'll find that you can operate practically all commonly used Window functions and programs with a huge number of shortcuts (and many of these use the Function keys). The majority of casual PC users doesn't know this and doesn't use them, but I believe many professionals in text entry\/editing related jobs DO use these. By excluding Function keys, these potentials buyers are - maybe - lost. Yes, obviously it can work, which is why I'm definitely interested, but - like I said - it will decrease efficiency. Are there any numbers on which OS people who are interested are using? While I appreciate this keyboard may be intended\/designed more for other OS, if (at any point) this project would turn more commercial, considering the needs of Window users may make the difference between success and failure. Just by sheer numbers of potential buyers. Ah well, I'm guessing there's no chance in hell adding Function keys will be considered at this point... and I certainly don't want to sidetrack this initiative, so moving on! Surger, Unfortunately, as I told someone else who wanted to make some hardware changes, the design has pretty much been set in stone. That doesn't mean a v2 won't ever happen, but for this go around, there won't be any additional keys on top of the 76. It was proposed early on that more keys were added, but sadly it wasn't to be. I can tell you that the OS numbers will likely be skewed. Many of those who frequently chime in on the forums strike me as Unix\/Linux developers. AFAIK I am one of the few who do Windows development. This doesn't mean that many do not use MSFT products, only that at work, where the greatest use of the keyboard occurs, a linux environment is preferable, and they use an editor like Vi\/Vim, which allows them to pretty much never use a mouse. I apologize in advance for any characterizations of the community. I do not mean any disrespect, as I love Unix ans work with it daily. These are just my impressions. I hope that you pick one of these up, I feel pretty confident it is going to fill a very unique and desired niche in the Keyboard market. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 19 June 2012, 09:28:55 I'm probably going to have function keys for the ones on the edges (and maybe the bottom). The \"inside\" two keys can be modifiers (for obvious reasons) you could also assign some of the keys near the thumbs to funciton keys. I see how people don't like not having an extra row of keys across the top, but I don't think it's really needed, especially with so many assignable keys at your disposal. You can tailor the layout to include your most commonly used keys in the most easily hit positions. If you want, I can Download a graphics program and show you on the image. --- To answer another one of your questions (I should add a FAQ: Good idea) It will likely be sold as a \"parts kit\" form, but several members, myself included, are willing to do the assembly, though I imagine most will want some money for their time. My goal would be to get as many of these ergoDOX's in the hands of people as possible. Title: [Interest Check] Custom split ergo keyboard. Post by: Surger on Tue, 19 June 2012, 10:08:26 OrangeJewce, thanks for your comments. Yes, I gathered that most users here were developers, and appreciate they have different needs. Don't mistake my comments for criticism; just offering a slightly different perspective from a different potential target group. Quote from: dorkvader;616983 I'm probably going to have function keys for the ones on the edges (and maybe the bottom). The \"inside\" two keys can be modifiers (for obvious reasons) you could also assign some of the keys near the thumbs to funciton keys. Yes, I can see that as an option. I will certainly try to 'work around' the missing f-keys. No need for an image; I can think of several solutions, such as positioning my X-keys (http:\/\/www.piengineering.com\/xkeys\/xk24.php) in between the two sections. Quote from: dorkvader;616983 To answer another one of your questions (I should add a FAQ: Good idea) It will likely be sold as a \"parts kit\" form, but several members, myself included, are willing to do the assembly, though I imagine most will want some money for their time. My goal would be to get as many of these ergoDOX's in the hands of people as possible. OK. Excellent. Completely agree with compensating members for their time and effort! Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 19 June 2012, 10:44:13 Quote from: Surger;617009 OrangeJewce, thanks for your comments. Yes, I gathered that most users here were developers, and appreciate they have different needs. Don't mistake my comments for criticism; just offering a slightly different perspective from a different potential target group. Yes, I can see that as an option. I will certainly try to 'work around' the missing f-keys. No need for an image; I can think of several solutions, such as positioning my X-keys (http:\/\/www.piengineering.com\/xkeys\/xk24.php) in between the two sections. OK. Excellent. Completely agree with compensating members for their time and effort! The great thing, in my opinion about this community, is that they are willing to go so above and beyond what normal forums do for their members. For instance, we have I think 4 developers working on the firmware and layout modifying GUI (myself included). Just recently the community came together to help a member out who had an immediate need to come up with some capital to help is sick dog, and GH rallied around him through direct and keycap donations to help raise the funds. The reason I bring any of this up is that many of us really just like giving back to the community of Mechanical enthusiasts, and so we give our time and money without expecting something in return. That's why I really enjoy coming to GH. But this is just my take on that issue. I don't think it's wrong at all that GH offers services to its members for a fee, just that what really amazes me about this place is how the community will come together to help each other out and to really innovate in the mechanical world, like with this project! No worries Surge, I was merely clarifying some of why certain design decisions were made, and to hopefully put some of it in perspective for you. I am a Windows guy. At work, all the other developers tease me because I am stuck doing UI and automated testing, which has to be MSFT side, solely because that's what our customers use and we have to cater to their needs. I really enjoy that role, but I also understand that it's rather unique unless you're working on a very large windows application which has many collaborators. So I am with you in trying to make the keyboard for those of us who aren't hacking away at Unix programs frequently. That is why I took the lead in trying to develop a UI for people to modify, create, and share ErgoDox layouts. effh is helping me out by doing some of the interpreting work between the firmware hex and the output which will be edited in my program. Anyways, I'll get off the soap box now, I only meant to say that there are others who are Windows dominant, and I do see why the F keys would be very useful for you. Cheers, OJ Title: [Interest Check] Custom split ergo keyboard. Post by: mSSM on Tue, 19 June 2012, 11:00:17 Quote from: Surger;616971 Windows, which is perfectly suited for cutting back on using the mouse. You'll find that you can operate practically all commonly used Window functions and programs with a huge number of shortcuts (and many of these use the Function keys). The majority of casual PC users doesn't know this and doesn't use them, but I believe many professionals in text entry\/editing related jobs DO use these. By excluding Function keys, these potentials buyers are - maybe - lost. I understand perfectly well that you can have those functions in Windows, and that people who actually care about what their OS is capable of will use those features. However, the workflow you have mentioned is very specific to the needs of Windows users, and there are many people on Geekhack and especially in this thread who do not need the functions-keys (the amount of people using HHKBs and Pokers here speaks volumes). So, I believe a rewrite of the firmware and a redesign of the PCB as well as the keyboard's case to accomodate function keys would not really be adequate. Title: [Interest Check] Custom split ergo keyboard. Post by: Surger on Tue, 19 June 2012, 11:26:17 Thanks for elaborating, OJ. Perfectly clear. By the way, is stating my intention to buy enough or do I need to do something to be added to an 'official list'. Just want to make sure I don't miss out... Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 19 June 2012, 11:28:30 Quote from: Surger;617043 Thanks for elaborating, OJ. Perfectly clear. By the way, is stating my intention to buy enough or do I need to do something to be added to an 'official list'. Just want to make sure I don't miss out... Dork will add you to his list I'm sure. When the time comes, You'll get a PM for more information regarding payment etc. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Tue, 19 June 2012, 11:31:24 Adding a \"function modifier key\", much like a shift or ctrl key that only momentarily turns on the function layer when pressed, shouldn't add to much discomfort using F keys. F keys on a regular keyboard are far enough away to lose home row anyways. Title: [Interest Check] Custom split ergo keyboard. Post by: Djuzuh on Tue, 19 June 2012, 11:53:42 Quote from: PrinsValium;617050 Adding a \"function modifier key\", much like a shift or ctrl key that only momentarily turns on the function layer when pressed, shouldn't add to much discomfort using F keys. F keys on a regular keyboard are far enough away to lose home row anyways. you can even use a switch lock for this key \\o\/ Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Tue, 19 June 2012, 12:09:40 Quote from: Djuzuh;617070 you can even use a switch lock for this key \\o\/ Why on earth would you want to do that? Title: [Interest Check] Custom split ergo keyboard. Post by: Djuzuh on Tue, 19 June 2012, 12:10:33 sorry, meant a mxlock swtch >> Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Tue, 19 June 2012, 12:41:02 Quote from: Djuzuh;617077 sorry, meant a mxlock swtch >> Why on earth would you want to do that? Title: [Interest Check] Custom split ergo keyboard. Post by: Djuzuh on Tue, 19 June 2012, 13:03:21 so you don't need to hold the button down? Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 19 June 2012, 13:27:29 Quote from: Djuzuh;617106 so you don't need to hold the button down? The other option is to implement it as a type of \"fn\" key commonly seen on lenovo\/laptop keyboards. This would have to be done on the firmware level, and I do not think that the GUI will be able to control that directly in its first iteration. If you want it try to make a feature request on the Git repository! Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Tue, 19 June 2012, 14:26:52 Without having looked to close on the code, I think it should be really simple adding a if(my-fun-layer-key is pressed) send function key; else send regular key; This should be possible to do on a higher level than the I\/O communication between the keyboard halves. And on this higher level nothing is particularly tricky to do yourself. There should probably be some way of accessing the function keys no matter what. Although I use them next to never myself, sometimes they are actually necessary. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 19 June 2012, 14:56:58 Quote from: PrinsValium;617147 Without having looked to close on the code, I think it should be really simple adding a if(my-fun-layer-key is pressed) send function key; else send regular key; This should be possible to do on a higher level than the I\/O communication between the keyboard halves. And on this higher level nothing is particularly tricky to do yourself. There should probably be some way of accessing the function keys no matter what. Although I use them next to never myself, sometimes they are actually necessary. I think this is something to talk to ic07 about, and that someone should post on the codebase. I will dig up a link when I get home about it Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Tue, 19 June 2012, 16:11:56 Quote from: Djuzuh;617106 Quote from: PrinsValium;617092 Quote from: Djuzuh;617106 Quote from: PrinsValium;617092 Quote from: Djuzuh;617070 you can even use a switch lock for this key \\o\/ Why on earth would you want to do that? sorry, meant a mxlock swtch >> Why on earth would you want to do that? so you don't need to hold the button down? Had some cake, think I should dismiss your idea a bit more gently ;) If it is a locking switch to change between different layouts, of which one contains F-keys for situations where they are handy, along with other more heavily used keys in that same layer, it could certainly be a good idea. As a means to reach a layer of exclusively F-keys it sounds pretty useless. Imagine several locking layer switches enabling 2^(#layer keys) different layout choices. Did I hear someone saying DIP-switches? =D Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Tue, 19 June 2012, 16:24:46 I like my dip switches fancy, and large... Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Tue, 19 June 2012, 16:34:22 Quote from: Surger;617009 Yes, I can see that as an option. I will certainly try to 'work around' the missing f-keys. No need for an image; I can think of several solutions, such as positioning my X-keys (http:\/\/www.piengineering.com\/xkeys\/xk24.php) in between the two sections. Another option, if you think it's worth a dedicated key position on the home layer, would be to define a layer key that's also an alt key, so instead of pressing alt+fn#, you'd be pressing [alt,layer]+fn# - and the alt+number keys would stay the same. I'd probably be the one to add it to the firmware, but I think it'd be a fairly trivial addition if people thought it was worth having. Quote from: PrinsValium;617147 Without having looked to close on the code, I think it should be really simple adding a if(my-fun-layer-key is pressed) send function key; else send regular key; This should be possible to do on a higher level than the I\/O communication between the keyboard halves. And on this higher level nothing is particularly tricky to do yourself. There should probably be some way of accessing the function keys no matter what. Although I use them next to never myself, sometimes they are actually necessary. The keypress paradigm is a bit different in this firmware, but the general idea's correct: layer keys (and locking-layer keys) are implemented, and people can remap what they like. Fn keys are currently accessible (in the QWERTY map) on the 2nd layer, where the number keys are. Quote from: mSSM;616931 For my day to day tasks I mainly use mutt and vim in a terminal multiplexer (tmux), Firefox with the Pentadactyl plugin, and PDF readers such as llpp or mupdf, where all of the mentioned programs have vim-like keybindings. My window manager (Xmonad) also has vim-like keybindings. I *wish* I had a workflow like that, lol. Haven't had the patience to learn yet though... I currently use gvim, chrome, and thunderbird, mostly, in Ubuntu + Gnome. Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Tue, 19 June 2012, 16:56:24 I am going to have too look closer on that code some day =) Is the locking\/non-locking layer keys implemented as two separate functionalities? I had an idea to make shift locking (or act as a caps lock toggle) if it was pressed just shortly, and behave regularly when held for a longer period of time. I never got around to implement that though (as with many other things..). Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Tue, 19 June 2012, 20:58:48 Quote from: PrinsValium;617243 I am going to have too look closer on that code some day =) Is the locking\/non-locking layer keys implemented as two separate functionalities? I had an idea to make shift locking (or act as a caps lock toggle) if it was pressed just shortly, and behave regularly when held for a longer period of time. I never got around to implement that though (as with many other things..). I believe if you implement it as a hit to change, hit again to change back type layer switch, the MXlock works perfectly. I'm pretty sure you can set up the access-IS keyboards this way(as well as momentary) (though they don't have lock switches) I really need to get a MXlock switch, so when I make wy phantom, I can switch from dvorak-and numpad to dvorak-and-arrowkeys. It's two useful layers (with an identical alpha-area) that I'd be using long enough to justify it, and it's a really good solution in my book. I just need to PM 7bit about them :p --- Also, I updated the second post the other day (or so I thought). I normally keep the \"backup file\" more up to date, though. If you're not on the interest list now, feel free to PM me or post again in this topic. --- OJ is right: GH is a good community. I want to do my part keeping it that way. Title: [Interest Check] Custom split ergo keyboard. Post by: mSSM on Tue, 19 June 2012, 20:59:12 Quote from: ic07;617223 I *wish* I had a workflow like that, lol. Haven't had the patience to learn yet though... I currently use gvim, chrome, and thunderbird, mostly, in Ubuntu + Gnome. I strongly urge you not to do it. :D You are going to be entirely dependent on your very own setup, and you are going to _hate_ using anything but. Fun thing is that it sounds like a lot of work to learn that stuff, but in the end it's more for lazy people. ;-) Title: [Interest Check] Custom split ergo keyboard. Post by: Surger on Wed, 20 June 2012, 10:53:27 Quote from: ic07;617223 Another option, if you think it's worth a dedicated key position on the home layer, would be to define a layer key that's also an alt key, so instead of pressing alt+fn#, you'd be pressing [alt,layer]+fn# - and the alt+number keys would stay the same. I'd probably be the one to add it to the firmware, but I think it'd be a fairly trivial addition if people thought it was worth having. Yes, actually, adding that flexibility would be interesting: one would achieve an Alt+Function key press without increasing the number of keys to be pressed. Same for a Control+fn and Shift+fn. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Wed, 20 June 2012, 21:06:02 Ladies and Gentlemen, I am looking for an Icon to represent the ErgoDox UI. This will be used as the shortcut and installation Icon. I am also looking for a masthead to use as part of the installation project. Feel free to shoot me a PM with something that constitutes your own original work or an image that you have license to use. Please note that by submitting you agree in whole that I and the ErgoDox team can reproduce and freely use the images at our own discretion. Anyone is welcome to send me something and I will let you know what is selected in the end if there are many submissions. If nobody comes forward I'll just slap something together, but hopefully somebody who's a better artist than I can help us out! Really looking forward to it. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: bpiphany on Wed, 20 June 2012, 22:09:32 Since you already have transistors at each column, why not add the extra eight for the ROWn as well? This would allow you to use the full 500 USB mA. Say 480mA after the uC gets its share =) That would then be 60mA per ROWn. Brighter then that will not happen without extra power in any case. Using 8 rows on a regular board is a little bit of a pain when laying out the matrix. 6 is easier to work with, and gives ~21 columns on a full sized board. 8x13 is actually 104 for you ANSI people ;) Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Thu, 21 June 2012, 00:43:52 (http:\/\/i.imgur.com\/QF6MD.png) Minor update, still not satisfied with the look. Title: [Interest Check] Custom split ergo keyboard. Post by: Surger on Thu, 21 June 2012, 05:24:27 Quote from: REVENGE;618450 Show Image (http:\/\/i.imgur.com\/QF6MD.png) Minor update, still not satisfied with the look. Nice. IMO, the prev. version without the tool was a bit cleaner, more powerfull. When it comes to design, less is often more ;-) Have you considered flipping it? I.e.: buttons sticking out on the right. It will be easier to use the design in different locations\/situations; it will outline better when displayed amongst other icons, can be used easier on webpages etc. Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Thu, 21 June 2012, 10:04:42 What's the recommended size (in px) for an icon like that? Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Thu, 21 June 2012, 11:19:09 Quote from: dorkvader;618612 What's the recommended size (in px) for an icon like that? The ico needs to be pretty small, 16x16. (LxW) The Masthead should be roughly 500x70. (LxW) Sorry I hadn't specified earlier. I thin I will use the posted image on the About page, and use the DoX brand on the eula. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Thu, 21 June 2012, 12:50:38 For best results in Win 7 you should use 64x64 and either let it scale or also provide 32x32 and 16x16. Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Thu, 21 June 2012, 14:20:04 Quote from: alaricljs;618724 For best results in Win 7 you should use 64x64 and either let it scale or also provide 32x32 and 16x16. Eh? I thought you should make a high res 256 x 256 icon, then provide an alternate icon for 32 x 32 \/ 16 x 16. The text on my mockup, for example, will cease to be very visible at 16 x 16. Title: [Interest Check] Custom split ergo keyboard. Post by: mSSM on Thu, 21 June 2012, 14:29:13 Can't you make an SVG graphic? Can't Windows 7 handle that? Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Thu, 21 June 2012, 22:07:52 Quote from: mSSM;618805 Can't you make an SVG graphic? Can't Windows 7 handle that? Don't think so. Bitmaps or PNG, IIRC. Title: [Interest Check] Custom split ergo keyboard. Post by: ic07 on Thu, 21 June 2012, 23:07:49 Quote from: PrinsValium;617243 I am going to have too look closer on that code some day =) Is the locking\/non-locking layer keys implemented as two separate functionalities? I had an idea to make shift locking (or act as a caps lock toggle) if it was pressed just shortly, and behave regularly when held for a longer period of time. I never got around to implement that though (as with many other things..). :) To answer that question though, I think I'll have to write a quick overview of the firmware paradigm anyway - or feel free to skip the next two paragraphs, I won't be sad :) . In this firmware, each keypress and keyrelease generates a function call, which is responsible for doing all the actual work. The function is passed a uint8_t (usually a keycode), along with some other things. The assigned functions and keycodes are stored in 3 separate [layer][row][column] matrices; so for each key, on each layer, we have a keycode, keypress function, and keyrelease function. So, the functions dealing with layer increment and decrement all manipulate the layer matrix (each key also has its own layer) in the same way. Different behavior is implemented by changing which function gets called at what time. To implement a non-locking layer key, for instance, you'd assign an equal layer increment and decrement to that key's keypress function and keyrelease function. To implement a locking layer key, you'd assign an increment (or decrement) to that key's keypress function, and leave the keyrelease function null. There are a couple other behaviors that can be implemented as well. Long answer, sorry. And I left out a lot of details, but I hope it's still clear enough. Locking based on time sounds like a cool idea :) . I don't know much of anything about AVR timers though, so if I look into it it'll have to be after I've gotten some other stuff done. Quote from: mSSM;617428 I strongly urge you not to do it. :D You are going to be entirely dependent on your very own setup, and you are going to _hate_ using anything but. Fun thing is that it sounds like a lot of work to learn that stuff, but in the end it's more for lazy people. ;-) Haha. I realize that. I'm pretty sure this keyboard will be a definite step in the wrong direction then ;) Quote from: Surger;617814 Yes, actually, adding that flexibility would be interesting: one would achieve an Alt+Function key press without increasing the number of keys to be pressed. Same for a Control+fn and Shift+fn. Added to the 'dev' branch :) . Still to early to promise which features'll be in the final release, or be visible from the UI, but at least it's been through preliminary testing. Quote from: REVENGE;618450 [image] Looks good :) Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Fri, 22 June 2012, 02:17:55 Install: (http:\/\/i.imgur.com\/YzU8U.png) Config: (http:\/\/i.imgur.com\/mFtnJ.png) These would be more usable at resolutions down to 32 x 32. Dox: Did you use a font for your avatar, or is it custom? Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Fri, 22 June 2012, 06:08:23 Quote from: REVENGE;619288 Install: Show Image (http:\/\/i.imgur.com\/YzU8U.png) Config: Show Image (http:\/\/i.imgur.com\/mFtnJ.png) These would be more usable at resolutions down to 32 x 32. Dox: Did you use a font for your avatar, or is it custom? These are fantastic! Keep it all coming! I agree those would work great as Icons. Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Fri, 22 June 2012, 08:46:58 Quote from: REVENGE;619288 Dox: Did you use a font for your avatar, or is it custom? A GH'er made it for him somewhere in the DOXkb topic. --- Edit: I can't find it now. Maybe it wasn't in the DOXkb topic. Title: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Fri, 22 June 2012, 09:20:19 Quote from: REVENGE;619288 ...Dox: Did you use a font for your avatar, or is it custom? Quote from: dorkvader;619404 A GH'er made it for him somewhere in the DOXkb topic. --- Edit: I can't find it now. Maybe it wasn't in the DOXkb topic. You guys mean this? http:\/\/geekhack.org\/showthread.php?17374-My-keyboard-project&p=335210&viewfull=1#post335210 Cheers, Title: [Interest Check] Custom split ergo keyboard. Post by: REVENGE on Fri, 22 June 2012, 12:22:55 Quote from: OrangeJewce;619421 You guys mean this? http:\/\/geekhack.org\/showthread.php?17374-My-keyboard-project&p=335210&viewfull=1#post335210 Cheers, Thanks Jewce! I want to use that font for any text titles, Arial just doesn't cut it IMO. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Thu, 19 July 2012, 08:40:42 Are there any updates? I haven't really seen much on the github. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: dirge on Thu, 19 July 2012, 09:09:27 Are there any updates? I haven't really seen much on the github. Cheers, was quite a bit of progress on deskthority, imagine it'll make its way here. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Thu, 19 July 2012, 09:25:48 Can you link where they talked about this project over there? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Thu, 19 July 2012, 09:36:54 http:\/\/deskthority.net\/workshop-f7\/split-ergonomic-keyboard-project-t1753.html There's the topic on DT. Dox has a working prototype with a shapeways plastic case. I believe the case was$200 total.\n\nI'm hoping to have the case files updated this weekend, so we can get some quotes on the layer case from water\/laser cutters.\n---\nI'll be updating the interest list later this evening with all the interest garnered from DT over the break.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Thu, 19 July 2012, 10:06:14\n\nI will have to get in contact with ic07 and move up my timeline for completing the UI project prototype. I had no idea so much progress was being made! I figure I will have 4-6 weeks from the initiation of the group buy to get V 1.0 of the firmware stuff out so that should be pretty good I would think. I will keep up to date on both threads.\n\nCheers,\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Inf3rn0_44 on Sat, 28 July 2012, 18:52:04\nThis thread is amazing keep up the great work! I am holding off a Kinesis Advantage for one of these babies!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Sat, 28 July 2012, 18:56:34\nThis thread is amazing keep up the great work! I am holding off a Kinesis Advantage for one of these babies!\n\nSame here. Hopefully this will become a reality by the time school starts.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: fatchoi on Thu, 02 August 2012, 08:52:01\nHi guys, I'm interested in it, if it's under US$300 (all assembled and ready to use) and if you ship it international. Please keep me updated. Thanks ;) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Thu, 02 August 2012, 09:29:40 Hi guys, I'm interested in it, if it's under US$300 (all assembled and ready to use) and if you ship it international.\n\nPlease keep me updated. Thanks ;)\n\nCurrently I don't think you'll be able to get it for that price, from DT it seemed like aluminum cases were going to be in the $200 range, and after PCBs you'd be sitting at around$250. Switches and Caps are going to come in at around another $100 (depending on type). Then add assembly and international shipping, and I don't see it going for less than$400 :'(. If you can get in on a printed plastic case it may push the cost down by $100, but I am not sure what the status is on that. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Inf3rn0_44 on Thu, 02 August 2012, 10:21:42 oh damn, thats expensive! :o if there is a way to reduce overall costs, please go ahead. I really like the concept! best wishes Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Icarium on Thu, 02 August 2012, 12:25:06 We'll see how it turns out. In the end the PCB will probably be reasonably cheap, MX blacks are cheap if you harvest them from some other board and if need be a piece of cardboard will work as coaster case. I'd rather have it cheap and dirty than not at all. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: fatchoi on Thu, 02 August 2012, 22:58:26 Hi guys, I'm interested in it, if it's under US$300 (all assembled and ready to use) and if you ship it international.\n\nPlease keep me updated. Thanks ;)\n\nCurrently I don't think you'll be able to get it for that price, from DT it seemed like aluminum cases were going to be in the $200 range, and after PCBs you'd be sitting at around$250. Switches and Caps are going to come in at around another $100 (depending on type). Then add assembly and international shipping, and I don't see it going for less than$400 :'(. If you can get in on a printed plastic case it may push the cost down by $100, but I am not sure what the status is on that. Cheers, Hm... If excluding shipping, it's$350 or below, please count me in. ;)\n(Expects a shipping of $60) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Fri, 03 August 2012, 14:24:13 Hi guys, I'm interested in it, if it's under US$300 (all assembled and ready to use) and if you ship it international.\n\nPlease keep me updated. Thanks ;)\n\nCurrently I don't think you'll be able to get it for that price, from DT it seemed like aluminum cases were going to be in the $200 range, and after PCBs you'd be sitting at around$250. Switches and Caps are going to come in at around another $100 (depending on type). Then add assembly and international shipping, and I don't see it going for less than$400 :'(. If you can get in on a printed plastic case it may push the cost down by $100, but I am not sure what the status is on that. Cheers, Hm... If excluding shipping, it's$350 or below, please count me in. ;)\n(Expects a shipping of $60) What it will all come down to is the case material. It seemed like, based on the DT discussions, DoX was going to offer only Aluminum in the official group buy, but I think The_Beast was investigating 3D printing options for plastic cases, which is where my reduced amount for cases came from. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Fri, 03 August 2012, 14:34:02 Hi! I'm new to geekhack, but I'd like to register interest in this. I found the site at ergodox.org (based on a reference to it in my introduction thread here on geekhack), but it's a little bare. How do I go about getting one of these? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Djuzuh on Fri, 03 August 2012, 14:44:05 Hi! I'm new to geekhack, but I'd like to register interest in this. I found the site at ergodox.org (based on a reference to it in my introduction thread here on geekhack), but it's a little bare. How do I go about getting one of these? You wait until orders go public. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: fatchoi on Fri, 03 August 2012, 23:17:36 What it will all come down to is the case material. It seemed like, based on the DT discussions, DoX was going to offer only Aluminum in the official group buy, but I think The_Beast was investigating 3D printing options for plastic cases, which is where my reduced amount for cases came from. Cheers, Let's see how it goes :D If the end product is great, don't mind paying a bit more. :) Thanks for your quick reply. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Sun, 05 August 2012, 18:58:09 So after reading through this thread (and the accompanying thread on deskthaurity), I think I've gleaned the following: \u2022 The design of the device is all but set in stone at this point. \u2022 Dox already has a prototype, has put it through the paces, and loves it. \u2022 No official order has been placed yet, so most (if not all) others don't have one yet. \u2022 At one point geekhack went down, and the deskthaurity spread started up in its absence. \u2022 Price is looking to be over$400 at this point, bottom line.\n\nWhich site are people treating as the home for this now? GH was first, and appears to be back now, but it seems to be fairly stalled compared to the DT thread.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Sun, 05 August 2012, 23:13:45\nI'd like to add my interest in buying two sets of PCBs.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: braaaiiins on Mon, 06 August 2012, 01:42:55\nIf the PCBs are under under $100 for a set, I'm in for one. