text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
package com.bzf.jianxin.main.widget;
import android.view.LayoutInflater;
import android.view.View;
import android.view.ViewGroup;
import com.bzf.jianxin.R;
import com.jude.easyrecyclerview.adapter.RecyclerArrayAdapter;
/**
* 通讯录头部
* com.bzf.jianxin.main.widget
* Author: baizhengfu
* Email:709889312@qq.com
*/
public class ContactListHeadView implements RecyclerArrayAdapter.ItemView {
@Override
public View onCreateView(ViewGroup parent) {
return LayoutInflater.from(parent.getContext()).inflate(R.layout.item_contact_list_footer,null);
}
@Override
public void onBindView(View headerView) {
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,168 |
{"url":"http:\/\/www.mzan.com\/article\/48238036-create-the-complete-symmetric-matrix-by-copying-the-lower-triangular-of-a-sparse.shtml","text":"Home create the complete symmetric matrix by copying the lower triangular of a sparse matrix in triplet format\n\n# create the complete symmetric matrix by copying the lower triangular of a sparse matrix in triplet format\n\nUmut Tabak\n1#\nUmut Tabak Published in 2018-01-13 08:02:21Z\n As the subject line suggests, what would be the most efficient way to copy the lower triangular part of a sparse matrix to the upper triangular part and complete the matrix entries to create the symmetric sparse matrix? Assume that I have the triplets I, J, X for the lower triangle including the diagonal. I am reading these arrays from a commercial program and for storage space reasons, I believe, they only store the lower triangular part. Well I will start testing different options soon, but wanted to see if someone else has experienced this before or not.\nrahnema1\n2#\n You can use sparse: idx = I ~= J; %index of nondiagonals result = sparse([I;J(idx)], [J;I(idx)], [X;X(idx)]); Because sparse adds together elements in X that have duplicate subscripts in I and J we exclude diagonal elements when concatenating vectors.","date":"2018-01-16 11:00:41","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\": 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\": 0.456730455160141, \"perplexity\": 983.2433929880817}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-05\/segments\/1516084886416.17\/warc\/CC-MAIN-20180116105522-20180116125522-00261.warc.gz\"}"} | null | null |
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<pre class="code"><span class="info file"># File 'lib/thinner/command_line.rb', line 21</span>
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<span class='options! fid id'>options!</span>
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\section*{\centering \huge {Supplementary Note 1} }
\vspace{10ex}
\subsection*{Empirical Spectrum of Interaction Matrices $W$}
The initial interaction matrix $J_0 \triangleq J(t=o)$ is defined as a random Gaussian matrix with mean $0$ and variance $\dfrac{{g_0}^2}{\langle K\rangle}$, where $\langle K \rangle$ is the mean in and out degree, and
$g_0$ (the network gain) determines the spectral radius of the combined interaction matrix $W$ at $t=0$ (see Methods section in main text).
Empirically we find that for matrices of relevant size the spectral radius of $W$ is not greatly affected by topology and it remains $\sim g_0$ following the above normalization $Var({J_0}_{ij})=\dfrac{{g_0}^2}{\langle K\rangle}$ , however the distribution is highly non-uniform (Sup. Fig. 1)
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS1}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Eigenvalues of finite size matrices with N=1500}. The eigenvalues of full Gaussian (A), sparse Gaussian (B) and scale-free/binomial (C) matrices are plotted. The eigenvalues of all three matrices are almost entirely contained within a disc of radius $g_0$ (broken red) and all three have a largest norm of eigenvalue $\sim g_0$ (green dot). However, the distribution of eigenvalues in the disc differs considerably between the three matrices. The number of non-zero elements in the sparse Gaussian matrix (B) is distributed with Binomial distribution in both columns and rows. The scale-free/binomial matrix (C) has a Binomial distribution for the number of non-zero elements in the rows and a scale-free distribution in the columns. All matrices have the form $W=T\circ J$, with ${J}_{ij} \sim \mathcal{N}\bigl( 0, \dfrac{{g_0}^2}{\langle K\rangle}\bigr)$ and $g_0=10$. Binomial distributions in (B) and (C) have parameters $p\simeq \dfrac{5}{N}$ and scale-free distribution in (C) has parameters $a=1$, $\gamma = 2.2$.}
\label{fig:Spectra}
\end{figure}
\subsection*{Distributions of Phenotype $y$}
The variable representing the macroscopic phenotype is defined as $y(\mathbf{x})=\mathbf{b}\cdot \mathbf{x}$. The arbitrary weight vector $\mathbf{b}$ is characterized by a degree of sparseness $c$, i.e. the fraction of nonzero components, $\dfrac{1}{N}\!\!<c\!<1$. The non-zero components of $\mathbf{b}$ are thus distributed $b_{i} \sim \mathcal{N}(0, \dfrac{1}{{g_0}^2\cdot cN}\cdot\alpha)$ (see Methods section in main text). Sup. Fig.
2(A-C) depicts distributions of the values of $y$ for $\alpha = 100$ with various types of interaction matrices $W$. As can be seen, these distributions are similarly shaped for a broad range of network sizes (Sup. Fig.
2A) and gains, $g_0$ (Sup. Fig.
2B), and do not change for various network topologies (Sup. Fig.
2C). These results verify that $y$ and $J_0$ are appropriately normalized.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS2}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Distributions of phenotype $y$ over trajectories for various network ensembles} The distribution of the values of the macroscopic phenotype $y=\mathbf{b}\cdot\mathbf{x}$ are plotted for various ensembles of networks with fixed interaction strengths. These include networks of various sizes (A), network gains (B) and topologies (C). For all ensembles the $y$ values are similarly distributed. This indicates that $y$ and $J_0$ are appropriately normalized. For all networks $\alpha = 100$. Networks in (A) and (B) have Scale-free out-degree distribution and Binomial in-degree distribution; Networks in (A) and (C) have $g = 10$ and networks in (B) and (C) have $N=1000$. In all panels scale-free in/out distributions have parameters $a=1$ and $\gamma=2.4$, exponential distributions have parameter $\beta =3.5$ and binomial distributions have parameters $p= \dfrac{3.5}{N}$ and $N$. }
\label{fig:YNorm}
\end{figure}
\subsection*{Convergence of Different Network Ensembles}
The topological ensembles in our model includes both quenched and annealed disorder. The random topology of the network, namely the specific adjacency matrix $T$ , is quenched and remains the same throughout the course of any single simulation run. The strengths of the network interactions, $J(t$), on the other hand, are dynamic and change via a random walk, thus presenting an annealed disorder. Convergence fractions are computed by averaging over such simulations; one needs to determine what is the relevant ensemble to average over.
\par Given a choice of the model parameters, one possible ensemble $\{(T^j,J_0^j, \mathbf{x}_0^j)\}_{j=1}^{m}$, consists of a set of $m$ networks, each with a different topology $T^j$, different initial interaction strengths $J_0^j \triangleq J^j(t=0)$ and different initial conditions $\mathbf{x}_0^j \triangleq \mathbf{x}^j(t=0)$. Another potential ensemble, $\{(T^0,J_0^j, \mathbf{x}_0^j)\}_{j=1}^{m}$, contains of a set of networks which all share the same adjacency matrix $T^0$, but differ in the initial network strengths $J_0^j$, and initial conditions $\mathbf{x}_0^0$; A third possibility is constructing an ensemble by varying only the initial conditions $\mathbf{x}_0^j$ and using the same initial network $W^0 =T^0\circ J_0^0$, $\{(T^0,J_0^0, \mathbf{x}_0^j)\}_{j=1}^{m}$, and finally, one can simulate the dynamics consecutively keeping both the initial network $W^0$ and initial dynamical conditions $\mathbf{x}_0^0$ constant, $\{(T^0,J_0^0, \mathbf{x}_0^0)\}_{j=1}^{m}$, with different realizations of the exploration process. Whether or not these various ensembles show qualitatively similar statistical properties or not is \textit{a-priori} known and depends on the self-averaging properties of the system.
\par We tested these properties by computing the distribution of convergence times for the various ensembles. Sup Fig.
3 shows that these distributions are similarly shaped for all ensembles.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS7}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure} Convergence Time distributions for Different Network Ensembles.} (i) An ensemble in which each network has random $T^j$, $J_0^j$ and $\mathbf{x}_0^j$ (blue); (ii) An ensemble in which all networks share the same topology $T^0$, but differ in $J_0^j$, and $\mathbf{x}_0^j$ (red); (iii) An ensemble in which initial network $W =T^0\circ J_0^0$ is the the same for all networks but initial conditions $\mathbf{x}_0^j$ are unique (green) (iv) An ensemble in which both the initial network $W^0$ and the initial dynamical conditions $\mathbf{x}_0^0$ are the same for all networks. All Ensembles have SF out-degree distribution and Binomial in-degree distribution. The backbone $T$ is the same matrix for ensembles (ii), (iii) and (iv) and the initial interactions strengths $J_0$ is the same in ensembles (iii) and (iv). For all ensembles $N=1500$, $g_0 = 10$, $\alpha = 100$, $\mathcal M_0 = 2$, $c=0.2$, $\varepsilon = 3$, $D=10^{-3}$ and $y*=0$. SF out-degree distribution has parameters $a=1$, $\gamma=2.2$, and Binomial in-degree distributions has parameters $p= \dfrac{5}{N}$ and $N$.}
\label{fig:EnsembleAveraging}
\end{figure}
\newpage
\section*{\centering \huge {Supplementary Note 2} }
\vspace{10ex}
\setcounter{equation}{0}
\subsection*{Robustness of Model to Saturating Function $\phi$}
The dynamics of the microscopic variables $\mathbf{x}$ prior to any exploration in $W$ is given by
\begin{eqnarray}
\dot{ \mathbf{x}}&=&W\phi(\mathbf{x})-\mathbf{x}.
\end{eqnarray}
The results shown in the main text were obtained using the element-wise saturating function $\phi(x_i) = \tanh(x_i)$. However, we find that these main results hold also for other types of saturating functions, specifically piece-wise linear and Sign function. In all cases convergence fractions depend on the topology of the networks, with higher fractions for those with scale-free out-degree distribution (Sup. Fig. 4A,B).
The slope of the saturating function at zero has little impact on convergence fractions (Sup. Fig. 4C,D)
\begin{figure}[H]
\refstepcounter{figure}
\begin{center}
\includegraphics[width=13cm]{FigS3_2}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Convergence fractions for dfferent saturating functions.} (A) Functional from of three saturating functions examined: $\tanh(x_i)$ (blue), piece-wise linear (purple) and Sign function (broken green) (B) Convergence fractions for ensembles with the three functional forms and two types of topology SF-Binom and Binom-SF within a time window of 2000 units .(C) Functional from of saturating functions with various slops at zero. (D) Convergence fractions for ensembles with functional forms of $\phi$ shown in (C) with SF-Binom topology, within a time window of 2000 units. The ensemble samples in (B) and (D) consist of 500 networks each. For all networks $g_0 = 10$, $\alpha = 100$, $c=0.2$ $\mathcal M_0 = 2$, $D=10^{-3}$ and $\varepsilon = 3$, $y*=0$. Scale-free in/out distributions have parameters $a=1$ and $\gamma=2.4$, $\beta \sim 3.5$ and Binomial distributions have parameters $p\simeq \dfrac{3.5}{N}$ and $N=1000$. }
\label{fig:SatFn}
\end{figure}
\subsection*{Robustness of Model to Position of Saturating Function $\phi$}
In the model described in the main text the saturating function $\phi(x_j)$ operates directly on $x_i$ prior to the interactions, while the interactions $w_{ij}$ multiply $\phi(x_j)$ (See Eq. 1 above). However, it is of interest to examine a possible alternative model in which the saturating function $\phi$ operates on $W\mathbf{x}$ and the equation of motion is
\begin{eqnarray}
\dot{ \mathbf{x}}&=&\phi(W\mathbf{x})-\mathbf{x}.
\end{eqnarray}
or equivalently
\begin{eqnarray}
\dot{x_i}&=&\phi\left(\sum\limits_{j} Wx_j\right)-x_i.
\end{eqnarray}
Similar equations are often used to describe the dynamics of neural networks, as well as gene interactions.
It is not \textit{a-priori} whether these two formulations will result in similar convergence properties in the context of the exploratory adaption protocol described here. Remarkably, we find convergence fractions of the two models to be almost identical (Sup. Fig. 5), as long as the macroscopic phenotype $y$ is appropriately normalized (see Sup. Fig. 2).
Recall that for the model described in the main text the elements of the vector $\mathbf{b}$ which defines the phenotype $y$ are given by $b_{i} \sim \mathcal{N}(0, \dfrac{1}{{g_0}^2\cdot cN}\cdot\alpha)$. The normalizing factor $\dfrac{1}{{g_0}^2\cdot cN}$ ensures $y \sim \mathcal{N}(0,\alpha)$ prior to convergence. The variance of $b_i$ is normalized by $\dfrac{1}{{g_0}^2}$ due to the empirical distribution of $x_i$ prior to convergence: $x_i \sim \mathcal{N}(0,\sim {g_0}^2)$. In the alternative model described by Eqs. 2,3 this is not the case. For $g_0 >> 1$, $x_i$ mostly attains the saturated values of $\phi$ which are $\pm 1$ with equal probability and $Var(x_i)\sim 1$. Thus the normalizing factor $\dfrac{1}{{g_0}^2}$ can be dropped and $b_{i} \sim \mathcal{N}(0, \dfrac{1}{cN}\cdot\alpha)$ results in $y \sim \mathcal{N}(0,\alpha)$ as in the former case.
\begin{figure}[H]
\refstepcounter{figure}
\begin{center}
\includegraphics[width=16cm]{FigS3_4}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Convergence Fractions with saturating functions inside and outside the summation.} Convergence fractions within a time window of 2000 units for the model described in the main text (Blue) and a similar model in which the saturating function is placed outside the summation (Green). Convergence Fractions are shown for ensembles with two types of topology: SF-Binom (out-in) and Binom-SF (out-in) for both models. For all networks $g_0 = 10$, $\alpha = 100$, $c=0.2$ $\mathcal M_0 = 2$, $D=10^{-3}$ and $\varepsilon = 3$, $y*=0$. Scale-free in/out distributions have parameters $a=1$ and $\gamma=2.4$, $\beta \sim 3.5$ and Binomial distributions have parameters $p\simeq \dfrac{3.5}{N}$ and $N=1000$. }
\label{fig:InsideOut}
\end{figure}
\subsection*{Robusntess of Model to Mismatch function ${\cal M}(y)$}
For all computations shown in the main text, the mismatch function ${\cal M}(y)$ is defined as a symmetric sigmoid around $y*$
\begin{eqnarray}
{\cal M}(y) = \dfrac{{\cal M}_0}{2}\Big[1+\tanh \Big(\dfrac{|y-y*|-\varepsilon}{\mu}\Big)\Big],
\end{eqnarray}
\noindent where $2\varepsilon$ is the size of the low mismatch comfort zone around zero, $\mu$ controls the steepness of the sigmoid in its dynamic range, and ${\cal M}_0$ is its maximal value (see Sup. Fig. 6, blue line). An alternative linear mismatch function
\begin{eqnarray}
{\cal M}(y)=
\begin{cases}
\hfill |y-y*|- \varepsilon \hfill & |y-y*|>\varepsilon \\
\hfill 0 \hfill & |y-y*|\leq \varepsilon \\
\end{cases}
\end{eqnarray}
\noindent was examined (see Sup. Fig. 6, red line), resulting in similar convergence properties.
However, using a parabolic function for the mismatch resulted in poor convergence fractions for the same parameters displayed in the main text. Thus, the existence of a broad region of zero mismatch, rather than a well-defined minimum at a point, seems essential for convergence by exploratory adaptation, but the detailed shape of the function does not seem to have a large impact on the results.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS3}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Mismatch Functions} Two examples of mismatch functions ${\cal M}(y)$ that result in similar convergence behavior. The results shown in the main text and supplementary were obtained using a sigmoidal mismatch function (blue); similar convergence results can be obtained with a linear mismatch function (red) as well (convergence results not shown). The sigmoidal function in the figure has parameters $\varepsilon = 3$, $mu = 0.5$ and ${\cal M}_0=4$.}
\end{figure}
\newpage
\section*{\centering \huge {Supplementary Note 3} }
\vspace{10ex}
\setcounter{equation}{0}
\subsection*{Convergence to a Limit Cycle}
An example of convergence to a fixed-point which satisfies the constraint is shown in the main text (Fig. 1 B-D).
However, the non stringent constraint which is reflected in the "comfort zone" of the mismatch function ${\cal{M}}(y)$ allows for a time-varying solutions with small amplitude which are not fixed-points.
Indeed, many simulations converge to a limit cycle solution (example shown in Sup. Fig. 7 A,B). Such a solution satisfies the constraint only if the amplitude of macroscopic phenotype $y$ is confined in the range $(-\varepsilon, +\varepsilon)$ (Sup. Fig. 7A). The microscopic variables $x_i$ also converge to limit cycles, but these can vary in amplitude and values (Sup. Fig. 7B). Interestingly for a broad range of network sizes and different network topologies the ratio between convergence of exploratory dynamics to fixed-points and to limit-cycles is largely preserved. For the ensembles shown in Sup Fig. 7C roughly $35\%$ of the solutions are limit cycles and the rest are fixed-points.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS4}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Convergence to Limit Cycles.} (A) The macroscopic phenotype $y$ as a function of time in one simulation which converged to a small-amplitude limit tycle around $y^*$. (B) Several microscopic variable $x_i$ as a function of time in the same simulation; $x_i$ also converged to limit cycles but with various amplitudes and centers. (C) Fraction of networks that converged to limit cycles within a time window of 2000 time units, as a function of network size. Results are shown for different ensembles, each composed of a sample of 500 networks. Networks in each of the ensembles has a random $T$, $J_0$ and $\mathbf{x}_0$. The network in (A) has SF out-degree and Binomial in-degree distributions. For all networks in (A) (B) and (C) $g_0 = 10$, $\alpha = 100$, $c=0.2$ $\mathcal M_0 = 2$, $D=10^{-3}$ and $\varepsilon = 3$. In (A) and (B) $y*=10$ and in (C) $y*=0$. In all panels scale-free in/out distributions have parameters $a=1$ and $\gamma=2.4$, exponential distributions have parameter $\beta \sim 3.5$ and Binomial distributions have parameters $p\simeq \dfrac{3.5}{N}$ and $N$. }
\end{figure}
\subsection*{Dependence of Convergence in Scale-Free Networks on Pareto Distribution Parameters}
As mentioned above, scale-free degree distributions were sampled by discretesizing the continuous Pareto distribution
\begin{eqnarray}
P(k) =\dfrac{(\gamma-1)a^{\gamma-1}}{k^\gamma},
\end{eqnarray}
\noindent where the parameter $a$ controls the minimal value of the support and $\gamma$ controls the power law tail of the distribution. In contrast to directly sampling from a discrete distribution such as the Zeta distribution, such a sampling method allows additional control of the lower part of the distribution. After discretization the minimal possible degree, $k_{min}$ is the integer which is nearest to $a$ regardless of non-integer values assigned to $a$. However, the exact value of $a$ affects the weight of the distribution at its minimal value $k_{min}$ and the overall shape of the discrete distribution at its lower part.
For example, for every $a\in [1, 1.5)$ the minimal degree in the network would be 1. However for $a=1.1$ there would be a higher probability for nodes with degree 1 then with $a=1.4$. This allows us to examine with detail the effect of the lower part of the scale-free distribution on the convergence properties of the model.
We find that convergence of exploratory adaptation is indeed sensitive to the the weights at the lower part of the out-going distribution (Sup. Fig. 8A), and occurs with high fractions only for networks with a large enough number of nodes with out-going degree 1 ($a \in (0.4, 1.4)$). In contrast, convergence is weakly dependent on the exact power law of the distribution $\gamma$ (Sup. Fig. 8B).
\par While $a$ and $\gamma$ have a very different effect on the distribution, they both influence the mean degree $\langle k \rangle$ of the network. Sup Fig. 8C shows the same convergence fractions plotted as a function of the mean degree. The results indicate that $\langle k \rangle$ does not directly influence convergence fractions, and highlights the sensitivity to the lower-part of the distribution which is controlled by $a$. Recent findings have shown that the controllability of random networks is strongly affected by the minimal degree of the nodes with a transition when the minimal degree is increased to $k_{min} \geq 2$ \cite{Menichetti2014}. For our model we conclude that both the existence of hubs and the existence of a large number nodes with out-going degree 1 are indicative of convergence to a stable state.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS5}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Dependence of convergence fractions on parameters of out-degree Pareto Distribution.} Scale-free degree distributions are sampled by discretesizing the continues Pareto distribution (Eq. 6). (A) Convergence fracion as a function of $a$, a parameter which controls the lower part of the distribution. (B) Convergence fraction as a function of $\gamma$, which controls the power-law tail of the distribution. (C) Convergence fraction as a function of mean degree $\langle K \rangle$; changes in this mean degree can be obtained by varying either $a$ (red line) or $\gamma$ (blue line). Each data point in (A), (B) and (C) represents the fraction of network which converged within a time window of 2000 time units from a different ensemble of 500 networks. Networks in each of the ensembles has a random $T$, $J_0$ and $\mathbf{x}_0$. All Ensembles have SF out-degree distribution and Binomial in-degree distribution. For all results $N=1000$, $g_0 = 10$, $\alpha = 100$, $c=0.2$ $\mathcal M_0 = 2$, $\varepsilon = 3$, $D=10^{-3}$ and $y*=10$. Scale-free out-degree distributions have parameters $a=1$, $\gamma=2.4$, and Binomial in-degree distributions have $p=\dfrac{3.5}{N}$. }
\end{figure}
\subsection*{Dependence of Convergence on Sparseness of Macroscopic Phenotype}
As mentioned above the macroscopic state, $y(\mathbf{x})=\mathbf{b}\cdot \mathbf{x}$, can have a varying degree of sparseness $c$.
However, we find that convergence properties are not affected by changing the sparseness of macroscopic state (Sup. Fig. 9). This is intuitively understood since the dimensionality of the constraint in the high-dimensional space of microscopic states is the same for all $c$.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=13cm]{FigS6}
\end{center}
\small{
\textbf{Supplementary Figure \arabic{figure}. Dependence of convergence fractions on the sparseness of macroscopic state vector.} Convergence properties are not affected by changing the sparseness of macroscopic state, $c$ (A). Each data point represents the fraction of network which converged within a time window of 2000 time units from a different ensemble of 500 networks. Networks in each of the ensembles have random $T$, $J_0$ and $\mathbf{x}_0$. All Ensembles have SF out-degree distribution and Binomial in-degree distribution. For all results $N=1000$, $g_0 = 10$, $\alpha = 100$, $\mathcal M_0 = 2$ and $D=10^{-3}$, $\varepsilon = 3$. SF out-degree distribution has parameters $a=1$, $\gamma=2.4$, and Binomial in-degree distributions has parameters $p\simeq \dfrac{3.5}{N}$ and $N$.}
\end{figure}
\subsection*{Dependence of Convergence on Network Motifs}
Network motifs are specific local sub-graphs which are thought to be significantly over-represented in gene regulatory networks. We examined the effect of motifs on convergence by creating an ensemble of networks in which motifs are over-represented and comparing the convergence fractions of the motif-enriched networks to an appropriate null model. The single node motif of auto-regulation was discussed in the main text of the article. In this Supplementary section we shall further discuss this motif as well as motifs of higher order. \par
\bigskip
\noindent
\textbf{\textit{Autoregulation}} \par
\noindent the effect of auto regulation of the hubs and positive auto-regulation to random nodes was discussed in the main text. Here we examined separately the effect of adding negative ($W_{ii}<0$) and positive ($W_{ii}>0$) self connections. We assessed the contributions of this motif by creating an ensemble of 500 random networks of size N=1000 and adding auto regulation randomly to 10\% of the nodes (Sup Fig. 10 dark green and dark blue). Such additions change the in and out degrees of some nodes in the networks and consequently affect the overall in and out degree statistics of the network. This is, in general, expected to affect convergence regardless of the auto-regulatory loops. Therefore, for each enriched network we created a null control which shares the same exact in and out degree sequence but does not include an over-representation of the auto-regulatory motif (Sup Fig. 10 light green and light blue). The control was created by randomly re-connecting out half-stubs to in half-stubs until the network is well mixed (see \cite{shen2002network}) for details of the half-stubs method). Another control is the convergence fractions of the networks prior to any addition (Sup Fig. 10 gray).
We find that both positive and negative auto regulation increases convergence, yet positive auto regulation has a considerably larger effect.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS10_3_5}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure} Effect of adding auto-regulation loops to convergence.} An ensemble of 500 networks, in which auto-regulation was added randomly to 10\% of the nodes was tested for convergence. The added connections are either positive (dark green) or negative (dark blue). Results are compared to random networks with the same degree sequence (light green and light blue) and networks prior to enriching the networks with auto regulation loops (grey). Initial networks prior to the addition of auto regulation loops have SF out-degree distributions with $a=1$, $\gamma=2.4$ and Binomial in-degree distribution with $p= \dfrac{3.5}{N}$ and $N$. Other parameters are $N=1000$, $g_0 = 10$, $\alpha = 100$, $\mathcal M_0 = 2$, $\varepsilon = 3$, $c=0.2$, $D=10^{-3}$ and $y*=0$. }
\end{figure}
\newpage
\noindent
\textbf{\textit{Feed-Forward Loops}} \par
\noindent The 3-node motif which is thought to be most significantly over-represented in regulatory networks is the feed-forward (FF) loop in which $A\Rightarrow B \Rightarrow C$ and $A \Rightarrow C$. We note that the equations governing our model are symmetric around zero and so are the connections strengths $W_{ij}$. Therefore there is no clear interpretation for coherent or incoherent feed-forward loops, and the signs of the connections within each motif were chosen randomly. We over-represented feed-forward loops in our networks by initially picking a random fraction of existing sequences of the form $A\Rightarrow B \Rightarrow C$ , and adding to these sequences the connection $A \Rightarrow C$ which was not previously part of the network. The strengths of these added connection was drawn from the same distribution as the existing connections in the network. As in the auto-regulation motif we compare these results to a control with the same in and out degree sequence (Sup Fig. 11, blue) and to the original network prior to any addition (Sup Fig. 11, orange).
Networks in the FF ensemble are enriched with 300 feed-forward loops, which increases the over-all number of FF loops by ~50\% on average.
We find that over-representing this motif increases convergence by ~12\% compared to random networks with the same degree sequences (Sup Fig. 11, FF and Null 1). However they do not contribute nor harm the convergence of the network prior to adding the loops (Sup Fig. 11, FF and Null 2).
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS10_4}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure} Convergence of networks enriched with feed-forward loops.} An ensemble of 500 networks, each enriched with 300 additional feed-forward loops, was tested for convergence (green). Results are compared to random networks with the same degree sequence (blue) and networks prior to enriching the networks with feed-forward loops (red). Initial networks prior to the addition of FF loops have SF out-degree distributions with $a=1$, $\gamma=2.4$ and Binomial in-degree distribution with $p= \dfrac{3.5}{N}$ and $N$. Other parameters are $N=1000$, $g_0 = 10$, $\alpha = 100$, $\mathcal M_0 = 2$, $\varepsilon = 3$, $c=0.2$, $D=10^{-3}$ and $y*=0$. }
\end{figure}
\par
\bigskip
\noindent
\textbf{\textit{Bi-Fans}} \par
\noindent The four-node motivf which is thought to be most significantly over-represented in regulatory networks is the bi-fan in which two regulators jointly regulate two target genes: $A \Rightarrow C$, $A \Rightarrow D$, $B \Rightarrow C$, $B \Rightarrow D$. We find that over representing this motif does not have strong positive or negative effect compared to the network prior to adding the loops or the null model.
\subsection*{Stretched Exponential Fit to the Distribution of Convergence Times}
Convergence times of exploratory adaptation can be well fit by a stretched exponential (main text Fig. 4).
The fit is calculated by fitting $1-log(CDF)$ of convergence times to a power law. Thus, the fit to the CDF has the stretched exponential form $1-e^{-{x/\lambda}^k}$ which implies a Weibull distribution, with PDF
\begin{eqnarray}
f(t) =
\begin{cases}
\hfill \frac{k}{\lambda}{(\frac{t}{\lambda})^{k-1}}e^{-{t/\lambda}^k} \hfill & x>0 \\
\hfill 0 \hfill & x\leq0 \\
\end{cases}
\end{eqnarray}
\par For the distributions shown in the main text (Fig. 12), the fit of $1-log(CDF)$ to a power law is excellent with ${R^2}\geq0.995$. To gain further understanding of the distribution of convergence times, we computed the empirical mean and standard deviation for increasingly larger time windows. Results show that both moments monotonically increase with the window size (even for very large time windows - Sup. Fig. 12A and 12B blue lines). In addition we calculated the stretched exponential fit for each time window. We did not use all the data points in each window, but rather a fixed number of 200 data points for all windows which were evenly distributed in the window. Thus we avoid the possibility of erroneous estimations of the quality of the fit stability which might result from an increase in the size of the data set for large time windows. Using this fit protocol we obtained excellent fits of $1-log(CDF)$ to a power law For all time windows above t=3000 (${R^2}\geq0.995$). We also found that the fit is stable and that after an initial transient the fit parameters fluctuate very little with increased windows sizes (Sup. Fig. 12A and 12B red lines). These findings increase our confidence in the stretched exponential fit. Moreover, although we observed an increase in mean and std with window size, they do not diverge. The stability of the fit and its large mean and std may indicate that the first two moments of the convergence times distribution are finite but can only be estimated faithfully using much larger time windows.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS8}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure} Stability of stretched exponential fit to the distribution of convergence times.} the empirical mean and standard deviation for increasingly larger time windows is shown (A and B blue lines). Both monotonically increase with window size for all times tested. Mean and variance estimated from parameters of the stretched exponential fit (see text for detail) are stable and after an initial transient fluctuate very little with increased windows sizes (A and B reds). Ensemble has SF out-degree distribution with $a=1$, $\gamma=2.4$ and Binomial in-degree distribution with $p= \dfrac{3.5}{N}$ and $N$. Other parameters are $N=1500$, $g_0 = 10$, $\alpha = 100$, $\mathcal M_0 = 2$, $\varepsilon = 3$, $c=0.2$, $D=10^{-3}$ and $y*=0$. }
\end{figure}
\subsection*{Stability of the Adapted State}
As shown in the main text, a large fraction of the networks with appropriate topology converge to a stable state for which the phenotype $y$ remains sufficiently close to the demand $y*$. From a biological point of view these final states are likely to be perturbed. Therefore it is of interest to examine the resilience of the final stable state to perturbations both in the nodes' states $x_i$ and the interactions $W_{ij}$. The system at hand is high-dimensional, nonlinear and includes a stochastic feedback in the form of a random-walk in its parameters. These properties make the analytical assessment of the stability of the full model very difficult Therefore, we shall address the question of stability numerically.
\bigskip\\
\noindent
\textbf{\textit{Perturbations to $\mathbf{x}$}} \par
\noindent A standard linear stability analysis can be employed for network parameters $W_{ij}$ at the values they reached following exploration. Examinations of the Jacobian matrix at such a fixed-point reveals that its eigenvalues mostly cluster around -1, with a few outliers eigenvalues (Sup Fig. 13A Inset). This is not surprising given the structure of the equation of motion $\dot{x}_i = -x_i + \sum W_{ij}\phi \left(x_j\right)$. At a fixed-point one may expect the linear term $-x_i$ to dominate typically while the other term may average out, resulting in an eigenvalue which is close to -1. The overall stability of the fixed-point can be quantified by the largest eigenvalue of the Jacobian at the fixed-point. The distribution of the largest eigenvalues, computed across and ensemble of converged networks at their respective fixed-points, are mostly located near -1 as well (Sup Fig. 13A).
While such analysis provides some information as to the stability of fixed-points, it has three major disadvantages: (i) It is limited to the case where the converged state is a fixed point; (ii) It is relevant only to constant parameters $W_{ij}$, in contrast to the exploratory dynamics we described. Any large enough perturbation in $\mathbf{x}$ will be naturally accompanied by change in $W_{ij}$ due to the divergence of $y$ from the $\epsilon$ comfort-zone around $y*$. (iii) Even for constant $W_ij$, linear stability analysis is only valid locally around the fixed-point. For nonlinear dynamics with a large number of dimensions, the basin of attraction around a fixed point may be very small and beyond it the linear analysis does not hold. In such cases even relatively small perturbation to a system with negative eigenvalues my cause the system to lose its stability. \par
Given these disadvantages of linear stability analysis, we employ an additional method to assess the stability of the system to a perturbations in $\mathbf{x}$. Stability is assessed numerically by directly employing the full exploratory dynamics to perturbed variables and computing the convergence times. More specifically, we examined an ensemble of 500 networks which converged to a stable state. For each network we perturbed the final state $\mathbf{x}_{converged}$ randomly by 5\%, 10\%, 20\%, 50\%, 100\% and 200\%, and simulated the dynamics with the perturbed state $\mathbf{x}_0 \coloneqq \mathbf{x}_{pertubed}$ and final interaction matrix $W_{converged}$ as initial condition, and the same phenotype vector $\mathbf{b}$. Convergence times for these simulation were recorded. Results are shown in Sup. Fig. 13B, alongside a control (labeled "Null") which is composed of an ensemble of 500 networks with the same parameters as the converged networks.
As can be seen for perturbations of 5\%, nearly all networks re-adapted within 2000 time units and a large number of these networks re-converged very rapidly. For larger perturbation,
we find a higher convergence than in the control and a lager fraction of rapid convergences. This suggests that the stability of the converged state in $\mathbf{x}$ space is non-local and that the basin of attraction covers a large area of the $\mathbf{x}$ space.