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Mon, 06 August 2012, 14:18:35 So after reading through this thread (and the accompanying thread on deskthaurity), I think I've gleaned the following: \u2022 The design of the device is all but set in stone at this point. \u2022 Dox already has a prototype, has put it through the paces, and loves it. \u2022 No official order has been placed yet, so most (if not all) others don't have one yet. \u2022 At one point geekhack went down, and the deskthaurity spread started up in its absence. \u2022 Price is looking to be over$400 at this point, bottom line.\n\nWhich site are people treating as the home for this now? GH was first, and appears to be back now, but it seems to be fairly stalled compared to the DT thread.\n\nI cruise both forums, and so does Dork. As for the rest of the community, I'd say that more discussion exists on DT. However, I would not rely on that to contain anything official outside of what is occurring with PCB development. For official announcements, etc., I would encourage you to look at www.ergodox.org and maintain a presence here because the official GB will most definitely have a thread here.''\n\nCheers,\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Tue, 07 August 2012, 01:42:46\nSo after reading through this thread (and the accompanying thread on deskthaurity), I think I've gleaned the following:\n\n\u2022 The design of the device is all but set in stone at this point.\n\u2022 Dox already has a prototype, has put it through the paces, and loves it.\n\u2022 No official order has been placed yet, so most (if not all) others don't have one yet.\n\u2022 At one point geekhack went down, and the deskthaurity spread started up in its absence.\n\u2022 Price is looking to be over $400 at this point, bottom line. Which site are people treating as the home for this now? GH was first, and appears to be back now, but it seems to be fairly stalled compared to the DT thread. I forgot my DT Password, so I can't update then until I remember or reset it. I've updated the info: Will update the post later. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: litster on Sun, 19 August 2012, 22:25:54 Just realized Lister is on the list, but not Litster. Don't believe that Lister imposer. I am the real deal. Litster is the real deal! I am in since post 6 on this thread (http:\/\/geekhack.org\/index.php?topic=22780.msg428686#msg428686)! ;D Title: Re: [Interest Check] Custom split ergo keyboard. Post by: tsangan on Sun, 19 August 2012, 22:39:24 Didn't want to commit before but after seeing Dox working proto I will be in on this Title: Re: [Interest Check] Custom split ergo keyboard. Post by: mkawa on Mon, 20 August 2012, 01:20:31 in to help as usual. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Mon, 20 August 2012, 11:18:40 Hopefully next month I'll be able to begin working on the meat of the UI, as IC hands me a relatively stable version of the firmware. I think Dox is still working out some issues with the case, and Prins just shipped the updated PCBs to both Dox and IC last week. I would estimate at least 2 months before a GB still. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: funkymeeba on Mon, 20 August 2012, 13:44:44 My price limitation may be a bit higher, as I have had income for a few weeks now, and am due for a nice pay bump in just a couple more weeks. Timing is everything! :D Title: Re: [Interest Check] Custom split ergo keyboard. Post by: StaCT13 on Tue, 28 August 2012, 23:02:26 If interest is still high in this and progress is still being made, I'd be willing to buy one for about$500, assuming the price includes everything needed to get it working and a set of blank keycaps.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: damorgue on Tue, 28 August 2012, 23:13:43\nIf interest is still high in this and progress is still being made, I'd be willing to buy one for about $500, assuming the price includes everything needed to get it working and a set of blank keycaps. The case will determine if it ends up costing more or less than$500 I believe. A milled aluminium case will ofc make it cost quite a bit, but there are other options in the works.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: The_Beast on Mon, 10 September 2012, 00:35:26\nI thought I registered interest in a PCB\n\nAnyways, I'm interested in a pcb :D\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: TheProfosist on Mon, 10 September 2012, 01:06:01\nInterested\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Ian S on Tue, 11 September 2012, 08:50:21\nI've not read the whole 29 pages.\u00a0 Is there an option for Topre switches?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: damorgue on Tue, 11 September 2012, 08:52:41\nI've not read the whole 29 pages.\u00a0 Is there an option for Topre switches?\n\nNot a chance.\n\nThis is only for Cherry MX. Making one for alps wouldn't be that difficult, but it would require a new pcb to be made. Topre is just way to different unfortunately.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Ian S on Tue, 11 September 2012, 09:09:13\nWould that be related to a controller to work with the capacitive switches?\u00a0 Oh well. :(\u00a0 I anyway half expected all that and the switches too would be propriety and not for third party products.\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: dirge on Tue, 11 September 2012, 10:31:10\nMaking one for alps wouldn't be that difficult, but it would require a new pcb to be made.\n\nALPS!!!! make it happen! just moar ALPS!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Tue, 11 September 2012, 11:46:50\nFor a split ergonomic keyboard with topre switches, there is the \u03bcTron \/ uTron ... here, Amazon-Japan has it:\n\nWould that be related to a controller to work with the capacitive switches?\u00a0 Oh well. :(\u00a0 I anyway half expected all that and the switches too would be propriety and not for third party products.\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Icarium on Tue, 11 September 2012, 12:00:06\nIf you can't figure out what it costs from that page: Be glad.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: docomoz on Thu, 20 September 2012, 09:12:07\nI'm in. No matter the cost.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Pyrolistical on Thu, 20 September 2012, 15:55:46\nI'm in. No matter the cost.\n\nBoy, do I have a keyboard for you sir!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Ian S on Thu, 20 September 2012, 16:19:13\nFor a split ergonomic keyboard with topre switches, there is the \u03bcTron\nAh, thanks, yes I saw that a little while ago together with a video and that board seemed to be 'wrong' in a couple or so ways, not least, the price, but I recall the slope and angle looked wrong, maybe had too few keys, either way, unlike docomoz above, alas or me price is a factor.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: kta on Sat, 22 September 2012, 06:16:48\nThis is really promising, it looks like the perfect input device to me:)\n\nif the price is in the 500$range, I am interested for at least one set. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: litster on Wed, 26 September 2012, 19:24:15 anyone interested in pooling together to print some ergodox cases? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: litster on Fri, 28 September 2012, 12:43:43 bpiphany enlisted me as his beta tester. I soldered diodes and a teensy on to the right hand PCB (no connectors or resistors). After I flashed the firmware from github on to the teensy, the keyboard is not recognized by Windows at all when I plug it in. Do I need to connect the two halves together in order for the teensy to boot correctly? Do I need to flash both .hex and .eep files onto the teensy? the 1.06 loader doesn't seem to know how to flash the .eep file. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Fri, 28 September 2012, 12:56:01 yeah... the .eep is in the same exact format as .hex, if you rename it then it'll load... I just don't know how the teensy loader determines where to load it to. The file should tell it, but does it listen? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Fri, 28 September 2012, 12:56:18 anyone interested in pooling together to print some ergodox cases? Absolutely. If you haven't seen it though you might want to check out JesuswasaZombie's GB IC thread (http:\/\/geekhack.org\/index.php?topic=35439.0) as I think there are also moves being made there to coordinate this. Either way, I'm in! I'd like to see this happen as soon as possible. bpiphany enlisted me as his beta tester. AWESOME. I'm really excited to get the kind of info from the field that you're providing. Hope you keep the thread posted! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Fri, 28 September 2012, 12:57:37 Maybe some clues here: see updates to rev 1.05 http:\/\/www.pjrc.com\/teensy\/loader.html (http:\/\/www.pjrc.com\/teensy\/loader.html) and more here (https:\/\/groups.google.com\/forum\/?fromgroups=#!topic\/lufa-support\/Qookbb9v_YE): Hi guys! Here's the EEPROM-writing asm code the GUI-based Teensy Loader uses. Actually, a binary copy of this is built into the Teensy Loader. When opening the .hex file, the Teensy Loader checks if there's an .elf file which matches the .hex file, and if so the .eeprom section is extracted from the .elf and appended to the binary data from of tiny program. Once downloaded and run, it just writes to the eeprom and then jumps back to the bootloader. Seems you need the original elf, or a way to put them back together. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: sordna on Mon, 01 October 2012, 09:18:57 Why does deskthority get all the nice pictures (http:\/\/deskthority.net\/workshop-f7\/split-ergonomic-keyboard-project-t1753-480.html) ?? Copying couple of ic07's pics here, it looks sooooo nice Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Sifo on Mon, 01 October 2012, 09:32:13 Looking good Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wiredPANDA on Mon, 01 October 2012, 09:47:45 Thanks for cross-posting those from DT. =D Title: Re: [Interest Check] Custom split ergo keyboard. Post by: tiarnachutch on Sun, 07 October 2012, 17:47:59 What's the current ETA on having final designs and beginning production? The mock-ups look amazing. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Sinzz on Sun, 07 October 2012, 21:09:42 hmmm.. interested.. but will have to see the final designs first. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Mon, 08 October 2012, 09:21:05 Prototypes are out in the field and are being beta-tested right now. The last remaining hurdle is the case, and even I still have no idea when we can expect that to be completed. You can always check out this thread on Deskthority for engineering related info. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Mon, 08 October 2012, 15:37:19 The last remaining hurdle is the case I'd beta test on a yoga mat case like ic07 if it meant getting this thing sooner. Function over form! Case important, but less important; not sure if I'm alone in this opinion though. Also I'm in between contracts right now so I've got a bunch of time I could dump into this. And a nice camera to indulge forum readers! :) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Matias on Mon, 08 October 2012, 16:39:24 Why does deskthority get all the nice pictures (http:\/\/deskthority.net\/workshop-f7\/split-ergonomic-keyboard-project-t1753-480.html) ?? Copying couple of ic07's pics here, it looks sooooo nice Prototypes are out in the field and are being beta-tested right now. The last remaining hurdle is the case, and even I still have no idea when we can expect that to be completed. You can always check out this thread on Deskthority for engineering related info. This is VERY cool. Nice work! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Mon, 08 October 2012, 20:15:21 The last remaining hurdle is the case I'd beta test on a yoga mat case like ic07 if it meant getting this thing sooner. Function over form! Case important, but less important; not sure if I'm alone in this opinion though. Also I'm in between contracts right now so I've got a bunch of time I could dump into this. And a nice camera to indulge forum readers! :) Hah, I am one to disagree with you, because IMO it holds the greatest design and production challenge of the entire keyboard! Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Mon, 08 October 2012, 20:36:02 yeah, without the case where is the 'ergo'? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Tue, 09 October 2012, 00:21:52 yeah, without the case where is the 'ergo'? Respectfully: without the case, the keys are still laid out the same. If I were to guess, you'd opt for one of the sloped bottom designs? Personally, I'm going flat, so the keyboard will be just as ergo for me without the case as it will be with it. Hah, I am one to disagree with you, because IMO it holds the greatest design and production challenge of the entire keyboard! Totally conceded! I'd be interested to know if there is anything that can be done to help this challenge progress. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: jwaz on Tue, 09 October 2012, 00:33:28 yeah, without the case where is the 'ergo'? The staggering of the keys? The split between sections? I'm sure you could do a tent design without a case... Title: Re: [Interest Check] Custom split ergo keyboard. Post by: sordna on Tue, 09 October 2012, 01:30:28 I haven't heard anything about this case being \"ergo\", so unless they can make it adjustable (which would be very difficult), it should be as flat and low profile as possible! Then it would be up to each of us to prop\/tilt\/tent it as we please. I'll probably build a stand out of cardboard, or out of a coat-hanger or something, that can prop the keyboard halves to an angle of at least 45\u00b0 Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Tue, 09 October 2012, 05:13:50 I haven't heard anything about this case being \"ergo\", so unless they can make it adjustable (which would be very difficult), it should be as flat and low profile as possible! The diagrams for the case parts are on the ergodox website--there is one case top, and case bottoms of three different types: flat: (http:\/\/www.ergodox.org\/Images\/Downloads\/Flat_BottomLeftCase2.JPG) sloped (vertical) (http:\/\/www.ergodox.org\/Images\/Downloads\/Single_BottomLeftCase2.JPG) double-sloped (horizontal and vertical). (http:\/\/www.ergodox.org\/Images\/Downloads\/Double_BottomLeftCase2.JPG) So while not being adjustable per se, it does appear as though there are options in the works. Not sure about 45\u00b0 though. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Tue, 09 October 2012, 07:39:00 yeah, I was referring to the angled bottoms Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Workoft on Thu, 11 October 2012, 09:02:50 Hi, This looks really good. Unfortunately, I didn't see this any earlier and now 30 pages are a lot to work through. I have a few questions about the design. What's the motivation for those extra keys on the bottom? I find keys like Alt, Ctrl and Alt-Gr on a conventional keyboard hard to reach with my fingers when my hands are in normal typing position, so I would think on an ergonomic keyboard there shouldn't be an extra row on the bottom. Also the center keys are relatively hard to reach because it requires reaching over two columns. Those who tried the prototype should know best, what's you experience with these? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: litster on Thu, 11 October 2012, 23:58:22 Here it is. A couple of mistakes like the 3.5mm opening is too narrow, forgot the make room for the USB connector on the layers that sandwich the acrylic plate. I want to have a built-in wrist rest to the case as well. I will have to make all those changes for the next prototype. (http:\/\/i.imgur.com\/TPVLf.jpg) Top view: (http:\/\/i.imgur.com\/zZOAy.jpg) BTW, to use this case, you will need to solder SMD diodes or through-hole diodes on the bottom of the PCB. SMD diodes on the bottom is better as you would not need to worry about the diode legs sticking up from the bottom. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: dirge on Fri, 12 October 2012, 03:14:08 Outstanding work litster! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: The_Beast on Fri, 12 October 2012, 03:16:44 Nice to see some progress being made on this. Hopfully too many custom boards don't come out at once, sounds dumb but I don't want to have to pick between custom boards. I WANT THEM ALL ^___^ Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bebuxe on Fri, 12 October 2012, 03:56:27 You have officially have me bought. No matter the price. I'll buy a one, and any others for my friends. Need money now for more materials and stuff? I am wondering if we can process these for bulk orders. Nah, thinking way too ahead. Better yet, want some server space to host your stuff? Or you got it covered? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Fri, 12 October 2012, 08:50:58 Nice to see some progress being made on this. Hopfully too many custom boards don't come out at once, sounds dumb but I don't want to have to pick between custom boards. I WANT THEM ALL ^___^ Honestly, the eDox is too unique compared to all the other custom boards. I think owning one really will make you special compared to the numerous custom TKLs. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: The_Beast on Fri, 12 October 2012, 12:58:11 Nice to see some progress being made on this. Hopfully too many custom boards don't come out at once, sounds dumb but I don't want to have to pick between custom boards. I WANT THEM ALL ^___^ Honestly, the eDox is too unique compared to all the other custom boards. I think owning one really will make you special compared to the numerous custom TKLs. Cheers, Your right, but I'm not even sure I'll like an ergo keyboard yet. Plus I'm really like the GH60 Title: [Interest Check] Custom split ergo keyboard. Post by: jwaz on Fri, 12 October 2012, 13:25:45 Looks good Lit, will similar colors be available as the filco\/ Phantom acrylic cases? Definitely hope the aluminum ones are reasonable. That design looks great. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: funkymeeba on Fri, 12 October 2012, 16:51:22 I tend to agree, litster. That case is funky, and I definitely liked what I saw of the Phantom cases. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: litster on Mon, 15 October 2012, 22:08:15 I have added a built-in wrist rest. Also now I have a proper top layer thanks to DOX. (http:\/\/i.imgur.com\/QG4S3.png) click the picture to see the larger version that is not weird :-) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wiredPANDA on Mon, 15 October 2012, 22:15:55 Nice idea, litster. Interested to see the new prototype case with wrist rest. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: tiarnachutch on Mon, 15 October 2012, 22:31:10 I have added a built-in wrist rest. Also now I have a proper top layer thanks to DOX. Show Image (http:\/\/i.imgur.com\/QG4S3.png) click the picture to see the larger version that is not weird :-) Excellent! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Mon, 15 October 2012, 23:44:19 I have added a built-in wrist rest. I like the idea of a built-in wrist rest, but I'd be worried about disagreements stemming from details surrounding it (padding\/firmness, surface texture, wrist rest dimensions for different hand sizes, etc), and potential setbacks surrounding the discussion. Is this just for the prototype that you've been testing or are you suggesting this for the full run of cases? Is there a plan for people who don't want it? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 16 October 2012, 14:18:05 I have added a built-in wrist rest. I like the idea of a built-in wrist rest, but I'd be worried about disagreements stemming from details surrounding it (padding\/firmness, surface texture, wrist rest dimensions for different hand sizes, etc), and potential setbacks surrounding the discussion. Is this just for the prototype that you've been testing or are you suggesting this for the full run of cases? Is there a plan for people who don't want it? Yeah I would rather not have a builtin wrist rest, not only for the materials cost increase, but also because it'll take a lot of space. Cool though, and to each their own. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: litster on Sat, 20 October 2012, 20:01:44 Now with wrist rest: (http:\/\/i.imgur.com\/0azLl.jpg) And a view of the encased Teensy and other parts: (http:\/\/i.imgur.com\/pCBXf.jpg) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Sifo on Sat, 20 October 2012, 20:29:59 Wow litster that is beautiful. Great work ! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: TheProfosist on Sat, 20 October 2012, 21:59:30 I agree looking good. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: tiarnachutch on Sun, 21 October 2012, 14:56:46 Looking good! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Sun, 21 October 2012, 16:52:47 Now with wrist rest Out of curiosity, how are you making these? Are you sending the designs out to a shop somewhere or is this maybe the work of a 3D printer or something? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: litster on Sun, 21 October 2012, 17:24:08 They are acrylic sheets cut with a laser cutter fed with my drawings I design on my computer. I cut these myself. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: sordna on Sun, 21 October 2012, 18:02:49 Now with wrist rest: Show Image (http:\/\/i.imgur.com\/0azLl.jpg) And a view of the encased Teensy and other parts: Show Image (http:\/\/i.imgur.com\/pCBXf.jpg) Wow, that's amazing! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: WhiteFireDragon on Sun, 21 October 2012, 18:11:43 Glad to see this is still progressing. Is this a working prototype? Why do you need to make a different revision prototype? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: litster on Sun, 21 October 2012, 19:58:24 The pair is done. It was a lot of fun building the case. (http:\/\/i.imgur.com\/kTRGM.jpg) It is exactly as I expect, a very good ergo keyboard, very much like my Kinesis Advantage. Personally I enjoy typing on traditional layout more. I am too used to that. bpiphany, please make a split keyboard laid out like the MX5000 with a proper 6-pack cluster. I will design a case for it. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: gdaian on Mon, 22 October 2012, 18:26:02 I am so happy to have stumbled upon this marvelous project. Just knowing of its existence has relieved me of immense frustration. I've been fumbling with a recently bought Typematrix and scouring the internet for alternatives, cursing the cluelessness of industrial keyboard designs, until I almost at random landed on the key64 page. The moment I saw the design, I burst out in maniacal laughter; it was as if my every plea had been answered. Thanks to this thread, I now live with the hope of seeing these answers materialize under my running fingers. At last, I rest. Anyway, I'm in for USD ~350. Accept Bitcoin for payment, and I'll send some delicious Danish beer on top. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 23 October 2012, 11:21:40 I am so happy to have stumbled upon this marvelous project. Just knowing of its existence has relieved me of immense frustration. I've been fumbling with a recently bought Typematrix and scouring the internet for alternatives, cursing the cluelessness of industrial keyboard designs, until I almost at random landed on the key64 page. The moment I saw the design, I burst out in maniacal laughter; it was as if my every plea had been answered. Thanks to this thread, I now live with the hope of seeing these answers materialize under my running fingers. At last, I rest. Anyway, I'm in for USD ~350. Accept Bitcoin for payment, and I'll send some delicious Danish beer on top. Unfortunately, I highly doubt bitcoin will be an accepted currency ( since the GB will almost assuredly be using paypal ). But more is merrier! Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: litster on Tue, 23 October 2012, 13:40:55 I know some people like the small, regular version, while some other people like the design with wrist rest. But the switches are soldered to the PCBs with the mounting plate layer sandwiched in-between. Switching between regular and the wrist rest version would require desoldering and resoldering switches I can re-design the mounting plate layer so that you always use the smaller, regular mounting plate, and you can move that mounting plate layer to go with the regular version of the case or the wrist rest version. When you use the wrist rest version, you just add an extension to the mounting-plate in the wrist rest area. The top two and the bottom two layers will be whichever design you choose to use. Everything is screwed down tightly so it should still be as sturdy as before. I should do that to my Filco\/Phantom case as well :-) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: TheProfosist on Tue, 23 October 2012, 13:49:19 I <3 that clear acrylic case with the built in wrist rests only thing about me i need my wrist rests to be 4.25in in width so it may or may not work for me. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: thp777 on Thu, 25 October 2012, 15:23:15 what about having the wrist wrest area a separate piece and attach with neo magnets so you can snap it on and off. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Thu, 01 November 2012, 18:09:57 what about having the wrist wrest area a separate piece and attach with neo magnets so you can snap it on and off. This is a good idea: I have about 20 of these from broken magsafe boards out of apple computers (Apple doesn't want the old magsafe 'boards back) Bytheway, I've updated the list. If you're not on it, PM me please. Sholud I put the pictures in the post as well to tantalize people? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Thu, 01 November 2012, 18:17:33 Hey dorkvader! On the offchance that you haven't been over to the DT thread recently, we're trying to start talking logistics with regards to moving forward. Can you take a look and weigh in? Actually, I suppose the game goes for anyone following this thread here--here's the link. (http:\/\/deskthority.net\/workshop-f7\/split-ergonomic-keyboard-project-t1753.html) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: TDub on Fri, 02 November 2012, 05:06:19 The transparent case with wristrest looks seriously awesome. Can't wait for a GB for this keyboard. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: AloisiusFauxly on Mon, 05 November 2012, 15:25:14 I posted this over at DT: This is a great time for crowd funding to get the project moving forward, and fits perfectly with the working-prototype stage the project is at: PCBs\/electronics basically done, case options coming together. Discrete levels of funding through perks\/rewards matches our varied interest here at DT and GH (just pcbs, pcbs+electronics, full kits, plastic vs metal case, etc). It also opens up the possibility to make a more attractive package by offering keycap sets, switches, and\/or assembly. Having the closest we can to a complete keyboard will help attract more people outside of GH\/DT, which is better for everyone's bottom line. It also takes care of the pre-order money issue as it's a large entity holding the funds. Now, this all hinges on people getting behind the project, handling things like shipping logistics and communication. Since I just rolled into this project a couple weeks ago, I don't really know what roles people have stepped up to. If no one has done so already I'll start crunching some numbers to get a good idea of costs and target prices for something like indiegogo. This looks like a great keyboard, and I'd like to help make it a reality. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 06 November 2012, 09:26:04 I posted this over at DT: This is a great time for crowd funding to get the project moving forward, and fits perfectly with the working-prototype stage the project is at: PCBs\/electronics basically done, case options coming together. Discrete levels of funding through perks\/rewards matches our varied interest here at DT and GH (just pcbs, pcbs+electronics, full kits, plastic vs metal case, etc). It also opens up the possibility to make a more attractive package by offering keycap sets, switches, and\/or assembly. Having the closest we can to a complete keyboard will help attract more people outside of GH\/DT, which is better for everyone's bottom line. It also takes care of the pre-order money issue as it's a large entity holding the funds. Now, this all hinges on people getting behind the project, handling things like shipping logistics and communication. Since I just rolled into this project a couple weeks ago, I don't really know what roles people have stepped up to. If no one has done so already I'll start crunching some numbers to get a good idea of costs and target prices for something like indiegogo. This looks like a great keyboard, and I'd like to help make it a reality. I think this is a pretty dead horse tbh. Overall crowdsourcing this was ruled to be too costly upfront, and the logistics of handling all the money wasn't great. Secondly, it's hard enough trying to keep people settled whilst waiting for the case (many want pcbs NAO), It'd be really tough if we package caps now (since it can take a long time for a production run), to ask for an additional 2-3 months. When I get the UI done I plan on putting together something for a cap buy, since it seems there might not be a lot of interest in a WASD set. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: AloisiusFauxly on Tue, 06 November 2012, 17:43:41 Why was crowdsourcing ruled to be too costly up front? AFAIK, indiegogo would run the campaign and if it was successful, they would take their 4% cut and release the money to the organizers who could then make the purchases for everything in bulk and get those balls rolling. We get 30-60 days to collect money and target a completed product\/kit 2-4 months down the road from that. It seems like the optimal model for getting as much money up front to order at higher qty. It also creates a sense of legitimacy to mitigate people's aversion to handing over a few hundo to a GH\/DT user before we have everything together. This legitimacy would also be much more attractive to people outside of this community, leading to higher qty. Once that chunk of money is available, we can start placing orders for the PCBs, electronics, and\/or switches and ship them out as kits earlier while the case designs and keycaps get sorted out. So it would benefit people like me, who are card-carrying members of PCBNAO. This is definitely more work than a simple group buy would be. But the scope of the project and the costs involved might require something more than simple group buy organization. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Tue, 06 November 2012, 23:17:31 Why was crowdsourcing ruled to be too costly up front? AFAIK, indiegogo would run the campaign and if it was successful, they would take their 4% cut and release the money to the organizers who could then make the purchases for everything in bulk and get those balls rolling. We get 30-60 days to collect money and target a completed product\/kit 2-4 months down the road from that. It seems like the optimal model for getting as much money up front to order at higher qty. It also creates a sense of legitimacy to mitigate people's aversion to handing over a few hundo to a GH\/DT user before we have everything together. This legitimacy would also be much more attractive to people outside of this community, leading to higher qty. Once that chunk of money is available, we can start placing orders for the PCBs, electronics, and\/or switches and ship them out as kits earlier while the case designs and keycaps get sorted out. So it would benefit people like me, who are card-carrying members of PCBNAO. This is definitely more work than a simple group buy would be. But the scope of the project and the costs involved might require something more than simple group buy organization. Few months ago when kickstarter was initially proposed. At that time the idea went nowhere and was shot down. I'm not going to dredge it up because...well this thread is 31 pages long and the DT thread is 22. 53 pages of searching ain't worth it. Just note this issue has been discussed before, and while what happens may have changed between then and now, I won't hold my breath. We don't know what type of quantity we are dealing with. We still don't have a case. Dealbreaker. Switches won't be part of the buy, neither will keycaps. This is really, really firm. It's been stated over and over there won't be a buy before the case is done. I don't see how this is going to alleviate such concern in the short term, if we still have to wait for everyone to submit payment, only to receive their goods piecemeal. I don't like it personally, and I would rather not have my money tied up for an extra 3-4 weeks while some others get PCBs earlier because that's all they want. I understand that people really want to get their hands on these things right now, but in the best interests of everyone who wants something I firmly believe we should wait for a final case design that can be mass produced. Once we have the R&D done I'm all ears on how to streamline the ordering and distribution process. One thing to consider is this board is already expensive. 15% on top of a$200-$300 board really isn't cheap, since that won't include caps or switches. I'm still concerned about the IP related to these designs, we don't know what license everything will be covered under. Cheers, P.S. Found Dox's original post from last December: Quote Quote Have you thought about broadening the audience a bit? Throw it on Kickstarter and get 100 people to pay$300. It couldn't hurt.\nI thought about it but with my current job, I don't have the time to manage something like this.\n\nP.P.S.\nI have mispoke, and \"costly\" was incorrect of me. I will remand that, and instead would rather say that the issue was previously discussed hella long time ago (longer than I thought actually), no idea if Dox's situation has changed.