Moreover, the convergence process following the perturbation involves changes of the parameters $W$. The rapid convergence for large number of networks suggests that the phase space of the dynamics in $\mathbf{x}$ deforms continuously with the parameters $W_{ij}$ and that in many cases the existence of a stable attractor in not affected by small perturbations to these parameters.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS10_1}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Perturbation to the state vector $\mathbf{x}$ after convergence.} (A) PDF of the maximal real-part of eigenvalues of the Jacobian matrix at the fixed-point, across an ensemble of 700 networks. Typical distribution eigenvalues in the complex plane for a single network is shown in the inset. Largest real part of eigenvalue in blue. (B) Convergence fraction of networks for which the final state $\mathbf{x}_{converged}$ was perturbed and a null control. All networks have SF out-degree distributions with $a=1$, $\gamma=2.4$ and Binomial in-degree distribution with $p= {3.5}/{N}$ and $N$. Other parameters are $N=1000$, $g_0 = 10$, $\alpha = 100$, $\mathcal M_0 = 2$, $\varepsilon = 3$, $c=0.2$, $D=10^{-3}$ and $y*=0$. }
\end{figure}
\noindent \textbf{\textit{Perturbations to $W_{ij}$}} \par
\noindent In order to asset the effect of perturbations to $W_{ij}$ we examined 10 distinct networks $\left\lbrace W^1,..W^{10}\right\rbrace $ with SF-Binom connectivity after they converged to an adapted state. For each network $W^i$ we perturbed all non zero connections $W_{ij}$ randomly by 1\% 250 times thus obtaining 250 new networks. Simulations were then run for these 250 perturbed networks using the same phenotype vector $\mathbf{b}$ used for $W^i$ and initial conditions $\mathbf{x}_0$ equal to the converged state $\mathbf{x}_{converged}$ of the network $W^i$. Re-adaptation convergence times for these perturbed networks were then recorded. This protocol was repeated for perturbations of magnitude 5\%, 10\%, 20\% and 50\%, using as a basis the same converged network $W^i$. In addition we constructed a null control for each converged network $W^i$ by running 500 simulation with random choices of $W_{ij}$ and $x_i$, while using the same backbone $T^i$ which corresponds to $W^i$. Thus the statistics of convergence for the perturbed networks can be compared to random networks with the same backbone $T^i$. All of these simulation were repeated for each of the 10 networks $\left\lbrace W^1,..W^{10}\right\rbrace $. The results, averaged over the 10 networks, are shown in Sup Fig. 14.
As can be seen in Sup Fig. 14A, for small perturbations of 1\% nearly all networks re-adapted within 2000 time units and a large number of these networks re-converged very rapidly. For larger perturbation
(5\% and 10\%) convergence was at lower fractions and less rapid but still more than the control (Sup. Fig. 14A.). These findings suggest a continuous picture: small perturbations re-converge rapidly in high fractions, intermediate perturbations (20\%) less so, and for large perturbations (50\%) convergence statistics is similar to that of random networks with the same backbone. Consistently with this picture, Sup. Fig. 14B shows that the coordinates of the new fixed-points move away from the original one in a continuous manner.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS10_2}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Perturbation to network connection strengths after convergence.} Non-zero connection strengths, $W_{ij}$, of 10 networks were randomly perturbed following convergence to fixed points. For each perturbation size an ensemble of 250 networks was constructed. In addition, a control ensemble was constructed consisting of 500 networks with random connection strengths $W_{ij}$ and the same topological backbone as the original network. Results are averaged over the 10 networks.(A) Convergence fraction of perturbed networks and null control. (B) Average Euclidean distance between the initial converged state $\mathbf{x}_0$ before perturbation and the converged state after the perturbation $\mathbf{x}_{readapted}$. All networks have SF out-degree distributions with $a=1$, $\gamma=2.4$ and Binomial in-degree distribution with $p={3.5}/{N}$ and $N$. Other parameters are $N=1000$, $g_0 = 10$, $\alpha = 100$, $\mathcal M_0 = 2$, $\varepsilon = 3$, $c=0.2$, $D=10^{-3}$ and $y*=0$. }
\end{figure}
\noindent
\textbf{\textit{Perturbations to $T$}} \par
\noindent The effect of perturbations to the backbone $T$ were assessed similarly manner to the perturbations in $W_{ij}$ described above. We examined 10 distinct networks $\left\lbrace W^1,..W^{10}\right\rbrace $ with SF-Binom connectivity after convergence; each backbone $T$ was perturbed by adding or deleting a random fraction of connections to the network. Each such perturbation was applied 250 times and simulations were then run with the same phenotype vector $\mathbf{b}$ used for $W^i$. Initial conditions $\mathbf{x}_0$ for these runs were the converged state reached for $W^i$ prior the perturbation. For new connections $T_{ij} = 1$ that were added, the statistics of the connection strength $W_{ij}$ was chosen randomly from the same distribution as the existing connection strengths in the network. \par
The results, averaged over the 10 networks, are shown in Sup Fig. 15.
For both additions and deletions convergence is relatively stable for small perturbations, And for such perturbations many network quickly return to a converged state (Sup Fig. 15A and 15B).
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=16cm]{FigS10_3}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure} Perturbation to topology of converged networks.} Topology, $T$, of 10 converged networks was randomly perturbed by deleting and adding connections. A varying number of random connections have been removed (A) or added (B) to the converged networks. For each magnitude of perturbation an ensemble of 250 perturbed networks was constructed. Network in these ensembles were then simulated and convergence times were tracked. Results are averaged over the 10 initial networks. Initial converged networks have SF out-degree distributions with $a=1$, $\gamma=2.4$ and Binomial in-degree distribution with $p= {3.5}/{N}$ and $N$. Other parameters are $N=1000$, $g_0 = 10$, $\alpha = 100$, $\mathcal M_0 = 2$, $\varepsilon = 3$, $c=0.2$, $D=10^{-3}$ and $y*=0$. }
\end{figure}
\newpage
\section*{\centering \huge {Supplementary Note 4} }
\vspace{10ex}
\setcounter{equation}{0}
\subsection*{Dependence of Convergence of Fixed Networks on Largest Hub}
We have seen that convergence of exploratory adaptation correlates with the fraction of fixed networks (constant networks and no constraint - Fig. 7 in the main text) in which the intrinsic dynamics of Eq. (1) converges to fixed points. Here we investigate further the dependence of constant networks on the network hubs. In particular, we ask whether the existence of larger hubs in a network correlates with larger probability of convergence to fixed point. In order to examine this property we randomly constructed backbones $T$ of size N=1500 with SF out-degree and Binomial in-degree distributions. We picked 20 such backbones $\{T_1...T_{20}\}$ for which the largest hub has outgoing degrees between ${{K_1}} \sim 100$ and ${{K_{20}}} \sim 1100$. Next we created for each backbone $T_i$ an ensembles of 500 networks, each with random interactions strengths $\{J^{i,1}...J^{i,500}\}$, $1\leq i \leq 20$. For each ensemble we computed the fraction of networks which converged to a fixed-point in the open-loop setting. Sup. Fig. 16 depicts this fraction as a function of the largest degree, showing a noisy but significant correlation. The large fluctuation indicate that there are other properties in addition to the largest hub that have a significant influence on convergence.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=13cm]{FigS9}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Dependence of convergence fractions to fixed points in constant networks on largest hub.} Twenty backbones $\{T_1...T_{20}\}$ were used to generate 20 ensembles, each composed of 500 random realizations of interaction strengths $J$. Each backbone $T_i$ has a different maximal degree of the largest out-going hub, between ${{k_1}} \sim 100$ and ${{k_{20}}} \sim 1100$. Each data point represents the fraction of networks within the ensemble which converged to a fixed-point within a time window of 2000 in the ensemble, plotted as a function of the maximal out-degree. All backbones are drawn from a SF out-degree distribution with $a=1$, $\gamma=2.4$ and Binomial in-degree distribution with $p\simeq \dfrac{3.5}{N}$ and $N$ . $N=1500$ and $g_0 = 10$.}
\end{figure}
\subsection*{Dependence of Convergence of Fixed Networks on Network Gain}
Convergence fractions under exploratory adaptation dynamics are weakly dependent on the network gain $g$ (Fig. 2 D in the main text). We examined the analogous property for constant networks by randomly constructing 5 backbones with SF out-degree and Binomial in-degree, $\{T^1...T^{5}\}$. For each backbone $T^i$ we created seven ensembles of 500 networks, each with a different g, $\{(T^i,J_g^j)\}_{j=1}^{500}$, $1\leq i \leq 5$ , $g\in\{2,3,6,8,10,12,15\}$ (a total of 35 ensembles). For each ensemble we computed the fraction of networks for which the intrinsic dynamics converges to a fixed-point (fixed network no constraint - Sup Fig. 17 doted lines). In addition we averaged over backbones by constructing seven ensembles with $g\in\{2,3,6,8,10,12,15\}$ in which each network has a different $T$ and $J$, $\{(T^j,J_g^j)\}_{j=1}^{500}$ (Sup. Fig. 17 dark blue). Both types of ensembles show a weak dependence on $g$ after an initial decline for small $g$ . In addition convergence fractions are also dependent on the specific topology $T^i$.
\begin{figure}[H]
\refstepcounter{figure}
\label{fig:eigen}
\begin{center}
\includegraphics[width=13cm]{FigS10}
\end{center}
\renewcommand{\baselinestretch}{1}
\small{
\textbf{Supplementary Figure \arabic{figure}. Dependence of convergence fractions to fixed points in constant networks on network gain.} Ensembles of 500 networks with fixed $T^i$, and different g, $\{(T^i,J_g^j)\}_{j=1}^{500}$, $1\leq i \leq 5$ , $g\in\{2,3,6,8,10,12,15\}$ (doted lines), were tested for converged to a fixed-point with a fixed network and no constraint. Mixing of the different backbones into ensembles characterized by $g$ results in the thick blue line. Ensembles have SF out-degree distribution with $a=1$, $\gamma=2.4$ and Binomial in-degree distribution with $p\simeq \dfrac{3.5}{N}$ and $N$, $N=1500$.
}
\end{figure}
\bibliographystyle{unsrt}
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From G5316; shining, that is, apparent (literally or figuratively); neuter (as adverb) publicly, externally:—abroad, + appear, known, manifest, open [+ -ly], outward ([+ -ly]).
NASB - apparent(1), disclosed(2), evident(6), light(2), obvious(1), outward(1), outwardly*(1), tell(2), well known(2).
Matthew 12:16. Mark 3:12. Acts 7:13.
Luke 8:17. Acts 4:16. Romans 1:19. 1 Corinthians 3:13; 11:19; 14:25. Galatians 5:19. Philippians 1:13. 1 John 3:10. | {
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} | 1,111 |
Deva (węg. Déva, niem. Diemrich) – miasto w zachodniej Rumunii, w Siedmiogrodzie, nad rzeką Maruszą. Jest stolicą okręgu Hunedoara. W mieście funkcjonuje słynna szkoła gimnastyki sportowej.
W starożytności była dacką fortecą, nazywaną Singidava. Właśnie w tym regionie Dakowie mieli główne ośrodki swojego państwa i tu ulegli w 106 r. przeważającym siłom rzymskich legionów cesarza Trajana.
W mieście rozwinął się przemysł maszynowy, materiałów budowlanych, drzewny, spożywczy, porcelanowy oraz hutniczy.
Merem miasta jest od 2000 Mircia Munteanu z Narodowej Partii Liberalnej.
Współpraca
Arras, Francja
Cherbourg-Octeville, Francja
Szigetvár, Węgry
Yancheng, Chińska Republika Ludowa
Przypisy
Bibliografia
Miasta w okręgu Hunedoara | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,891 |
Die 4-mal-400-Meter-Staffel der Männer bei den Leichtathletik-Europameisterschaften 2012 wurde am 30. Juni und 1. Juli 2012 im Estadi Olímpic Lluís Companys der finnischen Hauptstadt Helsinki ausgetragen.
Europameister wurde Belgien in der Besetzung Antoine Gillet, Jonathan Borlée (Finale), Jente Bouckaert und Kevin Borlée sowie dem im Vorlauf außerdem eingesetzten Nils Duerinck.Den zweiten Platz belegte Großbritannien mit Nigel Levine, Conrad Williams, Robert Tobin (Finale) und Richard Buck (Finale) sowie den im Vorlauf außerdem eingesetzten Luke Lennon-Ford und Michael Bingham.Bronze ging an Deutschland in der Besetzung Jonas Plass, Kamghe Gaba, Eric Krüger (Finale) und Thomas Schneider sowie dem im Vorlauf außerdem eingesetzten Niklas Zender.
Auch die nur im Vorlauf eingesetzten Läufer erhielten entsprechendes Edelmetall.
Rekorde
Bestehende Rekorde
Der bestehende EM-Rekord wurde bei diesen Europameisterschaften nicht erreicht. Die schnellste Zeit erzielte Europameister Belgien mit 3:01,09 min, womit das Quartett 2,87 s über dem Rekord blieb. Zum Europarekord fehlten 4,49 s, zum Weltrekord 6,80 s.
Rekordverbesserung
Es wurde ein neuer Landesrekord aufgestellt:
3:02,72 min – Tschechien (Daniel Němeček, Pavel Maslák, Josef Prorok, Jakub Holuša), Finale am 1. Juli
Legende
Kurze Übersicht zur Bedeutung der Symbolik – so üblicherweise auch in sonstigen Veröffentlichungen verwendet:
Vorrunde
30. Juni 2012, 13:05 Uhr
Die Vorrunde wurde in zwei Läufen durchgeführt. Die ersten drei Staffeln pro Lauf – hellblau unterlegt – sowie die darüber hinaus zwei zeitschnellsten Teams – hellgrün unterlegt – qualifizierten sich für das Finale.
Vorlauf 1
Vorlauf 2
Finale
1. Juli 2012, 19:45 Uhr
Weblinks
Helsinki European Championships european-athletics.com, abgerufen am 25. Februar 2023
Europameisterschaft in Helsinki (Finnland), leichtathletik.de, abgerufen am 25. Februar 2023
Men 4x400m Relay Athletics European Championship 2012 Helsinki (FIN), todor66.com, abgerufen am 25. Februar 2023
European Championships - Statistics Handbook Athletics, 22nd European Athletics Championships Helsinki FIN 27 JUN–01 JUL 2012 Olympiastadion, Men 4x400m, S. 688, englisch (PDF, 30.741 KB), downloads.european-athletics.com, abgerufen am 25. Februar 2023
XXI European Championship, Helsinki 2012, trackfield.brinkster.net (englisch), abgerufen am 25. Februar 2023
Videolink
ECH2012 Helsinki Day 5 Belgium 4x400m Relay Team (BEL), Interview, youtube.com, abgerufen am 25. Februar 2023
Einzelnachweise und Anmerkungen
Staffel 4x400 m Manner | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,350 |
<?php
require_once dirname(__FILE__) . '/../../../bootstrap.php';
class Elastica_Query_QueryStringTest extends Elastica_Test
{
public function testSearchMultipleFields()
{
$str = md5(rand());
$query = new Elastica_Query_QueryString($str);
$expected = array(
'query' => $str
);
$this->assertEquals(array('query_string' => $expected), $query->toArray());
$fields = array();
$max = rand() % 10 + 1;
for ($i = 0; $i < $max; $i++) {
$fields[] = md5(rand());
}
$query->setFields($fields);
$expected['fields'] = $fields;
$this->assertEquals(array('query_string' => $expected), $query->toArray());
foreach (array(false, true) as $val) {
$query->setUseDisMax($val);
$expected['use_dis_max'] = $val;
$this->assertEquals(array('query_string' => $expected), $query->toArray());
}
}
public function testSearch()
{
$client = new Elastica_Client();
$index = new Elastica_Index($client, 'test');
$index->create(array(), true);
$index->getSettings()->setNumberOfReplicas(0);
//$index->getSettings()->setNumberOfShards(1);
$type = new Elastica_Type($index, 'helloworld');
$doc = new Elastica_Document(1, array('email' => 'test@test.com', 'username' => 'hanswurst', 'test' => array('2', '3', '5')));
$type->addDocument($doc);
// Refresh index
$index->refresh();
$queryString = new Elastica_Query_QueryString('test*');
$resultSet = $type->search($queryString);
$this->assertEquals(1, $resultSet->count());
}
/**
* Tests if search in multiple fields is possible
*/
public function testSearchFields()
{
$index = $this->_createIndex();
$type = $index->getType('test');
$doc = new Elastica_Document(1, array('title' => 'hello world', 'firstname' => 'nicolas', 'lastname' => 'ruflin', 'price' => '102', 'year' => '2012'));
$type->addDocument($doc);
$index->refresh();
$query = new Elastica_Query_QueryString();
$query = $query->setQuery('ruf*');
$query = $query->setDefaultField('title');
$query = $query->setFields(array('title', 'firstname', 'lastname', 'price', 'year'));
$resultSet = $type->search($query);
$this->assertEquals(1, $resultSet->count());
}
public function testSetDefaultOperator()
{
$operator = 'AND';
$query = new Elastica_Query_QueryString('test');
$query->setDefaultOperator($operator);
$data = $query->toArray();
$this->assertEquals($data['query_string']['default_operator'], $operator);
}
public function testSetDefaultField()
{
$default = 'field1';
$query = new Elastica_Query_QueryString('test');
$query->setDefaultField($default);
$data = $query->toArray();
$this->assertEquals($data['query_string']['default_field'], $default);
}
public function testSetRewrite()
{
$rewrite = 'scoring_boolean';
$query = new Elastica_Query_QueryString('test');
$query->setRewrite($rewrite);
$data = $query->toArray();
$this->assertEquals($data['query_string']['rewrite'], $rewrite);
}
/**
* @expectedException Elastica_Exception_Invalid
*/
public function testSetQueryStringInvalid()
{
$query = new Elastica_Query_QueryString();
$query->setQueryString(array());
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,574 |
{"url":"https:\/\/www.jobilize.com\/physics\/section\/coordinate-systems-for-one-dimensional-motion-by-openstax?qcr=www.quizover.com","text":"# 2.2 Vectors, scalars, and coordinate systems\n\n Page 1 \/ 4\n\n## Learning objectives\n\nBy the end of this section, you will be able to:\n\n\u2022 Define and distinguish between scalar and vector quantities.\n\u2022 Assign a coordinate system for a scenario involving one-dimensional motion.\n\nThe information presented in this section supports the following AP\u00ae learning objectives and science practices:\n\n\u2022 3.A.1.2 The student is able to design an experimental investigation of the motion of an object.\n\nWhat is the difference between distance and displacement? Whereas displacement is defined by both direction and magnitude, distance is defined only by magnitude. Displacement is an example of a vector quantity. Distance is an example of a scalar quantity. A vector \u00a0 \u00a0is any quantity with both magnitude and direction . Other examples of vectors include a velocity of 90 km\/h east and a force of 500 newtons straight down.\n\nThe direction of a vector in one-dimensional motion is given simply by a plus $\\left(+\\right)$ or minus $\\left(-\\right)$ sign. Vectors are represented graphically by arrows. An arrow used to represent a vector has a length proportional to the vector's magnitude (e.g., the larger the magnitude, the longer the length of the vector) and points in the same direction as the vector.\n\nSome physical quantities, like distance, either have no direction or none is specified. A scalar \u00a0 \u00a0is any quantity that has a magnitude, but no direction. For example, a $\\text{20\u00baC}$ temperature, the 250 kilocalories (250 Calories) of energy in a candy bar, a 90 km\/h speed limit, a person's 1.8 m height, and a distance of 2.0 m are all scalars\u2014quantities with no specified direction. Note, however, that a scalar can be negative, such as a $-\\text{20\u00baC}$ temperature. In this case, the minus sign indicates a point on a scale rather than a direction. Scalars are never represented by arrows.\n\n## Coordinate systems for one-dimensional motion\n\nIn order to describe the direction of a vector quantity, you must designate a coordinate system within the reference frame. For one-dimensional motion, this is a simple coordinate system consisting of a one-dimensional coordinate line. In general, when describing horizontal motion, motion to the right is usually considered positive, and motion to the left is considered negative. With vertical motion, motion up is usually positive and motion down is negative. In some cases, however, as with the jet in [link] , it can be more convenient to switch the positive and negative directions. For example, if you are analyzing the motion of falling objects, it can be useful to define downwards as the positive direction. If people in a race are running to the left, it is useful to define left as the positive direction. It does not matter as long as the system is clear and consistent. Once you assign a positive direction and start solving a problem, you cannot change it.\n\nan 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit\nthanks so much. i undersooth well\nwhat is physics\nis the study of matter in relation to energy\nKintu\na submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole\nwhat is power?\npower P = Work done per second W\/ t. It means the more power, the stronger machine\nSphere\ne.g. heart Uses 2 W per beat.\nRohit\nA spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror\ndid you solve?\nShii\n1.75cm\nRidwan\nmy name is Abu m.konnek I am a student of a electrical engineer and I want you to help me\nAbu\nthe magnification k = f\/(f-d) with focus f = R\/2 =16 cm; d =12 cm k = 16\/4 =4\nSphere\nA weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a \u201cOne Way\u201d street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa\nhi\nGodfred\nGodfred\nIf a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?\nthe same behavior thru the prism out or in water bud abbot\nJu\nIf this will experimented with a hollow(vaccum) prism in water then what will be result ?\nAnurag\nWhat was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?\nWhat is the far point of a person whose eyes have a relaxed power of 50.5 D?\nJaydie\nWhat is the far point of a person whose eyes have a relaxed power of 50.5 D?\nJaydie\nA young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?\nJaydie\n29\/20 ? maybes\nJu\nIn what ways does physics affect the society both positively or negatively\nhow can I read physics...am finding it difficult to understand...pls help\ntry to read several books on phy don't just rely one. some authors explain better than other.\nJu\nAnd don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.\nJu\nhope that helps\nJu\nI have a exam on 12 february\nwhat is velocity\nJiti\nthe speed of something in a given direction.\nJu\nwhat is a magnitude in physics\nPropose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.\nWhat is meant by dielectric charge?","date":"2019-11-13 17:41:40","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 5, \"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\": 0.6553951501846313, \"perplexity\": 868.1621310286865}, \"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-2019-47\/segments\/1573496667319.87\/warc\/CC-MAIN-20191113164312-20191113192312-00364.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.thearmchaircritic.org\/mansplainings\/difficulty-adjustment-in-blockchain","text":"We looked at the Proof-of-Work algorithm in the previous article, and in this article, we shall look at how we adjust the target hash based on the difficulty value to keep the transaction time constant.\n\nFor starters, we calculate the target hash based on a difficulty value. It is this difficulty value that we adjust to keep the time taken to produce a transaction constant. Let\u2019s see how we adjust this difficulty value.\n\nBitcoin adjusts the difficulty value every 2016 transactions (it\u2019s actually blocks and we shall discuss blocks later). Bitcoin expects each transaction (block) to take around 10 minutes. Therefore, effectively, Bitcoin adjusts the difficulty value every 20160 minutes, which is equal to two weeks. To make sure that transactions on average take 10 minutes, we need to measure the time taken for each transaction.\n\nSo, we timestamp every transaction. A timestamp is the number of milliseconds that have elapsed since the Unix epoch, which is 00:00:00 01 January 1970. We can find the difference between the timestamp of the 2016th block in the current batch and the 2016th block of the previous batch to find out the total time taken to complete these 2016 transactions.\n\n## Calculating difficulty\n\nOnce we have this value, we can compare this with the expected value, which is 20160 minutes, by dividing the expected value by the actual value. If both the values are the same, we will get a value of one. If the transactions have taken place quicker, then the result would be greater than one. Similarly, if the transactions take longer, we will get a value of less than one.\n\n={\\text{expected value (20160)} \\over \\text{actual value}}\n\nWe can then use this value to calculate difficulty. If the transactions were quicker, then that means we should increase the difficulty. We have already seen that by dividing the expected value by the actual value, we get a value greater than one if the transactions were quicker. Consequently, if we multiply this value by the existing difficulty, we will end up with a higher difficulty value.\n\n\\text{new difficulty}={\\text{difficulty} \\times {\\text{expected value (20160)} \\over \\text{actual value}}}\n\nNow, let\u2019s look at a few examples. Assuming the actual value was 30,000, and the difficulty value is 100, let\u2019s see what the new difficulty value would be.\n\n\\text{new difficulty}={100 \\times {20160 \\over 30000}}\n\\text{new difficulty}={100 \\times 0.672}\n\\text{new difficulty}={67.2}\n\nAs you can see, the difficulty value has come down since the transactions have taken longer.\n\nLet\u2019s take another example with an actual value of 15,000 and a difficulty value of 100:\n\n\\text{new difficulty}={100 \\times {20160 \\over 15000}}\n\\text{new difficulty}={100 \\times 1.334}\n\\text{new difficulty}={133.4}\n\nThe difficulty value has gone up since the transactions were quicker.\n\n## Calculating target hash based on difficulty\n\nLet\u2019s now see how we calculate the target hash based on the difficulty value. We have seen that the theoretical maximum hash value is 2255. But in actuality, the maximum hash value is set to:\n\n0x00000000FFFF0000000000000000000000000000000000000000000000000000\n\nWe obtain the target hash value by dividing this maximum hash value by the difficulty value.\n\n\\text{target hash}={\\text{maximum hash value} \\over \\text{difficulty}}\n\nWhen a blockchain network is incepted, the target hash would be the maximum hash value. So, the difficulty value will be 1. As a result, the difficulty value can never be lower than 1 since a lower difficulty value will mean that the target hash will be higher than the maximum hash value.\n\nThe target hash becomes smaller and smaller as many computers join the network or as the processing power of the existing computers increases. This increases the difficulty of solving the puzzle and consequently, ensures that the time taken to solve the puzzle remains 10 minutes.\n\n## Storing target hash\n\nHowever, we don\u2019t store the target hash as a 256-bit hash in blocks (We shall learn about blocks later. For the time being, consider blocks as same as transactions.). In order to conserve space, we store it as a 32-bit (4-bytes) integer value. For example, the maximum possible hash is defined as 486604799, which is 0x1d00ffff in the hexadecimal format. This integer is called bits.\n\nLet\u2019s see how the bits are then converted back to the hash format. First, the value of the bits is converted to the hexadecimal format, which is 0x1d00ffff. This is, as aforementioned, a 4-byte number. The most significant byte of this (0x1d) is called the index. The 3 least significant bytes of this (0x00ffff) are called the coefficient. Now, we can use the following formula to find out the target hash value.\n\n\\text{target hash} = \\text{coefficient} \\times 2^{8 {(\\text{index}-3)}}\n\nLet\u2019s try to plug the coefficient and the index into this formula to obtain the target hash.\n\n\\text{target hash} = \\text{coefficient} \\times 2^{8 {(\\text{0x1d}-3)}}\n\nThis will give an output of\n\n0xFFFEFFD1A3A429BFBCB8A4188E09DA06491A6841F000000000000000\n\nWe can round this off to\n\n0xFFFF0000000000000000000000000000000000000000000000000000\n\nNote that this has only 224 bits. To make it 256 bits, we can add zeroes in front.\n\n0x00000000FFFF0000000000000000000000000000000000000000000000000000\n\nThis is the computed target hash.\n\n## Another method to calculate the target hash\n\nHowever, there is an easier way to calculate this as well. Consider the index as the number of bytes and the coefficient as a prefix. In our example, the index is 0x1d, which converted to decimal is 29. So, the calculated value should have 29 bytes. The prefix, 0x00ffff, has only 3 bytes. So, append 52 zeroes to the prefix to obtain the remaining 26 bytes. And then add zeroes in front of this value to get a 256-bit hash.\n\nOne should also keep in mind that a maximum hash value of 0x00000000FFFF0000000000000000000000000000000000000000000000000000 is not applicable to pool miners (We shall see about pool mining in detail later). Pool miners use a maximum hash value of 0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF.\n\nSo, the difficulty value calculated by pool miners would differ from the one calculated by others. The difficulty value calculated by pool miners is called pdiff whereas the one calculated by others is called bdiff.\n\nNow that we understand how we adjust the target hash value, let\u2019s see how we create blocks out of transactions in the next article.","date":"2023-03-29 03:38:09","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8330579996109009, \"perplexity\": 947.7365193695758}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296948932.75\/warc\/CC-MAIN-20230329023546-20230329053546-00719.warc.gz\"}"} | null | null |
/**
*
*
*
*/
var ArrayProto = Array.prototype
, ObjProto = Object.prototype
, FuncProto = Function.prototype
var nativeIsArray = Array.isArray
, nativeKeys = Object.keys
, nativeBind = FuncProto.bind
, nativeCreate = Object.create
, hasOwnProperty = ObjProto.hasOwnProperty
, toString = ObjProto.toString
, push = ArrayProto.push
, slice = ArrayProto.slice
, nativeAssign = Object.assign
export const isUndefined = function (obj){
return obj === void 0
}
export const isObject = function (obj){
var type = typeof obj
return type === 'function' || type === 'object' && !!obj
}
export const isPlainObject = function (obj){
if(typeof obj !== 'object'){
return false
}
if ( obj.constructor &&
!hasOwnProperty.call( obj.constructor.prototype, 'isPrototypeOf' ) ) {
return false
}
return true
}
export const isArray = nativeIsArray || function (obj){
return toString.call(obj) === '[object Array]'
}
export const isFunction = function (obj){
return typeof obj == 'function' || false
}
export const has = function (obj, key){
return obj != null && hasOwnProperty.call(obj, key)
}
export const keys = nativeKeys || function (obj){
var keys = []
for (var key in obj) if (has(obj, key)) keys.push(key)
return keys
}
export const assign = nativeAssign || function(target, ...sources){
sources.forEach((source) => {
keys(source).forEach((key) => {
target[key] = source[key]
})
})
return target
}
export const clone = function (obj){
if(!obj) return obj
if(isArray(obj)){
return obj.slice()
}else{
return assign({}, obj)
}
}
export const range = function range(start, stop, step){
if (stop == null) {
stop = start || 0
start = 0
}
step = step || 1
var length = Math.max(Math.ceil((stop - start) / step), 0)
var range = Array(length)
for (var idx = 0; idx < length; idx++, start += step) {
range[idx] = start
}
return range
}
export function stackProcess(expr, fns, context = {}){
var head = fns[0]
, tails = fns.slice(1)
, preProcessor = head[0]
, postProcessor = head[1] || ((a) => a)
var preResult = preProcessor(expr, context)
if(!tails.length){
return postProcessor(preResult, context)
}else{
return postProcessor(stackProcess(preResult, tails, context), context)
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,213 |
Q: When separation in $L^1$ is possible? Let $A$, $B$ be disjoint convex closed subsets of the Banach space $L^1[0,1]$. Assume additionally that $A$ is bounded and $A$, $B$ are closed under convergence in measure. Then there exists a closed hyperplane, which strictly separates $A$ and $B$.
This follows almost immediately from the Komlós lemma (if the distance between $A$ and $B$ is positive, then usual Hahn-Banach theorem works, if not, let $a_n\in A$, $b_n\in B$ be so that $\|a_n-b_n\|\rightarrow 0$, by Komlós lemma we may without loss of generality suppose that $c_n:=(a_1+\dots+a_n)/n$, $d_n:=(b_1+\dots+b_n)/n$ converge in measure to $c\in A$, $d\in B$ respectively, but $\|c_n-d_n\|\rightarrow 0$, hence $c=d$, a contradiction.)
Two questions are:
1) This looks like a very classical subject, what is appropriate reference?
2) Are there some weaker general assumptions for the existence of separator in $L^1$ or maybe in more general spaces?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,172 |
{"url":"https:\/\/www.physicsforums.com\/threads\/the-infinite-square-well.113274\/","text":"# The infinite square well\n\nA particle is in ground state of an infinite square well. Find the probabilirt of finding the particle in the interval $$\\Delta x = 0.002L$$ at x=L. (since delta x is small, do not integrate)\n\nhere's what I have:\n\n$$\\Psi*\\Psi = P(x) = \\frac{2}{L} sin^2 \\left(\\frac{ \\pi x}{L} \\right) \\Delta x$$\n\n$$P = \\frac{2}{L} sin^2 \\left(\\frac{ \\pi L}{L} \\right) 0.002L$$\n$$P = 2sin^2 \\left(\\pi \\right) 0.002$$\n$$P=0.004$$\n\nis this the correct method?\n\nLast edited:\n\nRelated Advanced Physics Homework Help News on Phys.org\nyou can't just ignore the sin(Pi) term because it is 0. You need to use a first order approximation of sin(Pi+delta) and square the first order approximation in order to get the result you want.\n\n~Lyuokdea\n\nwhat is a first order approximation? and why would I use sin(Pi+delta) ?\n\nMeir Achuz\nHomework Helper\nGold Member\nUrbanXrisis said:\nA particle is in ground state of an infinite square well. Find the probabilirt of finding the particle in the interval $$\\Delta x = 0.002L$$ at x=L. (since delta x is small, do not integrate)\n\nhere's what I have:\n\n$$\\Psi*\\Psi = P(x) = \\frac{2}{L} sin^2 \\left(\\frac{ \\pi x}{L} \\right) \\Delta x$$\n\n$$P = \\frac{2}{L} sin^2 \\left(\\frac{ \\pi L}{L} \\right) 0.002L$$\n$$P = 2sin^2 \\left(\\pi \\right) 0.002$$\n$$P=0.004$$\n\nis this the correct method?\nYou made a trig mistake with $$sin(\\pi)$$.\nIt should = zero.\nI disagree with the hint.\nYou can expand $$sin^2(\\pi-z)$$ for small z, and then integrate from L-\\delta x to L. You could also integrate without the expansion, and just be careful about the numbers.\n\nsorry, i used bad terminology in the hint, use Meir Archuz's hint, try to do a taylor series expansion for sin(x) around x=0 and see how that applies to your problem.\n\n~Lyuokdea\n\nwouldnt the possibilty be just = 0? I dont think this question was designed for the use of the taylor series.\n\nPhysics Monkey\nHomework Helper\nThe probability is not zero. You only get zero because you've made too rough of an approximation to the integral. To get a better estimate of the propability, try evaluating the wavefunction somewhere else in the interval, say at the midpoint.\n\ndelta x=L\/2\n$$P = \\frac{2}{L} sin^2 \\left(\\frac{ \\pi }{2} \\right) 0.002L$$\nP=0.004?\n\nPhysics Monkey\nHomework Helper\nHi UrbanXrisis,\n\nYou have misunderstood me, but let me ask you, do you think your answer makes sense? Should the probability depend on the value of the wavefunction in the middle of the box? To clarify, what I mean was that you should perhaps look at the midpoint of the interval $$[ L - .002 L, L]$$.\n\ni'm not sure. there is an example in my text that is exacly the same problem. \"what would be the probability of finding an electron while in ground state in a very narrow region delta x = 0.01L wide centered at x=5L\/8\"\n\nThe way that the book goes about solving this question was using:\n$$P = \\frac{2}{L} sin^2 \\left(\\frac{ \\pi (5L\/8)}{L} \\right) 0.01L=0.017$$\n\nso I am following their procedure\n\nwhy would the probability not be zero at x=L ??\nit should be zero AT the boundary but little to the left say $L-\\Delta x$ it will be almost zero but very small\n\nUrbanXrisis said:\ni'm not sure. there is an example in my text that is exacly the same problem. \"what would be the probability of finding an electron while in ground state in a very narrow region delta x = 0.01L wide centered at x=5L\/8\"\n\nThe way that the book goes about solving this question was using:\n$$P = \\frac{2}{L} sin^2 \\left(\\frac{ \\pi (5L\/8)}{L} \\right) 0.01L=0.017$$\n\nso I am following their procedure\nbut is this what I should follow when doing my problem?\n\nno, because then you will get an answer that is zero.\n\nFor the spread centered around a point like x=5L\/8, the above approximation is ok, because you can assume that (5+.01)L\/8 is approximately similar to 5L\/8.\n\nHowever, you cannot do this for the point x=L because sin(Pi*x\/L) is exactly 0 at that point. Thus sin(Pi*(1-.01)*L\/L) is not approximately the same as sin(Pi).\n\nHave you done work with Taylor Series? How does sin(x) change when x is close to zero? Find the first non-zero term in the taylor expansion, and use that in order to find a non-zero answer. For most classes, the first non-zero term is a good enough answer.\n\n~Lyuokdea\n\nbut according to qpt:\n\nqtp said:\nwhy would the probability not be zero at x=L ??\nit should be zero AT the boundary but little to the left say $L-\\Delta x$ it will be almost zero but very small\n\nthat's exactly right, but your answer gives you a number that is exactly zero, because the sin (Pi) is 0. To find the small but non-zero answer, you need to expand sin(Pi) into it's taylor series.\n\nPhysics monkey gave another good suggestion which gives you a non-zero answer without depending on Taylor series, simply find the midpoint of the range [L-.002, L] and then use that value, as shown in the example which you quoted from the book, to find a first order approximation of the answer.\n\n~Lyuokdea\n\nMeir Achuz","date":"2021-03-01 20:39:24","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8972861766815186, \"perplexity\": 520.0462578051736}, \"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-2021-10\/segments\/1614178362899.14\/warc\/CC-MAIN-20210301182445-20210301212445-00406.warc.gz\"}"} | null | null |
Q: ng-repeat list doesn't update immediately after api call My web app view lists folders and their children in a nested list:
<ul>
<li class="folderLi" ng-repeat="folder in folders">
<a href="" ng-click="listFolderFiles( folder )">{{folder.title}}</a>
<ul >
<li ng-repeat="child in folder.children">
{{child.title}}
</li>
</ul>
</li>
</ul>
When I load the initial list of folders, the list updates immediately to display the folders. However, there is no children object on each folder at that point. That is filled out when the folder is clicked and the app calls the Google Drive API to retrieve the folder's children. The controller includes this function:
$scope.listFolderFiles = function( folder ) {
var request = gapi.client.request({
'path': '/drive/v2/files',
'method': 'GET',
'params' : {
'q' : "'" + folder.id + "' in parents"
}
});
request.then(function(response){
//log successful response
console.log(response);
folder.children = response.result.items;
}, function(response) {
//log error
console.log(response);
})
}
This function correctly retrieves the information and updates the model. However, the ng-repeat list of children is not updated and displayed immediately. Instead, it is updated and displayed the next time a folder is clicked. It seems like this function is updating the view before the api call is finished, so the next time the function runs the view gets updated to show the last API call's response. Thoughts?
A: You are trying to update outside angular's knowledge. So your view is not updated. You need to use $scope.$apply() or $timeout to run a digest cycle.
request.then(function(response){
//log successful response
console.log(response);
//folder.children = response.result.items; //Required in case of $scope.$apply()
$timeout(function(){folder.children = response.result.items;}); //Or $scope.$apply(); (Don't forget to inject $timeout in your controller)
}, function(response) {
//log error
console.log(response);
})
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,436 |
be:longing
exploring personal experiences of migration, cross-culture, nostalgia and belonging
Thoughts + Stories
Photos + Art
Folk + Food
by belongingmag November 21, 20179:46 am December 3, 2017
Memories and play
Courtney Neville is a recruitment specialist who spends her time between PNG and Australia. She was a boarder at Girls Grammar school in Canberra and then attended Narrabundah College before moving to Queensland. Courtney lived in and around Brisbane for 7 years, studying and working, and then moved to Townsville with her two youngest siblings (and three dogs) to join their army sister.
Photographer's statement:
For me, these photos symbolise the different worlds and cultures that bring PNG and Australia together. Although they are so close geographically and are in some senses sister countries, I recall being struck by distinctions between the two places as a child when I visited my Nan and Pop in Canberra for a fair bit of time every year. The photo of my sister and me was taken at their place, where we loved to run through the sprinklers and roll around in the mud, baking mud pies. We did this back home in PNG, too, and continued to play our games wherever our parents took us. Apparently, you can take the girl out of PNG, but you can't take PNG out of the girl. Some of our cousins in Canberra were a lot more "posh" than us, and didn't know how to take their grubby and carefree PNG cousins, but kids will be kids anywhere in the world and playing games always unites people – play is a universal language.
The first photograph in this piece was taken in Mendi, in the Southern Highlands in PNG, and is of myself and my father at a marketplace on the side of the road. From what I have gathered, the pig was a household pet and was not for sale – we were just playing with it when my mother took the photo. It is actually one of my favourite photographs of my father and me. The marketplaces in Mendi still look similar and driving around there these days reminds me of my childhood and being carefree.
I was lucky to go back to PNG in September 2017 to commemorate the 75th anniversary of the Battle of Milne Bay. Kids were dancing and selling artifacts to the tourists who came in on the Pacific Ocean cruise, to raise funds for school tuition. Observing this brought back memories of when I used to dance and participate in similar school cultural events. The excitement and nerves were always present, but talking and hugging it out with school friends is a memory that you cherish forever. The smiles on the kids' faces were so big and their eyes so bright – they were so proud of themselves, as well they should be, contributing as they were to fundraising for their school tuition and making lifelong memories – just as I did.
© Courtney Neville, 2017
Tagged with: courtneyneville
belongingmag | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,794 |
package org.apache.flex.swf.types;
/**
* Sound Envelope record.
*
* @see SoundInfo
*/
public class SoundEnvelope implements IDataType
{
private long pos44;
private int leftLevel;
private int rightLevel;
/**
* @return the pos44
*/
public long getPos44()
{
return pos44;
}
/**
* @param pos44 the pos44 to set
*/
public void setPos44(long pos44)
{
this.pos44 = pos44;
}
/**
* @return the leftLevel
*/
public int getLeftLevel()
{
return leftLevel;
}
/**
* @param leftLevel the leftLevel to set
*/
public void setLeftLevel(int leftLevel)
{
this.leftLevel = leftLevel;
}
/**
* @return the rightLevel
*/
public int getRightLevel()
{
return rightLevel;
}
/**
* @param rightLevel the rightLevel to set
*/
public void setRightLevel(int rightLevel)
{
this.rightLevel = rightLevel;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,752 |
\section{Conclusion}
\section{Introduction}
As massive data is collected from social media, wearable devices and internet of things, novel algorithms and platforms are highly desired to handle data-intensive computing tasks. Vector- and matrix-based methods can efficiently process $1$-way data (e.g., a sequence of voice data) or $2$-way data (e.g., a gray-scale image), but they are often inefficient to handle multi-way data. Representative examples includes $3$-way (or order-3) E-commerce data (which records customers' preference on massive products over a few months), $4$-way (or order-$4$) cardiac image data (which records the spatial data of $3$D at multiple time points). Processing such multi-way data often suffers from the curse of dimensionality.
Tensors are a high-order generalization of matrices and vectors, and they are a natural tool to represent and process multi-way data~\cite{kolda2009tensor}. Leveraging various tensor decomposition or factorization methods~\cite{kolda2009tensor,oseledets2010tt,de2000multilinear,de2000best}, the curse of dimensionality of storing and computing multi-way data can be avoided or significantly mitigated in many applications. For instance, the canonical polyadic (CP)~\cite{candecomp,harshman1970fpp} and tensor-train~\cite{oseledets2010tt} factorizations can reduce the storage cost and unknown variables from an exponential function to a linear one. Tucker factorization~\cite{de2000multilinear} can be used for high-order principle component analysis or facial recognition~\cite{vasilescu2002multilinear,vasilescu2003multilinear,vasilescu2005multilinear}. Tensor computation has achieved tremeonduous success in data mining~\cite{kolda2008scalable}, computer vision~\cite{vasilescu2002multilinear,vasilescu2003multilinear,vasilescu2005multilinear}, medical imaging~\cite{batmanghelich2011regularized}, electronic design automation~\cite{zhang2016big,zhang2014enabling,zhang2016tensor,luan2019prediction} and deep learning~\cite{novikov2015tensorizing,ttrnn2017icml,hawkins2019bayesian}.
The emerging tensor computation concept brings in massive research opportunities and challenges on the hardware level. Due to the fundamental difference between tensor and matrix computations, we may need to re-think many aspects of tensor computation (e.g., storage, computing and data movement) on specific platforms. Increasing research results have been reported to improve the tensor data storage and computing on the cloud and high-performance clusters ~\cite{kaya2016high,smith2017sparse,li2015input}. However, little work has been done on resource-constrained platforms. This becomes increasingly important as the need of energy-efficient machine learning and data privacy surges. In order to address this issues, some efforts have been made towards tensor-compressed neural networks on mobile devices~\cite{kim2015compression} and dense tensor operations on FPGA. For instance, some dense tensor operations including MTTKRP, TTM and TTMc were accelerated in~\cite{srivastava2019t2s}; a spectral analysis of Hankel tensors was reported in \cite{huang2019high}. To perform dense Tucker decomposition on FPGA, Zhang et al.~\cite{zhang2019tucker} divided the hardware architectures into three modules: tensor-times-matrix, singular value decomposition via Jacobi iterations and tensor permutation/reshaping. In addition, a warm-start algorithm was used to reduce the cost of Jacobi iterations. The resulting FPGA accelerator demonstrated significant speedup compared with both CPU and GPU. However, the FPGA accelerator~\cite{zhang2019tucker} cannot exploit data sparsity, and it becomes energy- and time-inefficient when dealing with sparse tensors. Ref.~\cite{srivastava2020tensaurus} reported some sparse tensor computation kernels. For instance, it demonstrated how to implement both dense and sparse tensor operations, such as sparse TTMc via sparse compute pattern $SF^3$. To our best knowledge, there is no FPGA accelerator available for sparse Tucker decomposition.
In this paper, we investigate the hardware acceleration of Tucker factorization for {\bf sparse} tensor data. Sparse tensors widely appear in practice due to the missing information in recommendation systems, medical image or E-commerce data. For instance, in magnetic resonance imaging (MRI), one can generate a sparse tensor by partial MRI scanning, then reconstruct the whole image with a low cost~\cite{roohi2016dynamic}. In neuroscience, researchers use sparse tensors to monitor the brain variability~\cite{fillard2005extrapolation}. In EDA, it is often too expensive to obtain all simulation or measurement data, thus one uses a partially sampled sparse tensor for process variation or performance uncertainty prediction~\cite{zhang2016big,zhang2016tensor,luan2019prediction}. Although extensive algorithms have been developed to process sparse tensors, their hardware/algorithm co-optimization remains a rarely explored field~\cite{zhang2019tucker}. This task has become increasingly important as energy efficiency and privacy cause lots of concerns in the data science and machine learning community.
\begin{figure*}[t]
\centering
\includegraphics[width=4.5in]{fig/MRI.pdf}
\caption{(a) A matrix is a $2$-D data array (e.g., one slice of MRI data), (b) a $3$-way tensor is a $3$-D data array (e.g., multiple slices of images).}
\label{fig:tensor}
\end{figure*}
\subsection{Paper Contributions and Organization}
This paper proposes to design an energy- and memory-efficient hybrid FPGA-CPU accelerator for sparse Tucker decomposition~\cite{kaya2016high}. This algorithm consists of three major components: tensor-times-matrix (TTM)~\cite{kolda2009tensor}, Kronecker product~\cite{van2000ubiquitous} and QR decomposition with column pivoting (QRP)~\cite{golub1996matrix}. Our specific contributions include:
\begin{itemize
\item On the hardware side, we present a high-level synthesis (HLS) FPGA implementation for sparse Tucker decomposition. We describe the design of two modules, TTM and Kronecker product, by exploiting the data sparsity.
\item On the algorithm side, we replace the conventional singular value decomposition (SVD)~\cite{golub1971singular} with the QR decomposition with column pivoting (QRP)~\cite{golub1996matrix} to reduce the data storage cost and to speed up the computation.
\item We implement our FPGA accelerator in a Xilinx FPGA on Amazon web service (AWS). Then we compare our hybrid FPGA-CPU accelerator with CPU and with the recently developed dense FPGA accelerator~\cite{zhang2019tucker} on synthetic and real-world sparse tensor benchmarks. Our hybrid FPGA-CPU accelerator
achieves $1.15 \times$$ \sim$$ 1091\times$ speedup and consumes $93.519\% $$\sim$$ 99.514 \%$ less energy. In addition, our proposed accelerator achieves significant speedup ($23.6\times$$\sim $$ 1091\times$) when the tensor is very large and sparse
\end{itemize}
This paper is organized as follows. Section~\ref{tensorref} introduces some background information about tensor operations. Section~\ref{sec:Sparse_tucker} presents the algorithm and our Vivado HLS FPGA design of a sparse Tucker decomposition. We compare our FPGA/CPU hybrid platform with CPU and the dense Tucker FPGA accelerator \cite{zhang2019tucker} in terms of run-time and energy efficiency in Section~\ref{sec:Experiments}. Finally, Section~\ref{sec:conclusion} concludes this paper.
\section{Preliminaries of Tensors}
\label{tensorref}
This section presents some background about tensors, which is necessary for understanding the ideas of this paper.
\begin{definition}
A tensor $\ten{X} \in \mathbb{R}^{I_1 \times I_2 \times \dots \times I_N}$ is a high-dimensional array of order $N$. Here the order $N$ (also known as ``way") is the total number of dimensions. A matrix $\mat{X} \in \mathbb{R}^{n_1\times n_2}$ is a $2$nd-order (or $2$-D) tensor, and its element indexed by $(i_1, i_2)$ can be denoted as $x_{i_1i_2}$. For a general $N$th-order (or $N$-way) tensor $\ten{X}$, its element indexed by $(i_1, i_2 \cdots, i_N)$ is denoted as $x_{i_1 i_2\cdots i_N}$.
\end{definition}
Fig.~\ref{fig:tensor} shows a matrix (e.g., one slice of MRI data) and a $3$-way tensor, respectively. In this paper, we use boldface lower-case letters (e.g., $\mat{x}$) to denote vectors, boldface upper-case letters (e.g., $\mat{X}$) to denote matrices, and boldface Euler script letters ( e.g.,$\ten{X}$) to denote tensors. A scalar is denoted by a lower-case letter, e.g., $x$.
\begin{definition}
The inner product of two tensors with the same size is defined as
\begin{equation}
\langle \ten{X}, \ten{Y} \rangle =\sum \limits_{i_1i_2 \cdots i_N} x_{i_1i_2 \cdots i_N} y_{i_1i_2 \cdots i_N}.
\end{equation}
Furthermore, the Frobenius norm (also known as F-norm) of a tensor $\ten{X}$ is defined as $|| \ten{X}||_{\rm F} =\sqrt{\langle \ten{X}, \ten{X} \rangle}$.
\end{definition}
\begin{definition}
A matricization operation, (also known as unfolding or flattening), reshapes a tensor into a matrix. The mode-$n$ matricization of a tensor $\ten{X} \in \mathbb{R}^{I_1 \times I_2 \times \dots \times I_N}$ is denoted as $\mathbf{X}_{(n)}$ which has $I_n$ rows and $\prod_{k\neq n}I_k$ columns. Element-wise, we have each entry of $\mathbf{X}_{(n)}$ as
\begin{equation}
\mathbf{X}_{(n)}({i_n, j})=x_{i_1i_2\cdots i_N} \\
{\text{with}}~j = 1 + \sum_{k=1, k \neq n}^{N} (i_k-1)\prod_{m=1, m\neq n}^{k-1} I_m.
\end{equation}
\end{definition}
\begin{definition}
The mode-$\mathbf{n}$ tensor matrix product [or tensor-times-matrix (TTM)], between a tensor $\ten{X} \in \mathbb{R}^{I_1 \times I_2 \times \dots \times I_N }$ and a matrix $\mathbf{U} \in \mathbb{R}^{J \times I_n}$ is denoted as
\begin{equation}
\ten{G} = \ten{X}\times_n \mathbf{U},~{\text{where}}~{\ten{G} \in \mathbb{R}^{I_1 \times \dots \times I_{n-1} \times J \times I_{n+1}\times \dots \times I_N}}.
\end{equation}
Element-wise, we can write this operation as
\begin{equation}
g_{i_1\dotsi_{n-1} j i_{n+1}\dots i_N} = \sum_{i_n=1}^{I_n} x_{i_1 i_2 \dots i_N}u_{j i_n}.
\end{equation}
We may also obtain a TTM product by using the unfolded tensors:
\begin{equation}
\ten{G} = \ten{X} \times_n \mathbf{U} \Leftrightarrow \mat{G}_{(n)} = \mat{U}\mat{X}_{(n)}.
\end{equation}
\end{definition}
We further introduce a matrix operation that will be used in our subsequent tensor computation.
\begin{definition}
Given a matrix $\mat{A} \in \mathbb{R}^{m\times n}$ and another matrix $\mat{B} \in \mathbb{R}^{p\times q}$, their Kronecker product $\mat{A}\otimes\mat{B}$ is the following matrix $\mat{C} \in \mathbb{R}^{mp\times nq}$
\begin{equation}
\mat{C}=\mat{A}\otimes\mat{B}=\begin{bmatrix}
a_{11}\mat{B} & \cdots & a_{1n}\mat{B}\\
\vdots & \ddots & \vdots\\
a_{m1}\mat{B} & \cdots & a_{mn}\mat{B}
\end{bmatrix}.
\end{equation}
\end{definition}
\begin{algorithm}[t]
\caption{Standard HOOI for Tucker Decomposition}
\label{alg:hooi}
\begin{algorithmic}[1]
\STATE { Initialize $\{\mat{U}_n\} _{k=1}^N$ via HOSVD}
\WHILE {not converge}
\FOR {$n=1,2, \ldots, N$}
\STATE {$\ten{Y} = \ten{X} \times_1 \mat{U}_1^T \dots \times_{n-1} \mat{U}_{n-1}^T \times_{n+1} \mat{U}_{n+1}^T \dots \times_N \mat{U}_N^T$}
\STATE {Unfold $\ten{Y}$ and perform SVD: $ \mat{Y}_{(n)}=\mat{U} \mat{S} \mat{V}^T $}
\STATE {$\mat{U}_n \leftarrow$ the first $R_n$ columns of $\mat{U}$.}
\ENDFOR
\ENDWHILE
\STATE {\textbf{return} $\{ \mat{U}_{n}\}_{n=1}^N$. }
\end{algorithmic}
\end{algorithm}
\section{Accelerator for Sparse Tucker Decomposition}
\label{sec:Sparse_tucker}
Given a tensor $\ten{X} \in \mathbb{R}^{I_1 \times I_2 \times \dots \times I_N}$, the Tucker decomposition~\cite{de2000best} approximates it with a small low-rank core tensor $\ten{G} \in \mathbb{R}^{R_1 \times R_2 \times \dots \times R_N}$ and $N$ factor matrices $\{ \mat{U}_n \in \mathbb{R}^{I_n \times R_n } \}_{n=1}^N$:
\begin{equation}
\ten{X}\approx \ten{G}\times_1 \mat{U}_1 \times_2 \mat{U}_2 \cdots \times_N \mat{U}_N.
\end{equation}
Here $(R_1, R_2, \cdots, R_N)$ is a multilinear tensor rank.
The Tucker decomposition can be regarded as a high-order generalization of singular value decomposition (SVD), and it is often implemented with the power iteration method called high-order orthogonal iteration (HOOI) in~\cite{de2000best}. As shown in Alg.~\ref{alg:hooi}, it aims to find the orthogonal matrices $\{ \mat{U}_n \in \mathbb{R}^{I_n \times R_n }\}_{n=1}^N$ to maximize the F-norm of
\begin{equation}
\label{TTM_G}
\ten{G} = \ten{X}\times_1\mathbf{U}_1^T \times_2 \mathbf{U}_2^T \dots \times_N \mathbf{U}_N^T.
\end{equation}
In every iteration, we need to compute the $R_n$ dominant left singular vectors of unfolded matrix $\mat Y_{(n)}$, where
\begin{equation}
\label{eqn:power_ite}
\ten{Y} = \ten{X} \times_1 \mathbf{U}_1^T \dots \times_{n-1} \mathbf{U}_{n-1}^T \times_{n+1} \mathbf{U}_{n+1}^T \dots \times_N \mathbf{U}_N^T.
\end{equation}
The orthogonal matrix is obtained by a SVD of the unfolded matrix $\mat Y_{(n)}$.
The standard HOOI becomes very inefficient for sparse tensors because Line 4 of Alg.~\ref{alg:hooi} does not exploit any data sparsity and always performs $N-1$ times of TTM operations.
\begin{algorithm}[t]
\caption{Sparse Tucker Decomposition}
\label{alg:sparse_tucker}
\textbf{Input: }
A sparse tensor $\ten X$
\\$R_1$,$\ldots$,$R_N$: rank of approximation
\begin{algorithmic}[1]
\STATE \textbf{initialize} $\mathbf{U_1},...,\mathbf{U_N}$ randomly.
\REPEAT
\FOR {$n=1, 2, \dots, N$}
\FOR {$x_{i_1,\dots,i_N} \neq 0$}
\STATE $\mathbf{Y}_{(n)}(i_n,:) \mathrel{+}= x_{i_1,\dots,i_N}[\otimes_{t\neq n}\mathbf{U}_t(i_t,:)]$
\ENDFOR
\STATE $\mathbf{U}_n \leftarrow \textbf{QRP}(\mathbf{Y}_{(n)}, R_n)$
\ENDFOR
\STATE $\ten{G} \leftarrow \ten{Y}\times_N \mathbf{U}_N^T$
\UNTIL{convergence or maximum number of iterations reached}
\end{algorithmic}
\textbf{Output: }
\\$\ten{G}$: a $R_1 \times $$\ldots$$\times R_N$ core tensor
\\$\mathbf{U_1},\ldots,\mathbf{U_N}$: $\mat{U}_n$ is a $R_n \times I_n $ factor matrix
\end{algorithm}
\begin{figure}[t]
\centering
\includegraphics[width=3.5 in]{fig/Block_Diagram.pdf}
\caption{A Hybrid FPGA-CPU platform for sparse Tucker factorization.}
\label{fig:Block_Diag}
\end{figure}
\begin{table}[t]
\caption{Coordinate (COO) format of a $5\times5\times5\times5$ sparse tensor. Here $(i,j,k,l)$ denotes an index, and $nnz$ is the value of an associated non-zero data element.}
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
$i$ & $j$ & $k$ & $l$ & $nnz$ \\ \hline \noalign{\hrule height 1.0pt}
1 & 1 & 1 & 1 & 2 \\ \hline
1 & 1 & 1 & 5 & 7.5 \\ \hline
1 & 1 & 3 & 5 & 4 \\ \hline
2 & 2 & 2 & 4 & 5 \\ \hline
\end{tabular}
\label{tab:COO}
\end{table}
\subsection{Overall Algorithm Flow}
In this paper, we design an FPGA-CPU hybrid accelerator based on~\cite{kaya2016high} to perform Tucker factorization for sparse tensors. Two formats can be used to represent sparse tensors:
\begin{itemize}
\item The coordinate format (COO) stores a sparse tensor with all nonzero elements and their associated coordinate vectors, shown in~Table \ref{tab:COO}. The first four columns represent the coordinate $(i,j,k,l) $ of 4 nonzero elements, and the last column represents the corresponding value. The COO format usually requires storage of $O(nnz*N)$ index values and $O(nnz)$ nonzero data values, where $nnz$ is the number of nonzero elements and $N$ is the mode of the tensor.
\item Compressed sparse fiber format (CSF) stores a sparse tensor by compressing the indices of nonzero elements that share the same coordinates. It is regarded as high dimensional version of the compressed sparse row (CSR) or compressed sparse column (CSC) formats used for matrices in \cite{gustavson1972some}. The CSF format requires $O(2*(nnz+s+f)+2)$ to store an order-$3$
tensor with $s$ slices, $f$ fibers and $nnz$ non-zero values.
\end{itemize}
In this paper, we use the COO format because of its flexibility and simplicity. Furthermore, the COO format provides better performance on merging-related TTM~\cite{tew2016investigation}. If we do not assume any special structure of the tensor and the non-zero elements are uniformly distributed, there will be rarely multiple nonzero elements in a given fiber. In such a general case, the CSF format barely has any advantages in storage compression.
The algorithm flow is summarized in Alg.~\ref{alg:sparse_tucker}. Compared with the standard dense Tucker factorization, the following techniques are used to exploit the data sparsity:
\begin{itemize}
\item Instead of storing the whole tensor, we only store the nonzero entries by specifying their values and indices.
\item When performing the tensor-times-matrix (TTM) in~\eqref{eqn:power_ite}, we do not perform $N-1$ levels of iterations over all modes except mode $n$. Instead, we only consider the non-zero elements of $\ten{X}$ and have a one-level iteration over the indices of all non-zero elements in $\ten{X}$.
\item In order to reduce the computational and memory cost of extracting orthogonal matrix factor $\mat{U}_n$, we replace the SVD of $\mat{Y}_{(n)}$ with a QR decomposition with column pivoting (QRP).
\end{itemize}
The proposed accelerator architecture is shown in Fig.~\ref{fig:Block_Diag}. Because it is difficult to parallelize the QRP operation, we implement it on CPU. Both \eqref{TTM_G} and~\eqref{eqn:power_ite} require TTM operations, but they are handled in different ways. For \eqref{TTM_G} we only need to compute
\begin{equation}
\label{eqn:core_ten}
\ten{G} = \ten{Y}\times_N \mat{U}_N
\end{equation}
once for each iteration after obtaining $\ten{Y}$ (which is often dense) by \eqref{eqn:power_ite}. Therefore, we design a specialized TTM module on FPGA in Section~\ref{subsec:TTMc}. For the power iteration in \eqref{eqn:power_ite}, we design a Kronecker product module on FPGA to accelerate the sparse operation, which is detailed in Section~\ref{subsec:kron}.
\subsection{Tensor-Times-Matrix (TTM) on FPGA}
\label{subsec:TTMc}
The computation of $\ten{G}$ in \eqref{TTM_G} requires $N$ tensor-matrix products on the original huge-size tensor $\ten{X}$. This expensive computation actually can be simplified.
Assuming that we have already done the power iteration \eqref{eqn:power_ite} for $n=N$, and obtained a small-size tensor $\ten{Y} \in \mathbb{R}^{R_1\times R_2\times \dots \times I_N}$ and an orthogonal factor matrix $\mathbf{U}_N\in \mathbb{R}^{I_N\times R_N}$. We only need to compute the mode-$N$ tensor-matrix product \eqref{eqn:core_ten} to obtain the core tensor $\ten{G}$ (line $9$, Alg. \ref{alg:sparse_tucker}). This TTM can be written in an element-wise manner:
\begin{equation}
\label{eqn:ttm_ele}
(\ten{Y}\times_N \mathbf{U}_N^T)_{r_1 r_2\dots r_N} = \sum_{i_N=1}^{I_N} y_{r_1 r_2 \dots i_N} \mat{U}_N (i_N, r_N).
\end{equation}
Equivalently, we can express this particular TTM with unfolded tensors as follows:
\begin{equation}
\label{eqn:core_unfolded}
\ten{G} = \ten{Y}\times_N \mat{U}_N^T \Leftrightarrow \mat{G}_{(N)} = \mat{U}_N^T \mat{Y}_{(N)}.
\end{equation}
Here $\ten{G}_{(N)}$ and $\mat{Y}_{(N)}$ are the mode-$N$ unfolding of the tensors $\ten{G}$ and $\ten{Y}$, respectively.
\begin{algorithm}[t]
\caption{Vivado HLS Implementation of TTM on $3$-way Tensors}
\label{alg:HLS_ttm}
\begin{algorithmic}[l]
\REQUIRE $\mat{Y} \in \mathbb{R}^{R_1R_2\times I_3}, \mat{U} \in \mathbb{R}^{R_3\times I_3}$
\STATE $\ell = R_1 R_2$, $b = 32$
\FOR {$(i_{b} = 0;i_{b} < \ell;i_{\delta} \mathrel{+}=b)$}
\STATE \textbf{initialize} $\textbf{tmp}$ as zero
\FOR{$(k =0;k<R_3;k\texttt{++})$}
\FOR{$(i_o = 0;i_o<b;i_o\texttt{++})$}
\FOR{$(t=0;t<I_3;t\texttt{++})$}
\STATE $\textbf{tmp}[i_o, k] \mathrel{+}= \mat{Y}[i_o+i_{b}, t]*\mat{U}[k, t]$
\ENDFOR
\ENDFOR
\ENDFOR
\FOR{$(k = 0;k<R_3;k\texttt{++})$}
\FOR{$(i_o=0;i_o<b;i_o\texttt{++})$}
\STATE $\mat{G}[i_o+i_{b}, k] = \textbf{tmp}[i_o, k]$
\ENDFOR
\ENDFOR
\ENDFOR
\end{algorithmic}
\textbf{Output: } $\mat{G} \in \mathbb{R}^{R_1 R_2\times R_3} $
\end{algorithm}
\begin{figure}[t]
\centering
\includegraphics[width=3 in]{fig/ttm.pdf}
\caption{Tensor-times-matrix (TTM) data flow.}
\label{fig:ttm_flow}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=1.6 in]{fig/PE_ttm.png}
\caption{Tensor-times-matrix (TTM) Processing Element (PE) \cite{zhang2019tucker}.}
\label{fig:pe_ttm}
\end{figure}
In FPGA design, the $3$-D sparse tensor $\ten{X} \in \mathbb{R}^{I_1\times I_2 \times I_3}$ is stored with a cost $O(nnz)$, where $nnz$ denotes the number of nonzero elements. However, the tensor $\ten{Y} \in \mathbb{R}^{R_1\times R_2\times I_3}$ in (\ref{eqn:core_ten}) is dense, and we need to store all of its elements. Although $\ten{Y}$ is multi-dimensional, it is unnecessary to create a new copy of this tensor. We can just reshape it into a 2-D matrix of size $R_1 R_2 \times I_3$.
Meanwhile, it is critical to process the entries of $\ten{Y}$ in several batches. The batch size, $b$, controls the number of entries in $\ten{Y}$, being processed in each iteration. If we set the batch size as $b = R_1R_2$, we will end up with 3 nested for-loops because the outermost for-loop is redundant. As a result, all the entries of $\ten{Y}$ have to be processed at the same time, resulting in an extremely large amount of loop unrolling, which is not practical when $R_1R_2$ is larger. To overcome this issue, we decrease our batch size to $32$, and separate this loop into two parts, resulting in 4 nested for-loops to compute the resultant tensor of the TTM. In this way, we could achieve optimal loop unrolling on memory-constrained FPGAs.
We provide the Vivado HLS implementation pseudo code of the TTM for a $3$-way tensor $\ten{X}$ in Alg. \ref{alg:HLS_ttm}. Given a $3$-way tensor, $\ten{X} \in \mathbb{R} ^{I_1 \times I_2 \times I_3}$, \eqref{eqn:core_ten} is a mode-$3$ TTM between $\ten{Y} \in \mathbb{R}^{R_1 \times R_2 \times I_3}$ and $\mathbf{U} \in \mathbb{R}^{I_3\times R_3}$, where $\ten{G} \in \mathbb{R} ^{R_1\times R_2\times R_3}$ is the result. In the pseudo code, we reshape our tensors $\ten{Y} \in \mathbb{R}^{R_1 \times R_2 \times I_3}$ and $\ten{G} \in \mathbb{R} ^{R_1\times R_2\times R_3}$ into matrices $\mat{Y} \in \mathbb{R}^{R_1 R_2 \times I_3}$ and $\mat{G} \in \mathbb{R}^{R_1R_2\times R_3}$. Basically, we divide our result, $\mat{G}$, into several portions such that we can update one portion of $\mat{G}$ in each batch:
\begin{itemize}
\item First, we initialize the temporary matrix, $\mathbf{tmp}$ as zero matrix of size $b \times R_3$, where $b$ is the batch size. This temporary matrix stores one portion of our result $\mat{G}$.
\item Then, we compute TTM by multiplying unfolded tensor $\mat{Y}$ and $\mat{U}$ based on (\ref{eqn:core_unfolded}) and store the results in $\mathbf{tmp}$.
\item Finally, we just update one portion of $\mat{G}$ with $\mathbf{tmp}$.
\end{itemize}
In order to optimize the Vivado HLS implementation, we reshape $\mat{U}$ in cyclic forms by a factor of $8$, and we reshape $\mat{Y}$ and $\mathbf{tmp}$ in cyclic forms by a factor of $16$. Furthermore, in order to save RAM usage, we assign only one port of RAM to the variables, $\mat{Y}$, $\mat{U}$, and $\mathbf{tmp}$. We also assign the intermediate variable $\mathbf{tmp}$ to registers instead of memory to minimize memory usage.
Fig.~\ref{fig:ttm_flow} shows the data flow in the TTM computation module on FPGA. According to the element-wise formula (\ref{eqn:ttm_ele}), each entry of the resultant tensor can be recognized as the sum of product between the entries from the original tensor $\ten{Y}$ and the entries from the matrix $\mathbf{U_N}$. In Fig.~\ref{fig:ttm_flow}, it shows that data from the tensor interface, $y_{r_1r_2\dots i_N}$ multiplies with the data from the matrix interface, $\mathbf{U_N}(i_N,r_N)$. After the multiplication, the results are summed up to obtain the entries in the resultant tensor, $(\ten{Y}\times_N \mathbf{U}_N^T)_{r_1 r_2\dots r_N}$.
A detailed data flow of the PE for TTM is shown in Fig.~\ref{fig:pe_ttm}, which was proposed in \cite{zhang2019tucker}. A buffer temporarily stores the intermediate result after multiplying the tensor and the matrix. For each batch, the multiplexer selects and adds the intermediate result to the new product. Once all batches are processed, the final result is stored the DRAM.
\subsection{Kronecker Products on FPGA}
\label{subsec:kron}
The power iteration \eqref{eqn:power_ite} requires $O(R^d\times n)$ operations, and it consumes most of the computational power and run-time in the sparse Tucker decomposition. Although an FPGA design was presented in~\cite{zhang2019tucker} to accelerate power iterations, existing design cannot handle sparse tensor data efficiently. Therefore, leveraging~\cite{kaya2016high,van2000ubiquitous}, we design an FPGA module to compute the power iteration via Kronecker products.