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Wed, 07 November 2012, 00:49:21\nOrangeJewce,\n\nI just summarized my first turnaround with MassDrop (http:\/\/deskthority.net\/post82080.html#p82080); I think it's very promising, and it addresses a lot of your concerns.\n\nA couple of quick highlights in direct response to your items here:\n\u2022 Massdrop is entirely different than Kickstarter, and much better suited to our needs.\n\u2022 Massdrop polling can help us elicit the current level of actionable interest so that they can plan accordingly.\n\u2022 The case doesn't seem far off; Dox's last images on DT look almost identical to the ones on ergodox.org, and he even said they were nearly complete. We can proceed with polling and massdrop setup; the case will only be required when the massdrop opens for purchase. If anyone can get in touch with Dox maybe we can get a time estimate to help with planning.\n\u2022 Massdrop can set up the buy such that everyone, PCB-only or full-components alike, will be fulfilled at the same time, with the same buy.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Wed, 07 November 2012, 08:05:28\nThanks bisl,\n\nThat alleviates a lot of concerns actually. I would be surprised if Dox would rather use a traditional buy for something like this. I agree, the primary concern with a standard GB is nobody can handle the money we're talking about here individually which may even reach the $100k mark. Paypal would freak the hell out, and if we put it in escrow, that's a huge amount of work that I am sure Dox wouldn't have time for. Not sure if we'll be able to get a good deal on switches or any of the more rare ones, but we'll see. As for caps, I think the amount of interest will be pretty weak by comparison, so a traditional GB could be done for that. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: AloisiusFauxly on Wed, 07 November 2012, 13:04:06 this thread is 31 pages long and the DT thread is 22. 53 pages of searching ain't worth it. I'll take your word for it! I would rather not have my money tied up for an extra 3-4 weeks while some others get PCBs earlier because that's all they want. Your money would only be held for an extra amount of time if the case designs were done and ready to order before the campaign was finished. It's not like anyone would sit around with the money while they twiddle their thumbs. When parts are ready to be ordered\/manufactured, they should be. When parts come in to fulfill orders, the orders get shipped out. People getting their PCBs sooner doesn't make the complete kit come any later. Is it just a lead time issue? You would only want to pay when the case design is finalized and you're only 2-3 weeks away from getting your parts instead of 6-8 weeks? One thing to consider is this board is already expensive. 15% on top... Indiegogo takes 4%. Where is this 15% coming from? This is a moot point as MassDrop looks much much better for our needs here, but I have a different understanding than you of how it would have worked with indiegogo. As far as the IP problems are concerned, ErgoDox is under the GPL so AFAIK, anyone could sell a version of it, but they might have to change the name. Having said that, I consider dox the owner of this project and wouldn't like to see anyone do a commercial run without his involvement or blessing. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: jwaz on Wed, 07 November 2012, 13:09:15 Massdrop works really well for the kit buy logistics solution but really unnecessary for buying key caps from SP. Anyone have any ideas oh how to get a custom PBT set for these unique layouts? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Wed, 07 November 2012, 13:10:14 this thread is 31 pages long and the DT thread is 22. 53 pages of searching ain't worth it. I'll take your word for it! I would rather not have my money tied up for an extra 3-4 weeks while some others get PCBs earlier because that's all they want. Your money would only be held for an extra amount of time if the case designs were done and ready to order before the campaign was finished. It's not like anyone would sit around with the money while they twiddle their thumbs. When parts are ready to be ordered\/manufactured, they should be. When parts come in to fulfill orders, the orders get shipped out. People getting their PCBs sooner doesn't make the complete kit come any later. Is it just a lead time issue? You would only want to pay when the case design is finalized and you're only 2-3 weeks away from getting your parts instead of 6-8 weeks? One thing to consider is this board is already expensive. 15% on top... Indiegogo takes 4%. Where is this 15% coming from? This is a moot point as MassDrop looks much much better for our needs here, but I have a different understanding than you of how it would have worked with indiegogo. As far as the IP problems are concerned, ErgoDox is under the GPL so AFAIK, anyone could sell a version of it, but they might have to change the name. Having said that, I consider dox the owner of this project and wouldn't like to see anyone do a commercial run without his involvement or blessing. 15% came from an off hand, poorly remembered post by someone somewhere who had talked to massdrop and the fee was high (probably not 15% but hey I haven't talked to them personally). If he's going to use GPL, no way to stop anyone from doing anything in regards to a commercial production. TBH the pcb would be changed and the controller most likely integrated, not to mention some other likely changes that would make mass production easier (no pcb mount switch holes). A lot of my concerns were put to rest by bisl's firsthand account with talking to a Massdrop rep. I still don't know what their fee would be, and it would be interesting to know. Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Wed, 07 November 2012, 13:10:53 Massdrop works really well for the kit buy logistics solution but really unnecessary for buying key caps from SP. Anyone have any ideas oh how to get a custom PBT set for these unique layouts? We start a GB for them! Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: jwaz on Wed, 07 November 2012, 13:15:00 But through who? IMSTO? MOQ is 500... Title: Re: [Interest Check] Custom split ergo keyboard. Post by: AloisiusFauxly on Wed, 07 November 2012, 13:17:29 A lot of my concerns were put to rest by bisl's firsthand account with talking to a Massdrop rep. I still don't know what their fee would be, and it would be interesting to know. Yeah, I'm curious about the business side of what they do, although I'm not sure that will be transparent. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: AloisiusFauxly on Wed, 07 November 2012, 13:18:43 But through who? IMSTO? MOQ is 500... Yeah, I was just relegated to getting an alphanum set and using blanks for the other keys. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: jwaz on Wed, 07 November 2012, 13:20:00 Multiple members met with them IN PERSON. Including myself... Basically the deeper the discount they get you the better cut they get. Hopefully BD will weigh in on this buy soon. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Wed, 07 November 2012, 14:58:00 Multiple members met with them IN PERSON. Including myself... Basically the deeper the discount they get you the better cut they get. Hopefully BD will weigh in on this buy soon. So we have to hope that the prices start low? Seems like a strange business model to me, since allegedly they are passing that additional tier savings back to us? Since when is imsto's moq 500? I thought it was 100? Cheers, Title: Re: [Interest Check] Custom split ergo keyboard. Post by: jwaz on Wed, 07 November 2012, 15:21:08 Multiple members met with them IN PERSON. Including myself... Basically the deeper the discount they get you the better cut they get. Hopefully BD will weigh in on this buy soon. So we have to hope that the prices start low? Seems like a strange business model to me, since allegedly they are passing that additional tier savings back to us? Since when is imsto's moq 500? I thought it was 100? Cheers, I mean, they aren't taking a huge cut off the top b\/c that would be detrimental to their business model (a Group Buy). They take a small percentage per transaction IIRC and it only increases if they get a really deep discount (example a$1000 car part for 1\/10th of that). This is all TMK, so hopefully BD will answer further questions.\n\nAs for IMSTO's keys, check this out http:\/\/geekhack.org\/index.php?topic=31861.0\n\nQuote\nMOQ: 300 sets, currently at: 205 paid sets.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: kurplop on Sun, 11 November 2012, 16:22:33\nI've been following this project with great interest from almost the beginning and have been impressed with the contributions made by several people to make this thing happen. I've also been impressed by how long the process takes when it's all done by volunteers whose interest is divided by also having to make a living.\n\nWould it help if someone was willing to put money up front to have the pcb's manufactured?\u00a0 It seems that there wouldn't be too great a risk to order 50 or so pairs of boards. At $40 per pair that would only be$2000. This would allow the less patient to get started sooner at volume buy pricing and I don't think it would hurt the other aspects of the development.\n\nI could fund the initial order but have no knowledge or time to distribute the orders.\n\nIf this can help the process let me know.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: mSSM on Tue, 13 November 2012, 04:18:33\nI've been following this project with great interest from almost the beginning and have been impressed with the contributions made by several people to make this thing happen. I've also been impressed by how long the process takes when it's all done by volunteers whose interest is divided by also having to make a living.\n\nWould it help if someone was willing to put money up front to have the pcb's manufactured?\u00a0 It seems that there wouldn't be too great a risk to order 50 or so pairs of boards. At $40 per pair that would only be$2000. This would allow the less patient to get started sooner at volume buy pricing and I don't think it would hurt the other aspects of the development.\n\nI could fund the initial order but have no knowledge or time to distribute the orders.\n\nIf this can help the process let me know.\n\nThe major part of the discussion about the keyboard has migrated to deskthority while geekhack was down:\nhttp:\/\/deskthority.net\/workshop-f7\/split-ergonomic-keyboard-project-t1753.html\n\nCurrently, the PCBs are still being finalized, and there is discussion about how exactly the group buy is going to happen (only PCB or all bits included). The problem is that the cases are not yet final, and that dox, being the driving force behind the project, seems to be busy with his real life. :-)\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: TheGrey on Thu, 15 November 2012, 12:32:36\nI'm really interested in this. Is there any idea of when its likely to be ready?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: BugBuster on Thu, 15 November 2012, 13:39:22\nI guess, there is a number of people, who are quietly tracking the topic and just waiting for the buy to happen. Like me :)\nSo put me to the list if there is any!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Thu, 15 November 2012, 13:45:08\nI am coordinating with Massdrop to construct a poll so that we can gauge actionable interest from all you quiet trackers. I'll reply when that's ready to go so everyone can head over there and declare their interest, and which parts they want; this will help them determine price breaks.\n\nI'll post back when that part is ready!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: vivalarevoluci\u00f3n on Sun, 18 November 2012, 13:30:19\nThe amount of interest in this keyboard makes me wonder if this thing can be taken beyond a group buy.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Sun, 18 November 2012, 18:42:07\nThe amount of interest in this keyboard makes me wonder if this thing can be taken beyond a group buy.\n\nThe answer is [IMO]: most likely. I have no qualms that dox could have done a kickstarter on this and started a small business around it. That being said, the designs will be made open source, so that possibility is still open.\n\nCheers,\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: SmallFry on Sun, 18 November 2012, 19:22:55\n*trolling* Hi OJ!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: mjtorn on Sun, 25 November 2012, 08:20:52\nI already expressed my interest on Deskthority but maybe I'll do that here as well. Bring it on!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Octane on Sun, 25 November 2012, 10:06:47\nI have never tried an ergo keyboard but am definitely interested in this. I might also pick one up for my wife, who has carpal tunnel and has had an operation on one of her hands already - other hand pending... Good work guys !!!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: TheGrey on Sat, 01 December 2012, 05:23:48\nbtw please count me in for the preassembled group buy list....also if ergodox could provide a wee update as to how thinks are going...like can this be coming before Crissssmass!?\u00a0 \u00a0:)\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ic07 on Sat, 01 December 2012, 19:52:27\nOoo.. Nope, no getting this by Christmas, sorry.. Lol. We're getting there though. Everything's done, except I think we're probably waiting in case options. Then we'll be waiting on massdrop to get the polling done, then the group buy. Then we'll be waiting for parts to ship (which might take a second for the PCBs, and maybe other parts depending on what you want). And then the people who want assembly will be waiting for that. Dunno enough to give better estimates of time right now, but that's how I'm understanding things at the moment - just to post a rough idea - :)\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: TheGrey on Tue, 04 December 2012, 07:51:20\nupdate much appreciated ic07 ! ;)\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Tue, 04 December 2012, 18:40:02\nI've been pretty silent with this for a while, and I apologize--I'm working with Massdrop on getting the polls set up, but I want to get all the bases covered before I start shopping links around to direct everyone there. They had a good prototype poll set up, but it was missing a crucial option for PCB + Case. Once it's up with all the major ordering options I'll hit the thread with links.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Wed, 05 December 2012, 09:06:06\nHey all! I heard back from Massdrop yesterday, and they have the poll set up for us (http:\/\/www.massdrop.com\/poll\/ergo-dox-full-or-partial). Please drop by and let them know what you'd like out of the Ergodox, be it the full kit, the PCB alone, or the PCB + Case, etc. This will help them work out price break information.\n\nThanks!\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: BugBuster on Wed, 05 December 2012, 10:10:01\nWhat's the difference between \"1. Full Kit\" and \"6. Full kit + Cases + PCBs\"? Is it about assembling?\n\nWhat kind of case we are voting for atm: aluminium, acryllic, smth else? Or is it still TBD?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Wed, 05 December 2012, 10:26:29\nWhat's the difference between \"1. Full Kit\" and \"6. Full kit + Cases + PCBs\"? Is it about assembling?\n\nWhat kind of case we are voting for atm: aluminium, acryllic, smth else? Or is it still TBD?\n\nThey've made a separate poll for the case type (http:\/\/www.massdrop.com\/poll\/ergo-dox-case). I don't believe this will be a winner-take-all thing, but rather just for them to gauge who wants what so they can shop the orders accordingly. I believe everyone is getting what they want in this case.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: asura on Wed, 05 December 2012, 17:40:29\nVoted.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Leandros on Fri, 07 December 2012, 06:54:03\nVoted, too.\n\nAlso I'am interested in buying one.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: engicoder on Fri, 07 December 2012, 08:10:07\nAnyone else having trouble with the Massdrop site. It annoying pops up a sign in doesn't seem to allow me to sign up. Clicking the signup button does nothing. I don't use Facebook, so that is not an option. There is no way to contact them for help as the signup popup has no such links.\n\nSolved: You can ignore the popup and click \"login\" in the upper right corner of the page even though it is greyed out...that will take you to a page with a \"Signup\" link on it.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Fri, 07 December 2012, 09:59:05\nWhat's the difference between \"1. Full Kit\" and \"6. Full kit + Cases + PCBs\"? Is it about assembling?\n\nWhat kind of case we are voting for atm: aluminium, acryllic, smth else? Or is it still TBD?\n\nThey've made a separate poll for the case type (http:\/\/www.massdrop.com\/poll\/ergo-dox-case). I don't believe this will be a winner-take-all thing, but rather just for them to gauge who wants what so they can shop the orders accordingly. I believe everyone is getting what they want in this case.\n\nThe case poll is now really skewed. I'd say it looks about tied between the two if you added all the Dox-Style cases together (maybe small advantage to litster style).\n\nCheers,\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Fri, 07 December 2012, 10:27:25\nI actually asked them to clean up the options on the case poll, since it's unclear whether litster votes are voting for the built-in wrist rest shape, or the acrylic plate design rather than 3d printed case (since litster cases were originally shaped like dox cases). Basically the options available are 3d printed (flat, slant, tent+slant) or acrylic (with\/without wrist rest) but the poll doesn't reflect that yet.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: BugBuster on Fri, 07 December 2012, 12:18:50\nDoes anyone know what could be the price difference between 3D-print vs acrylic case? At least some very rough numbers.\nIf the difference is actually not that big, then I would vote for 3D-printed with wrist support (which is currently missing in the poll)\u00a0 - personally don't like transparent cases.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Fri, 07 December 2012, 12:28:03\nAcrylic can be painted inside or out for interesting effects.\u00a0 It's the gloss that kills it, personally.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: damorgue on Fri, 07 December 2012, 12:45:48\nDoes anyone know what could be the price difference between 3D-print vs acrylic case? At least some very rough numbers.\nIf the difference is actually not that big, then I would vote for 3D-printed with wrist support (which is currently missing in the poll)\u00a0 - personally don't like transparent cases.\n\nThere are acrylics with absolutely solid colours.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Fri, 07 December 2012, 15:50:02\n3D-printed with wrist support (which is currently missing in the poll)\n\nIt's not a simple combination of features: the project started with case designs that had no wrist rests, and then Litster (while experimenting with acrylic plates) opted to create the wrist rest extension. There are no 3d printing designs that include wrist rests that I'm aware of.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: BugBuster on Fri, 07 December 2012, 16:37:33\nIt's not a simple combination of features: the project started with case designs that had no wrist rests, and then Litster (while experimenting with acrylic plates) opted to create the wrist rest extension. There are no 3d printing designs that include wrist rests that I'm aware of.\n\nI suspected that this is the case.\nBut it shouldn't be hard to change the designs for whose who have drawn it in the first place, is it? After all Litster was also cutting it with a machine, so he already has some 3D model. Or is it 2D for the laser cnc? Though together with the wrist rests it gets bigger and thus may not fit that easily into 3D printer.\n\nAnyway I'm actually ok if the acrylic will be cheaper to make and hopefully it will be not transparent.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Wed, 12 December 2012, 09:59:50\nHey all--I heard back from the Massdrop guys again today. Right now, it's looking like the Ergodox buy will be ready to go in January, and will probably run for about a month.\n\nAlso, because 3D printing doesn't scale well Massdrop will be offering only litster-style cases, although they will offer it with and without the wrist rest. Those that have their hearts set on the dox-style case can go PCB-only for the buy and order one up on their own since the total cost to the buyer would be the same either way.\n\nFinally, I brought the criticism to them concerning their registration wall, and while they sympathized (after all, it's something people don't like), they need to keep it in place to continue doing business with their suppliers, who from what I can tell essentially demand it. However, since there's no brand to keep happy with Ergodox, they've offered to try to make the Ergodox buy public and freely browsable, as a gesture of goodwill.\n\nHopefully this type of public implementation could be extended to other group buys in the future, for products that aren't simple retail goods (e.g. caps)? Those are my thoughts though, not their suggestion.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Wed, 12 December 2012, 15:53:06\nSo I'm guessing no one is planning a group buy in the U.S.?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: TheGrey on Wed, 12 December 2012, 16:24:47\nvoted!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Wed, 12 December 2012, 19:40:09\nMan how the hell did i miss this, there was even a sticky in the ergonomics section and i still missed it.\n\nI feel like such a noob reading this thread and section of geekhack! I would love to assemble something myself but i usually break something and i am horrible at soldering given my hand tremors.\n\nI've only been able to get through some of the recent pages of this but it seems that getting a assembled version of this in the US would be a bit expensive and just may not be possible at all, correct me if i am wrong....I'm actually unsure how this works i am a complete noob when i comes to this part of geek-hack.\n\nBut damn i want one of these really bad, especially after seeing the photos, I kind of miss split design now; i had a Kinesis Freestyle for almost 3 years but i always thought the layout wasn't good and obviously cheap switches that didn't survive my jackhammer touch.\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Thu, 13 December 2012, 08:19:07\nSo I'm guessing no one is planning a group buy in the U.S.?\n\nBy all means, anyone is free to do so; but practically speaking it hasn't happened, no.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Thu, 13 December 2012, 09:14:59\nSo I'm guessing no one is planning a group buy in the U.S.?\n\nMassDrop will ship to U.S. if it's used.........\n\ncheers,\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Thu, 13 December 2012, 09:25:36\nI meant other than massdrop\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Susan1430 on Thu, 13 December 2012, 09:57:26\nBf is interested. He'd probably prefer to give money to someone to handle the assembly than put it together himself.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: islisis on Thu, 13 December 2012, 11:46:29\nThis board should be _the_ ergonomic board for the masses... extended thumb keys, flat easy to manufacture pcb, even fittable on a notebook, trackpoint version in the works... ...PATENT FREE... I can only dream ;)\nKeep up the great work guys, I do hope this is the future, however far it may be!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Sat, 15 December 2012, 23:54:13\nSort of bumping my slightly incoherent drunk post above with a more coherent post\n\nIf this interest check is still active\/stands I am absolutely interested in either an assembled one directly or paying someone\u00a0 in the USA to assemble a kit\u00a0 for me with brown switches or at least partially assemble it and i attempt to complete the assembly with the correct parts.\n\nOther interest (not requirement) is a built in or add on 10-20 degree lateral slope and accompanying wrist rest similar to kinesis freestyle http:\/\/www.kinesis-ergo.com\/support\/freestyle_vip_insert.pdf\n\nI am hesitant to state how much i am willing to pay, i know its not cheap, but I WANT to own this.\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: haskellelephant on Sun, 16 December 2012, 19:43:09\nIt would be really great if all the cables would be detachable (mini usb to the computer, and between the parts of the keyboard). I imagine only connecting the one handed part would be great for gaming.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Sun, 16 December 2012, 20:35:35\nIt would be really great if all the cables would be detachable (mini usb to the computer, and between the parts of the keyboard). I imagine only connecting the one handed part would be great for gaming.\n\nCan't, the controller is in the right side\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Sun, 16 December 2012, 20:57:38\nCan't, the controller is in the right side\n\nIf you're a lefty, that's pretty perfect :)\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Sun, 16 December 2012, 22:46:29\nIt's not completely impossible to move the controller to the left hand side. The Teensy is simple enough to mount inverted. The USB connector is connected through wires which makes it easy to correct for mounting upside down. Bending all the legs of the expander IC over backwards makes it possible to mount it upside down, just like the Teensy. Depending on the case It may also be possible to just put the switches on the \"wrong\" side.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: haskellelephant on Mon, 17 December 2012, 15:06:44\nIt's not completely impossible to move the controller to the left hand side. The Teensy is simple enough to mount inverted. The USB connector is connected through wires which makes it easy to correct for mounting upside down. Bending all the legs of the expander IC over backwards makes it possible to mount it upside down, just like the Teensy. Depending on the case It may also be possible to just put the switches on the \"wrong\" side.\n\nSounds like a hastle. Since the connectors are in the front I guess it's enough to simply move the right one out of the way, but I wonder if there is ever any reason to just keep the right one connected unless you are a left hand mouse kind of person ( I am left handed but still use the mouse on the right hand).\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bpiphany on Mon, 17 December 2012, 16:22:32\nIt's not much of a hassle, you only need to bend the expander legs backwards, and perhaps think a bit to get everything hooked up correctly. Everything else fits just fine.\n\nThis of course also makes it possible to use the ErgoDox as either a left or right hand only keyboard.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Fri, 21 December 2012, 01:45:55\nQuote from: litster\nthere are 4 holes where you could screw in legs like the ones you get with KMACs.\n\nI brought the idea of adding KMAC legs to Massdrop, and they're interested in adding them to the buy; in fact given the scarcity\/difficulty of obtaining korean boards, they're planning on a sourcing trip to Korea. I personally don't know where to direct him, but if anyone's got a name or a number I'll certainly pass it along; otherwise I guess I just point him to kbdmania. In any case, the bottom line is that if we can put Massdrop in contact with a supplier, they'll try.\n\nQuote from: litster\nWhat i want to know is how they do quality control with a project like this.\n\nThe plan is still that they'll be sending the parts either to individual buyers, or at the buyer's discretion, a designated assembler from the volunteer list collected ages ago. Therefore, in terms of QA, they can't really do anything more than visually inspect the parts on the way through (specifically the cases). I'm sure the guys doing the assembly will give them love they deserve though.\n\nMassdrop emphasized however that they don't want to sound like they'd leave anyone out in the cold--they urge anyone somehow ending up with a bad product to contact them either via email or live chat on their site.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wasabah on Tue, 25 December 2012, 21:33:08\nHey guys,\nI'm totally new to the scene and here on geekhack.org, but I'm really interested in this keyboard.\nI was always looking for a keyboard like this to relieve my RSI - and also because it looks cool! :D\nIf this means that I have to assemble it myself - nice new hobby, right? :)\n\nUnfortunately, I somehow cannot access deskthority.net. (No idea if it's due to the fact that I'm in Japan or maybe some misconfiguration on my employers side. I will try later at home.)\nSo I'm very thankful for the few but informative updates here!\n\nAnyway, I voted on the massdrop.com poll. As far as I understand, they will start the group buy in January and ship to every country, right?\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Wed, 26 December 2012, 09:48:37\nAnyway, I voted on the massdrop.com poll. As far as I understand, they will start the group buy in January and ship to every country, right?\n\nI believe that's correct!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Wed, 09 January 2013, 11:45:12\nMassdrop has posted up a blog entry about the Ergodox (http:\/\/www.massdrop.com\/blog\/post\/40081950857\/ergodox-ergonomic-mechanical-keyboard). Some highlights:\n\n\u2022 Start date for the buy\n\u2022 Case material options\n\u2022 Shipping rates & details\n\u2022 Price details\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Wed, 09 January 2013, 12:21:25\noh man oh man oh man\n\nwith this, the phantom, and the GH60; My mind and wallet just exploded.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: jwaz on Wed, 09 January 2013, 12:23:35\nThey better not run the keyset in ABS and QWERTY!\n\nI vote for custom blank PBT set from IMSTO!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: jwaz on Wed, 09 January 2013, 13:25:56\nhttps:\/\/www.massdrop.com\/vote\/ergodox-keycap\n\nVote for blank PBTs in the poll!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: seferphier on Wed, 09 January 2013, 13:34:56\ndamn. i want an assembled one!!!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: jwaz on Wed, 09 January 2013, 13:36:14\nThere are tons of people who offer assembly services\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Wed, 09 January 2013, 13:46:53\nif i am reading this correctly the key caps will be a separate group buy?\n\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Wed, 09 January 2013, 13:53:08\nThere are tons of people who offer assembly services\n\nI established with them very early on that you'd be able to ship to an alternate location, so if you have a assembler who will build for you, you should be able to have your equipment sent to him\/her instead. However, I believe that's up to us to organize.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: jwaz on Wed, 09 January 2013, 13:54:12\nif i am reading this correctly the key caps will be a separate group buy?\n\n\n\nThat is correct, go vote in the poll!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Wed, 09 January 2013, 14:02:25\nif i am reading this correctly the key caps will be a separate group buy?\n\n\n\nThat is correct, go vote in the poll!\n\nI already voted for qwerty when it popped up\u00a0 :-[ sorry....\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Wed, 09 January 2013, 14:03:23\noh snap you can change votes\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Wed, 09 January 2013, 14:40:25\nThere are tons of people who offer assembly services\n\nThat is true, but no place to look them up directly. Might be a good idea to get an IC going, the number of people who may want assembled could overwhelm a single individual.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Wed, 09 January 2013, 15:02:09\nThere are tons of people who offer assembly services\n\nThat is true, but no place to look them up directly. Might be a good idea to get an IC going, the number of people who may want assembled could overwhelm a single individual.\n\nIndeed, you also have to factor in that the Phantom and GH60 assembly services are being planned as well right now with the Phantom services starting sign ups any day now. There will be a queue for assembly services AND parts.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Wed, 09 January 2013, 15:30:26\nThere are yet more people that do assembly that aren't working on Phantom\/GH60.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Wed, 09 January 2013, 15:38:57\nThere are yet more people that do assembly that aren't working on Phantom\/GH60.\n\ni know, i'm just saying its something to consider, Prof was originally offering services for the ErgoDox.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wasabah on Wed, 09 January 2013, 19:48:25\nOmg, it's here!!\u00a0 ;D\n\nQuote\nWith the screw based case construction you can experiment with different slants to find what position works best for you. In addition to slant customization, you can also fully customize the keyboard layout and reprogram the teensy board (uses Arduino software) to make the keys trigger whatever functions you desire.\n\nWhat do they mean by that? As far as I understand the cases available are flat and not slanted, right?\n\nThey also say there will be the choice between full hand and classic case.\nFull hand case means the one with hand rest?\nWhich do you think is the more ergonomic choice?\n\nAnother question I couldn't find the answer for:\nHow high (in cm) is the case? On the pictures it looks quite high which might be not really ergonomical.\n\nAnd last, but not least:\nI'm a total switch noob. I only know that I dislike switches that need a lot of force to push.