We consider a sparse $3$-way tensor $\ten{X}$ as an example. We investigate the power iteration of mode 1, which is written as $\ten{Y}$ = $\ten{X}$ $\times_2$ $\mathbf{U_2}^T$ $\times_3$ $\mathbf{U_3}^T$. To exploit the sparsity, we may choose to compute the Kronecker products and consider only nonzero elements $x_{ijk} \neq 0$~\cite{kaya2016high}:
\begin{equation}
\mathbf{Y_{(1)}}(i,:) =\mathbf{Y_{(1)}}(i,:)+ x_{ijk}[\mathbf{U_2}(j, :) \otimes \mathbf{U_3}(k, :)].
\end{equation}
The number of Kronecker products depends on the number of nonzero elements in $\ten{X}$, which is often very small for sparse tensors. Furthermore, a Kronecker product can be re-used for all non-zero elements that share the same indices $(j,k)$ for the $2$nd and $3$rd modes. Therefore, replacing TTM of \eqref{eqn:power_ite} with some Kronecker products can largely reduce the computational complexity. Additionally, directly computing TTM is memory-inefficient when the size and order of $\ten{X}$ are large, causing a high cost of RAM and registers on FPGA.
\begin{algorithm}[t]
\caption{Vivado HLS Implementation of Kronecker Product}
\label{alg:HLS_kron}
\begin{algorithmic}[1]
\STATE {\textbf{Input: } $\mathbf{a} \in \mathbb{R}^{1\times R_2}$, $\mathbf{b} \in \mathbb{R}^{1\times R_3}$ }
\FOR {$(i = 0; i < R_2; i++)$}
\FOR {$(j = 0; j<R_3;j++)$}
\STATE $\mathbf{c}[R_3 \times i + j] =\mathbf{a}[i] \times \mathbf{b}[j]$
\ENDFOR
\ENDFOR
\STATE{\textbf{Output: } $\mathbf{c}\in \mathbb{R}^{1\times R_2R_3}$}
\end{algorithmic}
\end{algorithm}
In the Vivado HLS implementation, we utilize nested for-loops to implement the Kronecker product (Alg. \ref{alg:HLS_kron}):
\begin{itemize}
\item In order to parallelize the Kronecker product on FPGA, we pipeline the first for-loop and unroll the second for-loop. The rank of approximation, $R_1$, $R_2$, and $R_3$, are usually very small compared with the mode sizes. Therefore, the available memory, lookup tables (LUTs) and registers are often sufficient for parallelization.
\item To update the corresponding rows of unfolded data $\mat{Y}_{(n)}$ in the the power iteration, we simply multiply the Kronecker product result in the LUTs with the corresponding nonzero element $y_{r_1 r_2 \dots i_N}$.
\item In addition, different nonzero elements may share the same index of some modes. In this case, we accumulate the multiplications between these nonzero elements and their corresponding Kronecker product results.
\end{itemize}
\begin{figure}[t]
\centering
\includegraphics[width=3 in]{fig/kronecker.pdf}
\caption{The data flow of a Kronecker product.}
\label{fig:Kronecker_flow}
\end{figure}
Fig.~\ref{fig:Kronecker_flow} shows the data flow inside our Kronecker product module on FPGA. To begin with, the indices of the non-zero elements in the original tensor are extracted. Then, based on the indices of the nonzero entries, the corresponding rows of the orthogonal matrix factor, $\mathbf{U}_t(i_t,:)$ are selected. Assuming there are two row vectors, every entry in one row vector multiply with every entry in the other row vector to generate the Kronecker product. Since we only compute the Kronecker product between two row vectors (not two matrices), the module only requires multiplication units (no addition units).
\begin{table}[t]
\centering
\caption{Accuracy comparison of Tucker decomposition with SVD and with QRP.}
\begin{tabular}{|c|c|c|}
\hline
Tensor Size & \begin{tabular}[c]{@{}c@{}}Tucker Decomposition \\ with SVD\end{tabular} & \begin{tabular}[c]{@{}c@{}}Tucker Decomposition \\ with QRP\end{tabular} \\ \hline
\noalign{\hrule height 1.0pt}
$50 \times 50 \times 50$ & $1.9222\times 10^{-09} $ & $1.9228\times 10^{-09}$ \\ \hline
$100 \times 100 \times 100$ & $1.3846\times 10^{-09}$ & $1.3820\times 10^{-09}$ \\ \hline
$200 \times 200 \times 200$ & $1.1588\times 10^{-09} $ & $1.1786\times 10^{-09}$ \\ \hline
$400 \times 400 \times 400$ & $1.2114\times 10^{-09}$ & $1.2115\times 10^{-09}$ \\ \hline
$800 \times 800 \times 800$ & $3.8450\times 10^{-10}$ & $3.8531\times 10^{-10}$ \\ \hline
\end{tabular}
\label{tab:svd_qrp}
\end{table}
\begin{table*}[t]
\centering
\caption{Performance comparison of FPGA and CPU on the TTM task.}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multicolumn{1}{|c|}{\multirow{2}{*}{Tensor Size}} & \multicolumn{1}{c|}{\multirow{2}{*}{Matrix Size}} & \multicolumn{2}{c|}{CPU} & \multicolumn{2}{c|}{FPGA} \\ \cline{3-6}
\multicolumn{1}{|c|}{} & \multicolumn{1}{c|}{} & Run-Time & Energy & Run-Time & Energy \\ \noalign{\hrule height 1.0pt}
$32 \times 32 \times 32$ & $32 \times 32$ & $0.493$ ms & $22.19$ mJ & $0.148$ ms & $0.4212$ mJ \\ \hline
$32 \times 32 \times 64$ & $32 \times 64$ & $0.596$ ms & $26.82$ mJ & $0.281$ ms & $0.8000$ mJ \\ \hline
$32 \times 32 \times 128$ & $32 \times 128$ & $1.165$ ms & $52.43$ mJ & $0.546$ ms & $1.556$ mJ \\ \hline
$32 \times 32 \times 256$ & $32 \times 256$ & $2.021$ ms & $90.95$ mJ & $1.077$ ms & $3.067$ mJ \\ \hline
\end{tabular}\normalsize
\label{table:ttm_whole}
\end{table*}
\begin{table*}[t]
\centering
\caption{Performance comparison of FPGA and CPU on the Kronecker product task.}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multicolumn{1}{|c|}{\multirow{2}{*}{Size of $\mat{x}_j$}} & \multicolumn{1}{c|}{\multirow{2}{*}{Size of $\mat{x}_k$}} & \multicolumn{2}{c|}{CPU} & \multicolumn{2}{c|}{FPGA} \\ \cline{3-6}
\multicolumn{1}{|c|}{} & \multicolumn{1}{c|}{} & Run-Time & Energy & Run-Time & Energy \\ \noalign{\hrule height 1.0pt}
$1 \times 32$ & $1 \times 32$ & $9.655$ $\mu$s & $0.4345$ mJ & $0.578$ $\mu$s & $2.111$ $\mu$J \\ \hline
$1 \times 64$ & $1 \times 64$ & $14.72$ $\mu$s & $0.6624$ mJ & $2.301$ $\mu$s & $8.403$ $\mu$J \\ \hline
$1 \times 128$ & $1 \times 128$ & $24.87$ $\mu$s & $1.119$ mJ & $9.195$ $\mu$s & $33.58$ $\mu$J \\ \hline
$1 \times 256$ & $1 \times 256$ & $48.24$ $\mu$s & $2.171$ mJ & $38.55$ $\mu$s & $140.7$ $\mu$J \\ \hline
\end{tabular}\normalsize
\label{table:kron_whole}
\end{table*}
\subsection{QR Decomposition with Column Pivoting}
\label{subsec:QRP}
In existing dense and sparse Tucker factorization~\cite{de2000best,kaya2016high}, the orthogonal matrix $\mat{U}_n$ is obtained with a singular value decomposition (SVD)~\cite{golub1971singular} of $\mat{Y}_{(n)}$. The SVD is accurate but extremely slow at computing the orthogonal matrices. In order to speed up the computation and minimize the memory usage, we propose to use QR decomposition with column pivoting (QRP)~\cite{golub1996matrix} to obtain $\mat{U}_n$. The QRP implementation does not lose any accuracy compared with the SVD implementation. This is clearly shown in Table~\ref{tab:svd_qrp}, which reports the errors of several low-rank Tucker decomposition with both SVD and QRP implementations, respectively.
Given a matrix $\mathbf{A}\in \mathbb{R}^{m\times n}$, the QRP get an orthogonal matrix $\mathbf{Q}\in \mathbb{R}^{m\times n}$ and an upper-triangular matrix $\mathbf{R}\in \mathbb{R}^{n \times n}$:
\begin{equation}
\mat{AP} = \mat{QR},
\end{equation}
with $\mat{P}$ being a permutation matrix.
The $\mathbf{P}$ is chosen so that the diagonal elements of $\mathbf{R}$ is non-increasing:
\begin{equation}
\mid r_{11}\mid \geq \mid r_{22}\mid \geq \dots \geq \mid r_{nn}\mid.
\end{equation}
A QRP costs about $2mn^2-2n^3/3$ flops, and an SVD costs about $ 2mn^2 + 11n^3$ flops, where $m \geq n$. In the sparse Tucker factorization of a tensor $\ten{X} \in \mathbb{R}^{I_1 \times I_2 \times \dots \times I_N }$, $\mat{A}$ is $\mat{Y}_{(n)}$, the mode-$n$ unfolding of the tensor $\ten{Y}$ obtained in \eqref{eqn:power_ite}. Consequently, $m=I_n$, $n=\prod \limits_{k\neq n} R_n$, and the computational saving is huge when the tensor order $N$ or multilinear rank parameters $(R_1, R_2, \cdots, R_N)$ are large. In some particular cases, we may end up with a fat rectangular matrix, $\mathbf{Y}_{(n)}$ ($n > m$). In this case, we can perform QRP on a square matrix, $\mathbf{Y}_{(n)}\mathbf{Y}_{(n)}^T$.
{\bf QRP Implementation.} The QRP in our implementation is based on the Householder reflection. This method computes the orthogonal matrix $\mathbf{Q}$ as the product of multiple Householder reflection matrices:
\begin{equation}
\label{eqn:house_reflect}
\mat{Q} = \mat{H_1}\mat{H_2}\dots \mat{H_{m-2}}\mat{H_{m-1}}.
\end{equation}
The $j$-th reflection matrix, $\mathbf{H}_j$, is defined as:
\begin{equation}
\mathbf{H}_j = \mathbf{I} - 2\mathbf{v}_j \mat{v}_j^T = \mathbf{I} - 2\frac{\mat{u}_j \mat{u}_j^T}{\mat{u}_j^T\mat{u}_j},
\end{equation}
where $\mathbf{u}_j$ is an unit vector and $\mathbf{u}_j = \frac{\mat{v}_j}{\left\lVert \mat{v}_j \right\rVert}$. Vector $\mat{v}_j$ can be chosen based the $j$th column of $\mat{A}$, $\mathbf{a}_j$:
\begin{equation}
\mathbf{v}_j = \mathbf{a}_j + {\text{sign}}(a_{jj})\left\lVert \mat{a}_n\right\rVert \mat{e}_1.
\end{equation}
During every iteration of QRP, we need to update $\mathbf{A}$ by multiplying it with the Householder matrix $\mathbf{H}$. In order to generate the permutation matrix, $\mathbf{P}$, we need to compare the norms of the columns of the updated matrix $\mathbf{A}$ at every iteration, arranging the columns so that the norms of the columns are in descending order. In this way, we can place the most weighted entries in the upper left corner of $\mathbf{Q}$, achieving the similar accuracy to SVD. Since we need to compare the norms of the columns at each iteration, the QRP operation is sequential. In other words, the comparison of the column norms made it very difficult to parallelize the algorithm on FPGA. Thus, we implement the Householder QR decomposition~\cite{golub1996matrix} with column pivoting on CPU.
\section{Results}
\label{sec:Experiments}
This section shows the performance of our hybrid FPGA-CPU accelerator on both synthetic and real-world datasets. We first verify the performance of individual FPGA modules for the TTM and Kronecker product. Afterwards, we verify the performance of the whole FPGA-CPU sparse Tucker accelerator and compare it with CPU. We use the FPGA model XCVU9P-FLGA2577-3-e in our experiment. The maximum frequency of the FPGA implementation is $890$MHz. The CPU model used is Intel(R) Core(TM) i7-6820HK CPU @ 2.70GHz. The size of the RAM is $16$GB. The CPU has a maximum memory bandwith of
34.1 GB/s and a thermal design power (TDP) of $45$W. In the experiments, we prioritize the computations on CPU to achieve the maximum performance, therefore, the energy consumption on CPU can be estimated as the product of runtime and TDP. We estimate the energy cost of sparse Tucker decomposition on FPGA on Xilinx Vivado via Amazon Web Service. The communication protocol between FPGA and CPU is PCI express, which has a maximum bandwidth of 10GB/s. Our design can also be implemented on a low-end FPGA such as Zynq-7100 as well. On a low-end FPGA, We may decrease the LUT utilization by adjusting the unroll factor in our TTM module implementation.
\subsection{Performance of Individual FPGA Modules}
\label{sec:result}
Firstly we verify the performance of the TTM and Kronecker-Product modules on some synthetic tensor data, and summarize their performance below:
\begin{itemize}
\item {\bf TTM Module:} We verify the performance by considering a set of 3-way tensors $\ten{Y} \in \mathbb{R}^{R_1\times R_2\times I_3}$ and factor matrices $\mathbf{U} \in \mathbb{R}^{R_3 \times I_3} $. The rank of approximate, $R_1$, $R_2$ and $R_3$, are always very small compared with the original tensor size for data compression. Thus, we set $R_1 = R_2 = R_3 = 32$. The original tensor size, $I_3$ is set to increase from $32$ to $256$ as shown in Table~\ref{table:ttm_whole}. In the real-life examples, the original tensor size $I_3$ can definitely be larger than $256$. And the performance of the tensor-times-matrix (TTM) module won't perform significantly worse when the original tensor size becomes extremely large. Here, we set the maximum of our tensor size to be $256$ for experimental purpose only. The FPGA achieves $1.560\times$ to $3.331\times$ speedup than CPU on these tensor-matrix products. We also compare the energy consumption between FPGA and CPU on the tensor-times-matrix task. As shown in Table~\ref{table:ttm_whole}, the FPGA saves $95.6\%$ to $98.1 \%$ of energy compared with CPU.
\item {\bf Kronecker-Product Module:} As shown in Section 4.3, the Kronecker product used in the sparse Tucker decomposition deals with two row vectors, $\mat{x}_j \in \mathbb{R}^{1 \times R_j}$ and $\mat{x}_k\in \mathbb{R}^{1 \times R_k}$. Therefore, we compare the performance of Kronecker products on FPGA and CPU by changing the rank parameters $R_1$ and $R_2$ from $32$ to $256$. The rank of approximation $R_1$ and $R_2$ does not necessarily need to be equal to each other. We set $R_1$ and $R_2$ to be equal for experimental purpose only. In addition, the rank of approximation $R_1$, $R_2$ and $R_3$ are usually very small compared with the original tensor size for data compression. We increase the rank from $32$ to $256$ to demonstrate the performance of Kronecker product module. We estimated the power of the CPU to be $45$W. The energy consumption of CPU is estimated by multiplying the power with the CPU time. The results are shown in Table~\ref{table:kron_whole}. The speedup of FPGA over CPU ranges from $1.251\times$ to $16.704\times$. As shown in Table~\ref{table:kron_whole}, FPGA consumes $93.519\%$ to $99.514\%$ less energy than CPU on the Kronecker-product tasks.
\end{itemize}
\begin{figure}[t]
\centering
\includegraphics[width=3.5in]{fig/sparsity_time.pdf}
\caption{Run-time comparison between the proposed hybrid platform, dense FPGA accelerator and CPU on a set of $200\times 200\times 200$ synthetic random tensors with different sparsity.}
\label{fig:sparsity_time}
\end{figure}
\subsection{Accelerator's Performance: Synthetic Datasets}
Now we evaluate the whole hybrid FPGA-CPU accelerator on some randomly generated synthetic sparse tensor data sets. Specifically, we consider a set of $3$-way tensors $\ten {X} \in \mathbb{R}^{200 \times 200 \times 200}$ with different sparsity. We fix the rank parameters $R_1$=$ R_2$=$R_3$=$16$.
Fig. \ref{fig:sparsity_time} compares the run-time of our hybrid FPGA-CPU platform with CPU and densor FPGA accelerator~\cite{zhang2019tucker}. The speedup of the hybrid FPGA-CPU accelerator is $27\times\sim853\times$ compared with CPU. The speedup of our sparse Tucker accelerator is $1.167\times\sim126\times$ faster than the FPGA accelerator designed for dense Tucker decompsition~\cite{zhang2019tucker}. In the whole sparse Tucker decomposition algorithm, the Kronecker product module takes the most amount of time. However, this module is parallelized in our design, and it is significantly sped up on FPGA as shown in Section \ref{sec:result}. When the tensor has more non-zero elements, more Kronecker-product operations are required, leading to a more significant speedup on FPGA.
\begin{table*}[]
\centering
\caption{Performance of Sparse Tucker Decomposition on real-world benchmarks.}
\begin{tabular}{|l|l|c|c|c|c|}
\hline
\multicolumn{2}{|l|}{Benchmarks} & Amazon & Nell-2 & Parallel Matrix Multiplication & Retinal Angiogram \\ \noalign{\hrule height 1.0pt}
\multicolumn{2}{|l|}{Tensor Size} & $20K \times 20K \times 20K $ & $1K \times 1K \times 1K$ & $25 \times 25 \times 25 $ & $130 \times 150$ \\ \hline
\multicolumn{2}{|l|}{Sparsity} & $1.128 \times 10^{-10}$ & $2.40 \times 10^{-5}$ & $8\times10^{-3}$ & $0.18$ \\ \hline
\multirow{2}{*}{CPU} & Run-Time & $100.045$ s & $7.355$ s & $8.175\times10^{-2}$ s & $0.1838$ s \\ \cline{2-6}
& Energy & $4502.03$ J & $330.98$ J & $3.68$ J & $8.27$ J \\ \hline
{Hybrid FPGA/CPU} & Run-Time & $86.785$ s & $0.403$ s & $2.179 \times 10^{-3}$ s & $9.898 \times 10^{-3}$ s \\ \cline{2-6}
(proposed) & Energy & $3896.08$ J & $17.10$ J & $0.1057$ J & $0.4667$ J \\ \hline
Dense FPGA Tucker~\cite{zhang2019tucker} & Run-Time & $9.47 \times 10^4$ s & $9.5$ s & $9.9 \times 10^{-3}$ s & $1.18 \times 10^{-2}$ s \\ \hline
\end{tabular}
\label{tab:realExample}
\end{table*}
\begin{table*}[]
\centering
\caption{Utilization of FPGA on real-world benchmarks. In the column of "memory" we list the number of BRAM, where each BRAM has $18\times 10^3$ bits.}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
\multicolumn{2}{|c|}{Name} & Expression & Instance & Memory & Multiplexer & Register & Total & Available & Utilization (\%) \\ \noalign{\hrule height 1.0pt}
\multirow{4}{*}{Amazon} & BRAM\_18K & - & - & $542$ & - & - & $542$ & $4320 $ & $13$ \\ \cline{2-10}
& DSP48E & - & $282$ & - & - & - & $282$ & $6840$ & $4$ \\ \cline{2-10}
& FF & 0 & $17257$ & - & - & $107670$ & $124927$ & $2364480$ & $5$ \\ \cline{2-10}
& LUT & $406251$ & $17649$ & -& $20587$ & - & $443268$ & $1182240$ & $37$ \\ \hline
\multirow{4}{*}{Nell-2} & BRAM\_18K & - & - & $63$ & - & - & $63$ & $4320 $ & $1$ \\ \cline{2-10}
& DSP48E & - & $470$ & - & - & - & $470$ & $6840$ & $7$ \\ \cline{2-10}
& FF & $0$ & $29495$ & - & - & $54691$ & $84186$ & $2364480$ & $4$ \\ \cline{2-10}
& LUT & $405656$ & $30863$ & - & $13972$ & - & $450491$ & $1182240$ & $38$ \\ \hline
\multirow{4}{*}{\begin{tabular}[c]{@{}c@{}}Parallel\\ Matrix \\ Multiplication\end{tabular}} & BRAM\_18K & - & - & $2$ & - & - & $2$ & $4320 $ & $\sim0$ \\ \cline{2-10}
& DSP48E & - & $16$ & - & - & -& $16$ & $6840$ & $\sim0$ \\ \cline{2-10}
& FF & $0$ & $759$ &- & - & $107$ & $866$ & $2364480$ & $\sim0$ \\ \cline{2-10}
& LUT & $49799$ & $778$ & - & $707$ & - & $51284$ & $1182240$ & $4$ \\ \hline
\multirow{4}{*}{\begin{tabular}[c]{@{}c@{}}Retinal \\ Angiogram\end{tabular}} & BRAM\_18K & - & - & $5$ & - & - & $5$ & $4320 $ & $\sim0$ \\ \cline{2-10}
& DSP48E & - & $21$ & - & - & - & $21$ & $6840$ & $\sim0$ \\ \cline{2-10}
& FF & $0$ & $1171$ & - & - & $9438$ & $10609$ & $2364480$ & $\sim0$ \\ \cline{2-10}
& LUT & $121303$ & $1089$ & - & $2256$ & - & $124648$ & $1182240$ & $11$ \\ \hline
\end{tabular}
\label{tab:utilization_real_world}
\end{table*}
\begin{figure*}[t]
\centering
\includegraphics[width=6.6in]{fig/sparse_image.pdf}
\caption{Left: the original retinal angiogram. Right: the approximated image by our sparse Tucker decomposition on the FPGA/CPU hybrid platform.}
\label{fig:sparse_image}
\end{figure*}
\subsection{Real-World Datasets}
Finally, we verify our accelerator on four real-world sparse tensor data sets~\cite{mcauley2013, BB15,Brent70,carlson2010toward}. In addition, we compare the performance of our accelerator with sparse Tucker decomposition on CPU and with the dense FPGA accelerator in~\cite{zhang2019tucker}. Table~\ref{tab:realExample} shows the detailed run-time and energy consumption of different methods on these datasets. Table~\ref{tab:utilization_real_world} further shows the overall hardware resource utilization of our method on FPGA. The FPGA design is compiled for each data set in order to achieve the maximum efficiency. We use BRAM\_18K, BDSP48E, FF and LUT to denote block random access memory, digital signal processing elements, flip flops and lookup tables, respectively.
The detailed experiments and results are summarized below:
\begin{itemize}
\item {\bf Amazon Reviews Datasets~\cite{mcauley2013}.} The modes of this three-way tensor represent users, products, and words, respectively. Each non-zero element in this tensor is the number of times a word appears in a given review. Additionally, we extract one portion of the Amazon reviews tensor of size $20000\times20000\times20000$ and choose the rank of approximation as $R_1=R_2=R_3=32$. We perform 2 power iterations on all modes. The sizes of the tensors and matrices in TTM \eqref{eqn:core_unfolded} are $32 \times 32 \times 20000$ and $32 \times 20000$, respectively. This sparse Tucker factorization involves $9$ calls of QR decomposition on a set of $20000\times 32$ matrices in total to compute the orthogonal factor matrices. Finally, there are totally $8,820$ calls of Kronecker products, which depends on the number of non-zero tensor entries. On this dataset, our hybrid FPGA/CPU platform achieves $1.15\times$ speedup than CPU with only $13.5\%$ energy consumption. Our method also achieves $1091\times$ speedup than the dense Tucker FPGA accelerator~\cite{zhang2019tucker}.
\item {\bf NELL-2 Datasets~\cite{carlson2010toward}.} This data set is extracted from the Never Ending Language Learner knowledge base. The non-zero entries represent some entity-relation-entity tuples. We extract one portion of the NELL-2 data set and obtain a sparse tensor of size $1000\times1000\times1000$. In addition, we choose our rank of approximation as $R_1=R_2=R_3=16$. We perform 5 power iterations on all modes. The sizes of the tensors and matrices in TTM \eqref{eqn:core_unfolded} are $16 \times 16 \times 1000$ and $16 \times 1000$, respectively. This sparse Tucker factorization involves $15$ calls of QR decomposition on a set of $1000\times 256$ matrices in total to compute the orthogonal factor matrices. Finally, there are totally $432,555$ calls of Kronecker products, which depends on the number of non-zero tensor entries. Our hybrid FPGA/CPU platform achieves $18\times$ speedup and $94.8\%$ energy saving compared with CPU. Our method is also $23.6\times$ faster than the dense FPGA accelerator~\cite{zhang2019tucker}.
\item {\bf Binary $3$-Way Tensor for Parallel Matrix Multiplication~\cite{BB15,Brent70}.} This binary tensor describes the parallel computation process of matrix multiplications. Given two matrices $\mathbf{A}\in{\mathbb{R}^{M \times K}}$ and $\mathbf{B}\in{\mathbb{R}^{K \times N}}$, their product results in a matrix $\mathbf{C}\in{\mathbb{R}^{M \times N}}$. Let $I_1=MK$, $I_2=KN$ and $I_3=MN$, then a binary 3-way tensor $\ten{X}$ can represent the parallel matrix multiplication. The first mode corresponds to the first input matrix $\mat{A}$ with entries in row-major order; the second mode corresponds to the input matrix $\mat{B}$ with entries in row-major order; the third mode corresponds to the output matrix $\mat{C}$ with entries in column-major order. A nonzero entry $x_{i_1 i_2 i_3}=1$ corresponds to a scalar multiplication within the classical matrix multiplication algorithm: the $i_1$-th entry of $\mat{A}$ is multiplied with the $i_2$-th entry of $\mat{B}$, and the result is accumulated into the $i_3$-th entry of $\mat{C}$. The number of nonzero elements in $\ten{X}$ is $nnz=MKN$. We consider the case $M=N=K=5$, which results in a binary tensor $\ten{X}$ with size $25\times 25\times 25$ and a sparsity of $8\times 10^{-3}$. To perform sparse Tucker decomposition on this 3-way binary tensor, we choose an approximation rank of $R_1=R_2=R_3=5$. We perform three steps of high-order power iterations on all modes, leading to 3 TTM in \eqref{eqn:core_unfolded} and totally 6 calls for QR decomposition with column pivoting. Finally, the number of Kronecker products used in this data set is $1,125$. Our meethod achieves $37\times$ and $1.52\times$ speedup than CPU and than the dense FPGA accelerator~\cite{zhang2019tucker}, respectively. Compared with the sparse Tucker decomposition on CPU, our accelerator saves $97.1\%$ energy.
\item {\bf Retinal Angiogram.} Angiogramy is a medical diagnoictic test that uses X-ray to take picture of the blood vessels. The images, angiogram, are always very sparse. Fig. 6 shows the retinal angiogram of a patient on the left. The size of the original retinal angiogram is $130 \times 150$~\cite{hoover2000locating}. Tucker factorization can also be employed to compress 2-D data, because a matrix is the special case of a tensor. Different from SVD compression of a matrix where the rank is a scalar, a Tucker decomposition allows one to set two rank parameters. We perform a sparse Tucker decomposition with rank
R = [30, 35] on this image. We performed $12$ steps of high-order power iterations on all modes, leading to $12$ TTM in \eqref{eqn:core_unfolded} and totally 24 calls for QR decomposition with column pivoting. We do not need any Kronecker products since the order of the tensor is $2$. Our proposed method achieves $19\times$ speedup than CPU and $1.91\times$ speedup than dense FPGA accelerator~\cite{zhang2019tucker}, and it saves $94.4\%$ energy compared with the sparse Tucker factorization on CPU. Fig.~\ref{fig:sparse_image} compares the original retinal angiogram and the resulting compressed image from our FPGA/CPU hybrid accelerator. The compression ratio is $18.57 \times$. While the image is highly compressed, the essential features, such as blood vessels, are still clearly preserved.
\end{itemize}
\section{Conclusion}
\label{sec:conclusion}
This paper has proposed a hybrid FPGA-CPU accelerator for sparse Tucker decomposition. On the algorithm level, the Kronecker products have exploited the data sparsity and has significantly reduced the computational complexity. The QR with pivoting method have dramatically reduced the complexity of obtaining the orthogonal mode-n matrix factors. The FPGA modules for the tensor-times-matrix and for the Kronecker products have achieved $93.519\%$ to $99.514 \%$ energy saving compared with CPU on synthetic benchmarks. The proposed hybrid FPGA-CPU accelerator has been evaluated with both synthetic and realistic sparse tensor data sets. It has achieved $27\times$$\sim$$853\times$ speedup over CPU and $1.167\times$$\sim $$126\times$ speedup over the recently developed dense Tucker FPGA accelerator~\cite{zhang2019tucker} on the synthetic datasets. Our proposed methods have also achieved $1.15\times $$\sim$$1091\times$ speedup and over $95\%$ energy savings on the tested real-world tensor datasets. Our proposed accelerator have significantly outperformed CPU and dense Tucker FPGA accelerator~\cite{zhang2019tucker} when the tensor is very large and sparse.
\bibliographystyle{IEEEtran}
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{"url":"http:\/\/evancordell.com\/2015\/09\/27\/macaroons-101-contextual-confinement.html","text":"# Macaroons 101: Contextual Confinement\n\n## Elegent authorization, for a more civilized age\n\nSeptember 27, 2015\n\nMacaroons, like Fezzes, are cool. If you find yourself disagreeing, it\u2019s possible you\u2019re thinking of the wrong sort of macaroons\n\n, or you\u2019ve yet to be convinced.11 or you have legitimate concerns This is the first in a series of posts in which I intend to explain why macaroons are so interesting. We\u2019ll start by motivating them and defining them, and later expand on the theory behind them and study examples of how they\u2019re applicable in the real world.\n\nThe name \u201cmacaroon\u201d comes from the Google research paper that introduced them, a play on the ubiquitous browser \u201ccookie.\u201d (Naturally, by naming them macaroons, Google has made them nigh on ungooglable.)\n\nWhat is a macaroon? Much like a signed cookie, a macaroon is a form of bearer credential that can be handed to a client and verified by a server at a later time. Unlike simple bearer tokens, macaroons embed \u201ccaveats\u201d that confine the context in which they can be used. This allows decentralized access control that can be difficult with other methods, and in particular is simple, efficient, and flexible.\n\nBefore delving into the technical details of macaroons, lets look at some interesting22 contrived authorization problems (and some non-macaroon solutions).\n\n## Protecting Frank\n\nAlice shares a home with a pretty adorable dachshund named Frank of whom she takes pretty adorable pictures. She likes to upload these to her Pics of Frank blog, but lately people have been hotlinking her images directly, which costs her a lot of bandwidth. She\u2019d prefer that any view of her images count as a page view of her entire blog - she has a couple of unobtrusive ads there and she\u2019d like to use the extra cash to buy toys for Frank.\n\n### Low Hanging Fruit: Checking the Referer\n\nAny request to the server should include a Referer header indicating from where the request originated. Alice can add some checks to all image requests to see if the referer is her own blog, and reject (or redirect) requests that don\u2019t match.\n\nThis works pretty well to prevent people who are innocently hotlinking her photos - but from monitoring her traffic she can see that there are some people who are intentionally stealing bandwidth by spoofing the Referer header!\n\n### Unique Image Keys\n\nAlice decides to take her attackers head on. She makes all of her image files private - only accessible from within her server. Before every page load, her blog now does the following:\n\n\u2022 finds all photos on the page about to be rendered\n\u2022 generates a unique, random id for each of them\n\u2022 stores those ids in a key-value store along with the image they reference Alice uses Redis\n\u2022 replaces references to the image files with urls that include the new random keys\n\nWhen a page on her blog renders, her server dereferences the unique urls into the corresponding image paths, and sends the image data. Her key-value store deletes the keys after 5 seconds, so that subsequent requests using them fail.\n\nThis strategy was a lot of work to implement, but it works well! Anyone who wishes to link to her photos directly must first render her blog in order to get access to them.\n\nUnfortunately, she finds that the money she\u2019s spending running her key-value store is greater than the additional money she\u2019s making from increased page views. There will be no new toys for Frank.\n\n## Sharing Frank\n\nAlice puts that problem aside for now. Her friend Bob is a dachshund fan and a photoshop wizard, and she\u2019d like to share her pictures with him so that he can touch them up for her.\n\nShe needs to give him write access to her dachshund photos, but doesn\u2019t want to give him full access to her server (she trusts him, but he\u2019d probably just screw something up).\n\nGiven that she already has a system in place for assigning unique ids to her images, she figures she can do the same to allow write access. She could generate non-expiring random ids that allow write access, and only give them to Bob (over a secure channel). But Bob, though a talented photo manipulator, is not very careful with security - she wouldn\u2019t be surprised if he shared the write-able link with someone, not realizing there was a difference between the read and write links.\n\nAfter some thought, she comes up with the following solution:\n\n\u2022 When Bob wants to work on one of the photos, he must first visit a special login page she made for him. \/bobs-login\/\n\u2022 The login page requires him to authenticate with Google OAuth as bob@example.com (she knows he has an account there already).\n\u2022 If he can do so successfully, the blog site creates a new record in the key value store: like before, the key is a unique, random id, but this time the value is Bob\u2019s ip address when he authenticated. This entry is set to expire in 30 minutes, and for good measure the id is also stored in a cookie on his browser.\n\u2022 When Bob is ready to upload an image, he visits a special upload page \/bob-upload\/. It can only be viewed if the request includes a cookie with the random id and originates from the corresponding stored ip address.\n\u2022 When loading, the page generates a unique id for each image, and appends Bob\u2019s unique key to each. These ids are only valid for 30 seconds.\n\u2022 Bob picks one of the images to overwrite, and issues a PUT request to the generated url.\n\u2022 If done within 30 seconds, the image is written.\n\nThis solution works pretty well for Alice. It effectively limits write-access to her photos to someone who can authenticate as Bob with Google, and places some limits to prevent him from sharing write access with anyone else. But she\u2019s not happy about a couple of things:\n\n\u2022 she has to host a login page just for Bob\n\u2022 she\u2019s storing a lot of state in the server\n\nAlice would like to redo this whole system without all of this rigmarole.\n\n## Going Stateless\n\nThere\u2019s a common pattern of keeping some server state in an authenticated browser cookie33 In its simplest form, an authenticated cookie is just a blob of data with a signature attached. The unforgeable signature is created on the server, and can be verified later by the server. This is commonly done with an HMAC. - Alice realizes that the same pattern would remove her need for a key value store. She generates a nice, random secret for her server, which she\u2019ll use to sign her new, stateless tokens.\n\nFor a reader of her blog, this is how it works:\n\n\u2022 When the page is requested, like before, the server replaces references to her photos with tokens. This time, though, the tokens aren\u2019t random, they are signed tokens that contain a reference to the file and a time that the tokens are no longer valid:\ntoken = (\n\"file.jpg,2015-09-16 21:13:23;\" +\nHMAC(secret_key, \"file.jpg,2015-09-16 21:13:23\")\n)\n\n\u2022 When the browser requests the photos, the server decodes the reference, verifies that it hasn\u2019t been tampered with by recalculating the signature, and only then streams the photo data to the client.\n\nBob, who would additionally need write access, still needs to authenticate with Google. But let\u2019s assume that Google provides Bob with a token that, when given to Alice\u2019s website, can be verified as his and from Google. Any write request that includes both the \u201cread\u201d token from above, and includes Bob\u2019s proof of authentication with Google, will be allowed. We\u2019ll assume the token from Google has additional restrictions to be safe (only valid for a certain period of time, etc).\n\nAt this point, Alice has essentially created an ad-hoc, inextensible, standard-less form of macaroons. Macaroons improve on this authenticated-cookie strategy by:\n\n\u2022 Defining a standard interface for specifying and verifying caveats (examples: proof of authentication as Bob at Google, time restrictions)\n\u2022 Unifying the interface between local assertions and remote assertions (i.e. freshness can be verified in the same way as external authentication)\n\u2022 Permitting extensibility and delegation - Macaroons are like \u201clayered\u201d authentication cookies, where additional restrictions can be trivially added by anyone, or even passed to a different client.\n\n# Introducing Macaroons\n\nOne of the problems with plain bearer tokens is that they authorize unconditionally. In the scenario above, Alice can\u2019t simply generate tokens to allow writing to her photos without worrying about who can get their hands on them (and then needs to go to great lengths to ensure they\u2019re not used by anyone but Bob).\n\nMacaroons solve this by introducing caveats. Caveats confine the context in which a macaroon is valid. A macaroon with appropriate caveats could confine a token to a user authorized as Bob with Google, restrict it to write access, and limit the time in which it can be used.\n\nA macaroon consists of:\n\n\u2022 an identifier used to differentiate between macaroons\n\u2022 a location that identifies the service from which the macaroon originated\n\u2022 a series of caveats which confine the context for which the macaroon is valid\n\u2022 first party caveats make assertions about the context of the target service 44 The term target service will be used to refer to service that will ultimately receive and verify a macaroon from here on.\n\u2022 third party caveats make assertions about the context of some third-party service (e.g. Google)\n\u2022 a signature that can be used to verify the macaroon has not been modified\n\nThe identifier and location fields of a macaroon serve to identify the key to use for verification of the signature. The signature itself is a chained-MAC of the previous fields. That is, given a secret key key and identifier id, the signature s1 would be\n\ns1 = HMAC(key, id)\n\n\nIf a validity-period caveat were added such as time < 2015-08-03T15:42:48, the new signature s2 would be\n\ns2 = HMAC(s1, 'time < 2012-08-03T15:42:48-04:00')\n\n\nThe chaining allows macaroons to be extended (attenuated) with further caveats. There are several practical implications of this property:\n\n\u2022 A client can pass their authority to someone else, while attenuating it further (delegation)\n\u2022 A macaroon with few or no caveats could be cached, and then attenuated for specific situations\n\u2022 Multiple services could coordinate access by passing macaroons to each other, attenuating as appropriate\n\u2022 After attenuation, the target service can still easily (and quickly) verify the macaroon\n\n### First- and Third-party Caveats\n\nCaveats come in two flavors: first- and third-party.\n\nFirst party caveats make assertions that the target service can verify. Some example restrictions include:\n\n\u2022 which resources can be accessed\n\u2022 what operations can be performed (read, write, share, etc)\n\u2022 how long a macaroon is valid\n\u2022 a specific user or group of users\n\u2022 a specific ip address or other connection-specific information\n\u2022 a check against a revocation service\n\nThese are all things that can be verified easily at the target service. If a macaroon restricts access to photo_of_frank.jpg and is read only, the server can reject any requests that are not for those specific actions.\n\nThird-party caveats make assertions about external systems. In order to verify those assertions, the target service must have some pre-arranged relationship with them.55 This relationship could be almost anything: a shared symmetric key, an explicit API for creating ad-hoc keys, or a public\/private key pair. The third-party caveat is actually the combination of the key for another macaroon that comes from the third party (a discharge macaroon66 The macaroon provided by a third-party service is called a discharge macaroon because it \u201cdischarges\u201d the caveat\u2019s assertion. Presence of a valid discharge macaroon means that the assertions made in the third-party caveat hold.), along with an identifier that matches the identifier of the discharge macaroon.\n\nThe target-service (Alice\u2019s blog) will embed a caveat requiring the third party (Google) to issue a specific macaroon that will prove a user is authenticated. Because discharging the third-party caveat is simply verification of another macaroon, additional caveats can be included by the third-party in the discharge macaroon. These caveats will also need to be verifiable (and verified) by the target service in order for the macaroon to be considered valid.\n\nAn example helps to clarify. Suppose Alice\u2019s blog wants to issue a macaroon for writing to photo_of_frank.jpg and needs to add a third-party caveat asserting that Bob can authenticate with Google.\n\n\u2022 First, Alice needs to get the key that will be used to sign the discharge macaroon. For the sake of example, lets say she makes a request to Google for a key. This key is included in the third-party caveat of the macaroon that will be handed to Bob.\n\u2022 Bob gets this macaroon, sees that it has a third-party caveat for authenticating with Google. He talks to Google\u2019s macaroon auth service and gets a discharge macaroon signed with the same key that Alice was given.\n\u2022 Bob sends both macaroons to Alice when he wants to write to photo_of_frank.jpg. Because the key to the discharge macaroon is embedded in the root macaroon\u2019s third-party caveat (and is encrypted, though I\u2019ve glossed over that so far), Alice can verify both macaroons and only allow the request through if they\u2019re valid.\n\u2022 Additionally, Google could add a time limit to the discharge macaroon, which would further limit the context for which the macaroon pair is valid.\n\n### Verification\n\nThe verification process for a macaroon is fairly simple:\n\n1. Collect all first party caveats from the root macaroon and all discharge macaroons.\n2. Verify that the first party caveats hold. If any fail, the request is rejected.\n3. Decrypt the keys for each discharge macaroon and verify their signatures.\n4. Find the key for the root macaroon and verify its signature.\n5. If none of the above verifications have failed, the request is allowed through.\n\nIt\u2019s important to note that the macaroon should not be \u201cread\u201d to see what request should occur. If a macaroon authorizes write access to photo_of_frank.jpg, any request that includes that macaroon should not be assumed to be a write request to that photo. A holder of a macaroon should have to explicitly specify what action is being performed. It would be even better if a client had to choose a specific authorization macaroon to present for a particular action, though that isn\u2019t possible when using macaroons as cookies.\n\n### Applications\n\nMacaroons are attractive because of their flexibility. Alice\u2019s dachshund blog is just one contrived example; macaroons can also be used for:\n\n\u2022 Distributing authorization data in a microservices architecture\n\u2022 Sharing structured auth information between external services\n\u2022 An alternative to JWTs for session management\n\u2022 Better management of session revocation and\/or network-less session refreshing\n\u2022 Unifying disparate auth systems\n\u2022 Meaningful OAuth2 tokens\n\nI intend to write more in-depth about these applications, but wanted to have some sort of \u201cfoundational\u201d post to refer to. Rest assured that anything that is hand-waved above will be clarified in a later post. A careful reader will have noticed a lack of detail on the actual format of tokens, no mention of a standard format for caveats, no discussion of the security properties of macaroons, and nowhere near enough technical detail around third-party caveats and discharge macaroons. It\u2019s also worth mentioning that although there are de-facto standards for macaroons, the definition in the research paper leaves a lot up to implementation.","date":"2018-05-22 11:26:52","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\": 0.17487594485282898, \"perplexity\": 2915.2517812207943}, \"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-2018-22\/segments\/1526794864725.4\/warc\/CC-MAIN-20180522112148-20180522132148-00299.warc.gz\"}"} | null | null |
The World Happiness Report is a landmark survey of the state of global happiness. The World Happiness Report 2018, ranks 156 countries by their happiness levels, and 117 countries by the happiness of their immigrants. The main focus of this year's report, in addition to its usual ranking of the levels and changes in happiness around the world, is on migration within and between countries. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,518 |
I have been fortunate enough to connect with a few people who have allowed me to work with them as models in the natural environment.
I love working in collaboration with people and their visions, allowing them the freedom to move about and explore the environment in as natural a fashion as possible. I try to avoid strict posing and prefer to work in a more organic fashion observing how each interacts with Nature's beauty, how they derive joy and inspiration from these interactions.
A printer's chop is either applied with ink and a stamp or by embossing the paper.
It is an acknowledgement not only of the expertise of the printer but also a confirmation that the print has been inspected and passed muster with the printer/printshop. A chop is, literally, the printmaker's stamp of approval.
For Flat Earth Photography, it is also a mark that distinguishes commercial photographic prints from fine art prints. The chop can only be applied to the heavier, fine art papers used for specific editions of photographs.
Prithvi is the Hindu earth and mother goddess. According to one such tradition, she is the personification of the Earth itself; according to another, its actual mother, being Prithvi Tattwa, the essence of the element earth.
As Prithvi Mata, or "Mother Earth", she contrasts with Dyaus Pita, "father sky". In the Rigveda, earth and sky are frequently addressed as a duality, often indicated by the idea of two complementary "half-shells." | {
"redpajama_set_name": "RedPajamaC4"
} | 733 |
export * from './home-root.component';
export * from './home-root.routes';
export * from './home-root.guard';
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,741 |
Subject: Fwd: Man is not god - Greenpeace Action goes to church!
>genetic manipulation of plants and animals.
>Cologne Cathedral against genetic manipulation of living creatures.
>"Man is not God - down with genetic manipulation".
>having an ethic duty to support the opponents of genetic engineering.
>visit to the Cathedral. Instead, we will remain outside.
Next by Date: Fwd: biggest Austrian dairy company goes GE-free!!!! | {
"redpajama_set_name": "RedPajamaC4"
} | 6,686 |
Home News More than half of services see reduction in frontline staff
More than half of services see reduction in frontline staff
More than half (53 per cent) of respondents to DrugScope's latest State of the sector survey have reported a reduction in the number of frontline staff, the charity states, with 40 per cent also reporting fewer managers and back office workers.
Based on a survey of 189 community, residential and prison services from across England, the State of the sector 2014-15 report records an average net funding reduction of 16.5 per cent – although this masked 'volatility and local variation' – following the previous State of the sector document's finding of 'no clear signs' of widespread disinvestment (DDN, March 2014, page 4). The new report also paints a picture of uncertainty around jobs and services, and de-motivated staff, with 'rapid commissioning cycles' one of the key concerns raised. Many respondents were worried that this could put clients at risk.
More than half of community services stated that they had been through tendering or contract renegotiation since September 2013, with a further 49 per cent expecting this to happen by September this year. The main gaps in provision identified by the report were housing support, dual diagnosis/complex needs and services for older clients, while more than 60 per cent of respondents also reported an increase in the use of volunteer 'recovery champions' and 47 per cent increased use of other volunteers.
'This is a period of far-reaching change for the services in our communities who support individuals and families affected by drug and alcohol problems,' said DrugScope chief executive Marcus Roberts. 'They are now part of a wider public health agenda, at a time when local authorities have increased discretion over their spending and are managing cuts to their budgets. It comes as no surprise that substantial disinvestment is expected and being planned for by service providers, nor that this will vary from place to place, with some areas more badly affected than others.'
The findings highlighted 'the impact of the constant cycle of local commissioning and recommissioning, which many respondents felt was disruptive to services and harmful both to clients and staff', he continued. 'Over three quarters of those surveyed were working to contracts of three years or less; one in four respondents reported that their contracts were getting shorter.'
It was vital, he stressed, that 'the benefits of effective drug and alcohol treatment that have been built up over decades are not lost in the coming years'.
DrugScope
State of the sector 2014-15 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,954 |
Phoenix Suns Schedule: Back Home Against The Warriors, Needing A Win
By Seth Pollack@sethpo Mar 18, 2011, 12:13pm MST
Share All sharing options for: Phoenix Suns Schedule: Back Home Against The Warriors, Needing A Win
The Phoenix Suns are technically out of the playoff hunt and while reality of how deep the hole is exists, they will continue to fight until they are eliminated. And from that point forward, as Coach Alvin Gentry stressed yesterday, they will play hard for 82 games because that's what they get paid to do.
"We are in critical situation now," center Marcin Gortat said yesterday, "Probably next lost game can cost us playoffs so we can't afford to come everyday now and just screw up and play some crap basketball."
The Suns have fallen from ninth to eleventh place in the West after losing their last four games, including critical losses to a team they are chasing (New Orleans) and a team that was chasing them (Houston).
Tonight's opponent, the Golden State Warriors (30-38), are 12th in the West and have lost to the Suns in their previous three meetings this season. The Warriors haven't won in Phoenix in their last 11 tries, but the Suns recently lost similar home winning streaks to the Nuggets and Magic.
Channing Frye will start tonight after missing the last five games with a dislocated right shoulder. He will wear a brace on the shoulder as he attempts to return ahead of schedule. The Suns were 1-4 without him.
The Warriors will be without center Andris Biedrins, who is expected to miss at least a week due to an ankle sprain.
The game tips at 7:00 p.m. local time on Fox Sports Arizona and will be broadcast on Sports 620 radio. Fans can follow along during the game with other Suns fans at the live game thread at Bright Side of the Sun.
Suns Down Warriors In Frye's Return, 108-97
Phoenix Suns Sweep Season Series With Warriors With 108-97 Win | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,591 |
namespace mirroring {
RemotingSender::RemotingSender(
scoped_refptr<media::cast::CastEnvironment> cast_environment,
media::cast::CastTransport* transport,
const media::cast::FrameSenderConfig& config,
mojo::ScopedDataPipeConsumerHandle pipe,
mojo::PendingReceiver<media::mojom::RemotingDataStreamSender> stream_sender,
base::OnceClosure error_callback)
: RemotingSender(cast_environment,
media::cast::FrameSender::Create(cast_environment,
config,
transport,
*this),
config,
std::move(pipe),
std::move(stream_sender),
std::move(error_callback)) {}
RemotingSender::RemotingSender(
scoped_refptr<media::cast::CastEnvironment> cast_environment,
openscreen::cast::Sender* sender,
const media::cast::FrameSenderConfig& config,
mojo::ScopedDataPipeConsumerHandle pipe,
mojo::PendingReceiver<media::mojom::RemotingDataStreamSender> stream_sender,
base::OnceClosure error_callback)
: RemotingSender(cast_environment,
media::cast::FrameSender::Create(cast_environment,
config,
sender,
*this),
config,
std::move(pipe),
std::move(stream_sender),
std::move(error_callback)) {
DCHECK(base::FeatureList::IsEnabled(media::kOpenscreenCastStreamingSession));
}
RemotingSender::RemotingSender(
scoped_refptr<media::cast::CastEnvironment> cast_environment,
std::unique_ptr<media::cast::FrameSender> frame_sender,
const media::cast::FrameSenderConfig& config,
mojo::ScopedDataPipeConsumerHandle pipe,
mojo::PendingReceiver<media::mojom::RemotingDataStreamSender> stream_sender,
base::OnceClosure error_callback)
: frame_sender_(std::move(frame_sender)),
clock_(cast_environment->Clock()),
error_callback_(std::move(error_callback)),
data_pipe_reader_(new media::MojoDataPipeReader(std::move(pipe))),
stream_sender_(this, std::move(stream_sender)),
input_queue_discards_remaining_(0),
is_reading_(false),
flow_restart_pending_(true) {
stream_sender_.set_disconnect_handler(base::BindOnce(
&RemotingSender::OnRemotingDataStreamError, base::Unretained(this)));
}
RemotingSender::~RemotingSender() {}
void RemotingSender::SendFrame(uint32_t frame_size) {
DCHECK_CALLED_ON_VALID_SEQUENCE(sequence_checker_);
const bool need_to_start_processing = input_queue_.empty();
input_queue_.push(base::BindRepeating(&RemotingSender::ReadFrame,
base::Unretained(this), frame_size));
input_queue_.push(base::BindRepeating(&RemotingSender::TrySendFrame,
base::Unretained(this)));
if (need_to_start_processing)
ProcessNextInputTask();
}
void RemotingSender::CancelInFlightData() {
DCHECK_CALLED_ON_VALID_SEQUENCE(sequence_checker_);
// Flag that all pending input operations should discard data.
input_queue_discards_remaining_ = input_queue_.size();
flow_restart_pending_ = true;
VLOG(1) << "Now restarting because in-flight data was just canceled.";
}
int RemotingSender::GetNumberOfFramesInEncoder() const {
NOTREACHED();
return 0;
}
base::TimeDelta RemotingSender::GetEncoderBacklogDuration() const {
NOTREACHED();
return base::TimeDelta();
}
void RemotingSender::OnFrameCanceled(media::cast::FrameId frame_id) {
// The frame cancellation may allow for the next input task to complete.
ProcessNextInputTask();
}
void RemotingSender::ProcessNextInputTask() {
DCHECK_CALLED_ON_VALID_SEQUENCE(sequence_checker_);
if (input_queue_.empty() || is_reading_)
return;
input_queue_.front().Run();
}
void RemotingSender::ReadFrame(uint32_t size) {
DCHECK_CALLED_ON_VALID_SEQUENCE(sequence_checker_);
DCHECK(!is_reading_);
if (HadError()) {
return;
}
if (!data_pipe_reader_->IsPipeValid()) {
VLOG(1) << "Data pipe handle no longer valid.";
OnRemotingDataStreamError();
return;
}
is_reading_ = true;
if (input_queue_discards_remaining_ > 0) {
data_pipe_reader_->Read(
nullptr, size,
base::BindOnce(&RemotingSender::OnFrameRead, base::Unretained(this)));
} else {
next_frame_data_.resize(size);
data_pipe_reader_->Read(
reinterpret_cast<uint8_t*>(std::data(next_frame_data_)), size,
base::BindOnce(&RemotingSender::OnFrameRead, base::Unretained(this)));
}
}
void RemotingSender::TrySendFrame() {
DCHECK_CALLED_ON_VALID_SEQUENCE(sequence_checker_);
DCHECK(!is_reading_);
if (input_queue_discards_remaining_ > 0) {
OnInputTaskComplete();
return;
}
// If there would be too many frames in-flight, do not proceed.
if (frame_sender_->GetUnacknowledgedFrameCount() >=
media::cast::kMaxUnackedFrames) {
VLOG(1) << "Cannot send frame now because too many frames are in flight.";
return;
}
const bool is_first_frame = (next_frame_id_ == media::cast::FrameId::first());
auto remoting_frame = std::make_unique<media::cast::SenderEncodedFrame>();
remoting_frame->frame_id = next_frame_id_;
if (flow_restart_pending_) {
remoting_frame->dependency = media::cast::EncodedFrame::KEY;
flow_restart_pending_ = false;
} else {
DCHECK(!is_first_frame);
remoting_frame->dependency = media::cast::EncodedFrame::DEPENDENT;
}
remoting_frame->referenced_frame_id =
remoting_frame->dependency == media::cast::EncodedFrame::KEY
? next_frame_id_
: next_frame_id_ - 1;
remoting_frame->reference_time = clock_->NowTicks();
remoting_frame->encode_completion_time = remoting_frame->reference_time;
base::TimeTicks last_frame_reference_time;
media::cast::RtpTimeTicks last_frame_rtp_timestamp;
if (is_first_frame) {
last_frame_reference_time = remoting_frame->reference_time;
last_frame_rtp_timestamp =
media::cast::RtpTimeTicks() - media::cast::RtpTimeDelta::FromTicks(1);
} else {
last_frame_reference_time = frame_sender_->LastSendTime();
last_frame_rtp_timestamp =
frame_sender_->GetRecordedRtpTimestamp(next_frame_id_ - 1);
}
// Ensure each successive frame's RTP timestamp is unique, but otherwise just
// base it on the reference time.
remoting_frame->rtp_timestamp =
last_frame_rtp_timestamp +
std::max(media::cast::RtpTimeDelta::FromTicks(1),
ToRtpTimeDelta(
remoting_frame->reference_time - last_frame_reference_time,
media::cast::kRemotingRtpTimebase));
remoting_frame->data.swap(next_frame_data_);
frame_sender_->EnqueueFrame(std::move(remoting_frame));
next_frame_id_++;
OnInputTaskComplete();
}
void RemotingSender::OnFrameRead(bool success) {
DCHECK_CALLED_ON_VALID_SEQUENCE(sequence_checker_);
DCHECK(is_reading_);
is_reading_ = false;
if (!success) {
OnRemotingDataStreamError();
return;
}
OnInputTaskComplete();
}
void RemotingSender::OnInputTaskComplete() {
DCHECK_CALLED_ON_VALID_SEQUENCE(sequence_checker_);
DCHECK(!input_queue_.empty());
input_queue_.pop();
if (input_queue_discards_remaining_ > 0)
--input_queue_discards_remaining_;
// Always force a post task to prevent the stack from growing too deep.
base::ThreadTaskRunnerHandle::Get()->PostTask(
FROM_HERE, base::BindOnce(&RemotingSender::ProcessNextInputTask,
weak_factory_.GetWeakPtr()));
}
void RemotingSender::OnRemotingDataStreamError() {
// NOTE: This method must be idemptotent as it may be called more than once.
data_pipe_reader_.reset();
stream_sender_.reset();
if (!error_callback_.is_null())
std::move(error_callback_).Run();
}
bool RemotingSender::HadError() const {
DCHECK_EQ(!data_pipe_reader_, !stream_sender_.is_bound());
return !data_pipe_reader_;
}
} // namespace mirroring
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,034 |
Виллем II, (, , ) полное имя Виллем Фредерик Георг Лодевейк (; ) — король Нидерландов и великий герцог Люксембургский с 7 октября 1840 года, герцог Лимбургский. Старший сын и преемник короля Виллема I.
Образование, наполеоновские войны
Воспитывался в Берлинской военной академии, завершил образование в Оксфордском университете и в 1811 году вступил подполковником в испанскую службу. В качестве нидерландского наследного принца он командовал в 1815 году, во время Ста дней, нидерландскими войсками. Виллем показал своё мужество и военные способности особенно в деле при Катр-Бра и в битве при Ватерлоо, в которой был ранен в плечо. Награждён 3 июля 1815 года орденом св. Георгия 2-го кл. № 75 «За участие в сражении при Ватерло».
22 июня 1814 года был награждён орденом Св. Андрея Первозванного.
В Петербурге в 1816 году он сочетался браком с сестрой императора Александра I, великой княжной Анной Павловной (1795—1865). К приезду принца юный Пушкин написал на заказ стихи «Принцу Оранскому».
Участие в бельгийских событиях
Когда в 1830 году вспыхнула революция в Бельгии, принц Оранский немедленно отправился в Антверпен и оттуда 1 сентября в Брюссель, где своим появлением произвел благоприятное впечатление. Несмотря на это, принц оказался в таком затруднительном положении, что превысил свои полномочия и 16 октября признал свободу Бельгии. Король отменил полномочия принца, который удалился в Англию. В следующем году он снова принял командование над нидерландскими войсками и вел войну с успехом, пока не был вынужден отступить перед вооруженным вмешательством Франции.
31 августа 1831 года получил звание фельдмаршала Нидерландов и должность главнокомандующего нидерландскими сухопутными войсками.
Царствование
Приняв трон после отречения отца в 1840 году, Виллем старался улучшить затруднительное финансовое положение страны, но опасался начать политические реформы, необходимость которых становилось все заметнее. Европейское революционное движение 1848 года сломило его сопротивление. Он согласился на полное преобразование конституции, финансовой и налоговой систем, но не дожил до окончания этих реформ и скончался 17 марта 1849 года. Его преемником стал сын Виллем III.
Виллем II умер в своём любимом городе Тилбурге, где подолгу пребывал со своим двором; его имя носит городской футбольный клуб «Виллем II».
Галерея
Генеалогия
Примечания
Литература
Залесский К. А. Наполеоновские войны 1799—1815. Биографический энциклопедический словарь, Москва, 2003.