\nSo I guess maybe the blue switches would be the right choice?\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Wed, 09 January 2013, 20:36:24\nOmg, it's here!!\u00a0 ;D\n\nQuote\nWith the screw based case construction you can experiment with different slants to find what position works best for you. In addition to slant customization, you can also fully customize the keyboard layout and reprogram the teensy board (uses Arduino software) to make the keys trigger whatever functions you desire.\n\nWhat do they mean by that? As far as I understand the cases available are flat and not slanted, right?\n\nThey also say there will be the choice between full hand and classic case.\nFull hand case means the one with hand rest?\nWhich do you think is the more ergonomic choice?\n\nAnother question I couldn't find the answer for:\nHow high (in cm) is the case? On the pictures it looks quite high which might be not really ergonomical.\n\nAnd last, but not least:\nI'm a total switch noob. I only know that I dislike switches that need a lot of force to push.\nSo I guess maybe the blue switches would be the right choice?\n\n1. I do not think they will offer a slant bottom in the group buy but the design could allow for a different bottom with a slant to be made. at least thats how i see it\n\n2. Full hand would be a wrist rest, Is it ergonomic? although i have had plenty people tell me having a wrist rest is not ergonomic but if you look at the other split ergo boards like the kinesis and truly ergonomic they have a rest, i think its a matter of what you are comfortable with; you also have to decide if you think it looks good with that rest\u00a0 :)), which i don't; ill use my own.\n\n3. That is a good question, they didn't go with the design on ergodox.org, it looks like its the Litster design, so i don't think this information has been made available, maybe the DT thread has something about it\n\n4. i'm a little bit surprised they are not offering browns as part of the group buy, blues are clicky, if you are OK with clicky that is the lighter switch. I'm going to get clears and swap out the springs with a lighter red or brown spring to make \"ergo clears\". If you are having someone assemble this for you most likely they will offer services for modifying the switches or ordering new switches altogether like browns, greens, and reds.\n\n-----\n\nMan we got to get the word out about this, there seemed to be a lot of interest in this and then it faded it looks like, maybe add something to the subject and OP. I would love to get this cheaper. I know there is some people that don't like massdrop though; ill rolling the dice.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Wed, 09 January 2013, 20:58:47\nBrowns are not on offer due to availability, no more than that.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: Glod on Wed, 09 January 2013, 21:00:31\nBrowns are not on offer due to availability, no more than that.\n\nah ok\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wasabah on Wed, 09 January 2013, 21:06:02\nI also hope we can get some more people to commit. 199$would be nice! After having read your comment about the switches, I read a bit more and it seems that browns might be good for me. Damn it, why don't they offer them! :) I confirmed with Massdrop via live chat: The case is 2.54cm high! For me, that creates a too steep angle for my wrist joint, so I definitely need a hand rest \/ the hand rest case. The live chat guy (Will) said he was writing on the keyboard while chatting with me and had the one with hand rest. Apparently he's still getting used to it and blamed his typos on that. ;) But he says it feels very natural and is really ergonomical. (With hand rest.) Also, they are checking about compatibility\/availability with the MX browns, and if possible they will update the buy. Apparently it is possible to change your order any time until the countdown is over! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Wed, 09 January 2013, 21:18:23 1\" high is about as tight as you can make it with a layer-cake acrylic case design. Only way to get it shorter is swapping a layer w\/ metal such as aluminum and that'll only get you a little over 1\/8\" Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wasabah on Wed, 09 January 2013, 21:22:56 Ah okay, I see. I didn't know that! :) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: OrangeJewce on Wed, 09 January 2013, 21:31:44 Yeah if we can get this down to$199, I'll probably get two, one blues and one clears.\n\nCheers,\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Wed, 09 January 2013, 21:36:31\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Wed, 09 January 2013, 21:55:21\nso I'm guessing we are not able to purchase an extra set of pcb's?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Wed, 09 January 2013, 22:05:29\nso I'm guessing we are not able to purchase an extra set of pcb's?\n\nLook to DT for a parts buy, Doesn't look like Massdrop will be selling anything less than a complete kit.\n\nCheers,\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Wed, 09 January 2013, 22:10:47\nYeah, I'll probably end up doing both group buys\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wasabah on Wed, 09 January 2013, 22:30:54\nYeah, I'll probably end up doing both group buys\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Wed, 09 January 2013, 22:32:10\nno, that's why I'm still participating in the massdrop. Not sure how long it will take before someone steps up and starts another group buy\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: jabar on Thu, 10 January 2013, 00:08:37\nlooks like this is live on that massdrop site...\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: reverkiller on Thu, 10 January 2013, 00:42:33\nlooks like this is live on that massdrop site...\n\nIt seems it is.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: mikelanding on Thu, 10 January 2013, 00:48:51\nGoing to place 2 x commit to buy.\nThey seem to be organised, good response via online chat, Cheap shipping to Non-US (especially Asia country) and fairly customisation for people like me who looking for complete set.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wasabah on Thu, 10 January 2013, 01:22:48\nThe option to purchase one or more extra PCB has just been added! (30$for each) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: kurplop on Thu, 10 January 2013, 04:38:18 PCB price is now$22.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: OrangeJewce on Thu, 10 January 2013, 07:10:42\nGiven how quickly they have reacted to feedback, I'm actually impressed by Massdrop thus far. They put together an assembly guide with photos, have added more customization at every turn when it's asked (pcb only or no switches), and finally changed its TOS (even if slightly).\n\nCheers,\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: seferphier on Thu, 10 January 2013, 09:12:07\ni really want red switches... why aren't they available?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: regack on Thu, 10 January 2013, 10:00:42\ni really want red switches... why aren't they available?\n\nI've found reds are hard to find.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: L!athus on Thu, 10 January 2013, 10:07:40\ni really want red switches... why aren't they available?\n\nI've found reds are hard to find.\n\nMy 1st post. Greetings to all @ GH. :) Base on mouser for mx switches. Reds are on backorder till march. Browns are supposely having shortages elsewhere. With demands there are bound to be shortages i guess.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: sherryton on Thu, 10 January 2013, 11:25:05\ni really want red switches... why aren't they available?\n\nI've found reds are hard to find.\n\nMy 1st post. Greetings to all @ GH. :) Base on mouser for mx switches. Reds are on backorder till march. Browns are supposely having shortages elsewhere. With demands there are bound to be shortages i guess.\n\nWelcome to GeekHack L!athus!\u00a0 I hope you will enjoy this place.\u00a0 I heard mx switches are backordered because of the recent orders.\u00a0 Hopefully, 2013-2014 will be okay.\u00a0 I hear Cherry does not have the machinery to fulfill all the orders :(\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: sordna on Thu, 10 January 2013, 11:29:47\nDid I read this correctly at the bottom of the link, a sweet price of $199 shipped for a complete kit ? http:\/\/www.massdrop.com\/blog\/post\/40081950857\/ergodox-ergonomic-mechanical-keyboard Title: Re: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Thu, 10 January 2013, 11:40:41 As long as we can get everyone who was interested to buy Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Glod on Thu, 10 January 2013, 11:45:47 get the word out lol, 199 would be nice. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Dgsbllx on Thu, 10 January 2013, 11:47:24 Asked them a few questions about it on the massdrop chat and if I like the responses I think i'll be down for one. Want to see the build guide first though because where they've put 'Here is a link to our instruction manual', I don't see a link? Title: Re: [Interest Check] Custom split ergo keyboard. Post by: ironman31 on Thu, 10 January 2013, 11:50:59 There's a link somewhere. I read it last night. I just don't see a video posted yet Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Halverson on Thu, 10 January 2013, 11:55:27 Well I commited to buy from massdrop, just want the board, and this seems the simplest way to go about it. I'll probably just end up selling the switches from it and using my abundant vintage blacks for it. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Glod on Thu, 10 January 2013, 12:03:36 Asked them a few questions about it on the massdrop chat and if I like the responses I think i'll be down for one. Want to see the build guide first though because where they've put 'Here is a link to our instruction manual', I don't see a link? the instructions are here https:\/\/www.massdrop.com\/dox-ergo.php Oddly i think they took down the link to this page, maybe they are making revisions Title: Re: [Interest Check] Custom split ergo keyboard. Post by: regack on Thu, 10 January 2013, 12:06:46 Well I commited to buy from massdrop, just want the board, and this seems the simplest way to go about it. I'll probably just end up selling the switches from it and using my abundant vintage blacks for it. Oh... that's a good idea... thanks! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Thu, 10 January 2013, 12:07:53 Asked them a few questions about it on the massdrop chat and if I like the responses I think i'll be down for one. Want to see the build guide first though because where they've put 'Here is a link to our instruction manual', I don't see a link? The link was in the blog. https:\/\/www.massdrop.com\/dox-ergo.php Title: Re: [Interest Check] Custom split ergo keyboard. Post by: L!athus on Thu, 10 January 2013, 12:16:08 Thanks sherryton. Getting comfortable as we speak. ;D For US, its great with freeship. Though shipping to the rest of the world @20 is attractive too. If price could get even lower will be a plus. :D Getting the 100+ commitments is the only hurdle to get that price. 18 days left to hit that target. Last i login it still stands @ 2 commited. IMO a complete kit isn't complete if its still missing keycaps. :)) Just thought that it would have been nice if, at least, those 1.5s were included as an option for the kit. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: jwaz on Thu, 10 January 2013, 12:25:48 I think we'll make it no problem. there is all kinds of crazy interest in this, especially once we spread the word. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Glod on Thu, 10 January 2013, 12:36:08 I hope those who were interested buy it, There was a lot of interest on DT as well it seems, but there is major hate towards mass-drop there. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wiredPANDA on Thu, 10 January 2013, 12:36:20 I'm going to be confirming 1 kit (maybe 2) today. Glad to see this. Now to decide if I want an aluminum\/acrylic and full\/classic cases. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: L!athus on Thu, 10 January 2013, 13:02:13 Well I commited to buy from massdrop, just want the board, and this seems the simplest way to go about it. I'll probably just end up selling the switches from it and using my abundant vintage blacks for it. In my email to MD, and i believed others on DT or GH here as well, have express my interest in a kit possible option to go without switches. I have just recieved an email reply. Now they have added an option to go \"switch-less\". Its -$44 off the final price if you choose to go with that option, if i understand correctly. Just check up on their site. The option is available under switches now.\n\nAnd for those outside of US interested in the buy but can't find your country under \"country\" just email your request to them. They will be added asap for you to procceed with it.\n\nAbout switches, MD expressed in the mail that they have a hard time sourcing well priced reds and browns. I'm not sure why but they will be running a seperate GB for brown switch only along with ergodox.\n\nThats all the answers i got from MD. Hope its helpful info for any.\n\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Thu, 10 January 2013, 13:02:59\nThere was a lot of interest on DT as well it seems, but there is major hate towards mass-drop there.\n\nDT is inexplicably toxic towards massdrop, or really towards progress of any kind. If I were acting in my own self-interest and not the best interest of the buy, I would have stopped posting there long ago and updated only here.\n\nBut hey, if there is a single person monitoring only the DT thread that ends up buying in, I guess it was worth it.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: asura on Thu, 10 January 2013, 13:07:58\nI'm going to hold off for a couple of days to see if they offer a case-less option...\u00a0 If not then I'll think obliquely...\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wiredPANDA on Thu, 10 January 2013, 13:18:40\n@asura:\nEmail or LiveChat MassDrop and ask about the option.\u00a0 They may decide to add it to the order form.\u00a0 They've been responding\/adding options today as they get suggestions.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: asura on Thu, 10 January 2013, 13:22:16\n\nWorst comes to the worst I can get someone to get an extra set of PCBs and post them out to me then sort out teensy, diodes, etcetera myself.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: L!athus on Thu, 10 January 2013, 13:31:33\nThere was a lot of interest on DT as well it seems, but there is major hate towards mass-drop there.\n\nDT is inexplicably toxic towards massdrop, or really towards progress of any kind. If I were acting in my own self-interest and not the best interest of the buy, I would have stopped posting there long ago and updated only here.\n\nBut hey, if there is a single person monitoring only the DT thread that ends up buying in, I guess it was worth it.\n\nLike it, go get it. Dislike it, just walk away.\u00a0 :))\n\nI would probably go with the kit w\/o switches. Looking to build it with reds.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Thu, 10 January 2013, 13:35:13\n\nWorst comes to the worst I can get someone to get an extra set of PCBs and post them out to me then sort out teensy, diodes, etcetera myself.\n\nYeah, I just talked to Will and he basically said that at the moment there is no way to purchase another full keyboard minus the case. Just the extra pcb's.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wiredPANDA on Thu, 10 January 2013, 14:55:43\nCurious - if anyone has ordered already, are you going with or without the wrist rest?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Thu, 10 January 2013, 17:05:58\nI will go with a wrist rest when I get one\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Thu, 10 January 2013, 17:11:08\nI went with no wrist rest, acrylic, black switches. I'm hoping that reds will be added mid-flight, and if not I'll probably get rested as well, just without switches. I can tolerate an extra set of blacks I don't like, but two sets I don't need.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: bisl on Thu, 10 January 2013, 17:23:22\nBasically, my line of thinking is that no matter what, I'll have some kind of squishy wrist rest under my hands--the built-in wrist rest basically just determines the height, and whether I have one big one (no rest) or two small ones (rest). Also, one thing to consider is that Ergodox enables you to have your two halves spaced as far apart as you want, so maybe the two-small-pad method is best; in that case the design with the rests is best. it's worth noting that having the pad sitting on the case's built-in rest keeps the pad in place relative to the keyboard, whereas the case without the rest could potentially scoot away from the rest or something.\n\nFood for thought.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: jabar on Thu, 10 January 2013, 17:25:13\nDoes the mounting plate allow for easy stem\/spring swaps, like Phantom?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: asura on Thu, 10 January 2013, 17:34:57\nLooking at the pictures in their instructions, I'd say yes.\u00a0 There are definitely recesses there.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wasabah on Thu, 10 January 2013, 19:00:50\nBasically, my line of thinking is that no matter what, I'll have some kind of squishy wrist rest under my hands--the built-in wrist rest basically just determines the height, and whether I have one big one (no rest) or two small ones (rest). Also, one thing to consider is that Ergodox enables you to have your two halves spaced as far apart as you want, so maybe the two-small-pad method is best; in that case the design with the rests is best. it's worth noting that having the pad sitting on the case's built-in rest keeps the pad in place relative to the keyboard, whereas the case without the rest could potentially scoot away from the rest or something.\n\nFood for thought.\n\nI think it's best to have two seperate wrist rests\/pads. And as you said, if you use seperate wrist rests, they might move around etc. (Of course depending on the wirst rest.)\nThis is why I will go for the Full hand option, although it looks not as cool.\n\nFor those people who want to buy extra PCBs, may I ask why?\nDo you use it for backup if you screw up or do you want to make more than one keyboard? If the latter, why? And where do you get the other supplies needed?\n\nAnd one last noob question: if I want to change the switches later on (because I have no idea which I want, will be my first mechanical keyboard\u00a0 ;D ), does it mean I need to unsolder all of the switches?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Thu, 10 January 2013, 19:11:17\nI would like to have an extra set so I can switch out having blues and browns\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wasabah on Thu, 10 January 2013, 19:24:50\nI would like to have an extra set so I can switch out having blues and browns\n\nBut for this you also need a second case or at least the plate between PCB and switches, right?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: regack on Thu, 10 January 2013, 19:25:53\n\nAnd one last noob question: if I want to change the switches later on (because I have no idea which I want, will be my first mechanical keyboard\u00a0 ;D ), does it mean I need to unsolder all of the switches?\n\nIt's possible to change out the stem\/spring without desoldering.\u00a0 There are some threads around here, and you can find videos on youtube.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Thu, 10 January 2013, 19:26:23\nHmm. Didn't notice there was a plate.. damn lol. I guess I would just get two\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Thu, 10 January 2013, 19:33:17\nI think we'll make it no problem. there is all kinds of crazy interest in this, especially once we spread the word.\nI'll be sending out a mass PM to everyone interested.\n\nWorst comes to the worst I can get someone to get an extra set of PCBs and post them out to me then sort out teensy, diodes, etcetera myself.\n\nHmm. Didn't notice there was a plate.. damn lol. I guess I would just get two\nThe PCB looks just like the one bpiphany designed, and has holes for PCb or plate-mount switches.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wasabah on Thu, 10 January 2013, 19:37:06\nHmm. Didn't notice there was a plate.. damn lol. I guess I would just get two\nYou can see it in the instructions: https:\/\/www.massdrop.com\/dox-ergo.php\n\nAnd one last noob question: if I want to change the switches later on (because I have no idea which I want, will be my first mechanical keyboard\u00a0 ;D ), does it mean I need to unsolder all of the switches?\n\nIt's possible to change out the stem\/spring without desoldering.\u00a0 There are some threads around here, and you can find videos on youtube.\n\nOkay, cool, thanks for this very helpful information! So I guess I can go with only one set then. :)\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: AloisiusFauxly on Thu, 10 January 2013, 19:45:02\nDT is inexplicably toxic towards massdrop\n\nI liked the occasional accusations of being paid by Massdrop. Oh, and being called a corporate apologist.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: StaCT13 on Thu, 10 January 2013, 19:49:28\n\nThe ultimate goal will be that when people get the keyboard, they will have access to our open source UI and firmware, which will allow them to use either the default QWerty \/ ic07 layout or any other layout of their choice (the software will automatically do any compiling and hardware flashing necessary). The UI will be Windows only, XP and above. If you're running linux, you'll have to manually edit the firmware, compile it, and flash the teensy 2.0 controller manually.\n\nMouse buttons won't be a part of the software as far as I know. I am not sure how the Teensy would handle this, seems to me it would almost have to register as two pieces of hardware to achieve. As far as we know, at the very least 2 layers will be available to the end users. A default and function layer. If you'd like to know what the default currently is, I point you to the source, or to sit tight until I can make a prototype UI available which will allow the designing of any custom layout of your choice. Let me know if you have any questions as I would be glad to help!\n\nCheers,\n\nOJ\n\nI don't remember\/know if there were any updates to this, but is the GUI still being developed? The Massdrop instructions page only references flashing the firmware using the Teensy Loader Application: I didn't see anything involving the GUI, or there even being a GUI in development. Is it just going to be released after launch?\n\nThanks for any help, and sorry for any previously answered questions.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: shawn on Thu, 10 January 2013, 19:51:07\napologies for the crosspost on deskauthority, but bisl asked me to do it.\u00a0 :)\n\nHey guys, I ordered 2 of the kits from massdrop. I also talked to Weyman @ wasdkeybaords.com (I have no affiliation with wasdkeyboards.com) because I want to get fancy laser etched keycaps with a custom pattern. here is what he said:\n\nQuote\nI didn't know Massdrop was going to run this. I put in an order myself today. We can definitely work something out for these kits. Pricing will be higher than a normal set due to the number of 1.5 keys needed. When we order in normal 104 key sets, so one of these sets would use up 6 sets worth of 1.5 keys. If there's some interest from at least several people, I can put together a new layout file for everyone to use specifically for the ErgoDox. For pricing, we would be looking at around $80 per set. Do you need custom pattern laser etched keycaps? No. Will it make a cool keyboard cooler? Yes.. Yes it will. Pretty awesome that Weyman ordered a keybaord as well. hehe. can't wait. I ordered both with 'full hand' (wrist rest). Title: Re: [Interest Check] Custom split ergo keyboard. Post by: AloisiusFauxly on Thu, 10 January 2013, 20:24:36 @StaCT13 If you can get the source compiling okay, you could always edit the layouts directly in source. It's meticulous but straight-forward once you wrap your head around it. Here's an example of the default QWERTY layer: https:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/master\/src\/keyboard\/ergodox\/layout\/qwerty-kinesis-mod.c#L27-45 Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wasabah on Thu, 10 January 2013, 20:25:37 Maybe we should do some more promotion.. put it on reddit or something ^^ I want to reach the 199$!!\u00a0 ;)\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Thu, 10 January 2013, 20:34:57\nWhat's the count at, or is it not published?\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: wasabah on Thu, 10 January 2013, 20:37:59\n18 sold, 11 buyers committed to buy if it reaches a certain price point and 59 people watching.\nWe need 100 sold to get to the 199$price point. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: dorkvader on Thu, 10 January 2013, 20:39:07 What's the count at, or is it not published? Currently at 18, the count is on the massdrop 'site https:\/\/www.massdrop.com\/buy\/ergodox (need to log in, I believe) Everyone interested should be Pm'd. Please Pm me back if you want to be taken off the list, Also Pm me if you want to be added to it. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: Halverson on Thu, 10 January 2013, 20:45:42 got your pm DV! Although I'm already committed to buy! Title: Re: [Interest Check] Custom split ergo keyboard. Post by: regack on Thu, 10 January 2013, 20:46:36 18 sold, 11 buyers committed to buy if it reaches a certain price point and 59 people watching. We need 100 sold to get to the 199$ price point.\n\nSo I assume that if Sold+Committed = 100 then it rolls over to $199? (ie. you could have 25 sold, and 74 committed, and as soon as there is one more commited, it becomes 100 sold?) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wasabah on Thu, 10 January 2013, 20:48:20 18 sold, 11 buyers committed to buy if it reaches a certain price point and 59 people watching. We need 100 sold to get to the 199$ price point.\n\nSo I assume that if Sold+Committed = 100 then it rolls over to $199? (ie. you could have 25 sold, and 74 committed, and as soon as there is one more commited, it becomes 100 sold?) Not sure, but I assume the same. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: kmiller8 on Thu, 10 January 2013, 20:48:27 So I assume that if Sold+Committed = 100 then it rolls over to$199?\u00a0 (ie. you could have 25 sold, and 74 committed, and as soon as there is one more commited, it becomes 100 sold?)\n\nyep, that's how the commitment button works on massdrop.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Thu, 10 January 2013, 20:51:09\nNot sure if it matters but I didn't receive a PM\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: dorkvader on Thu, 10 January 2013, 20:57:55\n\nYep, I added everyone, even if they already posted their commitment. Just trying to be thorough.\n\nNot sure if it matters but I didn't receive a PM\nThanks, I'll look into it. Yours should have gone out in the first batch. I'll send you one personally, so you can see what it looks like.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: regack on Thu, 10 January 2013, 21:00:17\n18 sold, 11 buyers committed to buy if it reaches a certain price point and 59 people watching.\nWe need 100 sold to get to the 199$price point. Even though there are 17 days left, I find myself hitting f5 a lot... it's now 20 sold... Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wasabah on Thu, 10 January 2013, 21:09:20 18 sold, 11 buyers committed to buy if it reaches a certain price point and 59 people watching. We need 100 sold to get to the 199$ price point.\n\nEven though there are 17 days left, I find myself hitting f5 a lot...\u00a0 it's now 20 sold...\n\nNow 23 sold btw. Keep up the pace!\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: ironman31 on Thu, 10 January 2013, 21:16:40\nThanks, I'll look into it. Yours should have gone out in the first batch. I'll send you one personally, so you can see what it looks like.\n\nThanks. Both actually just showed up in my inbox. lol.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: jabar on Thu, 10 January 2013, 21:17:00\nThe PM said this PCB supports PCB-mounted switches. Do the MX switches need to be PCB-mounted, or are you saying (dorkvader) either works?\n\nI am likely going to opt for third-party source of switches due to the mediocre switch offerings.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: jabar on Thu, 10 January 2013, 21:21:10\nSwitches are priced in the GB at about $0.50 each, unfortunately not enough to do a 1:1 swap for the aluminum case. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: alaricljs on Thu, 10 January 2013, 21:24:09 I would highly recommend PCB mount even with the acrylic plate, however they are not strictly necessary. I also do not know what MD is supplying. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: regack on Thu, 10 January 2013, 21:39:15 I would highly recommend PCB mount even with the acrylic plate, however they are not strictly necessary. I also do not know what MD is supplying. It doesn't say whether they are pcb or plate mount, but from what i've seen in the photos (https:\/\/www.massdrop.com\/dox-ergo.php) the examples that they have shown appear to be PCB mount switches. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wasabah on Thu, 10 January 2013, 21:43:04 Btw guys, if I would want to add a second keyboard but with different options (other case, other switches, etc), I need to buy it again, right? Because if I update the quantity in my history, the options are the same for every keyboard. That would add shipping costs again. (Germany) Guess I will ask them! Thinking about getting a second kit with the other case. That way I can compare what suits me best, and the assembled keyboard with the case I don't want to keep somebody will probably buy I guess. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wiredPANDA on Thu, 10 January 2013, 22:17:41 I'm sure you will be able to find a buyer wasabah. I'm leaning towards two kits so I can have one at work and one at home. I'm still debating if I want the full-hand or the standard cases, though. I wish they'd put up a image for the aluminum case. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: wasabah on Thu, 10 January 2013, 22:27:27 I'm sure you will be able to find a buyer wasabah. I'm leaning towards two kits so I can have one at work and one at home. I'm still debating if I want the full-hand or the standard cases, though. I wish they'd put up a image for the aluminum case. Work&Home: good idea.. damn! :D I'm also interested in the aluminium case. Especially with the hand rest, I think the feel might be nicer then the acrylic. If it looks cool I'll get one. They want to put up a picture in the next days. Edit: and we got 25 buyers! :) Title: Re: [Interest Check] Custom split ergo keyboard. Post by: bisl on Fri, 11 January 2013, 02:13:01 It doesn't say whether they are pcb or plate mount, but from what i've seen in the photos (https:\/\/www.massdrop.com\/dox-ergo.php) the examples that they have shown appear to be PCB mount switches. https:\/\/massdropinc.s3.amazonaws.com\/img_bucket\/ergo-dox-instruction\/_W3T1930.jpg Title: Re: [Interest Check] Custom split ergo keyboard. Post by: laffindude on Fri, 11 January 2013, 02:54:16 You can count me in for another but not counted in the page yet, I am waiting for a friend to reply to see if he wants one. Aiming for an aluminum full hand. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: TotalChaos on Fri, 11 January 2013, 05:20:02 It have a slope if you look at the side picture but it was easier to only model some flat spherical keycaps. Final keycap shape is not determined yet and my be left to the user. Yes the headers are for connecting the 2 halves. WTF. THis is really making me mad >:D I have been really interested in the Ergodox forever and ever! But I never, ever, ever clicked on this thread because the thread title does not say anything about ERGODOX so WHY would I click on this thread?! GRRR. I would really love flat spherical keycaps or flat cylindrical, or all keycaps have a small slant. If having a slant, then the front of the keycap should be a little higher than the back. I know this works perfectly because I have a rubberdome keyboard with keycaps like that. They are awesome! (The keycaps, not the rubberdomes). If all keycaps have same profile then the user may switch his keycaps around into any position they like any time they like. For example they could swap things around to try out COLEMAK or DVORAK layout. Or maybe just swap 2 keys with each other. Having all keys be the same profile is Awesome. Having all rows of keys be a different profile is rude and nonsensical. I wish this was available in red switches. Will this keyboard work with a PS\/2 adapter? If it works on PS\/2 and has red switches then I will buy 2 or 3 of them depending on how much it will cost me to pay someone to assemble it for me. I absolutely cannot assemble it myself. I don't mind spending the bucks to get 3 of them if the keyboard will do what I need it to do. Plus that way when the guy I hire to assemble them screws up my keyboard and gives it braindamage then I still have 2 left that will work out ;D For me, keyboarding is not a hobby, its a way of life. Title: Re: [Interest Check] Custom split ergo keyboard. Post by: BugBuster on Fri, 11 January 2013, 07:06:18 Switches are priced in the GB at about$0.50 each, unfortunately not enough to do a 1:1 swap for the aluminum case.\n\nCould you post a link to the source(s)? Would be nice to learn where I could get Browns cheaper than from WASD.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: regack on Fri, 11 January 2013, 07:25:24\nIt doesn't say whether they are pcb or plate mount, but from what \u00a0i've seen in the photos (https:\/\/www.massdrop.com\/dox-ergo.php) the examples that they have shown appear to be PCB mount switches.\n\nhttps:\/\/massdropinc.s3.amazonaws.com\/img_bucket\/ergo-dox-instruction\/_W3T1930.jpg\n\nI know there's a plate there, but I thought I saw the pins in one of the pictures where it showed the bottom of the assembled keyboard... I zoomed it in some more (https:\/\/massdropinc.s3.amazonaws.com\/img_bucket\/ergo-dox-instruction\/_W3T2121.jpg) and I guess you're right, it looks like they're not PCB mount.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: danielucf on Fri, 11 January 2013, 07:31:56\nSo ErgoDox needs to be in the title, and the link to massdrop should probably be in a group buy page, in the group buy section. If you want your numbers to grow, post this where people will see it (buying sections of the forum). I'm in for one, and am going to send the info out to friends just in case they are interested.\nTitle: Re: [Interest Check] Custom split ergo keyboard.\nPost by: alaricljs on Fri, 11 January 2013, 08:30:13\nTC - no PS\/2.\n\ndanielucf - it's posted in great finds...\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: sordna on Fri, 11 January 2013, 09:16:46\n\nI have been really interested in the Ergodox forever and ever!\n\nBut I never, ever, ever clicked on this thread because the thread title does not say anything about ERGODOX\u00a0 so WHY would I click on this thread?!\u00a0 GRRR.\n\nThis thread started before the ErgoDox name was decided\u00a0 \u00a0:)\n\nQuote\nI would really love flat spherical keycaps or flat cylindrical, or all keycaps have a small slant.\n...\nHaving all keys be the same profile is Awesome.\n\nThe keyboard comes without keycaps, so you can easily buy a set of keycaps all in the same profile, for example from WASD Keyboards, and use them.\n\nQuote\nI wish this was available in red switches.\n\nIf they don't offer them, you can buy the keyboard without switches, and buy the switches elsewhere.\n\nQuote\nWill this keyboard work with a PS\/2 adapter?\n\nDon't know, but for me, as long as I'm using a computer that accepts USB keyboard input in the BIOS (which all computers do for the last 10 years) then I'm sticking with USB.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: Doltoid on Fri, 11 January 2013, 09:31:23\nIt doesn't look like the case massdrop is using will allow the controller to be relocated to the left hand section. Is this just my faulty brain or is this true?\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: wiredPANDA on Fri, 11 January 2013, 09:39:46\nBelieve that is the case.\u00a0 I remember reading before that everything was created with the intention of the controller on the right half.\u00a0 May be able to get away with it on the left with a little hardware DIY\/hacking.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: bpiphany on Fri, 11 January 2013, 10:08:31\nI see no real reason to put the controller on the left side if you are not building a left hand only keyboard. And I didn't have a good look at the case either right now. But if it is layered wouldn't you be able to simply flip each layer upside down before putting them together to mirror the design?\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: BugBuster on Fri, 11 January 2013, 10:21:24\nI see no real reason to put the controller on the left side if you are not building a left hand only keyboard. And I didn't have a good look at the case either right now. But if it is layered wouldn't you be able to simply flip each layer upside down before putting them together to mirror the design?\n\nYou would have to flip Teensy and other stuff also.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: bpiphany on Fri, 11 January 2013, 10:42:31\nActually, flipping the Teensy is the easy part... You'd also need to put all the wires for the USB connector in the correct places, and make sure the communication between the halves ends up correct, and worst of all bend the IO-expander over backwards =P\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: wiredPANDA on Fri, 11 January 2013, 11:00:52\nHmmmm, debating if I want to try the mod when I get my ErgoDox.\u00a0 I'm interested in a left-hand only keyboard.\u00a0 Just not sure if I'm up for the work\/modding.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: litster on Fri, 11 January 2013, 11:34:33\nI assume that if you solder it as it is (teensy on right side), flip it over, and remap all the keys, you can have teensy on the left.\u00a0 But the thick teensy is now on the bottom of the PCB and my case design does not account for that, especially all the cutout areas.\u00a0 I am sure it is doable if changes are made to the CAD files.\u00a0 But seems a lot of work for one special edge case.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: bpiphany on Fri, 11 January 2013, 12:30:54\nThe Teensy can simply be soldered in, on top, upside down on the \"wrong\" side (if you get to choose which side of the Teensy the pins are that is). This in all effects \"mirrors\" it.\n\nTo do the same with the IO-expander you need to bend all the legs over backwards. This is probably not recommended by people who \"know\" about these things, but it should work =)\n\nAfter that you just need to figure the rest out. Everything else is only 2 pin components and mirror symmetric by nature =D\n\nLitster, wouldn't the right hand case be possible to assemble with all parts upside down to create a left hand case that would support a mirror of the right hand side electrics?\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: litster on Fri, 11 January 2013, 12:39:18\nYes, you could do it, if you also mirror all the components on the right hand side to the left hand side. I.e. Teeny on left hand side and on the top of PCB, IO expander on right hand side and on top of PCB.\u00a0 The only layer you would need to swap is to move the right hand side mounting plate to left and vis versa.\u00a0 other layers stay where they are.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: SmallFry on Fri, 11 January 2013, 12:54:55\nHey litster, do you have your E-Dox case files posted somewhere? http:\/\/www.kbdmania.net\/xe\/5705699\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: damorgue on Fri, 11 January 2013, 13:02:47\nHey litster, do you have your E-Dox case files posted somewhere? http:\/\/www.kbdmania.net\/xe\/5705699\n\nThose look like copies which they have made by themselves based on switch locations. They don't seem to have the tabs required to make allow the switches to be opened while mounted in the plate.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: SmallFry on Fri, 11 January 2013, 13:03:58\nAh. Well at least we know the other forums are excited about the E-Dox too! :D\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: litster on Fri, 11 January 2013, 13:26:18\nYes, unlike my other design, this is has been released for the public.\n\nhttp:\/\/deskthority.net\/workshop-f7\/split-ergonomic-keyboard-project-t1753-720.html#p85587\n\nI would not be surprised if the one on kbdmania is done based on my original design files.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: OrangeJewce on Fri, 11 January 2013, 13:43:00\nAh. Well at least we know the other forums are excited about the E-Dox too! :D\n\nSmalls ygpm.\n\nCheers,\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: ic07 on Fri, 11 January 2013, 15:31:23\nWill this keyboard work with a PS\/2 adapter?\n\nThe USB code is from PJRC for now, and conforms to the keyboard USB Boot Spec - i.e. the computer sees it as a regular, normal USB keyboard.\u00a0 Real PS\/2 adaptors should work, as far as I know.\u00a0 Passthrough adaptors (what the cheap ones usually are) almost certainly won't.\u00a0 I haven't tested either.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: ic07 on Fri, 11 January 2013, 15:38:57\nAlso, if anyone was interested in removing the right hand side without any modding, and didn't mind an extra altoids can on their desk, I don't think it'd be hard to put a Teensy in one, having the USB come out one end, and the I2C TRRS jack come out the other.\u00a0 I think all you'd have to do inside is 1) insulate the unused contacts (obviously), and 2) wire in the resistors to pull up the I2C lines...\u00a0 :)\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: wiredPANDA on Fri, 11 January 2013, 16:43:00\nFinally got my order placed, bringing us up to 29 orders.\u00a0 I'm still hoping we get red switches added to the GB (..and those aluminum case pics).\nTitle: Re: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: SmallFry on Fri, 11 January 2013, 16:57:22\nAh. Well at least we know the other forums are excited about the E-Dox too! :D\n\nSmalls ygpm.\n\nCheers,\nOJ ygpm.\n\nCheers,\u00a0 :))\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: litster on Fri, 11 January 2013, 17:01:49\nAh. Well at least we know the other forums are excited about the E-Dox too! :D\n\nSmalls ygpm.\n\nCheers,\nOJ ygpm.\n\nCheers,\u00a0 :))\n\nYou guys making your own acrylic cases?\nTitle: Re: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: SmallFry on Fri, 11 January 2013, 17:19:30\nAh. Well at least we know the other forums are excited about the E-Dox too! :D\n\nSmalls ygpm.\n\nCheers,\nOJ ygpm.\n\nCheers,\u00a0 :))\n\nYou guys making your own acrylic cases?\nNo sir, he was just asking me to build his board(s). :)\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: TotalChaos on Fri, 11 January 2013, 17:46:31\nWill this keyboard work with a PS\/2 adapter?\n\nThe USB code is from PJRC for now, and conforms to the keyboard USB Boot Spec - i.e. the computer sees it as a regular, normal USB keyboard.\u00a0 Real PS\/2 adaptors should work, as far as I know.\nDo u have any proof that these \"real PS\/2 adaptors\" actually exist and where could I buy one?\n\nPpl keep talking about them but its like the Loch Ness Monster, everyone \"knows\" they exist but there is no proof.\n\nI have already wasted many hours looking and I found lots and lots and lots of cheap adaptors to adapt a PS\/2 keyboard to work on USB.\u00a0 They are really cheap.\u00a0 But trying to adapt a USB keyboard that is hostile to PS\/2 seems like it is impossible. I am not saying it is electrically impossible, just saying that AFAICT nobody sells such adaptors.\u00a0 Either they never existed or they sold out long ago.\n\nQuote\nPassthrough adaptors (what the cheap ones usually are) almost certainly won't.\u00a0 I haven't tested either.\nI was already told they won't work.\n\nWhen the teensy controller gets upgraded to work on both USB and PS\/2 like the controller in WASD, Rosewill, Filco, etc. etc. ad nauseum then I will happily buy 3 Ergodox and pay someone to put them together for me.\n\nI might buy a 4th one to give to one of my friends who have hand pain.\n\nThanx\u00a0 :)\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: TotalChaos on Fri, 11 January 2013, 17:56:30\nI looked at a pic of the Ergodox and saw no FN key.\u00a0 Where is the FN key?\n\nHow does one generate the keycodes of the Function keys?\n\nCan all other ANSI standard keycodes (the standard keys available since at least 1985 or before) be generated?\n\nOr is this keyboard like the new Matias, CoolerMaster, etc. etc. etc. (lots of companies have been banishing keys) keyboards where certain standard keycodes are impossible to generate?\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: Glod on Fri, 11 January 2013, 18:08:09\nI looked at a pic of the Ergodox and saw no FN key.\u00a0 Where is the FN key?\n\nHow does one generate the keycodes of the Function keys?\n\nCan all other ANSI standard keycodes (the standard keys available since at least 1985 or before) be generated?\n\nOr is this keyboard like the new Matias, CoolerMaster, etc. etc. etc. (lots of companies have been banishing keys) keyboards where certain standard keycodes are impossible to generate?\n\n(https:\/\/massdropinc.s3.amazonaws.com\/product-images\/massdrop-product-ergodoxlayout.png)\n\nIs the layout massdrop gives instructions to use for qwerty\n\nIt only appears to show the first layer however visually\n\ncorrect me if im wrong guys but it is BASED ON but doesnt 100% mirror the kinesis layout\n\n(http:\/\/www.kinesis-ergo.com\/images\/qwerty.gif)\n\nRemember that you are not limited to the layout in the default\n\ngithub has a ergodox area\n\nhttps:\/\/github.com\/benblazak\/ergodox-firmware\n\nhttps:\/\/github.com\/benblazak\/ergodox-firmware\/blob\/master\/src\/keyboard\/ergodox\/layout\/qwerty-kinesis-mod.c\n\nsee layer 1, the picture i gave above is layer 0\n\nedit: i should mention that modifying the layout and creating new firmware is not exactly drag and drop, however if you have any trouble the geek hack community is here to help :D\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: ic07 on Fri, 11 January 2013, 18:57:30\nThanks Glod :) .\u00a0 Ya, it's based on the Kinesis layout, but I did change a few things.\u00a0 The function layer is based on that of the Arensito layout (though, I failed to mention that in the current version of the source).\u00a0 Here's a prettier picture of all the layers, just for reference.\u00a0 Similar things for all the currently compiled layouts can be found in the .zip files for the binaries (follow the link in the readme, here (https:\/\/github.com\/benblazak\/ergodox-firmware#downloading-binaries)).\n\n[attachurl=1]\n\n@TC:\nLol, nope, no proof... and a quick search didn't turn up anything either, sorry :\/ .\u00a0 I have no idea what the other keyboards you mention are using to make themselves work on both USB and PS\/2, so I dunno what to tell you about that.\u00a0 Guess I can't be much help :\/ .\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: Glod on Fri, 11 January 2013, 19:15:16\nThanks Glod :) .\u00a0 Ya, it's based on the Kinesis layout, but I did change a few things.\u00a0 The function layer is based on that of the Arensito layout (though, I failed to mention that in the current version of the source).\u00a0 Here's a prettier picture of all the layers, just for reference.\u00a0 Similar things for all the currently compiled layouts can be found in the .zip files for the binaries (follow the link in the readme, here (https:\/\/github.com\/benblazak\/ergodox-firmware#downloading-binaries)).\n\n@TC:\nLol, nope, no proof... and a quick search didn't turn up anything either, sorry :\/ .\u00a0 I have no idea what the other keyboards you mention are using to make themselves work on both USB and PS\/2, so I dunno what to tell you about that.\u00a0 Guess I can't be much help :\/ .\n\noh wow that file rocks, why could i not find this anywhere lol\n\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: sordna on Fri, 11 January 2013, 20:36:29\n\nDo u have any proof that these \"real PS\/2 adaptors\" actually exist and where could I buy one?\n\nHow about the famous blue cube (http:\/\/www.amazon.com\/PS2-Keyboard-To-USB-Adapter\/dp\/B000BSJFJS\/) adaptor? Works great with both my Model M and Kinesis Classic.\n\n(http:\/\/ecx.images-amazon.com\/images\/I\/21YWRCC1F7L._SL500_AA300_.jpg)\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: TotalChaos on Fri, 11 January 2013, 20:46:30\nOk so to press a function key on ErgoDox I must:\n1. Press a key to change the layer.\n2. Press whichever Function key I want.\n3. Press a key to the layer back.\n\nCorrect?\n\nBasically it appears the ErgoDox is like a flat Kinesis Advantage with the function keys chopped off and the PS\/2 connectivity removed.\n\nI never understood why the Kinesis Advantage forces ppl to use that\u00a0 keywell design.\u00a0 It is great for ppl who want that.\u00a0 And the price is totally reasonable.\u00a0 But I have never craved, desired or wanted my keys in a keywell.\u00a0 I also absolutely do not want my wrist resting on that high point of the Kinesis Advantage keyboard.\u00a0 I would have certainly already bought a Kinesis Advantage if it was available in a flat version.\n\nDoes ergodox have footpedal support?\n\nWhen I designed my ultimate dream keyboard in 2003 I put the shift keys down in the thumb area of Ergodox.\u00a0 And I left them in the original positions too.\u00a0 This greatly eases the transition of learning to use thumbs to shift.\u00a0 The trouble is that if I do that I lose 2 other extremely valuable keys.\n\nIn my design there were at least 12 keys in the middle of keyboard which could be assigned as whatever instead of the 6 of ergodox.\u00a0 \u00a0For example Enter and Backspace could go into the middle area, leaving 2 keys available in thumb area for 2 shift keys.\u00a0 Just an example.\u00a0 I am not saying that ergodox positioning of enter or backspace are bad at all.\u00a0 I am just saying that an Ergonomic keyboard needs some flexibility to it so that ppl like me who crave thumb-shifting can be 100% satisfied.\n\nFor ppl who develop hand pain it is a common complaint that the pinky fingers get overused.\u00a0 \u00a0Having to shift with my pinky fingers all the time hurts me.\u00a0 That is why I want to have the option of shifting with my thumbs.\n\nSadly there are no \"spare\" keys on the keyboard to allow easy ergonomical reassignment of keys.\u00a0 Even though there is a lot of room for extra keys in the middle.\n\nIs there some simple solution I have overlooked that would allow me to have 4 shift keys?\u00a0 The original 2 + 2 for the thumbs?\u00a0 Without destroying the layout in some other way?\n\nKeeping in mind that shifting and spacebar must be dead ez to actuate in all circumstances.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: TotalChaos on Fri, 11 January 2013, 20:59:05\n\nDo u have any proof that these \"real PS\/2 adaptors\" actually exist and where could I buy one?\n\nHow about the famous blue cube (http:\/\/www.amazon.com\/PS2-Keyboard-To-USB-Adapter\/dp\/B000BSJFJS\/) adaptor? Works great with both my Model M and Kinesis Classic.\n\nShow Image\n(http:\/\/ecx.images-amazon.com\/images\/I\/21YWRCC1F7L._SL500_AA300_.jpg)\n\nYou are saying exactly what I have been saying over and over and over and over and over and over and over and over again for 10 years.\n\nYou can easily connect a PS\/2 keyboard to ANY computer using a simple cheap adapter.\n\nBut you cannot connect a USB-only keyboard like Ergodox to a PS\/2 computer.\n\nSo if you are only going to support one standard in your keyboard controller it only makes sense to support PS\/2.\u00a0 Because as you showed, your blue cube adapter will allow it to connect to a computer that has its PS\/2 ports amputated.\n\nOf course, supporting both adds zero to the manufacturing costs so there is no reason not to support both.\u00a0 You downloaded your free opensource USB controller software and you can download some free opensource PS\/2 controller software too.\n\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: sordna on Fri, 11 January 2013, 21:39:21\nWe need the option to have an FN key be momentary (as opposed to toggle), or have 2 FN keys, one momentary, the other act like a toggle.\n\nRegarding extra shift keys, I'm in the same boat. I have 4 shift keys in my Kinesis Advantage. I plan to get the ErgoDox with the full hand case, so I can install a pair of palm keys for shift. I think it has some extra positions in the matrix, if not, I will just piggyback wires off the existing shift keys, I've done it before. (http:\/\/geekhack.org\/showwiki.php?title=Island:26579)\n\nNote the arcade buttons in the palm area of my keyboard acting as shifts... I've added 8 keys total, but the palm keys get the most use:\n\n(http:\/\/geekhack.org\/index.php?action=dlattach;topic=26579.0;attach=3388;image)\n\nI plan to add the same kind of arcade buttons (Seimitsu PS-15) on this type of case:\n\n(http:\/\/i.imgur.com\/kTRGM.jpg)\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: ic07 on Fri, 11 January 2013, 22:07:39\n@TC:\n\nThere are both layer shift and layer lock keys on the default QWERTY layout.\u00a0 And if you don't like where something is, you can always reassign it anywhere you like.\u00a0 Please read the documentation, it took a long time to write.\n\nAs far as footpedals go, they're entirely possible - but they'd be DIY.\n\nAs for PS\/2 support:\u00a0 The USB portion of the code is from PJRC.\u00a0 I haven't had time to rewrite it myself (though, I think the original author did a pretty good job).\u00a0 I know of one or two other libraries I could have used, but they looked harder to work with, and none of them supported PS\/2.\u00a0 The rest of the code I wrote myself, in my free time, for free (and fun :) ).\u00a0 Please don't ever tell a developer that (to paraphrase) they downloaded their free open source code, and they really should go downloaded a different one.\u00a0 It's quite a bit insulting.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: TotalChaos on Fri, 11 January 2013, 22:48:22\n@TC:\n\nThere are both layer shift and layer lock keys on the default QWERTY layout.\nOk good to know :)\n\nQuote\nAs for PS\/2 support:\u00a0 The USB portion of the code is from PJRC.\u00a0 I haven't had time to rewrite it myself (though, I think the original author did a pretty good job).\u00a0 I know of one or two other libraries I could have used, but they looked harder to work with, and none of them supported PS\/2.\u00a0 The rest of the code I wrote myself, in my free time, for free (and fun :) ).\u00a0 Please don't ever tell a developer that (to paraphrase) they downloaded their free open source code, and they really should go downloaded a different one.\u00a0 It's quite a bit insulting.\nI apologize if I did not word things well.\u00a0 I'm dying.\u00a0 I'm on hardcore drugz. I am wiped out tired.\u00a0 My POS Rosewill keyboard keeps flashing lights at me and doing freaky things (like eating my keys or making the alt key get stuck even though I never pressed the Alt key in the first place, etc.)\u00a0 Its hard for me to concentrate tbh.\u00a0 I am really sorry.\u00a0 I didn't mean to be insulting.\u00a0 :-[\n\nI didn't mean u should replace the code you have.\u00a0 Your code obviously works so no need to change it AFAICT.\u00a0 I just meant that there surely must be free PS\/2 controller code floating around somewhere that could be added in, in addition to the USB code, given that PS\/2 has been around for 30 years (or however long, I think PS\/2 is actually just a shrunken DIN5 which has been around way longer than 30 years).\n\nI have a vague memory that I saw a PS\/2 controller somewhere... it was probably on opencores.org\n\nI will offer you a $200.00 bribe :) but u can call it a bounty :) to add PS\/2 support to the controller. I am sorry that I cannot offer more but I don't have an ergodox, and there is no guarantee that I will ever get one, or that it will really and truly allow me to begin coding again. Also if I get an Ergodox it might cost a really HUGE amount of money to pay someone to put it together for me. Nobody has actually offered to put it together for me at any price. I absolutely cannot ever build one myself. I can barely sit in a chair and shove the mouse around. No way I can do anything more complicated than that. But I can send $$with AmazonPay. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: rknize on Fri, 11 January 2013, 23:55:57 Browns are not on offer due to availability, no more than that. ah ok If you are looking for a source for PCB-mount MX Browns, The_Ed is selling switches that were harvested from brand-new Cherry boards: http:\/\/deskthority.net\/marketplace-f11\/cherry-ds-capslock-bottom-rows-switches-relegendables-t3093.html Also, 7bit has a date of 01\/2013 for the same: http:\/\/deskthority.net\/marketplace-f11\/cherry-mx-taking-pre-orders-t2760.html Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: wasabah on Sat, 12 January 2013, 00:06:27 Also, 7bit has a date of 01\/2013 for the same: http:\/\/deskthority.net\/marketplace-f11\/cherry-mx-taking-pre-orders-t2760.html If I would want to order these for the Ergodox (complementing the Massdrop group buy), which would I need? PCB mount I guess? How many? 84? Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: rknize on Sat, 12 January 2013, 00:19:31 Yes you want to order: MXBROWN\/NW 84 Maybe a couple of extras. He recently switched his pricing to EUR instead of USD, so keep that in mind. The_Ed is selling his for 50 cents each plus shipping and Paypal fees. I've bought a bunch from him already for DIY pokers and the like. They do appear to be new, save for being desoldered. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: sordna on Sat, 12 January 2013, 00:24:46 Either PCB mount or plate mount would work, the ergodox PCB can accommodate both kinds (which is awesome). PCB mount might be better IMO, since they have a pair of strong plastic pins which go into additional holes of the PCB, making the construction sturdier. However PCB-mount switches usually cost a bit more. I think the keyboard has 76 keys, so 80 should be enough to cover any accidents, although I notice the massdrop assembly instructions mention they provide 88. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: wasabah on Sat, 12 January 2013, 01:53:41 Thanks for the fast answer guys! :) I think then I will order soon and order one more keyboard without switches. Cool! :) Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: seferphier on Sat, 12 January 2013, 02:27:32 can't we just buy a few extra pcbs and construct another Ergo Dox ourselves? Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: ic07 on Sat, 12 January 2013, 03:04:31 I apologize if I did not word things well. I'm dying. I'm on hardcore drugz. I am wiped out tired. My POS Rosewill keyboard keeps flashing lights at me and doing freaky things (like eating my keys or making the alt key get stuck even though I never pressed the Alt key in the first place, etc.) Its hard for me to concentrate tbh. I am really sorry. I didn't mean to be insulting. :-[ Thanks... I'm sorry too. I guess I'm a bit touchy at the moment, probably because of some of the more heated discussions that happened over on DT a little bit ago. I should have been more patient :\/ Quote I didn't mean u should replace the code you have. Your code obviously works so no need to change it AFAICT. I just meant that there surely must be free PS\/2 controller code floating around somewhere that could be added in, in addition to the USB code, given that PS\/2 has been around for 30 years (or however long, I think PS\/2 is actually just a shrunken DIN5 which has been around way longer than 30 years). I have a vague memory that I saw a PS\/2 controller somewhere... it was probably on opencores.org I will offer you a 200.00 bribe :) but u can call it a bounty :) to add PS\/2 support to the controller. I am sorry that I cannot offer more but I don't have an ergodox, and there is no guarantee that I will ever get one, or that it will really and truly allow me to begin coding again. Also if I get an Ergodox it might cost a really HUGE amount of money to pay someone to put it together for me. Nobody has actually offered to put it together for me at any price. I absolutely cannot ever build one myself. I can barely sit in a chair and shove the mouse around. No way I can do anything more complicated than that. But I can send$$$ with AmazonPay.\n\nYour bribe (*cough* bounty, lol) is very generous :) .\u00a0 And if it really means that much to you, I'd be very tempted to do it for free, if I could.\u00a0 Unfortunately, my main problem is that I don't have *time* :\/ or enough domain knowledge to do it quickly.\u00a0 This weekend I have work, the next two weeks I'm visiting my grandparents (who I can't very well neglect, lol), and for most of the next few months after that I'll be back in school...\u00a0 And as I've never dealt with PS\/2 before (or USB, for that matter, which is why I'm still using a library), or many of the Teensy functions a PS\/2 library would be using (interrupts and timers come to mind), I don't think my chances of success in any reasonable amount of time would be good.\u00a0 In fact, I had an experience not that long ago trying to integrate code I didn't have time to understand when I tried to get mousekeys into the firmware.\u00a0 There's a nice library for making the Teensy emulate a mouse, and lots of other people have done it - but I couldn't figure it out at the time, and I still haven't had time to go back and make it work.\u00a0 So, I'm sorry... but I'm sure you can understand.\n\nThat being said, if anyone else wants to try, my code is up on github (https:\/\/github.com\/benblazak\/ergodox-firmware) (though the unstable branch is in the middle of somewhat of a rewrite), and I'll do my best to help you out where I can.\u00a0 I also found this project (http:\/\/ps2avr.sourceforge.net), which might be worth checking out.\u00a0 More searching might turn up something better.\n\nIn the meantime, I was able to find an active USB -> PS\/2 converter (http:\/\/www.amazon.com\/StarTech-Keyboard-Mouse-Adapter-PS22USB\/dp\/B0055PKVZY) :) .\u00a0 It's crazy expensive, and it only has one (very bad...) review... but lol, at least it's proof they exist :) .\n\nAs for people willing to do assembly, here's a portion of Dorkvader's mass PM, which was sent out just recently:\n\nQuote\nFor those interested in a fully assembled product, below are a list of people on GH willing to help. PM and coordinate with them for a quote.\n\nTheProfosist (USA) (http:\/\/geekhack.org\/index.php?action=profile;u=12209)\nGeekabit (EU) (http:\/\/geekhack.org\/index.php?action=profile;u=16736)\nDirge (UK) (http:\/\/geekhack.org\/index.php?action=profile;u=16113)\n\nHope that helps!\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: TotalChaos on Sat, 12 January 2013, 03:50:07\nI apologize if I did not word things well.\u00a0 I'm dying.\u00a0 I'm on hardcore drugz. I am wiped out tired.\u00a0 My POS Rosewill keyboard keeps flashing lights at me and doing freaky things (like eating my keys or making the alt key get stuck even though I never pressed the Alt key in the first place, etc.)\u00a0 Its hard for me to concentrate tbh.\u00a0 I am really sorry.\u00a0 I didn't mean to be insulting.\u00a0 :-[\n\nThanks...\u00a0 I'm sorry too.\u00a0 I guess I'm a bit touchy at the moment, probably because of some of the more heated discussions that happened over on DT a little bit ago.\u00a0 I should have been more patient :\/\n\nQuote\nI didn't mean u should replace the code you have.\u00a0 Your code obviously works so no need to change it AFAICT.\u00a0 I just meant that there surely must be free PS\/2 controller code floating around somewhere that could be added in, in addition to the USB code, given that PS\/2 has been around for 30 years (or however long, I think PS\/2 is actually just a shrunken DIN5 which has been around way longer than 30 years).\n\nI have a vague memory that I saw a PS\/2 controller somewhere... it was probably on opencores.org\n\nI will offer you a $200.00 bribe :) but u can call it a bounty :) to add PS\/2 support to the controller. I am sorry that I cannot offer more but I don't have an ergodox, and there is no guarantee that I will ever get one, or that it will really and truly allow me to begin coding again. Also if I get an Ergodox it might cost a really HUGE amount of money to pay someone to put it together for me. Nobody has actually offered to put it together for me at any price. I absolutely cannot ever build one myself. I can barely sit in a chair and shove the mouse around. No way I can do anything more complicated than that. But I can send $$with AmazonPay. Your bribe (*cough* bounty, lol) is very generous :) . And if it really means that much to you, I'd be very tempted to do it for free, if I could. It does mean a lot to me and it means a lot to various other ppl out there who are reading this msg but are like I was, they are in READONLY mode and are unable to type due to their hands being trashed. The bountybribe offer is good for 1 year. After that we'll see. You can ask. If I can finish my current keyboard building project and my drugz keep working and my doctor doesn't quit and I don't die or have yet another pain attack then I might disappear into my codercave and never be seen on geekhack again. Quote Unfortunately, my main problem is that I don't have *time* :\/ or enough domain knowledge to do it quickly. This weekend I have work, the next two weeks I'm visiting my grandparents (who I can't very well neglect, lol), and for most of the next few months after that I'll be back in school... And as I've never dealt with PS\/2 before (or USB, for that matter, which is why I'm still using a library), or many of the Teensy functions a PS\/2 library would be using (interrupts and timers come to mind), I don't think my chances of success in any reasonable amount of time would be good. I was not expecting any progress for at least 3 months. Long after the group buy is over. That is why I was saying it may never benefit me in any way. Quote In fact, I had an experience not that long ago trying to integrate code I didn't have time to understand when I tried to get mousekeys into the firmware. There's a nice library for making the Teensy emulate a mouse, and lots of other people have done it - but I couldn't figure it out at the time, and I still haven't had time to go back and make it work. So, I'm sorry... but I'm sure you can understand. Coding alien systems is a batch. And I don't mean it like a file of script commands :)) Anywayz no pressure. If u feel like tackling it u will and if not then I just saved myself 200.00 which is enough for me to get that new Front-printed Filco I have been eyeing :) Quote In the meantime, I was able to find an active USB -> PS\/2 converter (http:\/\/www.amazon.com\/StarTech-Keyboard-Mouse-Adapter-PS22USB\/dp\/B0055PKVZY) :) . It's crazy expensive, and it only has one (very bad...) review... but lol, at least it's proof they exist :) . If it doesn't even work then it doesn't exist. :) I like how it says my brand new Intel core i5 is a legacy system :)) I don't really know how the USB protocol messages work but reading some msgs from guys who do know, they said it would be really complicated to make a working active adapter like that. It is really just better to buy a keyboard that is compatible with USB and PS\/2, like Filco, WASD, CoolerMaster, Rosewill, etc. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: sordna on Sat, 12 January 2013, 10:47:08 @TC If you have an i5 I bet the computer has USB ports. Why don't you simply use a USB port to connect the ErgoDox? Why is PS\/2 sooooo important that you won't even use a great ergonomic keyboard to help your health issues if it doesn't support it? Please educate us here. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: jabar on Sat, 12 January 2013, 12:11:15 a great ergonomic keyboard to help your health issues this remains to be seen Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: rknize on Sat, 12 January 2013, 12:45:44 Either PCB mount or plate mount would work, the ergodox PCB can accommodate both kinds (which is awesome). PCB mount might be better IMO, since they have a pair of strong plastic pins which go into additional holes of the PCB, making the construction sturdier. However PCB-mount switches usually cost a bit more. I think the keyboard has 76 keys, so 80 should be enough to cover any accidents, although I notice the massdrop assembly instructions mention they provide 88. More than anything else, the pins give the switch the proper orientation. One thing I noticed with the Phantom plate was that the switches could rotate slightly, especially the keys that had multiple positions (mods, space, etc). This is a problem for stabilized keys, especially space, which can't afford any rotation at all. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: oneproduct on Sat, 12 January 2013, 13:26:08 Anybody else having problems with paypal checkout on massdrop? I get a few different errors, but the main one seems to be \"total not set\" and it prints the array that's passed by the order page on screen and you can in fact see that the total is 0. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: sordna on Sat, 12 January 2013, 13:43:30 What other payment methods do they have available? Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: oneproduct on Sat, 12 January 2013, 15:08:40 They have credit card as well. At the moment I've got money in my paypal though so was hoping to be able to use that. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: haskellelephant on Sat, 12 January 2013, 15:40:16 There, my order is in. It seems that you have to choose \"N\/A\" on the extra pcb option since two pcb boards are already included in the price. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: Glod on Sat, 12 January 2013, 16:22:53 Man, 34 orders plus 12 committed to 199 aint bad for having more than 15 days left, I'm getting it no matter what so i'm pulling out the popcorn and watching this progress until the group buy date closes :) i had no problems with paypal btw.. they just send a notice that the processing is pending with massdrop and wont be billed until that is over. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: esoomenona on Sat, 12 January 2013, 16:28:03 If it gets down to 199 and I can spare the money, I will go in. I'm monitoring it until then. (http:\/\/www.bestmemes.com\/pix\/83950959.jpg) Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: ironman31 on Sat, 12 January 2013, 16:30:34 You can always commit to buying it only if it goes down to 199 Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: oneproduct on Sat, 12 January 2013, 16:48:32 This is what I keep getting :( https:\/\/www.massdrop.com\/php\/APIError.php PayPal API Error The PayPal API has returned an error! TIMESTAMP: 2013-01-12T22:47:45Z ACK: Failure VERSION: 65.1 BUILD: 4181146 L_ERRORCODE0: 10400 L_SHORTMESSAGE0: Transaction refused because of an invalid argument. See additional error messages for details. L_LONGMESSAGE0: Order total is missing. L_SEVERITYCODE0: Error Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: Halverson on Sat, 12 January 2013, 16:55:56 ^ Have you tried both buy and commit to buy? Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: oneproduct on Sat, 12 January 2013, 16:58:03 Yup, I get the same either way. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: Halverson on Sat, 12 January 2013, 17:00:33 Yup, I get the same either way. So strange, very strange. Maybe try changing your order, which you can always change back after? Order a full set, then remove switches after. Or something of that sort with different options. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: SubGothius on Sun, 13 January 2013, 02:44:21 More than anything else, the pins give the switch the proper orientation. One thing I noticed with the Phantom plate was that the switches could rotate slightly, especially the keys that had multiple positions (mods, space, etc). This is a problem for stabilized keys, especially space, which can't afford any rotation at all. ErgoDox doesn't use any stabliizers, and the assembly instructions have you mount the keyswitches in the plate before soldering them in place, so they should be locked into proper position when soldered. That said, if you still prefer PCB-pegged keyswitches, you can join the GB sans switches and source your own switches in some other GB or elsewhere. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: SubGothius on Sun, 13 January 2013, 02:49:44 This is what I keep getting :( https:\/\/www.massdrop.com\/php\/APIError.php PayPal API Error The PayPal API has returned an error! TIMESTAMP: 2013-01-12T22:47:45Z ACK: Failure VERSION: 65.1 BUILD: 4181146 L_ERRORCODE0: 10400 L_SHORTMESSAGE0: Transaction refused because of an invalid argument. See additional error messages for details. L_LONGMESSAGE0: Order total is missing. L_SEVERITYCODE0: Error Try clearing your cookies, or at least delete cookies for massdrop.com and paypal.com. Also make sure your browser settings aren't blocking third-party cookies; not sure if that's even relevant, but it's something to try. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: asura on Sun, 13 January 2013, 04:08:21 Want the PCB only? \"The best way to do this is to have you check out normally and notify one of our live chat reps so they can put a note on the transaction saying to only collect payment for the PCB (44 shipped to your door). Let me know what works best for you, - Will\" They really are bending over backwards. I'm sure everyone probably checking both posts, but just in case I'll pop it up in the other one too. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: oneproduct on Sun, 13 January 2013, 10:02:12 Okay, I think I managed to get in the group buy. I got the paypal confirmation email in any case. Is it suppose to show up in my purchase history, or is that only once the group buy actually completes? Just curious about whether it should be listed there as people mentioned being able to change your order (i.e. switch type or such) up until the group buy completes, but not sure where that would be done without something in my purchase history to be able to fiddle with. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: hoggy on Sun, 13 January 2013, 10:04:10 a great ergonomic keyboard to help your health issues this remains to be seen True, but I find it hard to believe that it won't help. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: haskellelephant on Sun, 13 January 2013, 11:47:22 Now that the keyboard is soon in hand, it's time to start looking for a wrist rest for split keyboard. I was think about getting some soft wrist rest for it. I am kinda hoping it would be possible to get something that would put the weight on the palms rather than the wrists like with the truly ergonomic keyboard and the kinesis advantage. Maybe two mouse wrist rests will do the trick? Ideas anyone? Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: sordna on Sun, 13 January 2013, 11:49:44 Folks, the debate here is about PS\/2. Even if PS\/2 is better in some technical aspects, the reality is that it makes no real difference to the user (unless you have 10+ year old computer). So if one has to choose between 2 similar keyboards, one with PS\/2 capability is preferable, but with unique keyboards like the ErgoDox it's really not worth to worry about it. I was hoping TC would explain why lack of PS\/2 is a total deal breaker for him. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: litster on Sun, 13 January 2013, 12:05:22 Now that the keyboard is soon in hand, it's time to start looking for a wrist rest for split keyboard. I was think about getting some soft wrist rest for it. I am kinda hoping it would be possible to get something that would put the weight on the palms rather than the wrists like with the truly ergonomic keyboard and the kinesis advantage. Maybe two mouse wrist rests will do the trick? Ideas anyone? Is my wrist rest case design not available from massdrop? Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: BugBuster on Sun, 13 January 2013, 12:12:04 Now that the keyboard is soon in hand, it's time to start looking for a wrist rest for split keyboard. I was think about getting some soft wrist rest for it. I am kinda hoping it would be possible to get something that would put the weight on the palms rather than the wrists like with the truly ergonomic keyboard and the kinesis advantage. Maybe two mouse wrist rests will do the trick? Ideas anyone? I'm thinking about a pair of http:\/\/www.ebay.co.uk\/itm\/3M-Gel-Mouse-Trackball-Wrist-Rest-Black-Leatherette-\/370723084235?pt=US_Mouse_Pads_Wrist_Rests&hash=item5650d157cb Or one big http:\/\/www.ebay.co.uk\/itm\/3M-WR314LE-KEYBOARD-WRIST-REST-ERGO-SPLIT-GEL-BLACK-LEATHERETTE-THIN-\/300595068203?pt=LH_DefaultDomain_0&hash=item45fcdcbd2b Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: regack on Sun, 13 January 2013, 12:14:26 Now that the keyboard is soon in hand, it's time to start looking for a wrist rest for split keyboard. I was think about getting some soft wrist rest for it. I am kinda hoping it would be possible to get something that would put the weight on the palms rather than the wrists like with the truly ergonomic keyboard and the kinesis advantage. Maybe two mouse wrist rests will do the trick? Ideas anyone? Is my wrist rest case design not available from massdrop? As far as I know it is. This is your design, yes?: (https:\/\/s3.amazonaws.com\/massdropinc\/product-images\/fullhandcase.jpeg) Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: haskellelephant on Sun, 13 January 2013, 12:27:50 Now that the keyboard is soon in hand, it's time to start looking for a wrist rest for split keyboard. I was think about getting some soft wrist rest for it. I am kinda hoping it would be possible to get something that would put the weight on the palms rather than the wrists like with the truly ergonomic keyboard and the kinesis advantage. Maybe two mouse wrist rests will do the trick? Ideas anyone? Is my wrist rest case design not available from massdrop? It is available, but I wanted something soft. I guess I could just add one of these: http:\/\/www.amazon.com\/GRIFITI-Notebook-Silicone-Reposition-Travelling\/dp\/B00897D3OQ\/ref=pd_sbs_pc_1 to it, but I think that a separate palm rest would be better for me. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: litster on Sun, 13 January 2013, 13:07:56 As far as I know it is. This is your design, yes?: Show Image (https:\/\/s3.amazonaws.com\/massdropinc\/product-images\/fullhandcase.jpeg) Yes. (http:\/\/i.imgur.com\/kTRGM.jpg) Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: bisl on Sun, 13 January 2013, 13:08:48 It is available, but I wanted something soft. I guess I could just add one of these: http:\/\/www.amazon.com\/GRIFITI-Notebook-Silicone-Reposition-Travelling\/dp\/B00897D3OQ\/ref=pd_sbs_pc_1 to it, but I think that a separate palm rest would be better for me. You know, I was originally against the wrist rest case design for exactly this reason--the balls of my wrists (\"pisiform,\" I believe) get really sore when typing on a hard surface. So when seeing litster's wrist rest case design, I thought \"Not for me! I need a soft rest.\" However! The more I think about it, the more I love that design because you can put a soft rest ON it, which does two things: 1) It provides extra height, which begins to approximate the Kinesis Advantage's keywell design. 2) Since the soft rest will sit on the case itself, this will help keep them positioned at a uniform distance from one another, in comparison to my current filco\/kensington setup, which I constantly fiddle with. That said, I'm getting both designs, so we'll see how it turns out :D Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: TotalChaos on Sun, 13 January 2013, 13:25:29 a great ergonomic keyboard to help your health issues this remains to be seen True, but I find it hard to believe that it won't help. The Ergodox is not my idea of my dream keyboard. It simply appears to be less crazy than a Kinesis Advantage and it seems like it is made by ppl who are actually trying to solve a problem. Since they seem like they are trying I am willing to go ahead and spend the bucks to buy it and pay someone to put it together for me if someone will fix the USB\/PS\/2 issue. Just because I am willing to take a risk on something does not mean it is perfect for me. It just means I am open minded and willing to give it a try and willing to help the project out. > How could it possibly not help you? 1. The thumb buttons are built into the hand buttons. I never asked for that and don't exactly want it due to this makes the keyboard as a whole take up a huge amount of deskspace. This means the keyboard either: A) Won't work for me. B) Will work for me but it will always be hanging off the edge of my lapmat or the edge of my rollerdesk and eventually will fall off and break. > Why can't you just be like me and keep your keyboard on a normal GDMF Desk?! Because I don't live a life of luxury and decadent pleasure like you. I am dying of pain. I can't use a keyboard PERIOD unless a huge number of strict rules are followed. Rule #13 The keyboard shall not be any higher than neccessary or extreme arm pain shall cause paralysis or death. Maybe there is some luxurious larger desk than this little thing I am using, that would have infinitely adjustable height like this... but I don't have it and I don't know how much such a thing costs or where to get it. I just recently gained the ability to do online shopping so there are probably an infinite number of little thingamajigs that u know about that I don't. Ok so even if I had the most perfect desk in the universe it still doesn't mean an ergodox will work for me because it just looks like the Ergodox intrudes greatly into my mouse space. > Oh dear God, he's going to quote another rule... Yes I am :) Under: Attempting to use a computer Rule #1. Don't Rule #2. If you break Rule#1 then you MUST keep the mouse right in front of you. None of this nonsense keeping the mouse way up on a tall desk out beyond your numeric keypad. I have to be hyper ergonomic at all times to even use my computer a little bit. If I had not come up with all these strict rules of Ergomania then I would not be here on GeekHack. I wouldn't be alive or I would still be in READONLY mode like I was for years just watching the world go by like a Dolphin, unable to use my hands. So yes, Ergodox allegedly lets me shift with my thumbs. That is kewl. And it is flat unlike Kinesis Advantage. That is great. But it consumes large amounts of deskspace. It uses a grid layout. I never asked for that and never thought I would like it. Normal layout is ok for me. Ergodox also uses a split layout with a really huge split. The only split keyboard I ever used before hurt me a lot but that is because it was some crappy fake \"ergo\" rubberdome keyboard with typical way overstiff rubberdomes that required a wildly painful impact in order to register a keypress. I am just hoping that my pain will be ok with the split and the grid of the ergodox. I know I can handle a small split. But the Ergodox split is hugely gigantamongous. For me, its a risk. If I stick with the Cherry Red keyboards I have now then I get real Function keys. I have coding stuff set up on my function keys so I can press a single button to trigger some text. On Ergodox I hafta press 2 keys. (2x the keys = 2x the pain) I only get to press a certain number of keys per day before the pain gets to high. I don't even know how SHIFT+F1 would work... I think to use the temp Layer key would require too much finger gymnastics which would hurt my hand immediately so that leaves using the Layer Switch key (whatever its called) but then I have to 1. Switch layer 2. Press SHIFT+1 3. Switch back to original layer. So that is 4 keypresses instead of 2. Some of the macros would no longer really be worth it. What if shifting with my thumbs doesn't work out for me? I would like to be able to shift with my fingers in the middle of keyboard. I need extra keys in the center of the board that are freely definable. In my dream keyboard there are at least 4 columns of keys in the center of the board. I have been wanting that since 2003. But Ergodox has only 2 columns and some of the keys are critically important layer keys and cannot be done away with. > Dude, you can like totally redefine the layer keys to be shift keys. How do you know it actually works? Have u tried it? What if there is a bug in the controller software so that you can redefine any key you want except the layer keys? That is exactly the kind of bug\/limitation I would expect. If I could redefine the layer keys to be elsewhere, which other keys would I destroy? This is why a keyboard needs a few extra keys on it so you don't get jammed up just because you want some extra shift keys. You see, switching to Ergodox is a risk. Now you can see why there is only a 50% chance of Ergodox actually helping me. If I stick to my brand new (complete garbage currently being held together with scotch tape) Rosewill then I at least get my cherry red switches with a beautiful spring under every key that works on PS\/2 and I get 12 function keys and a whole entire numeric keypad filled with keys that I can redefine to do special things. In fact, writing this msg has given me a great idea how to make an ergo keyboard out of a normal keyboard without having to pay someone thousands of$$$ to build my dream keyboard!\u00a0 Wow!\u00a0 Thank u Sordna for harassing me into writing this!\u00a0 ;D\u00a0 My new idea does not replace my dream keyboard but it might possibly maybe be \"barely good enough\" for me to squeak by with.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: AloisiusFauxly on Sun, 13 January 2013, 15:34:22\nif someone will fix the USB\/PS\/2 issue.\n\nWhy is it an issue for you that it needs to be PS2? Need more than 6KRO? Legacy pass-through devices, or using it on an old system?\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: SmallFry on Sun, 13 January 2013, 15:35:43\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: Glod on Sun, 13 January 2013, 15:51:40\nTC, i think you should have brought that and other posts into a separate thread. This thread is here for the interest, development, testing, and construction of the ErgoDox. Over the last year, feedback and interest was fielded by talented individuals that collectively made the final product. I have nothing but respect for the people involved in the Phantom, GH60, and ErgoDox projects.\n\nThis project's development is open source; you have had the honor of been given resources directly from the team and if you acquire a ErgoDox you are free to do and share whatever you want to do with it.\n\nIf you want to be critical of the ErgoDox and split keyboard designs, i wouldn't suggest doing that here, i would create a new thread doing so.\n\nIf you want to be critical of keyboards that do not support PS\/2 such as Topre and others then also create a thread doing so instead of doing that in a unrelated thread. Creating a new thread is easy and there are multiple forums with different categories to create threads in. You are likely to get more accomplished in a new thread about your concerns than in posts you drop in on.\n\nThe MassDrop GB seems to be a success, and people who are new to geekhack who were brought here by interest in the ErgoDox are going to see your posts in here and feel less inclined to participate altogether. This is exactly what happened lately in the Deskthority.net thread; things were very constructive in the thread and then it went to hell and actually caused people to loose interest in the ErgoDox the way i see it; thankfully DorkVader came to action.\n\nI am not trying to \"troll\" you and get you worked up but you have insulted me, you have insulted ic07, and i am 100% sure you have insulted other members of geekhack and the ergodox project with your last few posts in this thread.\n\nPlease keep this thread about the interest, construction, and testing of the ErgoDox. It is located in the \"making stuff together!\" area for a reason. Do not post threads that will discourage new\/existing geekhack members of participating in these discussions. Please create new threads related to your arguments and field interest from others that share your views.\n\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: bisl on Sun, 13 January 2013, 15:58:00\n\/snip\n\nNo offense man, but for someone dying of typing-related pain, you sure type a lot in here.\n\nYour criticisms are noteworthy, but this design is beyond finalized; rather than picking apart the ErgoDox, it might be time to start conceiving an ErgoChaos offshoot in a different thread. The Ergodox is a great advancement, but it wasn't tailor-made for you and you shouldn't treat it as such. I don't mean to shut you down, but your posts here are proving unproductive.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: haskellelephant on Sun, 13 January 2013, 16:11:41\n\n1. The thumb buttons are built into the hand buttons.\u00a0 I never asked for that and don't exactly want it due to this makes the keyboard as a whole take up a huge amount of deskspace.\u00a0 This means the keyboard either: A) Won't work for me.\u00a0 B) Will work for me but it will always be hanging off the edge of my lapmat or the edge of my rollerdesk and eventually will fall off and break.\n\nYour definition of huge is a bit weird. The roller board can handle a 15' laptop right, by my estimate it should also fit the keyboard although someone that actually have the dimensions\nof the keyboard must confirm this.\n\nRule #13 The keyboard shall not be any higher than neccessary or extreme arm pain shall cause paralysis or death.\n\nRule #2. If you break Rule#1 then you MUST keep the mouse right in front of you.\u00a0 None of this nonsense keeping the mouse way up on a tall desk out beyond your numeric keypad.\n\nYou could have the mouse between the parts of the keyboard if you want...\n\nHow do you know it actually works?\u00a0 Have u tried it?\u00a0 What if there is a bug in the controller software so that you can redefine any key you want except the layer keys?\u00a0 That is exactly the kind of bug\/limitation I would expect.\nThe board is built with a teensy microcontroller. If there is a bug in the software you can replace the software since the source is available. Looking at the source, it should be possible to change the layer keys. If there actually is a bug the rest of us would want to know about it and fix it.\nIf there is a problem with the teensy then 1) you might be eligable for a refund, and 2) they cost 16$. Title: Re: [Interest Check] ErgoDox - Custom split ergo keyboard. Post by: TotalChaos on Sun, 13 January 2013, 16:13:44 if someone will fix the USB\/PS\/2 issue. Why is it an issue for you that it needs to be PS2? Because PS\/2 keyboards work on everything. USB keyboards do not work on everything. And as a free added bonus PS\/2 is better than USB 1.1 Quote Need more than 6KRO? It is a very nice feature. And I respect nice features. It says to me \"This keyboard is WORTH the$800.00 you paid for it\".\u00a0 \u00a0But whatever.\n\nQuote\nLegacy pass-through devices,\nYes.\u00a0 This is required.\n\nQuote\nor using it on an old system?\nYes.\u00a0 This is required.\n\nWhy is it an issue for you that you need the PS\/2 broken?\n\nWhy can't u let me have my PS\/2 and be happy?\n\nRosewill is one of the worst keyboard companies around and they let me have PS\/2.\u00a0 Why not u?\n\nI have a gazillion computers and they all have PS\/2 ports.\u00a0 All my KVM switches have PS\/2 ports.\u00a0 They all work.\u00a0 I have never had a PS\/2 port fail yet.\n\nIf I take my USB 1.1 ergodox to the factory to use it on the robots, oh wait I CAN'T use it because it won't work on PS\/2 so forget that idea.\u00a0 That means I have just spent months training my hands to use Ergodox for nothing because I still have to keep switching back and forth from 1 keyboard to another.\n\nPart of Ergonomics is training your muscle memory to be really good with the keyboard you are using.\u00a0 If I keep randomly switching between 11 different keyboards I will never get any good at any of them.\u00a0 Pick something good, stick with it and get good at it.\n\nRemember I am not like you.\u00a0 I can't play keyboard games all day long.\u00a0 I am crippled with pain.\u00a0 I get a limited amount of keystrokes.\u00a0 When I first start to learn Ergodox layout it is going to hurt a lot.\u00a0 Why would I invest in learning a keyboard that doesn't actually work on millions of PS\/2 devices?\n\nI am trying to reduce my pain, not increase it.\u00a0 That means pick the best keyboard I can get and learn that one keyboard and use that ONE keyboard on everything all the time until something better comes along.\n\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: Glod on Sun, 13 January 2013, 16:22:47\nI asked you nicely above to not do this here again and you punched me in the stomach instead.\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: dorkvader on Sun, 13 January 2013, 16:24:18\n> Dude, you can like totally redefine the layer keys to be shift keys.\n\nHow do you know it actually works?\u00a0 Have u tried it?\u00a0 What if there is a bug in the controller software so that you can redefine any key you want except the layer keys?\u00a0 That is exactly the kind of bug\/limitation I would expect.\n\nIf I could redefine the layer keys to be elsewhere, which other keys would I destroy?\u00a0 This is why a keyboard needs a few extra keys on it so you don't get jammed up just because you want some extra shift keys.\n\nYou see, switching to Ergodox is a risk.\nFrom looking at the code, as far as I can tell, they define every key function from a matrix, and then assign them to their proper positions. This means that every key is arbitrarily assigned, generally speaking it should mean that if it works at all, it will work other ways, too. The function key position is not hardcoded, because no key is hardcoded. Even on my access-IS keyboards, you can arbitrarily assign the function keys. When I get my ErgoDOX, I fully plan on testing out some interesting custom layouts. Moving the function layer-swap key is a useful thing that I'm certain I'll try. I also want to play with a layout with my most-used Function keys on it without the need for pressing a fn key to get them. This is one of the many good parts about a programmable keyboard.\n\nAnd even if not, one of the best parts about open-source projects is that people can see what's there and fix bugs when they arise and are reported. This is pretty useful, especially if you offer bounties.\n\nAlso, why PS2? I don't think it has it now, but there is certainly a possibility of making this NKRO over USB, like what my soarer adapter does with my model F. I recognize it's good to have your preference, but I'm interested to know the reason.\n\n---\nAlso about active USB to PS2 adapters, you may be able to use a KVM box for that. I don't have one, but it seems feasible. One reason they're so expensive is dealing with\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: TotalChaos on Sun, 13 January 2013, 16:53:09\nIf you want to be critical of the ErgoDox and split keyboard designs, i wouldn't suggest doing that here, i would create a new thread doing so.\nI am not trying to be critical of the ErgoDox.\nI was just answering questions that ppl keep repeatedly bombing me with.\u00a0 Sordna asked me multiple times about the PS\/2 thing in multiple different threads for example and then some other guys did too.\u00a0 So I finally answered.\n\nDon't think of it as some sort of crucifixion of ErgoDox in my previous msgs.\n\nThink of it as me explaining that I really actually want to try an ErgoDox but I am in a specific situation and I answered ppl's questions to the best of my ability to explain this and that and the other.\n\nIf a mod wants to transfer the question that was asked of me and my \"critical\" response into a separate thread because some rule got broken or whatever then that is ok with me as long as the new thread maintains a logical coherency.\n\nI am sorry that you feel I have polluted your thread.\u00a0 But when I refuse to answer ppl's interrogations they get mad at me and say I am being evasive.\nThis has happened to me over and over again on GH.\n\nI just can't win.\u00a0 :(\n\nQuote\nIf you want to be critical of keyboards that do not support PS\/2 such as Topre and others then also create a thread doing so instead of doing that in a unrelated thread. Creating a new thread is easy and there are multiple forums with different categories to create threads in. You are likely to get more accomplished in a new thread about your concerns than in posts you drop in on.\nI will take that under consideration.\n\nBut I have a question: What are u going to do when the next person comes along who says \"I am interested in an Ergodox but _____\" ?\nAre you going to give this same speech to every person?\nOr is it something personal against me?\u00a0 Or ?\n\nQuote\nThe MassDrop GB seems to be a success, and people who are new to geekhack who were brought here by interest in the ErgoDox are going to see your posts in here and feel less inclined to participate altogether. This is exactly what happened lately in the Deskthority.net thread; things were very constructive in the thread and then it went to hell and actually caused people to loose interest in the ErgoDox the way i see it; thankfully DorkVader came to action.\n\nI am not trying to \"troll\" you and get you worked up but you have insulted me,\nI think you have misunderstood something.\u00a0 I like u and would not insult u.\nYou have a Mark VII Glue Gun (+12 vs. Rosewills)\u00a0 ;D\n\nQuote\nyou have insulted ic07,\nGRRR\n\nI insulted ic07?!?\n\nI offered him $200.00 to add PS\/2 support to ErgoDox even though this will likely never benefit me.... I am just throwing$200.00 into the project and now u say I am insulting him!???\n\n:'(\u00a0 \u00a0>:D\u00a0 \u00a0>:D\n\nDo you officially work for the Ergodox project?\n\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: AloisiusFauxly on Sun, 13 January 2013, 16:55:39\nWell TC, if you have legit needs for PS\/2 then that's just fine. But the stock ErgoDox is not for you then!\nTitle: Re: [Interest Check] ErgoDox - Custom split ergo keyboard.\nPost by: TotalChaos on Sun, 13 January 2013, 17:03:07","date":"2017-10-19 07:21:34","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\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.26150017976760864, \"perplexity\": 4590.779397801558}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-43\/segments\/1508187823255.12\/warc\/CC-MAIN-20171019065335-20171019085335-00256.warc.gz\"}"} | null | null |
The very young feline is quite clever and an agile lioness, do not let her fool you. She is very carefree and will run off into the unknown if you let one eye off of her due to her fearless personality. Her white coat and her luminous blue eyes make her very noticeable in every environment except lands with snowfall. Her figure is lean and long allowing her to climb and to be very agile. Once she grows up into a juvenile and then into an adult lioness, she will become very threatening and misleading to outsiders. Nalea is very determined and will do anything to for her pride. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,459 |
{"url":"https:\/\/tex.stackexchange.com\/questions\/475366\/full-page-figures-using-revtex","text":"# Full page figures using RevTeX?\n\nI am typesetting an article using the revtex4-2 document class (using the twocolumn option), and I was wondering if there is any way I can get a figure to be placed on its own separate page, like it is possible using the \\begin{figure}[p] option in other document classes. (RevTeX seems to be ignoring the [p] option entirely.)\n\nBackground: I have a few tall figures in my document, which\u2014in case there is no more space for regular text on the page\u2014result in the following error:\n\nOutput routine didn't use all of \\box255.\n\n\nwhich causes the figure to not be typeset at all (instead, I get an empty page). The following MWE should illustrate the problem:\n\n\\documentclass[twocolumn]{revtex4-2}\n\n\\usepackage{tikz}\n\\usepackage{lipsum}\n\\usepackage{standalone}\n\\usepackage{filecontents}\n\n\\begin{filecontents}{tall-figure.tex}\n\\documentclass[crop, tikz]{standalone}\n\\begin{document}\n\\begin{tikzpicture}\n% For a height of 20, everything is fine:\n\\draw (0, 0) rectangle (10, 21);\n\\end{tikzpicture}\n\\end{document}\n\\end{filecontents}\n\n\\begin{document}\n\\lipsum[1-5]\n\\begin{figure*}\n\\includestandalone{tall-figure}\n\\caption{Dummy Caption}\n\\label{fig:dummy}\n\\end{figure*}\n\\lipsum[5-10]\n\\end{document}\n\n\nAny hints and suggestions how to get full page figures with RevTeX would be greatly appreciated :)\n\n\u2022 I am trying to do the same thing and facing the same problem. Hopefully an answer exists.. \u2013\u00a0DanHickstein Apr 13 '19 at 3:42","date":"2021-07-24 08:39:26","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8249809145927429, \"perplexity\": 1182.4093550610205}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046150134.86\/warc\/CC-MAIN-20210724063259-20210724093259-00687.warc.gz\"}"} | null | null |
namespace FullContactDotNet.Shared
{
public class SocialProfile
{
/// <summary>
/// Gets or sets the bio.