Alberts, A., Koning Willem II, Den Haag: Kruseman, 1964
Hallema, Anne, Koning Willem II: een biografie ter gelegenheid van de herdenking van 's konings overlijden op 17 maart 1849, Assen: Born, 1949
Короли Нидерландов
Великие герцоги Люксембургские
Оранская династия
Фельдмаршалы (Великобритания)
Участники Наполеоновских и Революционных войн
Выпускники Оксфордского университета
Великие мастера ВВН
Принцы Нидерландов
Голландские командиры Наполеоновских и Революционных войн
Политики XIX века
Правители Европы XIX века | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,580 |
{"url":"https:\/\/codegolf.stackexchange.com\/questions\/231525\/happy-birthday-caird-coinheringaahing-chartz-belatedly\/231542#231542","text":"# Happy Birthday... caird coinheringaahing? ChartZ Belatedly?\n\nWhen this question was posted, it was caird coinheringaahing's birthday! (source: 1, 2, 3, 4) (It was also World Emoji Day.)\n\nAs a bit of some CGCC lore, caird's name came from a Jelly answer by Dennis (source) - the compressed form of \"Code Golf\" in Jelly is \u201c\u00bd\u010b\u1e6d6\u1ef4\u00bb, and if you insert a space (\u201c\u00bd\u010b\u1e6d6 \u1ef4\u00bb), it becomes \"caird coinheringaahing\" instead, which was important for this challenge as the former is lexicographically smaller than \"Programming Puzzles\", but the latter is larger.\n\nShifting the space around also gives some other resulting strings, and among them is \"ChartZ Belatedly\", which was caird's username during March of 2021.\n\n## Challenge\n\nOutput the string Happy Birthday, caird coinheringaahing! exactly.\n\nThe catch: for every character in your code, there must be at least one valid position that you can move it to such that the resulting program outputs Happy Birthday, ChartZ Belatedly! exactly.\n\nFor example, if abcd outputs the first string and bcad, acdb, cabd, and abdc output the second string, then this would be a valid program (a can be moved to the third position, b to the fourth, c to the first, and d to the third).\n\n(The idea for this came from caird themself, actually, so thanks to them :P)\n\n## Rules\n\n\u2022 You may output any amount of leading or trailing whitespace, and it does not have to be consistent either between the two strings or between varying programs printing the second string. For example, printing \"Happy Birthday, ChartZ Belatedly! \" for bcad and \" \\nHappy Birthday, ChartZ Belatedly! \\t \\r\\n\" for acdb would be valid.\n\u2022 No input will be given (the standard rules like allowing accepting an empty\/null input apply).\n\u2022 Your output method must be consistent though, so for example, if you print to STDOUT for the first string, you must do so for all other strings.\n\u2022 You must not output anything else with the chosen output method, but you can output to other methods (what I mean by this is if you output to STDOUT, you can flood STDERR with random garbage, and if your submission is a function that produces the result, you can output freely to STDOUT, etc.)\n\n## Scoring\n\nThis is a challenge still, so the shortest answer in bytes wins among submissions in its language.\n\n# Zsh-y, 145 148 144 142 131 130 bytes\n\n1=\"echo Happy Birthday, \";$1caird coinheringaahing!>x \"\\\";$1ChartZ Belatedly!>x #\"\n\"\\\";echo Happy Birthday, ChartZ Belatedly!>x #\"\n\nAttempt This Online!\n\nOutputs to a file called x, which allows us to save bytes exiting because we can overwrite the file to change the output instead of needing to exit the program.\n\n\u2022 Any character on the first line, including its trailing newline, should go between the \\ and \" on the third line\n\u2022 The final \" on the second line should go at the end of the third, and vice versa\n\u2022 Any other character on the second line, including its trailing newline, should go between the \\ and \" on the third line, and vice versa\n\nSome of the modified programs are highly cursed. For instance, moving the x on the first line:\n\n1=\"echo Happy Birthday, \";$1caird coinheringaahing!> \"\\\";$1ChartZ Belatedly!>x #\"\n\"\\x\";echo Happy Birthday, ChartZ Belatedly!>x #\"\n\n\nThis produces a \"parse error\" because of the trailing >, but zsh ...just continues executing the program??\n\n\u2022 Where do you move the newlines? Jul 18, 2021 at 7:23\n\u2022 @xigoi The first newline is considered a character on the first line, and the same for the second. So the first newline goes between the \\\" on the second line and vice versa Jul 18, 2021 at 7:57\n\n# Jelly, 88 69 bytes\n\nFLe33,39\u1e37\u00b6\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\n\n\nTry it online!\n\nThanks to @JonathanAllan for pointing out I could save 19 bytes by changing the last string to a compressed one.\n\nExplanation of base script:\n\nF | Flatten\nL | Length\ne33,39 | Is one of 33 or 39\n\u1e37 | Left (effectively a no-op here)\n\n\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb | [\"\", \"Happy Birthday, caird coinheringaahing!\"]\n\u00c7? | If helper link returns truthy:\n\u00b9 | - Identity function\n\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb | Else: [\"\", \"Happy Birthday, ChartZ Belatedly!\"]\n\u00c7\u0227$| helper(x) logical and x \u00c7\u0227$ | helper(x) logical and x\n\u1e37 | Left (effectively a no-op here)\n\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb | logical or [\"\", \"Happy Birthday, ChartZ Belatedly!\"]\n\n\nHere are the variants (produced by this script) that print \"Happy Birthday, ChartZ Belatedly!\":\n\n 0 F 10 Le33,39\u1e37\u00b6\u201cF\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n1 L 10 Fe33,39\u1e37\u00b6\u201cL\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n2 e 26 FL33,39\u1e37\u00b6\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bbe\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n3 3 10 FLe3,39\u1e37\u00b6\u201c3\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n4 3 10 FLe3,39\u1e37\u00b6\u201c3\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n5 , 10 FLe3339\u1e37\u00b6\u201c,\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n6 3 10 FLe33,9\u1e37\u00b6\u201c3\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n7 9 10 FLe33,3\u1e37\u00b6\u201c9\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n8 \u1e37 10 FLe33,39\u00b6\u201c\u1e37\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n9 \u00b6 1 F\u00b6Le33,39\u1e37\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n10 \u201c 13 FLe33,39\u1e37\u00b6\u201c\u1e42\u1e24\u201c\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n11 \u201c 13 FLe33,39\u1e37\u00b6\u201c\u1e42\u1e24\u201c\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n12 \u1e42 13 FLe33,39\u1e37\u00b6\u201c\u201c\u1e24\u1e42\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n13 \u1e24 11 FLe33,39\u1e37\u00b6\u201c\u1e24\u201c\u1e42\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n14 \u00bf 11 FLe33,39\u1e37\u00b6\u201c\u00bf\u201c\u1e42\u1e24\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n15 \u00a7 11 FLe33,39\u1e37\u00b6\u201c\u00a7\u201c\u1e42\u1e24\u00bf\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n16 \u2079 10 FLe33,39\u1e37\u00b6\u2079\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n17 \u1e6a 11 FLe33,39\u1e37\u00b6\u201c\u1e6a\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n18 \u00b6 11 FLe33,39\u1e37\u00b6\u201c\u00b6\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a3\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n19 3 10 FLe33,39\u1e37\u00b63\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b6\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n20 \u1e8a 11 FLe33,39\u1e37\u00b6\u201c\u1e8a\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n21 \u00f1 10 FLe33,39\u1e37\u00b6\u00f1\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n22 \u027c 11 FLe33,39\u1e37\u00b6\u201c\u027c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n23 \u1e43 10 FLe33,39\u1e37\u00b6\u1e43\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n24 \u1e40 11 FLe33,39\u1e37\u00b6\u201c\u1e40\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n25 \u0198 11 FLe33,39\u1e37\u00b6\u201c\u0198\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n26 \u00bb 10 FLe33,39\u1e37\u00b6\u00bb\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n27 \u00b9 10 FLe33,39\u1e37\u00b6\u00b9\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n28 \u201c 27 FLe33,39\u1e37\u00b6\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u201c\u00b9\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n29 \u00ae 11 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FLe33,39\u1e37\u00b6\u201c$\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online! 48 \u00c7 11 FLe33,39\u1e37\u00b6\u201c\u00c7\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online! 49 \u0227 43 FLe33,39\u1e37\u00b6\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u0227\u00c7?\u00c7\u0227$\u00c7$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online! 50$ 27 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FLe33,39\u1e37\u00b6\u201c\u201c\u1e42\u1e24\u201c\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n54 \u201c 14 FLe33,39\u1e37\u00b6\u201c\u201c\u1e42\u1e24\u201c\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n55 \u00ae 11 FLe33,39\u1e37\u00b6\u201c\u00ae\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n56 \u1e88 11 FLe33,39\u1e37\u00b6\u201c\u1e88\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n57 ' 11 FLe33,39\u1e37\u00b6\u201c'\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n58 \u00b6 11 FLe33,39\u1e37\u00b6\u201c\u00b6\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u1e92\u022ez\u1e42#jKgN\u00bb Try It Online!\n59 \u1e92 11 FLe33,39\u1e37\u00b6\u201c\u1e92\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u022ez\u1e42#jKgN\u00bb Try It Online!\n60 \u022e 11 FLe33,39\u1e37\u00b6\u201c\u022e\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92z\u1e42#jKgN\u00bb Try It Online!\n61 z 11 FLe33,39\u1e37\u00b6\u201cz\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022e\u1e42#jKgN\u00bb Try It Online!\n62 \u1e42 11 FLe33,39\u1e37\u00b6\u201c\u1e42\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez#jKgN\u00bb Try It Online!\n63 # 11 FLe33,39\u1e37\u00b6\u201c#\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42jKgN\u00bb Try It Online!\n64 j 10 FLe33,39\u1e37\u00b6j\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#KgN\u00bb Try It Online!\n65 K 11 FLe33,39\u1e37\u00b6\u201cK\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jgN\u00bb Try It Online!\n66 g 11 FLe33,39\u1e37\u00b6\u201cg\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKN\u00bb Try It Online!\n67 N 11 FLe33,39\u1e37\u00b6\u201cN\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKg\u00bb Try It Online!\n68 \u00bb 42 FLe33,39\u1e37\u00b6\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN Try It Online!\n\u2022 FLe33,39\u1e37\u00b6\u201c\u201c\u1e42\u1e24\u00bf\u00a7\u2079\u1e6a\u00b63\u1e8a\u00f1\u027c\u1e43\u1e40\u0198\u00bb\u00b9\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb\u00c7?\u00c7\u0227$\u00c7\u0227$\u1e37\u022f\u201c\u201c\u00ae\u1e88'\u00b6\u1e92\u022ez\u1e42#jKgN\u00bb works for 69. (Employed your Python script). Jul 18, 2021 at 19:59\n\n# C, 148 bytes\n\n\/**\/main(){printf(\"Happy Birthday, %s!\",'\\0'?\"ChartZ Belatedly\":\"caird coinheringaahing\");}\/\/\/*\/b;main(){puts(\"Happy Birthday, ChartZ Belatedly!\");}\n\n\u2022 Any character within the first main definition is moved to separate the first *\/, so the comment does not end there; it ends at the second *\/, and the second main definition applies.\n\u2022 Any of the first four characters \/**\/, except the first, is moved to make it \/*\/*, with the same effect.\n\u2022 The first character, \/, is moved one step right, making the program begin *\/*\/. This leaves * outside the comment, which combines with the later b; (a declaration of an implicit-int global variable) to form * b; (which declares b as a pointer to int).\n\u2022 Any other character (starting from \/\/\/*\/) is moved into '\\0', after the first ', to make it a multicharacter constant with a nonzero value, changing the string selected by the ? :; the last part originally beginning with three slashes ensures that it remains a line comment after any character is taken out from it.\n\n# Klein 000, 133, 120, 119, 111 bytes\n\n.\\\"Happy Birthday, \"\\\"ChartZ Belatedly!\"@\n>.\"Happy Birthday, ChartZ Belatedly!\"@\n\"oinheringaahing!\"@.>\"caird c\"\n\n\nTry it online!\n\nThe idea of this follows the classic klein \/ approach. We have 3 programs and we use the alignment to select which one we run. All of our swaps move one character to a different line breaking the alignment and putting it into a different program.\n\n## The breakdown\n\nIf the character is one of the first two then we swap them\n\n\\.\"Happy Birthday, \"\\\"ChartZ Belatedly!\"@\n>.\"Happy Birthday, ChartZ Belatedly!\"@\n\"oinheringaahing!\"@.>\"caird c\"\n\n\nAnything else on the first line we can put at the begining of the second line.\n\n.\\\"Happy Birhday, \"\\\"ChartZ Belatedly!\"@\nt>.\"Happy Birthday, ChartZ Belatedly!\"@\n\"oinheringaahing!\"@.>\"caird c\"\n\n\nFor the first two characters of the second line we can swap them too.\n\n.\\\"Happy Birthday, \"\\\"ChartZ Belatedly!\"@\n.>\"Happy Birthday, ChartZ Belatedly!\"@\n\"oinheringaahing!\"@.>\"caird c\"\n\n\nFor the rest of the line we can insert it before the . in the third line\n\n.\\\"Happy Birthday, \"\\\"ChartZ Belatedly!\"@\n>.\"Happy Birhday, ChartZ Belatedly!\"@\n\"oinheringaahing!\"@t.>\"caird c\"\n\n\nAny character on the third line can be inserted at the front of the second line.\n\n.\\\"Happy Birthday, \"\\\"ChartZ Belatedly!\"@\na>.\"Happy Birthday, ChartZ Belatedly!\"@\n\"oinheringahing!\"@.>\"caird c\"\n\n\nFinally we can do the newlines as follows:\n\n.\\\"Happy Birthday, \"\\\"ChartZ Belatedly!\"\n@>.\"Happy Birthday, ChartZ Belatedly!\"@\n\"oinheringaahing!\"@.>\"caird c\"\n\n.\\\"Happy Birthday, \"\\\"ChartZ Belatedly!\"@\n>.\"Happy Birthday, ChartZ Belatedly!\"@\"oinheringaahing!\"@.>\"caird c\n\"\n\n\n# Python 3, 130 bytes\n\n'''''';print(\"Happy Birthday,\",\"\"and\"ChartZ Belatedly!\"or\"caird coinheringaahing!\")#''';print('Happy Birthday, ChartZ Belatedly!')\n\n\nTry it online!\n\n## Alternate programs\n\n\u2022 Byte 1 to 6: The ' is moved behind the first ;, therefore characters 1 to 87 are a string and are disregarded. Characters 89+ are executed.\n\n''''';'print(\"Happy Birthday,\",\"\"and\"ChartZ Belatedly!\"or\"caird coinheringaahing!\")#''';print('Happy Birthday, ChartZ Belatedly!')\n\n\u2022 Byte 7 to 84: The byte is moved behind the fifth byte. As none of these characters is a ', this also creates a string from character 1 to character 87, with the same effects as above.\n\n'''''\"';print(Happy Birthday,\",\"\"and\"ChartZ Belatedly!\"or\"caird coinheringaahing!\")#''';print('Happy Birthday, ChartZ Belatedly!')\n\n\u2022 Byte 85-130: The byte is moved between the \"\" at position 32-33. This makes the string a truthy value and the other string is printed. There is no \" in byte 85-130, so this will always work. The second part of the program is not executed, because it is commented out.\n\n'''''';print(\"Happy Birthday,\",\"'\"and\"ChartZ Belatedly!\"or\"caird coinheringaahing!\")#''';print(Happy Birthday, ChartZ Belatedly!')\n\n\n# JavaScript (browser), 146 136 bytes\n\nBased off of the C and python answers.\n\nThis is too long and it still seems sketchy to me\n\n0\/**\/;;alert(\"Happy Birthday, \"+(\"\"?\"ChartZ Belatedly!\":\"caird coinheringaahing!\"))\/\/*\/-2;alert('Happy Birthday, ChartZ Belatedly!')\/\/*\/\n\n\n## Where to move:\n\n\u2022 The 0 goes after the second asterisk\n\u2022 The first slash moves to the right, forming 0* -1\n\u2022 The first two asterisks and the second slash can move to right anywhere before the \/\/*\/-1\n\u2022 The first two semicolons go inside the empty string\n\u2022 Any text between the two semicolons and the \/\/*\/-1 go after the second asterisk\n\u2022 Any text starting from \/\/*\/-1 goes inside the empty string\n\nTry this mess online!\n\nHope this is valid and it works aaaa\n\n\u2022 Looks valid now, aside from the fact that it should be caird (with a d, not a t) :P Jul 23, 2021 at 18:24\n\u2022 Oops, sorry! I\u2019m bad at names. I\u2019ve fixed it now Jul 23, 2021 at 18:27\n\u2022 It looks like you put the t back in. :) Aug 7, 2021 at 13:51\n\u2022 Oooops aaaaaaa, I modified the previous code I had stored somewhere, I guess I still forgot to change it there. Also I wonder if I have to change it to \u201cHappy birthday, Dude coinheringaahing\u201d because of the recent name change Aug 7, 2021 at 13:59\n\n# JavaScript, 123 bytes\n\n17\/**\/,x=>\"Happy Birthday, \"+(''?\"ChartZ Belatedly!\":\"caird coinheringaahing!\")\/\/**\/,x=>\"Happy Birthday, ChartZ Belatedly!\"\n\n\nTry it online!\n\n## Variations\n\n(full text omitted for brevity)\n\n17\/**\/,x=>\"HB\"+(''?\"CB\":\"cc\")\/\/**\/,x=>\"HBCB\"\n7\/**1\/,x=?\"HB\"+(''?\"CB\":\"cc\")\/\/**\/,x=>\"HBCB\"\n1\/**7\/,x=>\"HB\"+(''?\"CB\":\"cc\")\/\/**\/,x=>\"HBCB\"\n17**\/,x=>\"HB\"+(''?\"CB\":\"cc\")\/\/*\/*\/,x=>\"HBCB\" (syntax highlighting is broken, but runs ok)\n17\/*\/*,x=>\"HB\"+(''?\"CB\":\"cc\")\/\/**\/,x=>\"HBCB\"\n17\/**,\/x=>\"HB\"+(''?\"CB\":\"cc\")\/\/**\/,x=>\"HBCB\"\n17\/**x\/,=>\"HB\"+(''?\"CB\":\"cc\")\/\/**\/,x=>\"HBCB\"\n17\/**=\/,x>\"HB\"+(''?\"CB\":\"cc\")\/\/**\/,x=>\"HBCB\"\n\/\/ ...\n17\/**\"\/,x=>\"HB'+('\"?\"CB\":\"cc)\/\/**\/,x=>\"HBCB\"\n17\/**)\/,x=>\"HB\"+(''?\"CB\":\"cc\"\/\/**\/,x=>\"HBCB\"\n17\/**\/,x=>\"HB\"+('\/'?\"CB\":\"cc\")\/**\/,x=>\"HBCB\"\n17\/**\/,x=>\"HB\"+('*'?\"CB\":\"cc\")\/\/*\/,x=>\"HBCB\"\n17\/**\/,x=>\"HB\"+('\/'?\"CB\":\"cc\")\/\/**,x=>\"HBCB\"\n17\/**\/,x=>\"HB\"+('x'?\"CB\":\"cc\")\/\/**\/,=>\"HBCB\"\n\/\/ ...\n17\/**\/,x=>\"HB\"+('B'?\"CB\":\"cc\")\/\/**\/,x=>\"HBC\"\n17\/**\/,x=>\"HB\"+('\"'?\"CB\":\"cc\")\/\/**\/,x=>\"HBCB\n\n\u2022 This appears to be a snippet, which is not an allowed IO method on this site. You need to change it to use console.log or similar Jul 25, 2021 at 6:19\n\u2022 @pxeger Hmm, I thought an expression evaluating to the output was allowed, but I don't see it in the meta thread. I've updated my answer accordingly. Jul 25, 2021 at 14:57","date":"2022-07-06 16:26:34","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\": 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\": 0.3522307872772217, \"perplexity\": 9753.155134870885}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656104675818.94\/warc\/CC-MAIN-20220706151618-20220706181618-00274.warc.gz\"}"} | null | null |
package org.cobogw.gwt.user.client.ui;
import org.cobogw.gwt.user.client.CSS;
import com.google.gwt.user.client.ui.FlowPanel;
import com.google.gwt.user.client.ui.Widget;
/**
* The ButtonBar is horizontal panel on which {@link Button} widgets can be
* placed. When a {@link Button} is placed on the ButtonBar, depending on it's
* position on the bar left and right border effects are applied to create a
* aligned button effect. The ButtonBar is a {@link FlowPanel} that is set
* to <code>display</code> as an <code>inline-block</code>. It is therefore also
* possible to add non {@link Button} widgets to the ButtonBar. These widgets
* also are set to <code>display</code> as an <code>inline-block</code> to keep
* the horizontal state.
*
* <h3>CSS Style Rules</h3>
* <ul class='css'>
* <li>.cbg-ButtonBar { }</li>
* <li>.cbg-BCLeft { }</li>
* <li>.cbg-BCRight { }</li>
* </ul>
*/
public class ButtonBar extends FlowPanel {
//class style names.
public static final String CBG_BUTTON_BAR = "cbg-ButtonBar";
public static final String CBG_BUTTON_COLLAPSE_LEFT = "cbg-BCLeft";
public static final String CBG_BUTTON_COLLAPSE_RIGHT = "cbg-BCRight";
/**
* Creates a new empty ButtonBar.
*/
public ButtonBar() {
super();
CSS.setInlineBlock(getElement());
setStyleName(CBG_BUTTON_BAR);
}
/**
* Adds a new {@link Button} to the panel.
*
* @param button the Button to added
*/
public void add(Button button) {
super.add(button);
final int wc = getWidgetCount();
if (wc > 1) {
button.setInnerBorderColor(true, true);
setStyleName(button.getElement(), CBG_BUTTON_COLLAPSE_LEFT, true);
final Widget left = getWidget(wc-2);
if (left instanceof Button) {
((Button) left).setInnerBorderColor(true, false);
}
setStyleName(left.getElement(), CBG_BUTTON_COLLAPSE_RIGHT, true);
}
}
/**
* Adds a new child widget to the panel and set it to <code>display</code>
* as <code>inline-block</code>.
*
* @param w the widget to be added
*/
@Override
public void add(Widget w) {
super.add(w);
CSS.setInlineBlock(w.getElement());
}
@Override
public boolean remove(int index) {
final boolean present = super.remove(index);
if (present) {
final int cnt = getWidgetCount();
if (cnt > 0) {
if (index == 0) {
// correct the new first button, since the first was removed.
final Widget right = getWidget(0);
if (right instanceof Button) {
((Button) right).setInnerBorderColor(false, true);
}
setStyleName(right.getElement(), CBG_BUTTON_COLLAPSE_LEFT, false);
setStyleName(right.getElement(), CBG_BUTTON_COLLAPSE_RIGHT, false);
} else if (index == cnt) {
// correct the new last button, since the last button was removed.
final Widget left = getWidget(index-1);
if (left instanceof Button) {
((Button) left).setInnerBorderColor(false, false);
}
setStyleName(left.getElement(), CBG_BUTTON_COLLAPSE_RIGHT, false);
} // else button removed in between other buttons, so nothing to do
}
}
return present;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 623 |
A bored and domesticated Shrek pacts with deal-maker Rumpelstiltskin to get back to feeling like a real ogre again, but when he's duped and sent to a twisted version of Far Far Away—where Rumpelstiltskin is king, ogres are hunted, and he and Fiona have never met—he sets out to restore his world and reclaim his true love.
Max the terrier must cope with some major life changes when his owner gets married and has a baby. When the family takes a trip to the countryside, nervous Max has numerous run-ins with canine-intolerant cows, hostile foxes and a scary turkey. Luckily for Max, he soon catches a break when he meets Rooster, a gruff farm dog who tries to cure the lovable pooch of his neuroses.
Gru and his wife Lucy must stop former '80s child star Balthazar Bratt from achieving world domination.
A koala named Buster recruits his best friend to help him drum up business for his theater by hosting a singing competition.
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Drive-In Movies | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,078 |
\section{Introduction}
The development of radioactive-ion beams in the mid-80s has enabled the exploration of the
nuclear landscape away from stability. This technical breakthrough led to the discovery
of exotic nuclear structures such as hal\oe s \cite{Tan85b,Tan85l}.
Halo nuclei are light neutron-rich nuclei, which exhibit a matter radius significantly larger than their isobars.
This large size is qualitatively understood as resulting from their
small binding energy for one or two neutrons \cite{HJ87}:
Due to their loose binding, these valence neutrons can tunnel far away from
the core of the nucleus and exhibit a large probability of presence at a large distance
from the other nucleons. Halo nuclei have thus a strongly clusterised structure:
they can be seen as a core to which one or two neutrons are loosely bound.
These valence neutrons hence form a sort of diffuse halo around a compact core.
The best known halo nuclei are $^{11}$Be and $^{15}$C, with a one-neutron halo,
and $^6$He and $^{11}$Li, with a two-neutron halo.
Proton hal\oe s can also develop around proton-rich nuclei,
such as $^8$B or $^{17}$F.
Since their discovery, halo nuclei have been at the centre of many studies, both
experimental \cite{Tan96,Jon04} and theoretical \cite{AN03,BHT03}.
Due to their short lifetime, they cannot be studied with usual spectroscopic techniques,
and one must resort to indirect methods to deduce information about their structure.
Reactions are the most used tools to study halo nuclei. In particular, elastic scattering
\cite{Mat06,Dip10} and breakup \cite{Fuk04,BCG05} convey interesting information
about the structure of the projectile.
Recent experimental \cite{Dip10} and theoretical \cite{Mat06} studies of elastic scattering
indicate a strong coupling between scattering and breakup.
On the experimental side, the elastic scattering cross section for $^{11}$Be on Zn around
the Coulomb barrier is significantly reduced at large angles compared to that of non-halo
Be isotopes \cite{Dip10}. One explanation of this unexpected reduction is the transfer of
probability flux from the elastic channel to the breakup channel.
On the theoretical side, Matsumoto \etal have shown that for the elastic scattering of
$^6$He on Bi at low energy CDCC calculations agree with experimental data only if the
breakup channel is included in the model space.
To better investigate the interplay between elastic scattering and breakup, we analyse
theoretically the angular distributions for the elastic scattering and breakup of halo nuclei
within a near/far decomposition \cite{CFH85,HM84}.
We choose $^{11}$Be, the archetypical one-neutron halo nucleus, as testcase and
consider its collision on Pb at $69A$MeV, which corresponds to the conditions of the
RIKEN experiment \cite{Fuk04}.
The calculations are performed within the Dynamical Eikonal Approximation (DEA) \cite{BCG05,GBC06},
which is in excellent agreement with various experimental results.
After a brief reminder of the DEA and the near/far decomposition,
we apply this technique to the elastic-scattering cross section (\Sec{el}).
We then move to the analysis of the angular distribution for breakup
(\Sec{bu}) and show how similar both cross sections are at intermediate energies.
In \Sec{conclusion}, we emphasise the consequences of this analysis for
the study of halo nuclei and provide the prospects of this work.
\section{Theoretical framework}\label{theory}
\subsection{Dynamical eikonal approximation}\label{dea}
Most of the models of reactions involving one-neutron halo nuclei
rely on a three-body description of the colliding nuclei \cite{AN03,BC12}:
a two-body projectile $P$ made up of a fragment $f$ loosely bound to a core $c$
impinging on a structureless target $T$.
The two-body structure of the projectile is described by the phenomenological
Hamiltonian
\beq
H_0=-\frac{\hbar^2}{2\mu_{cf}}\Delta_{\ve{r}}+V_{cf}(\ve{r}),
\eeqn{e1}
where $\ve{r}$ is the $c$-$f$ relative coordinate, $\mu_{cf}$ is the $c$-$f$ reduced mass,
and $V_{cf}$ is a real potential adjusted to reproduce the binding energy of the fragment
to the core and some of the excited states of the projectile.
This potential usually exhibits a Woods-Saxon form factor and may include a spin-orbit coupling term.
The interaction between the projectile components $c$ and $f$ and the target $T$ are
simulated by the optical potentials $V_{cT}$ and $V_{fT}$, respectively.
Within this three-body framework, studying reactions involving one-neutron halo nuclei
reduces to solve the three-body \Sch equation
\beq
\left[-\frac{\hbar^2}{2\mu}\Delta_{\ve{R}}+H_0+V_{cT}(\ve{r},\ve{R})+V_{fT}(\ve{r},\ve{R})\right]
\Psi(\ve{r},\ve{R})=E_{\rm tot}\Psi(\ve{r},\ve{R}),
\eeqn{e2}
where $\ve{R}$ is the $P$-$T$ relative coordinate, $\mu$ is the $P$-$T$ reduced mass and
\beq
E_{\rm tot}=E_0+\frac{\hbar^2K^2}{2\mu}
\eeqn{e3}
is the total energy of the system, with $E_0$ the (negative) energy of the projectile ground state
$\phi_{l_0 j_0 m_0}$ and $\hbar K$ the initial $P$-$T$ relative momentum.
The quantum numbers $l_0$, $j_0$ and $m_0$ correspond to the $c$-$f$ orbital angular momentum,
the projectile total angular momentum and its projection, respectively.
To describe a reaction in which the halo nucleus $P$ impinges on the target $T$,
\Eq{e2} is solved with the initial condition
\beq
\Psi^{(m_0)}(\ve{r},\ve{b},Z)\flim{Z}{-\infty}e^{iKZ}\phi_{l_0 j_0 m_0},
\eeqn{e4}
where the dependence upon the transverse $\ve{b}$ and longitudinal $Z$ components
of $\ve{R}$ is made explicit.
Equation \eq{e2} must be solved for each value of $\ve{b}$ and of $m_0$.
At sufficiently high incident energy, the eikonal approximation can be performed to ease the
resolution of \Eq{e2}. That approximation consists in assuming that most of the rapid variation
of $\Psi$ in the $P$-$T$ relative coordinate $\ve{R}$ is included in the plane wave $e^{iKZ}$,
i.e. that the three-body wave function is well approximated by that plane wave times a function
$\widehat \Psi$ that does not vary much with $\ve{R}$:
\beq
\Psi(\ve{r},\ve{b},Z)=e^{iKZ}\widehat\Psi(\ve{r},\ve{b},Z).
\eeqn{e5}
Including the eikonal ansatz \eq{e5} within \Eq{e2} leads to
\beq
\left[-\frac{\hbar^2}{2\mu}\Delta_{\ve{R}}-i\frac{\hbar^2 K}{\mu} \frac{\partial}{\partial Z}
+\frac{\hbar^2K^2}{2\mu}
+H_0+V_{cT}(\ve{r},\ve{R})+V_{fT}(\ve{r},\ve{R})\right]
\widehat\Psi(\ve{r},\ve{R})=E_{\rm tot}\widehat\Psi(\ve{r},\ve{R}).
\eeqn{e6}
Since $\widehat\Psi$ varies smoothly with $\ve{R}$, its second-order derivative
$\Delta_{\ve{R}}\widehat\Psi$ can be neglected
in front of its first-oder derivative $K\partial/\partial Z \widehat\Psi$.
Then, considering the energy conservation \eq{e3}, the three-body \Sch equation \eq{e6}
reduces to the DEA equation \cite{BCG05,GBC06}
\beq
i\hbar v \frac{\partial}{\partial Z}\widehat\Psi(\ve{r},\ve{R})
=\left[H_0-E_0+V_{cT}(\ve{r},\ve{R})+V_{fT}(\ve{r},\ve{R})\right]
\widehat\Psi(\ve{r},\ve{R}),
\eeqn{e7}
with $v=\hbar K/\mu$ the initial $P$-$T$ relative velocity.
This equation is mathematically equivalent to a time-dependent \Sch equation
with straight-line trajectories posing $Z=vt$. It can thus been solved using appropriate algorithms,
such as the one described in \Ref{CBM03c}.
However, since the DEA does not assume any semiclassical treatment of the $P$-$T$ relative motion,
$\ve{b}$ and $Z$ are quantal variables. This implies that the DEA includes quantal interferences
such as between different trajectories, which
are missing in time-dependent models \cite{GBC06}.
The DEA therefore significantly improves these models.
The DEA differs also from what is usually called the eikonal approximation \cite{BC12}.
In its usual form, the eikonal approximation includes a subsequent adiabatic approximation to \Eq{e7}
in which the excitation energy of the projectile is neglected, i.e. $H_0-E_0\approx 0$.
In that case, the solution of \Eq{e7} is approximated by the eikonal form factor
\beq
\widehat\Psi^{(m_0)}_{\rm eik}(\ve{r},\ve{b},Z\rightarrow\infty)=e^{i\chi(\ve{r},\ve{b})}\phi_{l_0 j_0 m_0}(\ve{r}),
\eeqn{e8}
where the eikonal phase reads
\beq
\chi(\ve{r},\ve{b})=-\frac{1}{\hbar v}\int_{-\infty}^{\infty}[V_{cT}(\ve{r},\ve{b},Z)+V_{fT}(\ve{r},\ve{b},Z)]dZ.
\eeqn{e9}
The DEA thus improves the usual eikonal approximation by including dynamical effects that are
otherwise neglected. These effects may be very significant such as in Coulomb breakup,
for which the usual eikonal approximation diverges \cite{GBC06}.
The DEA has been used successfully to describe elastic scattering and breakup of one-neutron
halo nuclei on both light and heavy targets \cite{GBC06}. This approximation has also provided
a reliable description of the Coulomb breakup of the one-proton halo nucleus $^8$B \cite{GCB07}.
More recently, a comparison of various reaction models has shown that the DEA is in excellent
agreement with CDCC at intermediate energies \cite{CEN12} while being much less demanding
on a computational point of view.
The DEA is thus the most efficient model to study reactions involving one-neutron halo nuclei at intermediate energies.
Moreover as it describes simultaneously both elastic scattering and breakup, the DEA is ideal for the present study.
\subsection{Angular distributions and their near/far decompositions}\label{nf}
Within the DEA, the angular distribution for elastic scattering,
i.e. the elastic-scattering cross section, reads \cite{GBC06}
\beq
\frac{d\sigma_{\rm el}}{d\Omega}=K^2\frac{1}{2 j_0+1}\sum_{m_0 m'_0}
\left|\int_0^\infty b db J_{|m'_0-m_0|}(qb)S^{(m_0)}_{m'_0}(b)\right|^2,
\eeqn{e10}
where $J_\mu$ is a Bessel function \cite{AS70}, $q=2K\sin\theta/2$
is the transferred momentum and
\beq
S^{(m_0)}_{m'_0}(\ve{b})=\langle\phi_{l_0 j_0 m'_0} |
\widehat\Psi^{(m_0)}(\ve{b},Z\rightarrow\infty)\rangle-\delta_{m'_0 m_0}.
\eeqn{e11}
To have a better insight into the reaction mechanism that takes place during the scattering of
the projectile by the target, we perform a near/far decomposition of the elastic-scattering
cross section \eq{e10} \cite{CFH85,HM84}.
The idea behind this decomposition is to express the Bessel function as the sum of two
Hankel functions \cite{AS70}:
\beq
J_\mu(z)=\frac{1}{2}\left[H^{(1)}_\mu(z)+H^{(2)}_\mu(z)\right].
\eeqn{e12}
The elastic-scattering cross section can then be expressed as the sum of two terms
obtained by substituting $J_\mu$ by either $H_\mu^{(1)}/2$ or $H_\mu^{(2)}/2$ in \Eq{e10}.
The former is called the \emph{Far side} (F) of the angular distribution \eq{e10},
while the latter is its \emph{Near side} (N):
\beq
\frac{d\sigma_{\rm el}^{\rm F,N}}{d\Omega}=K^2\frac{1}{2 j_0+1}\sum_{m_0 m'_0}
\left|\int_0^\infty b db H_{|m'_0-m_0|}^{(1,2)}(qb)S^{(m_0)}_{m'_0}(b)\right|^2.
\eeqn{e13}
Since these two terms add coherently to form the elastic-scattering cross section,
they may interfere when they reach similar magnitude, which
explains some of the oscillatory patterns observed in angular distributions \cite{HM84}.
The physics behind this decomposition can be understood from the asymptotic
behaviour of the Hankel functions:
\beq
H_\mu^{(1,2)}\flim{z}{\infty}\sqrt{\frac{2}{\pi z}} e^{\pm i(z-\mu\pi/2-\pi/4)}.
\eeqn{e14}
Since $q\approx K\theta$, the N side corresponds to the positive deflection
i.e. repulsive forces (see \fig{f1}). On the contrary the F side carries information
about negative deflection, i.e. attractive forces.
\begin{figure}
\center
\includegraphics[width=6cm]{NFsketch.eps}
\caption{Schematic illustration of the Near and Far sides of the angular distribution.}\label{f1}
\end{figure}
The angular distribution for the breakup of the projectile can also be computed within the DEA
\cite{GBC06}. It corresponds to the breakup cross section expressed as a function of the
scattering angle $\Omega\equiv(\theta,\varphi)$ of the $c$-$f$ centre of mass after
dissociation at a $c$-$f$ relative energy $E=\hbar^2 k^2/2\mu_{cf}$. It reads
\beq
\frac{d\sigma_{\rm bu}}{dEd\Omega}=\frac{2\mu_{cf}KK'}{\pi \hbar^2k}\frac{1}{2 j_0+1}
\sum_{m_0}\sum_{ljm}\left|\int_0^\infty b db J_{|m-m_0|}(qb)S_{kljm}^{(m_0)}(b)\right|^2,
\eeqn{e15}
where
\beq
S_{kljm}^{(m_0)}(\ve{b})=\langle\phi_{k l j m} | \widehat\Psi^{(m_0)}(\ve{b},Z\rightarrow\infty)\rangle,
\eeqn{e16}
with $\phi_{k l j m}$ the continuum wave function describing the broken up projectile in partial
wave $ljm$.
To study the breakup process, we extend the N/F analysis to the angular distribution \eq{e15}.
As for the elastic scattering, the Bessel function is decomposed into the sum of two Hankel
functions \eq{e12}, which provide both N and F sides of the breakup cross section with the
same interpretation, i.e. the contribution to breakup of the repulsive and attractive forces,
respectively.
\section{Elastic scattering}\label{el}
\subsection{{\rm $^{11}$Be} on {\rm Pb} at $69A$MeV}
As a first step in our analysis, we study the elastic scattering of $^{11}$Be on Pb
at $69A$MeV.
As mentioned earlier, $^{11}$Be is the archetypical one-neutron halo nucleus. In our
analysis, it is described as a $^{10}$Be core in its $0^+$ ground state
to which one-neutron is loosely bound.
We choose for the $^{10}$Be-n interaction the potential developed in \Ref{CGB04},
which reproduces the $1/2^+$ ground state in the $1s1/2$ partial wave at 504~keV
below the one-neutron separation threshold. This potential also reproduces the $1/2^-$
bound excited state in the $0p1/2$ orbital and the $5/2^+$ resonance in the $d5/2$
partial wave.
We use the numerical parameters and the potentials $V_{cT}$ and $V_{fT}$ detailed in
\Ref{GBC06}. The numerical technique used to solve the DEA equation \eq{e7} is
explained in \Ref{CBM03c}
The DEA elastic-scattering cross section is plotted in \fig{f2} as a ratio to Rutherford \cite{CHB10}.
It presents a usual shape with a Coulomb rainbow at about $2^\circ$ followed by
an exponential drop. At larger angles, the angular distribution presents significant
oscillations.
The N/F decomposition shows that at forward angles the process is fully dominated
by the N side, as expected for a (repulsive) Coulomb-dominated reaction \cite{HM84}.
Note that the forward-angles oscillations (i.e. below $2^\circ$) are observed in both
the total cross section and its N side. The N/F interferences therefore cannot explain
this feature of the angular distribution.
\begin{figure}
\center
\includegraphics[width=8cm]{NFfig1pres.eps}
\caption{N/F analysis of the elastic scattering of $^{11}$Be on Pb at $69A$MeV
\cite{CHB10}.}\label{f2}
\end{figure}
At larger angles, i.e. around $8^\circ$, the N and F sides cross, explaining the
oscillatory pattern of the total cross section. This shows in particular that attractive
nuclear forces affect the elastic scattering mostly at large angles, as is expected from
semiclassical models.
The whole interpretation of the N/F decomposition is based on the asymptotic behaviour of
the Hankel functions \eq{e14}. To validate this interpretation, we repeat the calculation of
the cross section, its N and F sides using the asymptotics of the Bessel and Hankel functions.
The angular distributions obtained in this way (dotted lines) are in excellent agreement
with the exact ones, confirming our analysis of this N/F decomposition.
\subsection{Influence of $P$-$T$ interaction}\label{vpt}
To better apprehend the influence of the choice of $P$-$T$ interaction on the elastic scattering,
we repeat the calculation with the sole Coulomb term of the nuclear optical potential
(i.e. a point-sphere potential, P-S) and a purely point-point Coulomb interaction (P-P).
The dominant N sides of the corresponding elastic-scattering cross sections are plotted in \fig{f3}~(left).
This change of potentials causes dramatic changes in the angular distribution.
It mostly modifies the Coulomb rainbow.
As the full optical potentials, the P-S interaction leads to a Coulomb rainbow,
but its location is shifted from $2^\circ$ to about $4^\circ$.
On the contrary, no Coulomb rainbow is observed with the P-P interaction.
This confirms that the features of the elastic-scattering cross section strongly
depends on the choice of the optical potentials $V_{cT}$ and $V_{fT}$.
Interestingly, the change in the elastic scattering cross section cannot be simply
related to a transfer of flux towards the breakup channel, as postulated in \Ref{Dip10}.
Although the elastic scattering increases at large angles from the Coulomb + nuclear
potential to the purely Coulomb interaction (first with P-S and then even more with P-P),
the total breakup cross section increases as well, as shown in \tbl{t1}.
Since the Coulomb rainbow appears only for the $P$-$T$ potentials that account for
the extension of the projectile and the target (i.e. the full optical potential or just its Coulomb
component P-S), we now analyse the influence of the extension of the halo on these distributions.
\begin{figure}
\center
\includegraphics[width=8cm]{NFfig2pres.eps}\hspace{-2mm}
\includegraphics[width=8cm]{NFfig3pres.eps}
\caption{Sensitivity of the elastic-scattering cross section to the $P$-$T$ interaction (left)
and the extension of the halo (right).}\label{f3}
\end{figure}
\begin{table}
\center
\begin{tabular}{l | c | c | c c c}
\hline \hline
Iteraction & P-P & P-S & \multicolumn{3}{c}{C.+N.}\\ \hline
$|E_0|$ (MeV) & 0.5 & 0.5 & 0.5 & 0.05 & 5\\
$\sigma_{\rm bu}$ (b) & 2.58 & 2.10 & 1.70 & 23.57 & 0.07 \\
\hline \hline
\end{tabular}
\caption{Total breakup cross sections corresponding to the calculations shown in Secs.~\ref{vpt}
and \ref{e0} \cite{CHB10}.}\label{t1}
\end{table}
\subsection{Influence of the size of the halo}\label{e0}
To study the sensitivity of our results to the size of the halo, we repeat the DEA calculations
adjusting the $^{10}$Be-n potential to increase (reduce) the neutron separation energy $|E_0|$
of the $^{11}$Be-like projectile in order to shrink (resp. expand) its halo.
The N side of the elastic-scattering cross section is plotted as a ratio to Rutherford in \fig{f3}~(right).
The slope of the exponential drop after the Coulomb rainbow is sensitive to $E_0$: Reducing
the one-neutron separation energy of the projectile, i.e. expanding its halo, slightly reduces the
elastic-scattering cross section. This effect could therefore be used to get information about the
extension of the halo. However, this dependence remains small in comparison to the influence
of the $P$-$T$ potential [see \fig{f3}~(left)]. There is thus little hope that observing the sole
elastic-scattering cross section could provide unbiased information about the extension of the halo.
Since reducing $|E_0|$ increases the breakup cross section (see \tbl{t1}), we could believe that
the transfer of flux to the breakup channel explains the change in the elastic-scattering cross section.
However, since this increase is much more significant than the drop in the elastic-scattering cross
section, our analysis confirms that there is no direct link between both effects,
as suggested in \Sec{vpt}.
\section{Breakup of {\rm $^{11}$Be} on {\rm Pb} at $69A$MeV}\label{bu}
To better comprehend the link between angular distributions for elastic scattering and breakup,
we perform the same analysis as in \Sec{el} for the breakup cross section \eq{e15}.
For the breakup of $^{11}$Be on Pb at $69A$MeV, the angular distribution (solid line)
and its N (short-dashed line) and F (long-dashed line) sides are plotted as a function of
the scattering angle $\theta$ of the $^{10}$Be-n centre of mass after dissociation \cite{CHB10}
(see \fig{f4}). The $^{10}$Be-n relative energy is $E=0.5$~MeV.
\begin{figure}
\center
\includegraphics[width=8cm]{NFfig4pres.eps}
\caption{N/F decomposition of the breakup angular distribution for $^{11}$Be on Pb at $69A$MeV.
The $^{10}$Be-n relative energy is $E=0.5$~MeV.}\label{f4}
\end{figure}
The features of the breakup angular distribution are very similar to those of the elastic-scattering
cross section. First, the full calculation exhibits small oscillations at forward angles before an exponential
drop starting at $2^\circ$, which is reminiscent of the Coulomb rainbow observed in the
elastic-scattering cross section (see \fig{f2}). Second, at forward angles, the breakup is dominated
by its N side, just as in the elastic scattering.
Finally, at larger angles, the total cross section exhibits
oscillations that are explained by interferences between the N and F side, which cross at about $8^\circ$.
\fig{f5} shows the sensitivity of the breakup cross section to the $P$-$T$ potential (left)
and to the binding energy of the neutron $|E_0|$ (right).
The similarity between elastic scattering and breakup is also observed here.
Using the sole Coulomb part of the optical potentials (P-S) shifts the start of the exponential
drop of the breakup cross section to $4^\circ$, as in the elastic-scattering one [see \fig{f3}~(left)],
and using the purely point-point Coulomb interaction (P-P) leads to no rainbow-like behaviour.
Note that the larger breakup cross section obtained in the P-P case (see \tbl{t1})
is explained by this absence of
Coulomb rainbow in the angular distribution for breakup.
The sensitivity of breakup calculations to the neutron separation energy is also
similar to that observed in the elastic channel. In particular for the slope
of the drop after $2^\circ$, which becomes steeper when $|E_0|$ is reduced [see \fig{f3}~(right)].
This confirms that there is no
direct link between the drop observed in the elastic-scattering cross section and a possible loss of flux
towards the breakup channel since both angular distributions vary in the same way when either
the $P$-$T$ interaction or the projectile structure are modified.
\begin{figure}
\center
\includegraphics[width=8cm]{NFfig5pres.eps}\hspace{-2mm}
\includegraphics[width=8cm]{NFfig6pres.eps}
\caption{Sensitivity of the angular distribution for breakup to the $P$-$T$ interaction (left)
and the extension of the halo (right).}\label{f5}
\end{figure}
As shown in \Ref{CJN11}, these similarities
can be semi-quantitatively explained within the
Recoil Excitation and Breakup (REB) model developed by Johnson \etal \cite{JAT97}.
Within this adiabatic model, the angular distributions elegantly factorise into the product
of an elastic-scattering cross section for a pointlike projectile and a form factor that accounts
for the extension of the halo \cite{JAT97,CJN11}. The fact that the former appears in both
factorisations and that it contains most of the angular dependence
explains the similarity between the angular distributions.
That analysis also suggests a new observable to study more precisely the halo
structure. As observed in \fig{f3}~(left) and \fig{f5}~(left), the angular distributions are
very sensitive to the choice of optical potentials.
Since this sensitivity is very similar in both processes,
taking the ratio of two angular distributions removes most of the dependence on the choice
of the $P$-$T$ potentials.
Such a ratio emphasises the nuclear-structure content of the angular distributions \cite{CJN11}.
\section{Conclusion and prospect}\label{conclusion}
In this work, we analyse theoretically elastic-scattering and breakup reactions of halo nuclei
through a N/F decomposition of their angular distributions \cite{CHB10}.
The calculations are performed for $^{11}$Be, the archetypical one-neutron halo nucleus,
impinging on Pb at $69A$MeV, which corresponds to the experimental conditions of \Ref{Fuk04}.
The calculations are performed with the DEA, a reliable and accurate reaction model in which
elastic scatering and breakup are described simultaneously \cite{BCG05,GBC06}.
Our analysis shows that at intermediate energy,
the angular distribution for breakup is very similar to the elastic-scattering cross section:
Both present a Coulomb rainbow at the same scattering angle $\theta$,
they are both N-side dominated at forward angles,
they both exhibit similar sensitivity to the choice of $P$-$T$ interaction
and to the binding energy of the halo neutron.
These results suggest that the projectile is scattered by the target in
a similar way whether it remains bound or it is broken up.
This can be semi-quantitatively understood within the REB model \cite{CJN11,JAT97}.
The present analysis also suggests that
there is no obvious link between the drop observed in the elastic-scattering cross section
and a possible transfer of probability flux towards the breakup channel, as postulated in
\Ref{Dip10}. Since the work of Di Pietro \etal has been performed at lower energy
(around the Coulomb barrier), our conclusions cannot be directly transposed to their study.
A similar analysis within the CDCC framework \cite{DBD10} is planned to see how
elastic scattering and breakup are related to each other at low energy.
Moreover, recent progresses having been made in the modelling of reactions involving
two-neutron halo nuclei \cite{BCD09,PDB12},
an extension of this work for Borromean systems is also planned.
\section*{Acknowledgement}
M.~H. is supported by the Brazilian agencies CNPq and FAPESP.
This text presents research results of the Belgian Research Initiative
on eXotic nuclei (BriX), programme P6/23 on interuniversity
attraction poles of the Belgian Federal Science Policy Office.
\section*{References}
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"redpajama_set_name": "RedPajamaArXiv"
} | 952 |
{"url":"https:\/\/lavelle.chem.ucla.edu\/forum\/viewtopic.php?f=151&t=62203","text":"## Activated Complex vs Transition State\n\nArrhenius Equation: $\\ln k = - \\frac{E_{a}}{RT} + \\ln A$\n\nJasmine 2C\nPosts: 184\nJoined: Wed Sep 18, 2019 12:18 am\n\n### Activated Complex vs Transition State\n\nWhat's the difference between activated complex and transition state in the transition-state theory?\n\nJared_Yuge\nPosts: 100\nJoined: Sat Aug 17, 2019 12:17 am\n\n### Re: Activated Complex vs Transition State\n\nActivated complex refers to a range of configurations near the transition state that the atoms pass through in the transformation from products, while the transition state refers to only the highest potential energy configuration of the atoms during the reaction.\n\n805307623\nPosts: 99\nJoined: Fri Aug 09, 2019 12:17 am\n\n### Re: Activated Complex vs Transition State\n\nActivated Complex- collection of intermediate molecules that are created as a chemical reaction progresses\nTransition state- intermediate of a chemical reaction that makes up the highest potential energy\n\nMatt F\nPosts: 100\nJoined: Sat Aug 17, 2019 12:17 am\n\n### Re: Activated Complex vs Transition State\n\nWould it be correct to say that the activated complex is part of the transition state (or vise versa)? Or are they completely separate from each other\n\nPosts: 102\nJoined: Tue Oct 02, 2018 12:16 am\n\n### Re: Activated Complex vs Transition State\n\nAn activated complex can be a varying number of configurations between two molecules. In the activated complex, the complex can either form products or disassociate to form the original reactants. The transition state is the one of highest potential energy and when this energy level is reached, the complex will form products.\n\n805097738\nPosts: 180\nJoined: Wed Sep 18, 2019 12:20 am\n\n### Re: Activated Complex vs Transition State\n\n805307623 wrote:Activated Complex- collection of intermediate molecules that are created as a chemical reaction progresses\nTransition state- intermediate of a chemical reaction that makes up the highest potential energy\n\nWhen do we use these concepts in the material that we have learned and will be tested on?","date":"2020-11-23 22:51:47","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 1, \"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\": 0.24284136295318604, \"perplexity\": 3242.5456722764843}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-50\/segments\/1606141168074.3\/warc\/CC-MAIN-20201123211528-20201124001528-00135.warc.gz\"}"} | null | null |
I hope you guys aren't sick of these Sheet Music pages yet! I've had this one for years and totally forgot about it! I happened to be browsing on Pinterest last night and saw another page from this book, that I posted a couple of years ago, and it jogged my memory! Anyway, this one is Titled "The Happy Pilgrim" which I thought would be great for your Thanksgiving Projects!
What a great music sheet.
The sheet music is awesome, thanks so much for sharing!
Thanks! I don't think I will ever be tired of the sheet music! I love it.
You Have the greatest stuff and I always get inspired by your blog!! Thank you for all your beautiful images!! | {
"redpajama_set_name": "RedPajamaC4"
} | 1,330 |
Byron Scott admits he could have been better at communicating with Lakers' young players
Understatement of the year candidate.
By Harrison Faigen@hmfaigen Apr 6, 2016, 6:39pm PDT
Share All sharing options for: Byron Scott admits he could have been better at communicating with Lakers' young players
Richard Mackson-USA TODAY Sports
Less than 24 hours after calling the play of his younger players "soft and passive," Los Angeles Lakers head coach Byron Scott admitted the way he's communicated with the team's young players has been an issue.
"With our young guys, could I have probably done a better job [communicating]? Probably so," Scott told Bill Oram of the O.C. Register before the Lakers hosted the Los Angeles Clippers on Thursday night. Scott has repeatedly called out his younger players for their lack of effort, or most often for "not being ready to play," following the Lakers' many losses so far this season.
The approach hasn't worked, with the team losing 61 games to guarantee at least a tie for the worst record in franchise history, a tie they can only achieve if they win their final five games.
The futility has seemingly given Scott some perspective, and the head coach was self-critical of his coaching on Wednesday:
Byron on job he's done this seasons self-assessing: "I'm very critical of myself. I think I could have done better. I can do better."
— Shahan Ahmed (@shahanLA) April 7, 2016
Scott also blamed the times we live in for the ineffectiveness of his communication with the Lakers' young core:
In 1980s, Scott said, "it was more coach said, 'Do this,' you'd do it." Now? "You tell them, 'Do this,' they say, 'Why?'"
— Bill Oram (@billoram) April 7, 2016
Whether or not he can change his communication style remains to be seen, but with Scott reportedly coaching for his job, it will likely be one of many factors the front office looks at heading into the offseason when deciding whether or not to retain him for next year.
You can follow this author on Twitter at @hmfaigen. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,947 |
git clone git://github.com/lt/php-curve25519-ext.git
cd php-curve25519-ext
phpize
./configure
make
sudo make install
cd ..
rm -rf php-curve25519-ext
echo "extension = curve25519.so" >> ~/.phpenv/versions/$(phpenv version-name)/etc/php.ini
git clone git://github.com/encedo/php-ed25519-ext.git
cd php-ed25519-ext
phpize
./configure
make
sudo make install
cd ..
rm -rf php-ed25519-ext
echo "extension = ed25519.so" >> ~/.phpenv/versions/$(phpenv version-name)/etc/php.ini
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,508 |
\section*{Introduction}
\input{introduction.tex}
\section{Preliminaries and main result}\label{sec_preliminaries}
\input{preliminaries.tex}
\section{Tools for both maximal operators}\label{sec_both}
\input{general.tex}
\section{The dyadic maximal function}\label{sec_dyadic}
\input{characteristicf_levelsets.tex}
\section{The uncentered maximal function}\label{sec_uncentered}
\input{uncentered.tex}
\section{The optimal rate in \texorpdfstring{\(\lambda\)}{lambda}}\label{sec_optimal}
\input{optimal.tex}
\nocite{*}
\bibliographystyle{plain}
\subsection{The global case \texorpdfstring{\(\Omega=\mathbb{R}^d\)}{Omega=Rd}}
In this subsection we present a proof of \Cref{pro_levelsets_finite_l}.
It already contains some of the ideas for the general local case \Cref{pro_levelsets_finite_l_local}.
\input{small_average.tex}
\subsection{The general local case \texorpdfstring{\(\Omega\subset\mathbb{R}^d\)}{Omega is a subset of Rd}}
In this subsection we present a proof of \Cref{pro_levelsets_finite_l_local}.
It requires a few more steps than the proof of \Cref{pro_levelsets_finite_l}.
\input{small_average_local.tex}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,383 |
Q: How to delete all the recordings from the Voice Memos app on iOS? I need to delete all the tracks from Voice Memos app in iOS, in order to free up storage on my device. Deleting tracks one at a time is not an option since I have hundreds of them.
I am using an iPod touch 4G.
A: Open the app and you'll find a little symbol with 3 horizontal stripes in the right bottom corner.
You'll get a list and you can tap the memo and click "delete" right afterwards.
Or in iTunes you can select all voice memo's after you've synced them to your PC and delete them from there.
A: I just found another easy way to keep them on your computer and get them off your iPhone!
Just go to the playlist with all your voice memos in iTunes, Select All, press Cmd + i or right click and select information from contextual menu, go to options and change media type to music from voice memos. It will also be transferred within your finder structure to a new artist folder that's called "alan smithees iPhone 5" or whatever and will not be included in your synched voicemail anymore.
A: With iOS 14.4 (the one I have today):
Tap the Edit button on top right corner and scroll through all the recording's selection circles, then after having all recordings selected tap Delete on right corner right corner.
It's not as fast as a 'delete all' option but it think it scales well enough with hundreds of recordings as you keep your finger on the bottom left corner for continuous scrolling.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 513 |
Kaizen Costing System is one of the cost management systems in "lean accounting" concept. Kaizen Costing System was developed in the 1970's and has been practiced since then by leading Japanese firms. There are two fundamental aims in Kaizen Costing System which applies into the manufacturing process of a product. The first aim is to obtain a cost reduction by applying Kaizen Philosophy on the manufacturing process. The second aim of this costing system is to prevent the waste by eliminating nonvalue added activities from the manufacturing process. Based on the related literature and applications, the major aim of this study is to provide a comprehensive discussion of Kaizen Costing System. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,472 |
package com.yahoo.athenz.common.server.util;
import static org.testng.Assert.assertEquals;
import org.testng.annotations.Test;
public class ConfigPropertiesTest {
@Test
public void testGetPortNumberDefault() {
assertEquals(ConfigProperties.getPortNumber("NotExistantProperty", 4080), 4080);
}
@Test
public void testGetPortNumberValid() {
System.setProperty("athenz.port", "4085");
assertEquals(ConfigProperties.getPortNumber("athenz.port", 4080), 4085);
}
@Test
public void testGetPortNumberInvalidFormat() {
System.setProperty("athenz.port", "abc");
assertEquals(ConfigProperties.getPortNumber("athenz.port", 4080), 4080);
}
@Test
public void testGetPortNumberOutOfRangeNegative() {
System.setProperty("athenz.port", "-1");
assertEquals(ConfigProperties.getPortNumber("athenz.port", 4080), 4080);
}
@Test
public void testGetPortNumberOutOfRangePositive() {
System.setProperty("athenz.port", "65536");
assertEquals(ConfigProperties.getPortNumber("athenz.port", 4080), 4080);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,006 |
San Francisco has one of the most "open data" policies of any large city. In this lab, we are going to download about 400M of data (1,968,080 records) describing all police incidents since 2003 (I'm grabbing data on October 6, 2016).
## Getting started
Download all [San Francisco police department incident since 1 January 2003](https://data.sfgov.org/Public-Safety/SFPD-Incidents-from-1-January-2003/tmnf-yvry). Save in "CSV for Excel" format.
We can easily figure out how many records there are:
```bash
$ wc -l ~/data/SFPD_Incidents_from_1_January_2003.csv
1968081 /Users/parrt/data/SFPD_Incidents_from_1_January_2003.csv
```
So 1,968,080 not including the header row. Let's kill that first row using `tail`:
```bash
$ tail +2 SFPD_Incidents_from_1_January_2003.csv > SFPD.csv
```
In Python, that would be equivalent to `data[1:]` (it counts from 0 not 1 like `tail`). You can name that data file whatever you want but I will call it `SFPD.csv` for these exercises.
## Sniffing the data
To get an idea of what the data looks like, let's do a simple histogram of the categories and crime descriptions. Here is the category histogram:
```bash
$ python histo.py ~/data/SFPD.csv
406342 LARCENY/THEFT
279619 OTHER OFFENSES
210564 NON-CRIMINAL
172414 ASSAULT
117467 VEHICLE THEFT
113708 DRUG/NARCOTIC
100802 VANDALISM
93082 WARRANTS
81932 BURGLARY
70707 SUSPICIOUS OCC
57810 MISSING PERSON
50477 ROBBERY
37409 FRAUD
22549 SECONDARY CODES
22157 FORGERY/COUNTERFEITING
19415 WEAPON LAWS
16750 TRESPASS
15932 PROSTITUTION
10586 STOLEN PROPERTY
10065 SEX OFFENSES, FORCIBLE
9331 DISORDERLY CONDUCT
9281 DRUNKENNESS
7779 RECOVERED VEHICLE
5147 DRIVING UNDER THE INFLUENCE
4989 KIDNAPPING
4062 RUNAWAY
3956 LIQUOR LAWS
3430 ARSON
2688 EMBEZZLEMENT
2377 LOITERING
1164 SUICIDE
1114 FAMILY OFFENSES
880 BAD CHECKS
707 BRIBERY
643 EXTORTION
365 SEX OFFENSES, NON FORCIBLE
319 GAMBLING
49 PORNOGRAPHY/OBSCENE MAT
12 TREA
```
and here is the start of the crime description histogram:
```bash
143903 GRAND THEFT FROM LOCKED AUTO
70123 LOST PROPERTY
60593 BATTERY
59892 STOLEN AUTOMOBILE
59412 DRIVERS LICENSE, SUSPENDED OR REVOKED
52218 WARRANT ARREST
49375 AIDED CASE, MENTAL DISTURBED
47935 SUSPICIOUS OCCURRENCE
45227 PETTY THEFT FROM LOCKED AUTO
39820 MALICIOUS MISCHIEF, VANDALISM OF VEHICLES
38117 PETTY THEFT OF PROPERTY
36992 MALICIOUS MISCHIEF, VANDALISM
35278 TRAFFIC VIOLATION
31879 THREATS AGAINST LIFE
28655 FOUND PROPERTY
25815 ENROUTE TO OUTSIDE JURISDICTION
25254 GRAND THEFT OF PROPERTY
22830 PETTY THEFT FROM A BUILDING
21511 PETTY THEFT SHOPLIFTING
21340 POSSESSION OF NARCOTICS PARAPHERNALIA
21336 FOUND PERSON
20757 GRAND THEFT FROM A BUILDING
20068 CREDIT CARD, THEFT BY USE OF
...
```
**Exercise**: Create a helper function in `csvcols.py` that opens a CSV file in Excel format given a `filename` and returns the indicated column number:
```python
import csv
from collections import Counter
def get_column(filename,col):
"""
Load CSV in Excel format, return Counter created from column of data indicated by
integer col parameter.
"""
data = []
with open(filename, 'rb') as f:
reader = csv.reader(f, dialect='excel')
...
data = Counter(data)
return data
```
Then in `histo.py`, we can use it to get a particular column:
```python
categories = get_column(sys.argv[1],col=1)
```
Print out the histograms as shown above for categories and descriptions to finish off the exercise.
## Word clouds
A more interesting way to visualize differences in term frequency is using a so-called word cloud. For example, here is a word cloud showing the categories from 2003 to the present.
<img src=figures/SFPD-wordcloud.png width=400>
Python has a nice library you can use:
```bash
$ pip install wordcloud
```
**Exercise**: In a file called `catcloud.py`, once again get the categories and then create a word cloud object and display it:
```python
from wordcloud import WordCloud
from csvcols import get_column
import matplotlib.pyplot as plt
import sys
...
wordcloud = WordCloud(width=1800,
height=1400,
max_words=10000,
random_state=1,
relative_scaling=0.25)
... get tuples with (word,count) from categories Counter ...
wordcloud.fit_words(wordtuples)
plt.imshow(wordcloud)
plt.axis("off")
plt.show()
```
### Which neighborhood is the "worst"?
**Exercise**: Now, pullout the police district and do a word cloud on that in `hoodcloud.py` (it's ok to cut/paste):
<img src=figures/SFPD-hood-wordcloud.png width=400>
### Crimes per neighborhood
**Exercise**: Filter the CSV file using `grep` from the commandline to get just the rows from a particular precinct, such as MISSION:
```bash
$ grep MISSION ~/data/SFPD.csv > /tmp/mission.csv
$ grep RICHMOND ~/data/SFPD.csv > /tmp/richmond.csv
```
Run the `wordcloud.py` script on those files to get an idea of the types of crimes per those two neighborhoods. Here is the mission and richmond districts crime category clouds.
<img src=figures/SFPD-mission-wordcloud.png width=300> <img src=figures/SFPD-richmond-wordcloud.png width=300>
### Which neighborhood has most car break-ins?
**Exercise**: Filter the SFPD.csv for `GRAND THEFT FROM LOCKED AUTO` and then run `hoodcloud.py` on the resulting csv.
<img src=figures/SFPD-car-breakin-hood-wordcloud.png width=300>
Hmm..ok, so parking in the Mission is ok, but Northern, Central, and Southern precincts are bad news.
If you get stuck in any of these exercises, you can look at the [code associated with this notes](https://github.com/parrt/msds692/tree/master/notes/code/sfpd).
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,751 |
import React, { ComponentProps } from 'react';
import { Room } from 'matrix-js-sdk/src/models/room';
import { MatrixEvent } from 'matrix-js-sdk/src/models/event';
import { RoomStateEvent } from "matrix-js-sdk/src/models/room-state";
import classNames from "classnames";
import { EventType, RoomType } from "matrix-js-sdk/src/@types/event";
import BaseAvatar from './BaseAvatar';
import ImageView from '../elements/ImageView';
import { MatrixClientPeg } from '../../../MatrixClientPeg';
import Modal from '../../../Modal';
import * as Avatar from '../../../Avatar';
import DMRoomMap from "../../../utils/DMRoomMap";
import { mediaFromMxc } from "../../../customisations/Media";
import { IOOBData } from '../../../stores/ThreepidInviteStore';
interface IProps extends Omit<ComponentProps<typeof BaseAvatar>, "name" | "idName" | "url" | "onClick"> {
// Room may be left unset here, but if it is,
// oobData.avatarUrl should be set (else there
// would be nowhere to get the avatar from)
room?: Room;
oobData?: IOOBData & {
roomId?: string;
};
viewAvatarOnClick?: boolean;
onClick?(): void;
}
interface IState {
urls: string[];
}
export default class RoomAvatar extends React.Component<IProps, IState> {
public static defaultProps = {
width: 36,
height: 36,
resizeMethod: 'crop',
oobData: {},
};
constructor(props: IProps) {
super(props);
this.state = {
urls: RoomAvatar.getImageUrls(this.props),
};
}
public componentDidMount() {
MatrixClientPeg.get().on(RoomStateEvent.Events, this.onRoomStateEvents);
}
public componentWillUnmount() {
MatrixClientPeg.get()?.removeListener(RoomStateEvent.Events, this.onRoomStateEvents);
}
public static getDerivedStateFromProps(nextProps: IProps): IState {
return {
urls: RoomAvatar.getImageUrls(nextProps),
};
}
private onRoomStateEvents = (ev: MatrixEvent) => {
if (ev.getRoomId() !== this.props.room?.roomId || ev.getType() !== EventType.RoomAvatar) return;
this.setState({
urls: RoomAvatar.getImageUrls(this.props),
});
};
private static getImageUrls(props: IProps): string[] {
let oobAvatar = null;
if (props.oobData.avatarUrl) {
oobAvatar = mediaFromMxc(props.oobData.avatarUrl).getThumbnailOfSourceHttp(
props.width,
props.height,
props.resizeMethod,
);
}
return [
oobAvatar, // highest priority
RoomAvatar.getRoomAvatarUrl(props),
].filter(function(url) {
return (url !== null && url !== "");
});
}
private static getRoomAvatarUrl(props: IProps): string {
if (!props.room) return null;
return Avatar.avatarUrlForRoom(props.room, props.width, props.height, props.resizeMethod);
}
private onRoomAvatarClick = () => {
const avatarUrl = Avatar.avatarUrlForRoom(
this.props.room,
null,
null,
null,
);
const params = {
src: avatarUrl,
name: this.props.room.name,
};
Modal.createDialog(ImageView, params, "mx_Dialog_lightbox", null, true);
};
public render() {
const { room, oobData, viewAvatarOnClick, onClick, className, ...otherProps } = this.props;
const roomName = room?.name ?? oobData.name;
// If the room is a DM, we use the other user's ID for the color hash
// in order to match the room avatar with their avatar
const idName = room ? (DMRoomMap.shared().getUserIdForRoomId(room.roomId) ?? room.roomId) : oobData.roomId;
return (
<BaseAvatar
{...otherProps}
className={classNames(className, {
mx_RoomAvatar_isSpaceRoom: (room?.getType() ?? this.props.oobData?.roomType) === RoomType.Space,
})}
name={roomName}
idName={idName}
urls={this.state.urls}
onClick={viewAvatarOnClick && this.state.urls[0] ? this.onRoomAvatarClick : onClick}
/>
);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,168 |
Dieser Artikel gibt einen Überblick über die 2.-American-Football-Bundesliga-Saison 1997. Die 2. American-Football-Bundesliga 1997 war die 16. Saison der 2. Bundesliga, der zweithöchsten deutschen Spielklasse, in der Sportart American Football.
Modus
In der Saison 1997 nahmen an der 2. Bundesliga insgesamt 14 Teams teil, die gleichmäßig in die Gruppen Nord und Süd aufgeteilt waren. Die Gruppen spielten jeweils ein doppeltes Rundenturnier mit Heim- und Auswärtsspielen aus. Dadurch hatten alle Mannschaften je sechs Heim- und Auswärtsspiele.
Nach Abschluss dieser Runde wurden für beide Gruppen Abschlusstabellen erstellt. Die jeweils Erstplatzierten qualifizierten sich für die Aufstiegsrelegation, bei Platz 8 handelte es sich um einen direkten Abstiegsplatz zur Regionalliga.
Ligaaufteilung
Die Bremen Bravehearts hießen bis zu dieser Saison "Bremen Buccaneers", die Saarland Hurricanes "Dillingen Steelhawks".
Vorjahr = Liga des Vorjahres
RL = Regionalliga
(N) Aufsteiger aus der Regionalliga
Statistik
2. Bundesliga Nord
,
2. Bundesliga Süd
,
Aufstiegsrelegation
Nord
Die Paderborn Dolphins gewinnen die Relegation gegen die Berlin Adler aus der 1. Bundesliga Nord mit insgesamt 61:49 und steigen damit in die 1. Bundesliga Nord auf. Die Berlin Adler steigen in die 2. Bundesliga Nord ab.
Süd
Die Saarland Hurricanes verlieren die Relegation gegen die Stuttgart Scorpions aus der 1. Bundesliga Süd mit insgesamt 13:53 und verbleiben damit in der 2. Bundesliga Süd. Die Stuttgart Scorpions bleiben in der 1. Bundesliga Süd.
Weblinks
2. Bundesliga 1997 bei football-history.de
1997
Bundesliga 2 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,140 |
package org.seasar.doma.internal.jdbc.sql;
import java.util.List;
import java.util.function.Supplier;
import org.seasar.doma.internal.jdbc.scalar.BasicScalar;
import org.seasar.doma.wrapper.Wrapper;
/**
* @author taedium
*
*/
public class BasicListParameter<BASIC> extends
ScalarListParameter<BASIC, BASIC> {
public BasicListParameter(Supplier<Wrapper<BASIC>> supplier,
List<BASIC> list, String name) {
super(() -> new BasicScalar<>(supplier, false), list, name);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 291 |
{"url":"http:\/\/en.wikipedia.org\/wiki\/Ornstein%E2%80%93Uhlenbeck_process","text":"# Ornstein\u2013Uhlenbeck process\n\nNot to be confused with Ornstein\u2013Uhlenbeck operator.\n\nIn mathematics, the Ornstein\u2013Uhlenbeck process (named after Leonard Ornstein and George Eugene Uhlenbeck), is a stochastic process that, roughly speaking, describes the velocity of a massive Brownian particle under the influence of friction. The process is stationary, Gaussian, and Markovian, and is the only nontrivial process that satisfies these three conditions, up to allowing linear transformations of the space and time variables.[1] Over time, the process tends to drift towards its long-term mean: such a process is called mean-reverting.\n\nThe process can be considered to be a modification of the random walk in continuous time, or Wiener process, in which the properties of the process have been changed so that there is a tendency of the walk to move back towards a central location, with a greater attraction when the process is further away from the centre. The Ornstein\u2013Uhlenbeck process can also be considered as the continuous-time analogue of the discrete-time AR(1) process.\n\n## Representation via a stochastic differential equation\n\nAn Ornstein\u2013Uhlenbeck process, xt, satisfies the following stochastic differential equation:\n\n$dx_t = \\theta (\\mu-x_t)\\,dt + \\sigma\\, dW_t$\n\nwhere $\\theta > 0$, $\\mu$ and $\\sigma > 0$ are parameters and $W_t$ denotes the Wiener process.\n\nThe above representation can be taken as the primary definition of an Ornstein\u2013Uhlenbeck process.[1][citation needed].\n\n## Fokker\u2013Planck equation representation\n\nThe probability density function \u0192(xt) of the Ornstein\u2013Uhlenbeck process satisfies the Fokker\u2013Planck equation\n\n$\\frac{\\partial f}{\\partial t} = \\theta \\frac{\\partial}{\\partial x} [(x - \\mu) f] + \\frac{\\sigma^2}{2} \\frac{\\partial^2 f}{\\partial x^2}$\n\nThe Green function of this linear parabolic partial differential equation, taking $\\mu = 0$ and $D = \\sigma^2\/2$ for simplicity, and the initial condition consisting of a unit point mass at location $y$ is\n\n$f(x,t) = \\sqrt{\\frac{\\theta}{2 \\pi D (1-e^{-2\\theta t})}} \\exp\\left\\{\\frac{-\\theta}{2D}\\left[\\frac{(x - y e^{-\\theta t})^2}{1-e^{-2\\theta t}}\\right]\\right\\}$\n\nThe stationary solution of this equation is the limit for time tending to infinity which is a Gaussian distribution with mean $\\mu$ and variance $\\sigma^2\/(2\\theta)$\n\n$f_s(x) = \\sqrt{\\frac{\\theta}{\\pi \\sigma^2}}\\, e^{-\\theta (x-\\mu)^2\/\\sigma^2}.$\n\n## Application in physical sciences\n\nThe Ornstein\u2013Uhlenbeck process is a prototype of a noisy relaxation process. Consider for example a Hookean spring with spring constant $k$ whose dynamics is highly overdamped with friction coefficient $\\gamma$. In the presence of thermal fluctuations with temperature $T$, the length $x(t)$ of the spring will fluctuate stochastically around the spring rest length $x_0$; its stochastic dynamic is described by an Ornstein\u2013Uhlenbeck process with:\n\n\\begin{align} \\theta &=k\/\\gamma, \\\\ \\mu & =x_0, \\\\ \\sigma &=\\sqrt{2k_B T\/\\gamma}, \\end{align}\n\nwhere $\\sigma$ is derived from the Stokes\u2013Einstein equation $D=\\sigma^2\/2=k_B T\/\\gamma$ for the effective diffusion constant.\n\nIn physical sciences, the stochastic differential equation of an Ornstein\u2013Uhlenbeck process is rewritten as a Langevin equation\n\n$\\gamma\\dot{x}(t) = - k( x(t) - x_0 ) + \\xi(t)$\n\nwhere $\\xi(t)$ is white Gaussian noise with $\\langle\\xi(t_1)\\xi(t_2)\\rangle = 2 k_B T\\,\\gamma\\, \\delta(t_1-t_2).$\n\nAt equilibrium, the spring stores an average energy $\\langle E\\rangle = k \\langle (x-x_0)^2 \\rangle \/2=k_B T\/2$ in accordance with the equipartition theorem.\n\n## Application in financial mathematics\n\nThe Ornstein\u2013Uhlenbeck process is one of several approaches used to model (with modifications) interest rates, currency exchange rates, and commodity prices stochastically. The parameter $\\mu$ represents the equilibrium or mean value supported by fundamentals; $\\sigma$ the degree of volatility around it caused by shocks, and $\\theta$ the rate by which these shocks dissipate and the variable reverts towards the mean. One application of the process is a trading strategy known as pairs trade.[2][3][4]\n\n## Mathematical properties\n\nThe Ornstein\u2013Uhlenbeck process is an example of a Gaussian process that has a bounded variance and admits a stationary probability distribution, in contrast to the Wiener process; the difference between the two is in their \"drift\" term. For the Wiener process the drift term is constant, whereas for the Ornstein\u2013Uhlenbeck process it is dependent on the current value of the process: if the current value of the process is less than the (long-term) mean, the drift will be positive; if the current value of the process is greater than the (long-term) mean, the drift will be negative. In other words, the mean acts as an equilibrium level for the process. This gives the process its informative name, \"mean-reverting.\" The stationary (long-term) variance is given by\n\n$\\operatorname{var}(x_t)={\\sigma ^2 \\over 2\\theta}. \\,$\n\nThe Ornstein\u2013Uhlenbeck process is the continuous-time analogue of the discrete-time AR(1) process.\n\nthree sample paths of different OU-processes with \u03b8\u00a0=\u00a01, \u03bc\u00a0=\u00a01.2, \u03c3\u00a0=\u00a00.3:\nblue: initial value a\u00a0=\u00a00 (a.s.)\ngreen: initial value a\u00a0=\u00a02 (a.s.)\nred: initial value normally distributed so that the process has invariant measure\n\n## Solution\n\nThis stochastic differential equation is solved by variation of parameters.[citation needed] Apply It\u014d's lemma to the function\n\n$f(x_t, t) = x_t e^{\\theta t} \\,$\n\nto get\n\n\\begin{align} df(x_t,t) & = \\theta x_t e^{\\theta t}\\, dt + e^{\\theta t}\\, dx_t \\\\[6pt] & = e^{\\theta t}\\theta \\mu \\, dt + \\sigma e^{\\theta t}\\, dW_t. \\end{align}\n\nIntegrating from 0 to t we get\n\n$x_t e^{\\theta t} = x_0 + \\int_0^t e^{\\theta s}\\theta \\mu \\, ds + \\int_0^t \\sigma e^{\\theta s}\\, dW_s \\,$\n\nwhereupon we see\n\n$x_t = x_0 e^{-\\theta t} + \\mu(1-e^{-\\theta t}) + \\int_0^t \\sigma e^{\\theta (s-t)}\\, dW_s. \\,$\n\n### Formulas for moments of nonstationary processes\n\nFrom this representation, the first moment is given by (assuming that x0 is a constant)\n\n$E(x_t)=x_0 e^{-\\theta t}+\\mu(1-e^{-\\theta t}) \\!\\$\n\nThe It\u014d isometry can be used to calculate the covariance function by\n\n\\begin{align} \\operatorname{cov}(x_s,x_t) & = E[(x_s - E[x_s])(x_t - E[x_t])] \\\\ & = E \\left[ \\int_0^s \\sigma e^{\\theta (u-s)}\\, dW_u \\int_0^t \\sigma e^{\\theta (v-t)}\\, dW_v \\right] \\\\ & = \\sigma^2 e^{-\\theta (s+t)}E \\left[ \\int_0^s e^{\\theta u}\\, dW_u \\int_0^t e^{\\theta v}\\, dW_v \\right] \\\\ & = \\frac{\\sigma^2}{2\\theta} \\, e^{-\\theta (s+t)}(e^{2\\theta \\min(s,t)}-1). \\end{align}\n\nThus if s\u00a0<\u00a0t (so that min(st)\u00a0=\u00a0s), then we have\n\n$\\operatorname{cov}(x_s,x_t) = \\frac{\\sigma^2}{2\\theta}\\left( e^{-\\theta(t-s)} - e^{-\\theta(t+s)} \\right).$\n\n## Alternative representation for nonstationary processes\n\nIt is also possible (and often convenient) to represent xt (unconditionally, i.e. as $t\\rightarrow\\infty$) as a scaled time-transformed Wiener process[citation needed]:\n\n$x_t=\\mu+{\\sigma\\over\\sqrt{2\\theta}}e^{-\\theta t}W_{e^{2\\theta t}}$\n\nor conditionally (given x0) as\n\n$x_t=x_0 e^{-\\theta t} +\\mu (1-e^{-\\theta t})+ {\\sigma\\over\\sqrt{2\\theta}}e^{-\\theta t}W_{e^{2\\theta t}-1}.$\n\nThe time integral of this process can be used to generate noise with a 1\/\u0192 power spectrum.\n\n## Scaling limit interpretation\n\nThe Ornstein\u2013Uhlenbeck process can be interpreted as a scaling limit of a discrete process, in the same way that Brownian motion is a scaling limit of random walks. Consider an urn containing $n$ blue and yellow balls. At each step a ball is chosen at random and replaced by a ball of the opposite colour (equivalently, a ball chosen uniformly at random changes color). Let $X_n$ be the number of blue balls in the urn after $n$ steps. Then $\\frac{X_{[nt]} - n\/2}{\\sqrt{n}}$ converges in law to an Ornstein\u2013Uhlenbeck process as $n$ tends to infinity.\n\n## Generalizations\n\nIt is possible to extend Ornstein\u2013Uhlenbeck processes to processes where the background driving process is a L\u00e9vy process.[clarification needed] These processes are widely studied by Ole Barndorff-Nielsen and Neil Shephard,[citation needed] and others.[citation needed]\n\nIn addition, in finance, stochastic processes are used the volatility increases for larger values of $X$. In particular, the CKLS (Chan\u2013Karolyi\u2013Longstaff\u2013Sanders) process[5] with the volatility term replaced by $\\sigma\\,x^\\gamma\\, dW_t$ can be solved in closed form for $\\gamma=1\/2$ or 1, as well as for $\\gamma=0$, which corresponds to the conventional OU process.","date":"2014-09-17 04:31:04","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\": 48, \"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\": 0.984450101852417, \"perplexity\": 550.3109605117535}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-41\/segments\/1410657120974.20\/warc\/CC-MAIN-20140914011200-00174-ip-10-196-40-205.us-west-1.compute.internal.warc.gz\"}"} | null | null |
Cortisol Levels Predict Remission in Cushing's Patients Undergoing Transsphenoidal Surgery
Posted on September 25, 2019 by MaryO
In patients with Cushing's disease, removing the pituitary tumor via an endoscopic transsphenoidal surgery (TSS) leads to better remission rates than microscopic TSS, according to new research.