/// </summary>
/// <value>
/// The bio.
/// </value>
public string Bio { get; set; }
/// <summary>
/// Gets or sets the type identifier.
/// </summary>
/// <value>
/// The type identifier.
/// </value>
public string TypeId { get; set; }
/// <summary>
/// Gets or sets the name of the type.
/// </summary>
/// <value>
/// The name of the type.
/// </value>
public string TypeName { get; set; }
/// <summary>
/// Gets or sets the URL.
/// </summary>
/// <value>
/// The URL.
/// </value>
public string Url { get; set; }
/// <summary>
/// Gets or sets the identifier.
/// </summary>
/// <value>
/// The identifier.
/// </value>
public string Id { get; set; }
/// <summary>
/// Gets or sets the username.
/// </summary>
/// <value>
/// The username.
/// </value>
public string Username { get; set; }
/// <summary>
/// Gets or sets the followers.
/// </summary>
/// <value>
/// The followers.
/// </value>
public int? Followers { get; set; }
/// <summary>
/// Gets or sets the following.
/// </summary>
/// <value>
/// The following.
/// </value>
public int? Following { get; set; }
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,630 |
3.3 - Who's Using Who?
Welcome to the Tobacco Control virtual classroom!
Welcome to the Tobacco Control virtual classroom. Through this class, you will learn critical information about the history of smoking, the biology of smoking, the laws on smoking and, most importantly, how smoking affects you!
This space is pre-loaded with content designed to help you explore issues related to tobacco control with your students. All of the content that is here is completely editable by you, so you can keep what works, edit what you'd like to adapt, remove what doesn't meet your particular needs, and add more as you see fit!
• Connect your class with other classes around the world that are also utilizing the Tobacco Control virtual content in order to gain a global perspective, through the collaboration functionality.
• Invite guests to share their expertise and experiences related to the field of tobacco control. | {
"redpajama_set_name": "RedPajamaC4"
} | 637 |
1970sThink I Will Go For A Dip
Remember when this came out. . did u think twice about going into the ocean?
Tags: movie peter benchley steven spielberg shark amity roy scheider robert shaw martin brody
Posted By: sneakysnake
1970sFonzie Jumps The Shark
'Jumping the shark' is a term in the TV industry that describes when a show starts to go downhill. The term comes from this 1979 episode of Happy Days in which Fonzie...jumps a shark! The plot revolves around the cast heading west because Fonzie has been given a chance to take a Hollywood screen test. While in California, Fonzie develops a rivalry with a rich water skiing champion. The climax comes when the two challenge each other to jump a penned-up shark. The rich dude chickens out. Here's Fonzie's famous attempt.
Tags: Happy Days Fonzie jumps shark
1930s & EarlierKim Novak The Lavender Blonde
Kim Novak was born Marilyn Pauline Novak in Chicago, Illinois. She is perhaps best known for her performance in Alfred Hitchcock's Vertigo (1958). Her films include The French Line (1954) Pushover (1954) Phffft! (1954) Son of Sinbad (1955) 5 Against the House (1955) Picnic (1955) The Man with the Golden Arm (1955) The Eddy Duchin Story (1956) Jeanne Eagels (1957) Pal Joey (1957) Vertigo (1958) Bell, Book and Candle (1958) Middle of the Night (1959) Strangers When We Meet (1960) Pepe (1960) (Cameo) The Notorious Landlady (1962) Boys' Night Out (1962) Showman (1963) (documentary) Of Human Bondage (1964) Kiss Me, Stupid (1964) The Amorous Adventures of Moll Flanders (1965) The Legend of Lylah Clare (1968) The Great Bank Robbery (1969) The White Buffalo (1977) Just a Gigolo (1979) The Mirror Crack'd (1980) I Have Been Very Pleased (1987) (short subject) The Children (1990) Liebestraum (1991) She has always been one of my favorite actresses and I think she's one of the most underrated and overlooked actresses of her generation. Kim Novak was a unique phenomenon. As the last of the "manufactured" screen goddesses and Columbia's answer to Marilyn Monroe, Kim had a more refined sex appeal than the other blond goddesses of the 1950's. She radiated a kind of mystery that harked back to the days of Garbo and Dietrich. Onscreen Kim Novak seems distant, enigmatic, thoughtful and somehow sad. She has been referred to as the reluctant goddess, the melancholy blonde and the lavender blonde. The studio created the idea that lavender was Kim Novak's favorite color as part of her movie star image. However, I think the term Lavender Blonde fits Kim Novak - it sets her apart from the sunny Doris Day or the gilded Marilyn Monroe. Lavender is closer to blue - makes you think of Madeleine in Vertigo, lost in thought by the seashore.
Tags: kim novak actresses vertigo
1970sDid This Scare You Out Of The Water
For anyone who hasn't seen this film, Jaws is a 1975 thriller directed by Steven Spielberg, based on Peter Benchley's best-selling novel inspired by the Jersey Shore shark attacks of 1916. Jaws bears similarities to several literary and artistic works, most notably Moby-Dick by Herman Melville. The character of Quint strongly resembles Captain Ahab, the obsessed captain of the Pequod who devotes his life to hunting a sperm whale. Quint's monologue reveals his similar vendetta against sharks, and even his boat, the Orca, is named after the only natural enemy of sharks. A direct reference to these similarities may be found in the original screenplay, which introduced Quint by showing him watching the film version of Moby-Dick. His laughter throughout made people get up and leave the theater (Wesley Strick's screenplay for Cape Fear featured a similar scene). However, the scene from Moby-Dick could not be licensed from Gregory Peck, the owner of the rights. The final scenes of the film, in which the men chase the shark and try to harpoon it with flotation barrels, parallel the chase for Moby-Dick in the novel. We have this in our library and watch it usually once a month. There's something about this film that sticks in my memory, and no, I never went back into the water.
Tags: jaws peter bvenchley steven speilberg films 1975
1970sJohnny Carson Confronts Don Rickles
Despite not being particularly popular, this series is often remembered for an incident that occurred on The Tonight Show Starring Johnny Carson. During production of the series, Rickles appeared on Tonight Show with guest host Bob Newhart. While poking fun at Newhart, in faux-anger, Rickles slammed the cigarette box which Johnny Carson kept on his desk and broke it. When Carson returned to the show and discovered this, he took a camera crew to the studio next door where Sharkey was being taped. Carson disrupted the taping in order to tease Rickles about it, to the delight of the studio audiences of both shows. Carson also teased Harrison Page by speaking to him in an exaggerated AAVE accent. This incident was often replayed in Tonight Show retrospectives and was considered a highlight of the 1970s era of the show.
Tags: Johnny Carson Confronts Don Rickles
1980sShark Attack
British Commercial Funny
Tags: Funny
2000sEvel Knievel Dies 11 30 07
Evel Knievel, the red-white-and-blue-spangled motorcycle daredevil whose jumps over crazy obstacles including Greyhound buses, live sharks and Idaho's Snake River Canyon made him an international icon in the 1970s, died today. He was 69. His death was confirmed by his granddaughter, Krysten Knievel. He had been in failing health for years, suffering from diabetes and pulmonary fibrosis, an incurable condition that scarred his lungs. In 1999 he had undergone a liver transplant after nearly dying of hepatitis C, likely contracted through a blood transfusion after one of his bone-shattering spills.
Tags: evel knievel daredevil motorcyclists
2000sOlivia Newton John Hark The Herald Angels Sing
Tags: Olivia Newton John Hark The Herald Angels Sing
Added: 25th December 2007
2000sKodak Ad
We can all remember those Kodak Moment ads? Well here's a reasonably new one that harks back to those golden days, then blows them out of the water.
Tags: Kodak Ad Boo Yah
Added: 2nd September 2008
Comics On AgingThen And Now- Erin Murphy- Tabitha On Bewitched
The topless photo of Erin Murphy on the internet isn't what you think. Erin began her career while still in diapers. Discovered by an agent, as her mother pushed her stroller in Los Angeles, Erin got her first job, playing a boy in a commercial for Folgers Coffee, at eleven months. Her next job was a detergent commercial with future President Ronald Reagan. Right before her second birthday, ABC came calling, and Erin was cast as little witch Tabitha Stephens on the top ten sitcom, Bewitched. Millions of fans around the world tuned in to see if Tabitha had inherited magical powers from her mother Samantha. They delighted in Erin's antics as she turned bullies into bulldogs and bullfrogs, played piano like a maestro and skated like Dorothy Hamill. After eight seasons, 23 Emmy nominations, and 254 episodes, Bewitched gracefully ended without cancellation. Despite the fact that Bewitched was filmed in the 60's and 70's, the popularity of the show endures. Entertainment Weekly recently named Bewitched one of the "100 Greatest TV Shows of All Time" and for the 50th Anniversary of TV Guide. Immediately following Bewitched, Erin turned down a part on The Waltons to go to Girl Scout camp, but she didn't lose her love for the business. During her teens, Erin modeled and did numerous commercials. Today, she is 44 and has worked as a casting director, a makeup artist, a fashion stylist, an acting teacher, a motivational speaker. With her engaging personality, sense of humor and ability to appeal to audiences as diverse as Nickelodeon and Howard Stern, Erin is a popular celebrity host. She's been featured on numerous programs, look for her on as the host of the Ab Shark infomercial for Thane & the Bun Shaper infomercial for Emson!
Tags: Then and Now- Erin Murphy- Tabitha on Bewitched
Pages: [1] 2 of 2 | Random | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,128 |
\subsection{Procedure 1: Tier 1 Auction}
In the procedure, the relay SUE $r_i$ will conduct the auction virtually and decide winners. First, each SUE obtains the characteristics of computation abilities from SCBs, such as the number of available CPU cycles, remained energy, and geological information. These properties will be sent to MUEs with the help of SUE relays aiming to assist the decision made by MUEs. The SUE relay will receive the three-dimension bids for computation services for its MUEs which is demoted by $\{b_i^{j}(k),v_i^{j}(k),d_i^{j}(k)\}$. Let $OPT(b/d)$ be the unit budget of the optimal single-price auction denoted by
\begin{equation}\label{eq:bd}
OPT(b/d)=\max_{1\le i \le |b|} i\frac{b_i}{d_i},
\end{equation}\\
where $|b|$ denotes the length of the array, $b_i$ denotes the $i$th budget and $d_i$ denotes the $i$th demand.
In this stage, the designed algorithm should calculate the budget vector $F_i(k)$ for SCB $k$. We compute the budget for each SUE based on the random sampling profit extraction auction \cite{fiat2002competitive} and inspired by the work in \cite{goldberg2001competitive}, we partition the MUE set $S_i$ into two sets, $S_i^{1}$ and $S_i^{2}$ uniformly for sampling purpose. Then SUE $i$ computes $R^{1}=OPT(b^1/d^1)$ and $R^{2}=OPT(b^2/d^2)$. Depending on the values of $R^1$ and $R^2$, the budget of MUE is extracted from both vectors. The detail of the algorithm is shown in Algorithm \ref{alg:comptbgt} and \ref{alg:ph1}.
\begin{algorithm}[h]
\begin{algorithmic}[1]\caption{ComptBgt $(b/d,R,(v_i^{j}(k))_{j=1}^{n_i})$}\label{alg:comptbgt}
\REQUIRE{Sorted vector of b/d, potential budget R and valuation vector $(v_i^{j}(k))_{j=1}^{n_i}$}
\ENSURE{Budget with given valuation}
\STATE{Search for the maximum $j$ in $b/d$ such that $jb_j/d_j \ge R$}
\STATE{$p_c\leftarrow \frac{R}{j}$}
\STATE{$S_i^{w}(k)\leftarrow \emptyset$}
\STATE{$F_i(k)\leftarrow \emptyset$}
\FOR{$j\leftarrow 1$ to $n_i$}
\STATE{$p_i^{j}(k)\leftarrow p_c\cdot d_i^{j}(k)$}
\IF{$p_i^{j}(k)<b_i^{j}(k)$ and $p_i^{j}(k)<v_i^{j}(k)$}
\STATE{$S_i^w(k)\leftarrow S_i^{w}(k) \cup s_i^{j}$}
\STATE{$F_i(k)\leftarrow F_i(k)+p_i^{j}(k)$}
\ENDIF
\ENDFOR
\STATE{return $F_i(k)$}
\end{algorithmic}
\end{algorithm}
\begin{algorithm}[h]
\begin{algorithmic}[1]\caption{Phase I of TARCO for SUE $r_i$}\label{alg:ph1}
\FOR{$k\leftarrow 1$ to $K$}
\STATE{Let $b/d$ denote the sorted aray of $(b_i^{j}(k)/d_i^{j}(k))$ in non-increasing order}
\STATE{Divide $b/d$ uniformly at random into two arrays $b^1/d^1$ and $b^2/d^2$}
\STATE{$R^1 \leftarrow OPT(b^1/d^1), R^2 \leftarrow OPT(b^2/d^2)$}
\IF{$R^1<R^2$}
\STATE{$F_i(k)\leftarrow$ ComptBgt($b^2/d^2,R^1,(v_i^{j}(k))_{j=1}^{n_i}$)}
\ELSE
\IF{$R^1>R^2$}
\STATE{$F_i(k)\leftarrow$ ComptBgt($b^1/d^1,R^2,(v_i^{j}(k))_{j=1}^{n_i}$)}
\ELSE
\STATE{$F_i(k)\leftarrow$ [ComptBgt($b^2/d^2,R^1,(v_i^{j}(k))_{j=1}^{n_i}$)$+$\\ComptBgt($b^1/d^1,R^2,(v_i^{j}(k))_{j=1}^{n_i}$)]/2}
\ENDIF
\ENDIF
\ENDFOR
\end{algorithmic}
\end{algorithm}
From the view of relay $r_i$, $s_i^{j}$ can be regarded as the buyer with $d_i^{j}(k)$ computation resource to buy on budget $b_i^{j}(k)$. According to Algorithm \ref{alg:comptbgt}, the clearing price of $s_i^{j}$ for the $k$th SCB should not be greater than the unit budget $b_i^{j}(k)/d_i^{j}(k)$. Note that the value $R$ is extracted from smaller value group in the partition procedure of Algorithm \ref{alg:ph1} to ensure truthfulness. The decision process for winner set $S_i^{j}(k)$ and the gathering of $F_i(k)$ is regarded as the start for $r_i$ to bid SCB $k$ in the second phase, \ie phase II. The winners in $S_i(k)$ will get the desired CPU cycles if and only if SUE $r_i$ wins SCB $e_k$ in phase II.
To illustrate how Algorithm \ref{alg:ph1} works, we propose a simple example as follows. There are $5$ MUEs with their bids for SCB $e_k$ as $(30,4,35)$, $(20,3,26)$, $(18,6,9)$, $(13,2,16)$, $(8,3,14)$, where in each pair the first number is the bid, the second item is number of demand and the third item is the valuation, hence $b/d=\{7.5, 6.67, 3, 6.5, 2.67\}$. Assume that $b^1/d^1=\{7.5,6.5,2.67\}$, $b^2/d^2=\{6.67,3\}$ and we have $R^{1}=13$, $R^{2}=6.67$. Since $R^{2}<R^{1}$, we then extract $R^{2}$ from $b^2/d^2$. The mapping between the sorted value $b/d$ and valuation is illustrated in Fig. \ref{fig:example}. Obviously, it is shown that in Fig. \ref{fig:example}, for MUEs in group $i$, the clearing price $p_c^{i}(k)$ for SCB $k$, which is $p_c^{i}(k)=6.67/3=2.223$. Since the value $p_i^{1}(k)=p_c^{i}(k)\times d_{i}^{1}(k)=2.223\times 4=8.892<b_i^{1}(k)=30$ and $p_i^{1}(k)<v_i^{1}(k)=35$. Therefore, $s_i^{1}$ is added to the winner set $S_i^{w}(k)$ for the $k$th SCB. Similarly, $s_i^{2}$, $s_i^{4}$, $s_i^{5}$ are all winners. Therefore, the total budget of $r_i$ obtained from group $S_i$ for SCB $e_k$ is $26.676$.
\begin{figure}[h]
\includegraphics[width=3.5in]{example.eps}
\caption{Example of Algorithm \ref{alg:ph1}, where the dashed lines belong to $b^2/d^2$ and the remaining lines belong to $b^1/d^1$}\label{fig:example}
\end{figure}
\subsection{Procedure 2: Tier 2 Auction}
After the previous procedure, \ie phase I of auction which is conducted between MUEs and relay SUEs, the budget for SUE $r_i$ bids for SCB $e_k$ can be obtained and denoted as $F_i(k)$. $F_i(k)$ will be gathered when the SUE $r_i$ wins SCB $e_k$. In procedure 2 of the auction, there are multiple sellers and multiple buyer with heterogeneous items to bid since each SUE has different budgets for the corresponding SCBs. In this research, VCG auction is not adopted because of the high computational cost and the failure to ensure budget balance property. Meanwhile, the McAfee auction cannot be utilized since it only suits for the scenario where there are homogeneous goods to trade \cite{yang2011truthful}. Therefore, new auction mechanism should be invented in this procedure. Here, we propose a Random Matching based Efficient Allocation algorithm RMEA to trade the computation resource between SUEs and SCBs.
The detail of RMEA is shown in Algorithm \ref{algo:ph2}. The SCB assigns CPU cycles to each SUE relay node in a greedy manner. For each SUE relay $r_i$, the auctioneer try to maximize $B_i^{k}-A_k$. Note that the auctioneer always choose the minimum index of $k$ when there are multiple choices. The procedure resembles fixed price auction, which is proved to be truthful \cite{goldberg2001competitive}. RMEA charges each winning SUE $r_i$ the amount of $P_i$ and pays each winning SCB $e_k$ the payment $P_i$.
\begin{algorithm}[ht]
\begin{algorithmic}[1]\caption{Phase II of TARCO, the RMEA algorithm}\label{algo:ph2}
\REQUIRE{$B_i^{k}$, for $\forall 1\le i \le N$ and $1\le k \le M$}
\ENSURE{${\mathcal{R}}_w$, ${\mathcal{E}}_w$, $P_i$}
\STATE{$\mathcal{E}\leftarrow \{e_1,e_2,\cdots, e_M\}$, $\mathcal{E}_w \leftarrow \emptyset$, $\mathcal{R}_w \leftarrow \emptyset$}
\FOR{$i\leftarrow 1$ to $N$}
\STATE{$e_k \leftarrow \argmax_{e_k \in \mathcal{E}}(B_i^{k}-A_k)$}
\IF{$B_i^{k}-A_{k}\ge 0$}
\STATE{$\mathcal{R}_w \leftarrow \mathcal{R}_w \cup \{r_i\}$}
\STATE{$\mathcal{E}_w \leftarrow \mathcal{E}_w \cup \{e_k\}$}
\STATE{$P_i \leftarrow B_i^{k}$}
\STATE{$\mathcal{E}\leftarrow\mathcal{E}\setminus \{e_k\}$}
\ENDIF
\ENDFOR
\end{algorithmic}
\end{algorithm}
\subsection{Charge for MUEs}\label{subsec:charge}
As mentioned in previous subsection, the phase I of TARCO is conducted virtually by each SUE node and the auction results will not be executed unless the SUE wins the phase II auction. Next, we give a simple example to illustrate the charging procedure.
Assume there are $3$ SCBs and $3$ SUEs. At the end of phase I, we may have $F_1(k)=3$, $F_2(k)=5$, $F_3(k)=7$, for $\forall k\in [1,3]$. In phase II, $B_1^{k}=2$, $B_2^{k}=5$, $B_3^{k}=4$ and accordingly the ask price of SCBs are $A_1=1$, $A_2=3$, $A_3=5$. After the execution of algorithm
\ref{algo:ph2}, the winning SUE relays are $r_1$ and $r_2$, accrodingly, the winning SCBs are $e_1$ and $e_2$. Therefore, the utilities of SUEs are $U_1=F_1(k)-B_1^{k}=3-2=1$, $U_2=F_2(k)-B_2^{k}=5-5=0$ and the utilities of SCBs are $U^{1}=P_1-A_1=2-1=1$, $U^{2}=P_2-A_2=5-3=2$. Note that, the bid value of $B_i^k$ may be lower than $F_i(k)$.
\subsection{Non-incentive based schemes}
Some works study D2D based user association in HetNet \cite{xiao2016energy} \cite{liu2015device}. Xiao et al. \cite{xiao2016energy} proposed an energy efficient mode selection and user association scheme. The MCB acts as a central controller to determine which one of SCB and MCB that the mobile device should be attached to. Meanwhile, D2D relay mode and direct communication mode selection is also considered. Liu et al. \cite{liu2015device} adopted a D2D two-hop relay to help mobile users get access to neighbouring base stations. In this paper, tasks on MUEs in the two-tier HetNet are offloaded to SCBs instead of the far away MCB to conquer the high channel fading and low signal obstacles of MUEs.
Rahman et al. \cite{ur2015analysis} considered the downlink coverage extension from the MCB to MUEs via the D2D cooperation between SUEs and MUEs in a single macro cell. In this paper, we focus on the uplink transmission by offloading the computation task from MUEs to SCBs. The most recent work by Cao et al. \cite{cao2016cellular} designed a hybrid traffic offloading scheme for HetNets where mobile users can get access to SCBs with the help of mobile relays via D2D communication. Their objective is to maximize the number of mobile users admitted into the whole network, through MCB or SCBs. The problem is formulated as an integer linear programming and solved by dynamic programming. Different from \cite{cao2016cellular}, this paper mainly focuses on MUE's tasks offloading to the SCB with help of SUE relays. The benefits of both SUEs and SCBs can be ensured by the Tarco scheme. In \cite{kawamoto2014efficient}, a heuristic method was proposed to detour congested MCB traffic to uncongested SCBs with the help of D2D relay nodes. However, only skeletal numerical analysis is given by \cite{kawamoto2014efficient}, which cannot be directly deployed. Thus we carry out with a distributed implementation.
\subsection{Incentive based mechanisms}
Recently, the incentive based schemes have been proposed. Hua et al. \cite{hua2013truthful} proposed a truthful auction framework for femtocell access between MUEs and femtocell base stations. A dynamic game is designed by Zhu et al. \cite{zhu2014pricing} to offload traffic from the MCB to SCB service providers. However, both in \cite{hua2013truthful} and \cite{zhu2014pricing}, relay is not used.
LeAnh et al. \cite{leanh2015joint} came out with a Stackelberg game based offloading mechanism by transferring part of MUE's data to the SCB via SUE relay nodes. The MUE is the leader while candidate SUE relays are followers. The optimal power allocation and relay selection is conducted via leader-follower pricing. Later, Ho et al. \cite{ho2016coordinated} proposed a two-stage Stackelberg game for SCBs to admit MCB's traffic from the perspective of network fixed infrastructure, however, relay influence is not considered. Meanwhile, they do not consider SCB's heterogeneity.
Methods proposed by other literatures cannot be applied in this paper. Yang et al. \cite{yang2014truthful} studied the spectrum group auction in cognitive radio networks. Later, Wang et al. \cite{wang2015truthful} came out with a scheme to allocate both channels and cooperative relay nodes for cooperative cognitive radio networks with two-stage group auction. However, in their work, the ask price at each spectrum owner is same for different buyers. In computation offloading, the tasks are different and for each SCB, the ask price may not be constant for all buyers due to different location and channel fading conditions. In mobile cloud computing, Jin et al. \cite{jin2016auction} carefully designed an incentive-compatible auction scheme between cloudlets and mobile users. The cloudlets are edge servers to offload traffic of remote cloud. Similar to \cite{jin2016auction}, the SCBs can be regarded as cloudlets to admit computation tasks sent from mobile users.
Based on the observations, to offload the computation tasks of MUEs with relay SUEs and motivate both SUEs and SCBs should be properly handled. New schemes should deal with heterogeneous computation offloading tasks as well as SCB's heterogeneity.
\subsection{Simulation environment}
We consider a heterogeneous network structure shown in Fig. \ref{fig:network}, whose nodes are randomly distributed in a $100\times100$ area. The parameters for cooperative communications are adopted from \cite{chen2016two}.
By default, we set $M=10$, $N=10$. We vary $n_i$ from $10$ to $100$ with an increment of $10$ for any $i\in \{1,2,\cdots,N\}$. We assume that MUE $s_i^{j}$'s budget $b_i^{j}(k)$ is randomly distributed in $(0,v_i^{j})$ , where $v_i^{j}$ is computed as described in Section \ref{subsec:sysmodel}. In phase II of TARCO, the ask price $A_k$ is randomly distributed in $(0,1]$. The results are averaged for 100 repetitions.
To the best of authors' knowledge, this is the first incentive scheme proposed for cooperative computation offloading in heterogeneous network and there are no existing auction schemes to compare with. Instead, in this paper, we compare TARCO with the following two schemes, \ie the upper bound and random schemes. To derive the upper bound, we choose the maximum $p_i^j(k)$ as $b_i^j(k)$ to replace that of Line $9$ in Algorithm \ref{alg:comptbgt}. Note that through this change, we do not change the economic properties of TARCO. For the random scheme, it replace the phase I of TARCO by fistly choosing a MUE $s_i^{t}$, if the valuation of another SU $s_i^{j}$ is larger than $s_i^{t}$, where $j\ne t$ and $j\in [1,n_i]$, SUE will allocate the computation resource to it. Then we examine the performance of utility enhanced sceme VITA with the above mentioned schemes as well as the \textbf{m}ax \textbf{w}eighted matching based winner \textbf{d}etermination scheme (MWD).
\subsection{Simulation analysis}
Firstly, we investigate the running time of TARCO with different network settings shown in Fig. \ref{fig:tarcort}. In all simulations, the number of SUEs is set as same as that of SCBs' number, that is $N=M$. From Fig. \ref{fig:tarcort}, we observe that the running time is no more than $25$s when $n_i$ is lower than $80$. When $n_i$ is constant, the running time grows fast with the increasing of the SCB's number $M$ and meanwhile, when $M$ stays unchaged, the running time increases when $n_i$ becomes higher.
\begin{figure}[ht]
\centering
\includegraphics[width=4.5in]{RMEARunningtime.eps}
\caption{TARCO's running time with number of SUEs and number of SCBs (See digital or online version for color)}\label{fig:tarcort}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=4.5in]{rtvitatarcoscb.eps}
\caption{Running time comparisons between TARCO and VITA with number of SCBs }\label{fig:rtTVnumM}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=4.5in]{rtvitatarconi.eps}
\caption{Running time comparisons between TARCO and VITA with number of SUEs }\label{fig:rtTVnumni}
\end{figure}
Next, we compare the running time performance between TARCO and VITA with different number of SCBs and SUEs respectively. The results are shown in Fig. \ref{fig:rtTVnumM} and Fig. \ref{fig:rtTVnumni}. We can see the running time performance of VITA is as similar as that of TARCO. In Fig. \ref{fig:rtTVnumM}, we set the number of SUEs as $n_i=20$ while we set the number of SCBs as $M=4$. It is obvious that when network size becomes larger, the running time of VITA is slightly higher than TARCO on average. That's because VITA tries to maximize the total utility which consumes much more time than TARCO.
\begin{figure}[t]
\centering
\includegraphics[width=4.5in]{UMUEsvsnumMUEs.eps}
\caption{Average Utility of MUEs with the number of MUEs }\label{fig:UMUEsvsnumMUEs}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=4.5in]{USUEsvsnumMUEs.eps}
\caption{Average Utility of SUEs with the number of MUEs }\label{fig:USUEsvsnumMUEs}
\end{figure}
In the third experiment, we examine the utilities of network users for proposed schemes with $M=5$ and we vary $n_i$ from $50$ to $100$. As shown in Fig. \ref{fig:UMUEsvsnumMUEs}, we compre the average utility of MUEs with the increasing numnber of MUEs. As shown in Fig. \ref{fig:UMUEsvsnumMUEs}, with the increasing number of MUEs, the average utility of MUEs increases accordingly for MWD and VITA algorithms. For TARCO and OPTB, the average utility of MUEs varies around $2.0$ and $1.0$ respectively. Of all the algorithms, the random algorithm RND achieves the lowest utility in all situations. For MWD and VITA, the utility of MUEs grows fast when the number of MUEs is below $70$. That's because the competition for SUEs is not fierce since there are abundant resources. However, the utility gain decreases when the number of MUEs is above $70$ for MWD and VITA. That's because the CPU computation cycles obtained has reached to the limit and they cannot improve the utilities any longer. The utility of MUEs decreases with the increasing number of MUEs for the RND algorithm. That's because the RND algorithm tends to select inefficient MUEs. On average, OPTB achieves $46.90\%$ higher utility of MUEs than RND algorithm while TARCO is $104.90\%$ better than RND algorithm. What's more, VITA and MWD algorithms are the best two algorithms to enhance the utility of MUEs. VITA is $28.75\%$ better than TARCO and MWD outperforms TARCO for about $17.06\%$. That's because the two algorithms are based on max-weighted matching which greatly reduces the cost for MUEs.
Fig. \ref{fig:USUEsvsnumMUEs} shows the relationship between the average utility of SUEs and the number of MUEs. Generally, with the increasing number of MUEs, the average utility of SUEs grows accordingly. Different from Fig. \ref{fig:UMUEsvsnumMUEs}, the OPTB and MWD algorithms are among the best two algorithms. With the increasing number of MUEs, the utility gains of SUEs decrease for VITA, TARCO and RND algorithms when the number of MUEs is greater than $80$. For OPTB, it acquires the maximal $F_i(i)$ of all algorithms because $p_i^j(k)=b_i^j(k)$ for OPTB while for the other algorithms, $P_i^j(k)<b_i^j(k)$. Even though the utility gains of SUEs do not increase, the valuation of MUE $s_i^{j}$ is defined as (\ref{eq:vijkdef}), the SUE relay may select the MUEs with larger valuation and low capacity for direct communication, which result in the increase of utility of SUEs. On average, OPTB is about $317.65\%$ better than RND algorithm and TARCO achieves about $33.90\%$ utility gain than the RND algorithm on the utility of SUEs. Although VITA achieves almost the same utility of SUEs as TARCO, it outperforms TARCO by about $5.11\%$ whereas MWD outperforms TARCO by about $28.94\%$.
\begin{figure}[t]
\centering
\includegraphics[width=4.5in]{TWvsnumMUEs.eps}
\caption{Social Welfare with the number of MUEs }\label{fig:TWvsnumMUEs}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=4.5in]{USCBsvsnumMUEs.eps}
\caption{Average Utility of SCBs with the number of MUEs }\label{fig:USCBsvsnumMUEs}
\end{figure}
Fig. \ref{fig:TWvsnumMUEs} demonstrate almost the same trends as that of Fig. \ref{fig:USUEsvsnumMUEs}. Although OPTB achieves the best total social welfare, it cannot be achieved and it cannot fully guarantee the economic properties. Except for OPTB, MWD and VITA are among the best two algorithms that obtain the maximal utility. That's because the two algorithms try to maximize the sum utility of SCBs and SUEs, \ie
\begin{equation}
\sum_{i=1}^{N}\sum_{k=1}^{M}(F_i(k)-A_k),
\end{equation}
based on max weighted matching. In conclusion, the OPTB algorithm achieves higher social utility than RND algorithm for about $188.04\%$ and TARCO is about $12.05\%$ better than RND. Compared with RND, MWD and VITA outperform RND by $63.14\%$ and $28.01\%$ respectively.
Finally, Fig. \ref{fig:USCBsvsnumMUEs} depicts the average utility of SCBs with the varying number of MUEs. It is obvious that the three algorithms, \ie TARCO, MWD and RND, produce similar average utility of SCBs. That's because under the simulation setting, the budget acquired by the SUE from MUEs is close to $A_k$ for the three algorithms. In gerneraly, OPTB can ensure a higher utility of SCBs, which is $143.67\%$ higher than RND algorithm whereas VITA is about $12.42\%$ better than RND.
From the above experiments, we can see that VITA suits for the situation where all network participants' utility should be maximized at the same time. When the SCB is energy abundant and the cost can be neglected, TARCO, MWD and VITA demonstrate good qualities to ensure higher social welfare than the RND algorithm. In real situations, the SCB is a fixed network infrastructure, and is always full of computation resources as well as energy abundant. Therefore, TARCO, MWD and VITA can be deployed to motivate SUEs leasing resources to assist the computation offloading of MUEs.
\subsection{Main Idea of TARCO Scheme}
The main idea of our proposed TARCO scheme is to provide incentive and utilize D2D communications to assist the computation offloading of MUEs to local SCBs, with the aim to maximize utilities of both SCBs and MUEs. Take Fig. \ref{fig:network} as an example, when there are some MUEs in the high channel fading area or low signal region, they cannot directly to offload their computation tasks to neighbour SCBs without the help of SUE relays. The proposed TARCO scheme allows MUEs to access the SCBs by relaying the computation data via SUE relays in the coverage of corresponding SCBs. Intuitively, TARCO can improve the system performance by reducing the traffic flowed to MCB and reduce the MUE's energy consumption with a lower transmission power. It should be noted that for MUEs with high mobility and moving constantly, it may get access to MCB to avoid frequent handover, which is out of the scope of this paper.
\begin{figure}[ht]
\centering
\includegraphics[width=3.5in]{network.eps}
\caption{Network Model}\label{fig:network}
\end{figure}
\subsection{System Model}\label{subsec:sysmodel}
\begin{table}[t]
\centering
\small
\caption{Notations for system model}\label{tb:nt}
\begin{tabular}{l|p{6.5cm}}
\hline
Notations & Meaning \\ \hline
$s_i^{j}$, $S_i$ & The $j$th MUE in the $i$th SUE group, the $i$th group \\
$N$, $n_i$ & Number of SUEs and MUEs in the $i$th SUE group \\
$b_i^j(k)$, $v_i^j(k)$ & True bid and valuation of $s_i^{j}$ for the $k$th SCB \\
$d_i^j(k)$ & Demand of $s_i^{j}$ for the $k$th SCB \\
$\bar{b}_i^j(k)$, $\bar{v}_i^j(k)$ & Bid and valuation of $s_i^{j}$ for the $k$th SCB \\
$p_i^j(k)$, $P_i$ & $s_i^j(k)$'s and the $i$th SUE's payment for the $k$th SCB \\
$B_i^k$ & The $i$th SUE's bid for the $k$th SCB \\
$F_i(k)$ & The total payment of the $i$th SUE for the $k$th SCB \\
$A_k$ & Ask or reserve price of the $k$th SCB \\
$p_c$ & The clearing price \\
$u_i^j$ & The utility of MUE $s_i^j$ \\
$U_i$ & The utility of the $i$th SUE $r_i$ \\
$U_k$ & The utility of the $k$th SCB $e_k$ \\
$\mathcal{E}_w$, $\mathcal{R}_w$ & Winning set of SCBs, Winning set of SUEs \\
$S_i^w$ & Winning set of MUEs for SUE $r_i$ \\
\hline
\end{tabular}
\end{table}
In our scenario, we assume all nodes stay static in a given auction period. In the network shown in Fig. \ref{fig:network}, there is one MCB and $M$ SCBs in the coverage of the MCB and neighbouring SCBs have orthogonal frequency bands \cite{liu2016energy}. Meanwhile, MUEs are heterogeneous and need to perform different computation tasks. Each offloading task contains a QoS requirement information such as bandwidth and CPU cycles. Each MUE may have its own preference for the SCB based on its geological position, channel condition and distance from the SCB. Since MUEs within the same location may have similar relationships \cite{semiari2015context} and sense of channel conditions, they may get-together and form a communication social group. In total, there are $N$ groups of MUEs. By adopting interference mitigation technologies \cite{khawer2016usicic}, interferences between adjacent groups can be properly handled. Thus in this model, we do not consider the interference between small cells. Based on computation tasks, for the benefit of simplicity, we assume each MUE may require different number of CPU cycles. In the $i$th social group $S_i$, where $i\in [1,N]$, there are $n_i$ MUEs and $S_i=\{s_{i}^{1},s_{i}^{2},\cdots,s_{i}^{n_i}\}$. We use $\mathcal{E}=\{e_1,e_2,\cdots,e_M\}$ to denote the set of SCBs, i.e. the edge servers and $\mathcal{R}=\{r_1,r_2,\cdots,r_N\}$ to denote the set of SUEs. The $k$th SCB is denoted by $e_k$, $k\in [1,M]$. For each SCB $e_k$, each MUE $s_{i}^{j}$ has a CPU cycle demand $d_{i}^{j}(k)$, its valuation $v_{i}^{j}(k)$ and the budget $b_{i}^{j}(k)$ for the maximum payment. For the benefit to express the preference of MUE $s_i^{j}$ towards $e_k$, we define
\begin{equation}\label{eq:vijkdef}
v_{i}^{j}(k)=\max\{\frac{C_R(s_{i}^{j},r_{i},e_k)}{C_D(s_{i}^{j},e_k)},0\}.
\end{equation}
It should be noted that the CPU cycle demand may be different for different SCBs because of the location of SCBs and the traffic burden on them.
We design a two-stage hierarchical auction for the computation offloading. TARCO consists of two single round sealed bid auctions, they are tier I auction and tier II auction accordingly. The tier I auction is between each social group $S_i$ and SUE relay $r_i$. Each SUE relay $r_i$ is in charge of all the members in $S_i$. The tier II auction is between SUE $r_i$ and SCB $e_k$. Let $B_{i}^{k}$ be the $r_i$'s bid for SCB $e_k$, $i\in [1,N], k\in [1,M]$. Then the ask price of $e_k$ is $A_k$, which is the reserve price. We assume each social group can be served by one SCB at most because serving for multiple social groups will cause longer delays. Meanwhile, we also assume, each members inside the group will choose only one SCB.
In tier I aucton, for SCB $e_k$, each member of $S_i$ submits the bid $\beta_{i}^{j}(k)=\{{b}_{i}^{j}(k),{v}_{i}^{j}(k), d_{i}^{j}(k)\}$ to $r_i$. Note that $s_i^{j}$ may not be honest and report its true bid, therefore we have $\bar{\beta}_{i}^{j}(k)=\{\bar{b}_{i}^{j}(k),\bar{v}_{i}^{j}(k), d_{i}^{j}(k)\}$ if it may bring higher utility. For the SUE $r_i$, after gathering the group member's bids, the SUE $r_i$ will determine winning MUEs in $S_i(k)$, which is denoted by $S_i^{w}(k)$ and $S_i^{w}\subseteq S_i$. If $s_i^{j} \in S_i^{w}(k)$, and $e_k$ is selected by $r_i$, then $s_i^{j}$ will be charged $p_i^{j}(k)$. For $r_i$, the gathered bid is $F_i(k)$. In tier II, $r_i$ submits its bid for SCB $e_k$ as $B_i^{k}$, where $i\in [1,N], k\in [1,M]$. A double auction will be conducted to determine how many CPU cycles to allocate to relay SUEs and the payments for winners. If the SUE fails to obtain resources from the SCB, no transactions will happen and the utility of MUE members in the group will be zero.
Given the above settings, we denote $\mathcal{E}_w \subseteq \mathcal{E}$ as winning set of SCBs and $\mathcal{R}_w \subseteq \mathcal{R}$ as the winning relay set in tier II auction. Let $P_i$ be the price the wining SUE $r_i$ needs to pay for the SCB. If SUE $r_i$ wins then the payment of $r_i$ should not be greater than its gathered bid $F_i(e_i^{w})$, where $e_{i}^{w}\in \{0,1,2,\cdots,M\}$.
\subsection{Problem Formulation}
Let $u_{i}^{j}$ denote the utility of MUE $s_{i}^{j}$, for each MUE $s_{i}^{j}\in S_{i}^{w}$, SUE $r_i$ computes the payment $p_{i}^{j}$. Note that the payment for the winning MUE $s_i^{j}$ should not be higher than the true budget $b_{i}^{j}$. Hence the utility of MUE $s_i^{j}$ is
\begin{equation}\label{eq:uij}
u_i^{j}=
\begin{cases}
v_i^{j}(k)-p_i^{j}(k), &\text{if $s_i^{j} \in S_i^{w}$ and $p_i^{j}(k)\le b_{i}^{j}(k)$} \\
0, &\text{otherwise}.\\
\end{cases}
\end{equation}
Where we have $p_i^{j}(k)$, which is defined as \\
\begin{equation}\label{eq:pijk}
p_i^{j}(k)=p_c^{i}(k) d_i^{j}(k), \text{$k=e_i^{w}$ if and only if $s_i^{j} \in S_i^{w}$},\\
\end{equation}
where $p_c^{i}(k)$ is the clearing price. Accordingly, the utility of SUE $r_i$ is defined as\\
\begin{equation}\label{eq:Ui}
U_{i}=
\begin{cases}
F_i(k)-P_i, &\text{if $r_i \in \mathcal{R}_w$, $e_k \in \mathcal{E}_w$}\\
0, &\text{otherwise}.
\end{cases}
\end{equation}
Further more, the utility $U_k$ of SCB $e_k$ should not be negative, which is \\
\begin{equation}\label{eq:Uk}
U^k=
\begin{cases}
P_i-A_k, &\text{if $e_k \in \mathcal{E}_w$ and $r_i$ wins $e_k$} \\
0, & \text{otherwise}.
\end{cases}
\end{equation}
The first branch of (\ref{eq:Uk}) is the utility of $e_k$ when it wins the auction and gets enough payment from auctioneer in the transaction. The utility of $e_k$ should not be negative when it offloads computation tasks from MUEs.
\subsection{Economic Properties}\label{sec:subsececonoprop}
An auction will not be conducted until many economic properties are satisfied. In the following paragraphs, several critical economic properties of the auction are listed which TARCO would like to achieve.
\begin{definition}\label{def:truth}
(Truthful). An auction is truthful if any participant's utility is maximized by submitting its true valuation, regardless what others would like to behave. That is, no bidder can improve his utility by misreporting his bids.
\end{definition}
\begin{definition}\label{def:indivrat}
(Individual Rationality). The utility of each participant of the auction is non-negative. That is, $u_i^{j}$, $U_i$ and $U_k$ are non-negative in the TARCO auction scheme.
\end{definition}
\begin{definition}\label{def:budget}
(Budget Balance). An auction is budget balanced if total payment from buyers are no less than the sum paying paid to sellers. In TARCO scheme, this property is required in tier II auction to ensure the auctioneer a non-negative utility, \ie $\sum_{r_i\in R_w} P_i \le \sum_{e_k\in \mathcal{E}_w} P_k$.
\end{definition}
\begin{definition}\label{def:efficiency}
(Computational Efficiency). An auction is computational efficiency if the scheme can terminate in polynomial time in terms of the input.
\end{definition}
In this paper, TARCO is designed to achieve truthful, individual rationality, budget balance and computational efficiency. The mechanism is illustrated in detail in Section \ref{sec:auction} followed by proves in Section \ref{sec:analysis}.
\section{abstract}
\input{abstract.tex}
\begin{IEEEkeywords}
\emph{Auction, Computation Offloading, HetNet, incentive, Relay.}
\end{IEEEkeywords}
\section{Introduction}\label{sec:intro}
\input{into.tex}
\section{Related Work}\label{sec:relate}
\input{relate.tex}
\section{System Model and Problem Formulation}\label{sec:sysmodel}
\input{sysmodel.tex}
\section{Two-Stage Auction Mechanism}\label{sec:auction}
\input{auction.tex}
\section{Theoretical Analysis}\label{sec:analysis}
\input{analysis.tex}
\section{Improved Schemes VITA}\label{sec:improve}
\input{improve.tex}
\section{Performance Evaluation}\label{sec:simulation}
\input{simulation.tex}
\section{Conclusion}\label{sec:conclude}
\input{conclude.tex}
\bibliographystyle{IEEEtran}
| {
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Midtown KC Post Living here
KC criminal faces prison and murder charge after romance miscue
Aug 22nd, 2014 – by midtownkcposter1
Things went wrong for a Kansas City man after he hid his vehicle to cheat on his fiancé, at least that was his story.
A search of said vehicle led a federal jury on Thursday to convict Rashawn Long, 33, of illegally possessing firearms and a controlled substance.
After the federal conviction, Jackson County prosecutors also announced an unrelated murder charge against him for killing Kevin Jones last year in the 1800 block of East 77th Street.
According to a release from federal prosecutors:
On Oct. 26, 2013, a woman called police to her Kansas City home because a stranger had parked his Dodge Avenger in her back yard, banged on her door and left.
Officers called a tow truck and the resident found a note from Long addressed to another person, "thanking that person for letting him park the vehicle in her yard."
A few minutes later, Long ran down a hill yelling at officers. He said he knew the owner of the home and had parked there before.
"Long also told officers that he was trying to hide his car from his fiancé while he visited another woman who lived down the block, and did not want anyone to see him."
Police arrested Long, who had two warrants out for him.
A search of the Dodge found a stun gun, a can of pepper spray, a digital scale with residue and a digital video camera. They also found a Coke can with a false compartment that contained Buphedrone, a controlled substance similar to meth.
It got worse.
When police saw the video in the camera they found shots of Long flashing a Glock pistol.
As a person with former felony convictions that include second degree murder, armed criminal action and drug trafficking, it is illegal for Long to have a gun. He can be sentenced to to up to 40 years in prison for the federal charges.
In the new Jackson County case, Long's DNA matched that on a hat left at the scene of the shooting death, according to court records.
Tags: crime
Man killed KC mother and 3-year-old daughter, police say | Midtown KC Post | {
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Q: Gapped sentences Reading a gapped sentence aloud, what should we say to denote the part which is actually a gap?
For example, Gillian decided it was time to turn over a new _______ and forget her past mistakes. I heard people say "...new hm-hm-hm and..." But is there anything better than that?
A: I would use the word "blank" and read you sentence aloud like this:
Gillian decided it was time to turn over a new blank and forget her past mistakes.
Here are two relevant definitions (M-W):
blank
2 a : an empty space (as on a paper)
5 : a dash substituting for an omitted word
| {
"redpajama_set_name": "RedPajamaStackExchange"
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Home > New York > Suffolk County
St. John The Baptist Diocesan High School
Top Rankings Overview Student Body Academics and Faculty Tuition and Acceptance Rate Sports Extracurriculars Frequently Asked Questions Related Schools School Reviews Edit School Profile
1170 Montauk Highway
West Islip, NY 11795
www.stjohnthebaptistdhs.net
St. John The Baptist Diocesan High School serves 1394 students in grades 9-12, is a member of the Middle States Association of Colleges and Secondary Schools.
The student:teacher of St. John The Baptist Diocesan High School is 16:1 and the school's religious affiliation is Catholic.
Top Ranked NY School
St. John The Baptist Diocesan High School ranks among the top 20% of private schools in New York for:
List of Courses Offered
Link to List of Courses
http://www.stjohnthebaptistdhs.net/www/drvcny_stjohnthebaptistdhs/site/hosting/Course%20Catalog%202009-2010.pdf
(View more info)
Tuition for the 2012-2013 school year is $8,495.00 ---- which includes lab fees, guidance fees, testing fees, and a school ID card. An additional class fee is collected at the beginning of every school year.
Badminton, Baseball, Basketball, Bowling, Cheering, Crew, Cross Country, Dance, Diving, Equestrian, Field Hockey, Football, Golf, Gymnastics, Ice Hockey, Lacrosse, Sailing, Soccer, Softball, Surf Team, Swimming, Tennis, Track and Field, Volleyball, Winter Track, Wrestling
http://www.stjohnthebaptistdhs.net/site_res_view_template.aspx?id=e61a53f4-4bcc-44b0-9de9-e3702ce02cc6
How much does St. John The Baptist Diocesan High School cost?
St. John The Baptist Diocesan High School's tuition is approximately $8,495 for private students.
What schools are St. John The Baptist Diocesan High School often compared to?
St. John The Baptist Diocesan High Schoolis often viewed alongside schools like St. Anthony's High School by visitors of our site.
What sports does St. John The Baptist Diocesan High School offer?
St. John The Baptist Diocesan High School offers 26 interscholastic sports: Badminton, Baseball, Basketball, Bowling, Cheering, Crew, Cross Country, Dance, Diving, Equestrian, Field Hockey, Football, Golf, Gymnastics, Ice Hockey, Lacrosse, Sailing, Soccer, Softball, Surf Team, Swimming, Tennis, Track and Field, Volleyball, Winter Track and Wrestling. St. John The Baptist Diocesan High School is ranked as one of the top 20% of private schools in New York for most sports offered.
What is St. John The Baptist Diocesan High School's ranking?
St. John The Baptist Diocesan High School ranks among the top 20% of private schools in New York for: Largest student body and Most sports offered.
When is the application deadline for St. John The Baptist Diocesan High School?
The application deadline for St. John The Baptist Diocesan High School is rolling (applications are reviewed as they are received year-round).
Popular comparisons: St. John The Baptist Diocesan High School vs. St. Anthony's High School
People that viewed St. John The Baptist Diocesan High School also viewed these schools: St. Anthony's High School, Academy Of St. Joseph, Holy Trinity Diocesan High School, Victory Christian Academy and The Stony Brook School.
The nearest high school to St. John The Baptist Diocesan High School is Ascent School For Individuals With Autism (4.6 miles away)
The nearest elementary school and preschool is Bridges Academy (The) (0.3 miles away)
St. Anthony's High School
Grades: 9-12 | 2,385 students 9.4 miles 275 Wolf Hill Rd
Academy Of St. Joseph
Grades: K-12 | 385 students 6 miles 1725 Brentwood Road Bldg 2
Holy Trinity Diocesan High School
Grades: 9-12 | 809 students 13 miles 98 Cherry Ln
Victory Christian Academy
(Church of God)
Grades: PK-12 | 70 students 18.1 miles 1343 Montauk Hwy
The Stony Brook School
Grades: 7-12 | 454 students 17.8 miles 1 Chapman Parkway
5.00 out of 5 (2 reviews)
5 2/12/2020
I am a graduate of the class of 2018 and I can honestly say that my 4 years spent as an SJB cougar were the best 4 years of my life. This school was my second home and being in my second year of college I still say that I wish I could have spent more time at St. John's. SJB had such a family feel that I never experienced. The friends I had made here are friends that I hope to keep lifelong. The quality of education I had also received here was also amazing thanks to all the faculty in this school. I had graduated on honor roll and was not only accepted to all the colleges I had applied to, but received scholarships to all of them as well. I truly recommend SJB to anyone who considered a Catholic high school education. SJB 24/7
- Posted by Student/Alumni - 2018 grad
It's not just a school but a community- School administartors know all the kids by name and they are very interactive with all the students whether it be for academics , sports clubs etc. Also has other sports teams that that were not listed. Alot of Cougar pride
- Posted by Parent - my3so
Endorse St. John The Baptist Diocesan High School. Endorsements should be a few sentences in length. Please include any comments on:
The average private school tuition in Suffolk County, NY is $16,455 for elementary schools and $21,283 for high schools (read more about average private school tuition across the country).
The average acceptance rate in Suffolk County, NY is 82% (read more about average acceptance rates across the country).
St John The Baptist Diocesan High School
St John The Baptist Diocesan High School (2020)
We provide school information and parenting resources to help millions of American families ...
WILLIAM J. WEINELL (2020)
He was a graduate of St. John the Baptist Diocesan High School in Brentwood and SUNY Oneonta ...
St. John the Baptist Diocesan High School Wins $25,000 Celebrate my Drive Grant for Teen Driver Safety Efforts (2015)
WEST ISLIP, NY – St. John the Baptist Diocesan High School is proud to announce that it has won a $25,000 award from the ...
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,143 |
import React from 'react';
import {render} from 'react-dom';
import Root from './containers/Root';
import BigNumber from 'bignumber.js';
import {AppContainer} from 'react-hot-loader';
import {configureStore, history} from './store/configureStore';
const store = configureStore();
BigNumber.config({ DECIMAL_PLACES: 18 });
render(
<AppContainer>
<Root store={store} history={history}/>
</AppContainer>,
document.getElementById('root')
);
if (module.hot) {
module.hot.accept('./containers/Root', () => {
const NextRoot = require('./containers/Root'); // eslint-disable-line global-require
render(
<AppContainer>
<NextRoot store={store} history={history}/>
</AppContainer>,
document.getElementById('root')
);
});
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,145 |
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