But regardless of surgical approach, plasma cortisol levels one day after surgery are predictive of remission, researchers found.
The study, "Management of Cushing's disease: Changing trend from microscopic to endoscopic surgery," was published in the journal World Neurosurgery.
Because it improves visualization and accessibility, endoscopic TSS has been gaining popularity over microscopic TSS to remove pituitary tumors in Cushing's disease patients. Yet, although this surgery has been associated with high remission rates, whether it outperforms microscopic surgery and determining the factors affecting long-term outcomes may further ease disease recurrence after TSS.
A team with the All India Institute of Medical Sciences addressed this topic in 104 patients who underwent surgery from January 2009 to June 2017. Among these patients, 47 underwent microscopic surgery and 55 endoscopic surgery. At presentation, their ages ranged from 9 to 55 (mean age of 28). Also, patients had been experiencing Cushing's symptoms over a mean duration of 24 months.
Eighty-seven patients showed weight gain. Hypertension (high blood pressure) and diabetes mellitus were among the most common co-morbidities, found in 76 and 33 patients, respectively. Nineteen patients had osteoporosis and 12 osteopenia, which refers to lower-than-normal bone mineral density.
As assessed with magnetic resonance imaging, 68 patients had a microadenoma (a tumor diameter smaller than one centimeter) and 27 had a macroadenoma (a tumor one centimeter or larger). Only two patients had an invasive pituitary adenoma.
Two patients with larger tumors were operated on transcranially (through the skull). The surgery resulted in total tumor removal in 90 cases (86.5%). A blood loss greater than 100 milliliter was more common with endoscopic than with microscopic TSS.
Ten patients developed transient diabetes inspidus, two experienced seizures after surgery, and six of nine patients with macroadenoma and visual deterioration experienced vision improvements after TSS.
The incidence of intraoperative leak of cerebrospinal fluid — the liquid surrounding the brain and spinal cord — was 23.2%, while that of post-operative leak was 7.7% and was more common in microadenoma than macroadenoma surgery (9.8% vs. 5.0%).
Seventeen patients were lost to follow-up and two died due to metabolic complications and infections. The average follow-up was shorter for endoscopic than with microscopic surgery (18 months vs. 35 months).
Among the remaining 85 cases, 65 (76.5%) experienced remission, as defined by a morning cortisol level under 5.0 μg/dL, restored circadian rhythm (the body's internal clock, typically impaired in Cushing's patients), and suppression of serum cortisol to below 2 μg/dl after overnight dexamethasone suppression test.
The remission rate was 54.5% in pediatric patients and was higher with endoscopic than with microscopic TSS (88.2% vs. 56.6%). Also, patients with microadenoma showed a trend toward more frequent remission than those with macroadenoma (73.2% vs. 64.3%).
Ten of the remaining 20 patients experienced disease recurrence up to 28 months after surgery. Sixteen cases revealed signs of hypopituitarism, or pituitary insufficiency, which were managed with replacement therapy.
A subsequent analysis found that morning cortisol level on day one after surgery was the only significant predictor of remission. Specifically, a one-unit increase in cortisol lowered the likelihood of remission by 7%. A cortisol level lower than 10.7 μgm/dl was calculated as predicting remission.
Overall, the study showed that "postoperative plasma cortisol level is a strong independent predictor of remission," the researchers wrote, and that "remission provided by endoscopy is significantly better than microscopic approach."
From https://cushingsdiseasenews.com/2019/09/24/cortisol-levels-predict-remission-cushings-patients-undergoing-transsphenoidal-surgery/
Filed under: Cushing's, pituitary, Treatments | Tagged: cortisol, diabetes insipidus, diabetes mellitus, hypertension, hypopituitary, osteopenia, osteoporosis, plasma cortisol, remission, Transsphenoidal surgery, Weight gain | Leave a comment »
Metoclopramide Can Mask Adrenal Insufficiency After Gland Removal in BMAH Patients
Metoclopramide, a gastrointestinal medicine, can increase cortisol levels after unilateral adrenalectomy — the surgical removal of one adrenal gland — and conceal adrenal insufficiency in bilateral macronodular adrenal hyperplasia (BMAH) patients, a case report suggests.
The study, "Retention of aberrant cortisol secretion in a patient with bilateral macronodular adrenal hyperplasia after unilateral adrenalectomy," was published in Therapeutics and Clinical Risk Management.
BMAH is a subtype of adrenal Cushing's syndrome, characterized by the formation of nodules and enlargement of both adrenal glands.
In this condition, the production of cortisol does not depend on adrenocorticotropic hormone (ACTH) stimulation, as usually is the case. Instead, cortisol production is triggered by a variety of stimuli, such as maintaining an upright posture, eating mixed meals — those that contain fats, proteins, and carbohydrates — or exposure to certain substances.
A possible treatment for this condition is unilateral adrenalectomy. However, after the procedure, some patients cannot produce adequate amounts of cortisol. That makes it important for clinicians to closely monitor the changes in cortisol levels after surgery.
Metoclopramide, a medicine that alleviates gastrointestinal symptoms and is often used during the postoperative period, has been reported to increase the cortisol levels of BMAH patients. However, the effects of metoclopramide on BMAH patients who underwent unilateral adrenalectomy are not clear.
Researchers in Japan described the case of a 61-year-old postmenopausal woman whose levels of cortisol remained high after surgery due to metoclopramide ingestion.
The patient was first examined because she had experienced high blood pressure, abnormal lipid levels in the blood, and osteoporosis for ten years. She also was pre-obese.
She was given medication to control blood pressure with no results. The lab tests showed high serum cortisol and undetectable levels of ACTH, suggesting adrenal Cushing's syndrome.
Patients who have increased cortisol levels, but low levels of ACTH, often have poor communication between the hypothalamus, the pituitary, and the adrenal glands. These three glands — together known as the HPA axis — control the levels of cortisol in healthy people.
Imaging of the adrenal glands revealed they were both enlarged and presented nodules. The patient's cortisol levels peaked after taking metoclopramide, and her serum cortisol varied significantly during the day while ACTH remained undetectable. These results led to the BMAH diagnosis.
The doctors performed unilateral adrenalectomy to control cortisol levels. The surgery was successful, and the doctors reduced the dose of glucocorticoid replacement therapy on day 6.
Eight days after the surgery, however, the patient showed decreased levels of fasting serum cortisol, which indicated adrenal insufficiency — when the adrenal glands are unable to produce enough cortisol.
The doctors noticed that metoclopramide was causing an increase in serum cortisol levels, which made them appear normal and masked the adrenal insufficiency.
They stopped metoclopramide treatment and started replacement therapy (hydrocortisone) to control the adrenal insufficiency. The patient was discharged 10 days after the surgery.
The serum cortisol levels were monitored on days 72 and 109 after surgery, and they remained lower than average. Therefore she could not stop hydrocortisone treatment.
The levels of ACTH remained undetectable, suggesting that the communication between the HPA axis had not been restored.
"Habitual use of metoclopramide might suppress the hypothalamus and pituitary via negative feedback due to cortisol excess, and lead to a delayed recovery of the HPA axis," the researchers said.
Meanwhile, the patient's weight decreased, and high blood pressure was controlled.
"Detailed surveillance of aberrant cortisol secretion responses on a challenge with exogenous stimuli […] is clinically important in BMAH patients," the study concluded. "Caution is thus required for assessing the actual status of the HPA axis."
From https://cushingsdiseasenews.com/2019/05/07/metoclopramide-conceals-adrenal-insufficiency-after-gland-removal-bmah-patients-case-report/
Filed under: adrenal crisis, Treatments | Tagged: ACTH, adrenal insufficiency, bilateral macronodular adrenal hyperplasia, blood pressure, BMAH, cortisol, lipid, Metoclopramide, osteoporosis, unilateral | Leave a comment »
Mild Cases of Cushing's Syndrome Present Diagnostic Challenges
Posted on August 16, 2017 by MaryO
By Tori Rodriguez, MA, LPC
In the early 20th century, the term "pluriglandular syndrome" was coined by Harvey Cushing to describe the disorder that results from chronic tissue exposure to excessive levels of glucocorticoids.1 Now called Cushing's syndrome, the condition affects an estimated 10-15 million people annually, most often women and individuals between the ages of 20 and 50 years.2 Risk factors and common comorbidities include hypertension, obesity, osteoporosis, uncontrolled diabetes, depression, and anxiety.3
The clinical presentation of the disorder is heterogenous and varies by sex, age, and disease severity. Common signs and symptoms include central adiposity, roundness of the face or extra fat around the neck, thin skin, impaired short-term memory and concentration, irritability, hirsutism in women, fatigue, and menstrual irregularity.4 Because each of these features may be observed in a wide range of other conditions, it may be difficult to diagnose cases that are not severe.
"It can be challenging to differentiate the milder forms from pseudo-Cushing's states," which are characterized by altered cortisol production and many of the same clinical features as Cushing's syndrome, according to Roberto Salvatori, MD, the medical director of the Johns Hopkins Pituitary Center, Baltimore, Maryland. These may include alcoholism, obesity, eating disorders, and depression. "Because Cushing's can cause depression, for example, it is sometimes difficult to determine which came first," he says. In these states, however, hypercortisolism is believed to be driven by increased secretion of hypothalamic corticotropin-releasing hormone, which is suppressed in Cushing's syndrome.5
Causes and Diagnosis
If Cushing's syndrome is suspected on the basis of the patient's physical appearance, the diagnostic workup should include a thorough medical history, physical exam, and 1 or more of the following tests to establish hypercortisolism: the 24-hour urinary cortisol test, the low-dose dexamethasone suppression test, or the late-night salivary cortisol test. "We sometimes use 2 or 3 of these tests since 1 may not accurately reflect cortisol production in a particular patient," Dr Salvatori notes. The next step is to determine the source of the hypercortisolism, which may involve the high-dose dexamethasone suppression test, magnetic resonance imaging, or petrosal sinus sampling.2
Medication is the most common cause of Cushing's syndrome. These iatrogenic or exogenous cases typically result from corticosteroids administered for conditions such as asthma, allergies, and autoimmune disorders.6 More rarely, the disorder can be caused by the use of medroxyprogesterone. In these cases, corticosteroids should be reduced or discontinued under medical care, if possible.
Endogenous Cushing's syndrome results from the presence of benign or malignant tumors on the adrenal or pituitary glands or elsewhere in the body. These tumors can interfere with the adrenal glands' production of cortisol that is usually prompted by the adrenocorticotropic hormone (ACTH) released by the pituitary gland.6 There are 3 different mechanisms by which the process can occur.
Pituitary adenomas, which account for approximately 70% of endogenous cases of Cushing's syndrome, secrete ACTH and stimulate additional cortisol production. Because of the large proportion of cases this condition represents, it is specifically referred to as Cushing's disease. It is more common in women than men (with a ratio of 3 to 4:1), although in pediatric patients, it occurs more frequently in boys vs girls.5
Adrenal tumors (adenomas, malignant tumors, or micronodular hyperplasia) produce cortisol in their own tissue in addition to the amount produced by the adrenal glands. These tumors, which cause approximately 15% of endogenous Cushing's syndrome cases, are more common in children vs adults and in women vs men.
Benign or malignant tumors elsewhere in the body, most often the lungs, thyroid, thymus, and pancreas, secrete ACTH and trigger the excessive release of cortisol. An estimated 15% of endogenous cases are attributed to these types of tumors.
Surgery is the first-line treatment for Cushing's syndrome. "We first want to try to figure out the cause of the disorder," Dr Salvatori says. "Ideally, treatment involves surgery to remove the tumor that is causing it."
When surgery is unsuccessful, contraindicated, or delayed, other treatment options include radiation or medications that inhibit cortisol, modulate the release of ACTH, or inhibit steroidogenesis.5 Bilateral adrenalectomy may be indicated for patients who do not respond to medication or other surgery.
If surgical resection of the tumor is successful, then "all of the comorbidities reverse, but if it is unsuccessful or must be delayed, you would treat each comorbidity" with the appropriate medication; for example, antihypertensives for high blood pressure and antidiabetic medications for diabetes, Dr Salvatori advises. In severe cases, prophylactic antibiotics may be indicated for the prevention of severe infections such as pneumonia.
It is also important to inquire about and address psychiatric symptoms related to Cushing's syndrome, even in patients who are in remission. It has been proposed that the chronic hypercortisolism and dysfunction of the HPA axis may "lead to structural and functional changes in the central nervous system, developing brain atrophy, particularly in the hippocampus, which may determine the high prevalence of psychiatric disorders, such as affective and anxiety disorders or cognitive dysfunctions," according to a recently published paper on the topic.7 Patients should be screened with self-report questionnaires such as the Beck Depression Inventory and the Hospital Anxiety and Depression Scale, and management of psychiatric symptoms may include patient education, psychotropic medications, and referral to a mental health professional.
Several trials are currently planned or underway, including a phase 2 randomized, double-blind, placebo-controlled study of an oral medication called ATR-101 by Millendo Therapeutics, Inc. (ClinicalTrials.gov identifier: NCT03053271). In addition to the need for novel medical therapies, refined imaging techniques could improve surgical success rates in patients with Cushing's disease in particular, according to Dr Salvatori. "A significant portion of these patients have tumors too small to be detected by MRI, and the development of more sensitive MRI could improve detection and provide a surgical target" for neurosurgeons treating the patients, he says.
Milder cases of Cushing's syndrome present diagnostic challenges are a result overlapping features with various other conditions. Diagnosis may require careful observation as well as biochemical and imaging tests.
New Research Highlights Possible Genetic Cause of Cushing's Disease
Endocrine Society Releases Guidelines on Treatment of Cushing's Syndrome
Pediatric Endocrine Society Provides Guidance for Growth Hormone Use in Pediatric Patients
Loriaux DL. Diagnosis and differential diagnosis of Cushing's syndrome. N Engl J Med. 2017;376:1451-1459. doi:10.1056/NEJMra1505550
American Association of Neurological Surgeons. Cushing's syndrome/disease. http://www.aans.org/Patients/Neurosurgical-Conditions-and-Treatments/Cushings-Disease. Accessed August 1, 2017.
León-Justel A, Madrazo-Atutxa A, Alvarez-Rios AI, et al. A probabilistic model for cushing's syndrome screening in at-risk populations: a prospective multicenter study. J Clin Endocrinol Metab. 2016;101:3747-3754. doi:10.1210/jc.2016-1673
The Pituitary Society. Cushing's syndrome and disease–symptoms. https://pituitarysociety.org/patient-education/pituitary-disorders/cushings/symptoms-of-cushings-disease-and-cushings-syndrome. Accessed August 1, 2017.
Sharma ST, Nieman LK, Feelders RA. Cushing's syndrome: epidemiology and developments in disease management. Clin Epidemiol. 2015;7:281-293. doi:10.2147/CLEP.S44336
National Institutes of Health: Eunice Kennedy Shriver National Institute of Child Health and Human Development. What causes Cushing's syndrome?https://www.nichd.nih.gov/health/topics/cushing/conditioninfo/pages/causes.aspx. Accessed August 1, 2017.
Santos A, Resmini E, Pascual JC, Crespo I, Webb SM. Psychiatric symptoms in patients with Cushing's syndrome: prevalence, diagnosis and management. Drugs. 2017;77:829-842. doi:10.1007/s40265-017-0735-z
From http://www.endocrinologyadvisor.com/adrenal/cushings-syndrome-diagnosis-treatment/article/682302/
Filed under: adrenal, Cushing, Cushing's, pituitary | Tagged: adrenal, anxiety, cortisol, Cushing's Syndrome, depression, diabetes, Dr. Harvey Cushing, Dr. Roberto Salvatori, endogenous, Harvey Cushing, hypertension, obesity, osteoporosis, pituitary, pluriglandular syndrome, Pseudo-Cushing's | Leave a comment »
Who's at Risk for Cushing's?
by Kristen Monaco
Contributing Writer, MedPage Today
Researchers have developed a new method to assess specific populations for Cushing's syndrome, based on results from a multicenter study.
The prospective cohort study evaluated at-risk patients for Cushing's syndrome to create a novel type of scoring system in order to better predict the development of disease, stated lead author Antonio León-Justel, PhD,of the Seville Institute of Biomedicine in Spain, and colleagues.
Cushing's syndrome is identified by an excess of cortisol and/or glucocorticoids in the blood, which can result in myriad negative health outcomes, including an increased risk of death and morbidity, according to the study in The Journal of Clinical Endocrinology & Metabolism.
Because Cushing's syndrome (CS) is complex and difficult to diagnose, there is a necessity for new methods to assess at-risk populations in order to mitigate the rising prevalence of the disorder, the authors noted.
"The diagnosis of CS might pose a considerable challenge even for experienced endocrinologists since there are no pathognomonic symptoms or signs of CS and most of the symptoms and signs of CS are common in the general population including obesity, hypertension, bone loss, and diabetes," the senior author, Alfonso Leal Cerro, MD, toldMedPage Today via email. "Routine screening for CS remains impractical due to the estimated low prevalence of the disease. However this prevalence might be higher in at-risk populations."
The authors screened a total of 353 at-risk patients from 13 different hospitals across Spain between January 2012 and July 2013 to measure cortisol variability from saliva samples.
At-risk populations, which the authors note have a higher prevalence of Cushing's syndrome, included individuals with type 2 diabetes, hypertension, and osteoporosis.
The patients screened in the study were each identified as having at least two of the risk factors for Cushing's syndrome: high blood pressure (defined as taking two or more drugs and having a systolic blood pressure over 140 mmHg and/or a diastolic blood pressure over 90 mmHg), obesity (body mass index >30), uncontrolled diabetes (HbA1c>7.0%), osteoporosis (T-score ≥ -2.5 SD), and virilization syndrome (hirsutism) with menstrual disorders.
The researchers used clinical and biochemical methods of assessment. Clinical methods included inspection of physical characteristics, such as muscle atrophy, purple striae, and/or facial plethora. Biochemical methods included collecting saliva and blood samples from participants to test cortisol levels using a chemiluminescence method. Each individual was identified as either negative for hypercortisolism (late-night salivary cortisol [LNSC] ≤ 7.5 nmol/L and dexamethasone suppression test [DST] ≤ 50 nmol/L) or positive for hypercortisolism (LNSC > 7.5 nmol/L and DST > 50 nmol/L).
Univariate testing indicated the following significant characteristics to be positively correlated with the development of Cushing's syndrome:
Muscular atrophy (15.2, CI 95% 4.48-51.25);
Osteoporosis (4.60, 1.66-12.75); and
Dorsocervical fat pad (3.32, 1.48-7.5).
A logistic regression analysis of LNSC values also showed significant correlation between Cushing's syndrome and the following top three characteristics:
Muscular atrophy (9.04, CI 95% 2.36-34.65);
Osteoporosis (3.62, CI 95% 1.16-11.35); and
Dorsocervical fat pad (3.3, CI 95% 1.52-7.17).
Roberto Salvatori, MD, professor and medical director of the Johns Hopkins Pituitary Center, who was not involved with the study, commented to MedPage Today in an email: "Any endocrinologist would proceed with careful Cushing biochemical evaluation in the presence of the clinical features (muscular atrophy, osteoporosis, and dorsocervical fat pad) that are well known to be associated with hypercortisolism. Of notice, the odds ratio is further increased by an abnormal late-night salivary cortisol, which is already a screening test for hypercortisolism."
The researchers used their results to develop an equation to determine the level of risk a patient has for developing Cushing's syndrome, taking into account factors for osteoporosis, dorsocervical fat pads, muscular atrophy, and LNSC levels.
Although the study was able to develop a comprehensive risk model for the syndrome, when tested against the prevalence for Cushing's syndrome in the subject group, the equation generated a total of 56 false-positive and 25 true-positive results. Overall, the researchers wrote, 83% of patients were accurately classified as belonging to the at-risk population when using the equation.
Because the newly developed equation for identifying at-risk individuals involved factors that are relatively easy to test for, the authors noted that clinical application is broad and cost-effective in a primary care setting.
"We would like to test the scoring system in different clinical settings such as primary care or hypertension clinics," Leal Cerro said. "Primary care would be a particularly interesting setting since it might significantly decrease the time to diagnosis, something critical to avoid an excessive exposure to glucocorticoid excess and consequent deleterious effects."
Salvatori said that while the study was a good start at shedding light on some of the unknowns about Cushing's syndrome, more research is required. "The real question in my mind is when does a non-endocrinologist need to suspect Cushing in a general medicine, orthopedic, or other clinic? When the internal medicine residents ask me about guidelines for 'who to screen for hypercortisolism in my clinic,' I am unable to provide an evidence-based answer."
The study was funded by a grant from Novartis Oncology, Spain.
León-Justel and Leal Cerro disclosed financial relationships with Novartis Oncology, Spain.
Reviewed by F. Perry Wilson, MD, MSCEAssistant Professor, Section of Nephrology, Yale School of Medicine and Dorothy Caputo, MA, BSN, RN, Nurse Planner
Journal of Clinical Endocrinology & Metabolism
Source Reference: León-Justel, A, et al "A probabilistic model for Cushing's syndrome screening in at-risk populations: a prospective multicenter study " J Clin Endocrinol Metab 2016: DOI 10.1210/jc.2016-1673.
From http://www.medpagetoday.com/endocrinology/generalendocrinology/59688
Filed under: Cushing's | Tagged: cortisol, Cushing's Syndrome, Dr. Roberto Salvatori, fat pad, glucocorticoids, hypercortisolism, Johns Hopkins, Journal of Clinical Endocrinology & Metabolism, late-night salivary cortisol, muscle atrophy, osteoporosis | Leave a comment »
Screening tool accurately predicts Cushing's syndrome in most at-risk patients
Posted on August 9, 2016 by MaryO
León-Justel A, et al. J Clin Endocrinol Metab. 2016;doi:10.1210/jc.2016-1673.
A scoring system based on clinical signs and a late-night salivary cortisol test accurately predicted Cushing's syndrome in at-risk patients, with only one missed case, according to recent findings.
In a prospective, multicenter study, Antonio León-Justel, PhD, of the biochemistry department at the Hospital Universitario Virgen del Rocío in Seville, Spain, and colleagues analyzed data from 353 patients treated in endocrinology units in 13 university hospitals in Spain between 2012 and July 2013. All participants had at least two of five features compatible with Cushing's syndrome, including obesity, hypertension, poorly controlled diabetes,hirsutism with menstrual disorders and osteoporosis; none of the included patients was referred to clinic with the suspicion of Cushing's syndrome. All patients underwent late-night salivary cortisol and serum cortisol measurements after a low-dose (1 mg) dexamethasone test; those with discordant results were followed until December 2014 (mean follow-up time, 22.2 months).
Within the cohort, 26 (7.4%) patients were diagnosed with Cushing's syndrome (20 adrenocorticotropic hormone-dependent; six of adrenal origin). In univariate logistic regression analysis, researchers found that muscular atrophy (OR = 15.2), followed by osteoporosis (OR = 4.6), dorsocervical fat pad (OR = 3.32), absence of obesity (OR = 0.21) and absence of type 2 diabetes (OR = 0.26), were associated with Cushing's syndrome; late-night salivary cortisol values were also related (OR = 1.26). However, after multivariable adjustment, researchers found that muscular atrophy (OR = 9.04; 95% CI, 2.36-34.65), osteoporosis (OR = 3.62; 95% CI, 1.16-11.35) and dorsocervical fat (OR = 3.3; 95% CI, 1.52-7.17) remained as independent variables with Cushing's syndrome.
"Obesity and type 2 diabetes displayed a negative association with [Cushing's syndrome]," the researchers wrote. "These results might seem paradoxical a priori, but we want to stress that in our analyzed cohort, the prevalence of obesity and diabetes was exceedingly high (likely reflecting the reasons for referral to endocrinology units)."
In receiver operating characteristic (ROC) analysis, researchers determined that a cutoff value of 9.17 nmol/L for late-night salivary cortisol provided the best results, with an area under the curve of 0.893 (P < .001), a sensitivity of 88.5% and specificity of 83.2%.
Researchers developed a risk-scoring system, determining cutoff values from a ROC curve. The estimated area under the ROC curve was 0.93 (P < .001), with a sensitivity of 96.2% and specificity of 82.9%.
"Selecting this cutoff value of four, 271 of 327 subjects (83%) without [Cushing's syndrome] were correctly identified, while only 1 of 26 [Cushing's syndrome] cases was missed," the researchers wrote. "Our model yielded 56 false positives.
"Although all the assessments were performed by specialists (endocrinologists) in our study, this scoring system could be easily tested in independent cohorts and different settings such as primary care or hypertension clinics," the researchers wrote. "At the very least, our diagnostic prediction model could be used as a framework for future studies and potential improvements in diagnostic performance." – by Regina Schaffer
Disclosure: Leon-Justel and another researcher report receiving a research grant from Novartis Oncology, Spain.
From http://www.healio.com/endocrinology/adrenal/news/in-the-journals/%7B50d3d398-c8fe-41e9-b815-87626bfe8a4b%7D/screening-tool-accurately-predicts-cushings-syndrome-in-most-at-risk-patients
Filed under: Cushing's, symptoms | Tagged: Cushing's Syndrome, diabetes, hirsutism, hypertension, late-night salivary cortisol, menstrual disorder, obesity, osteoporosis | Leave a comment » | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,458 |
Copyright © 2013 by Nancy Collamer
All rights reserved.
Published in the United States by Ten Speed Press, an imprint of the Crown Publishing Group, a division of Random House, Inc., New York.
www.crownpublishing.com
www.tenspeed.com
Ten Speed Press and the Ten Speed Press colophon are registered trademarks of Random House, Inc.
Library of Congress Cataloging-in-Publication Data
Collamer, Nancy, 1957-
Second-act careers : 50+ ways to profit from your passions during semi-retirement / Nancy Collamer.—1st ed.
p. cm.
1. Career changes. 2. Retirees—Employment. I. Title.
HF5384.C65 2013
650.14086′96—dc23
eISBN: 978-1-60774-383-5
Cover design by Katy Brown
Interior design by Colleen Cain
v3.1
# Contents
_Cover_
_Title Page_
_Copyright_
Acknowledgments
Introduction
[**PART ONE**
**50+ WAYS TO GENERATE INCOME IN SEMI-RETIREMENT**](Coll_9781607743835_epub_p01_r1.htm)
**CHAPTER ONE** : Build Income from Your Expertise
**CHAPTER TWO** : Create an Information Empire
**CHAPTER THREE** : Start a Small Service Business
**CHAPTER FOUR** : Pursue a Business-in-a-Box Opportunity
**CHAPTER FIVE** : Trade Your Time for a Paycheck
**CHAPTER SIX** : Make a Living While Making a Difference
**CHAPTER SEVEN** : Get Paid to Travel
**CHAPTER EIGHT** : Ten Reinvention Lessons Learned
[**PART TWO**
**CREATING YOUR SECOND-ACT CAREER**](Coll_9781607743835_epub_p02_r1.htm)
**CHAPTER NINE** : Envision the Life You Want
**CHAPTER TEN** : Look to the Past for Clues to Your Future
**CHAPTER ELEVEN** : Ask, Analyze, and Assess
**CHAPTER TWELVE** : Research the World of Possibilities
**CHAPTER THIRTEEN** : Try It Out!
Conclusion: Some Final Tips on Creating Your Second-Act Career
Resources
About the Author
# Acknowledgments
This book would never have happened without the encouragement of my wonderful literary agent, Marilyn Allen. Marilyn, thank you for your friendship and belief in the importance of this book. I am so thrilled that we finally got the chance to work together! To the team at Ten Speed Press—in particular my editor, Sara Golski—thank you for your warm welcome, savvy advice, and editorial assistance. I am truly honored to be part of the Ten Speed family.
One of the aspects I enjoy most about my job is that I get to work in a profession filled with warm, smart, and supportive colleagues—and a few deserve special mention. To my "lunch bunch"—Karen Kirchner, Susan Gannon, and Linsey Levine—thank you for more than a decade of support, brainstorming, and wonderful holiday luncheons. Linsey, it was indeed serendipitous that we earned our master's degrees at the same time; you have been my personal "career counsel" on more occasions than I care to admit. To Susan Joyce of Job-hunt.org, thanks for showcasing me on your site; and to my accountability buddies, Shannon White and Pat Katepoo, much _mahalo_ for keeping me focused, on track, and productive—at least most of the time!
To the best clients in the world, thank you for allowing me to be part of your journey; you have inspired me with your brilliance and honored me with your trust. This book would never have been possible without you. And to all the remarkable people who agreed to be interviewed for this book, thank you for being so generous with your time, insights, and willingness to share your personal stories.
Much gratitude is also due to all my friends, gym buddies, UNC pals, Shir Ami supporters, and neighbors who have taken such great interest in this project. Your enthusiasm and "How are you holding up?" phone calls kept me going day after day.
A very special thank-you to my brother, David Jarmul, and his wife, Champa, for your brainstorming help and advice; and to my sister, Ruth Jarmul, and her husband, Irv Rosenthal, for your unfailing encouragement, love, and support. I am truly blessed to have such wonderful siblings. My one regret in writing this book is that our parents, Seymour and Lore Jarmul, are not alive to see this book in print. I was raised in a family of authors, and I know they would have been delighted to know I have joined their ranks. Thank you Mom and Dad for everything—I truly could not have asked for better role models.
To my two delightful daughters, Danielle and Juliana, who encouraged and cheered me every step of this journey, thank you for making me one proud "Nin." You enrich my life beyond measure, and I love you more than words can say.
And last, but never ever least, to my amazing husband, Joel Collamer: thanks for thirty-plus years of love, listening, and laughter. I know it sounds clichéd to say this wouldn't have been possible without your support, but it's true. Thank you for believing in me, cooking for me (although I've had enough of the cheese, thank you), entertaining me with your antics, and for being my best friend. This book is dedicated to you, with my love, thanks, and gratitude.
# Introduction
When I told people that I was writing a book about semi-retirement careers, I wasn't quite sure if people would understand what I meant. After all, by definition, "working during retirement" is an oxymoron. But I quickly found out that people weren't the least bit confused. In fact, not only were they not confused, but their reaction was also genuinely enthusiastic. It didn't take me long to realize that I was on to something important, and once word about the book spread, I started to receive a surprising number of calls from people asking, "Are you looking for people to interview? Because if you are, I know just the person you need to talk to."
I couldn't believe how many people had interesting stories to tell. It seemed that just about everyone had a neighbor, friend, or relative who was doing something fun and meaningful during semi-retirement. One woman told me about her grandmother, a retired teacher, who was selling an online course she'd written for special needs children; a neighbor spoke about a friend who was working as a travel blogger while enjoying free trips to exotic places; and my client shared stories about her father-in-law, a former advertising executive who was writing a movie script while working part-time as a tour guide for his local historical society. Others told me about their colleagues who had downshifted from full-time jobs into contract and part-time opportunities that enable them to continue to earn needed income while enjoying a less stressful lifestyle. The stories I heard were as diverse as the individuals who told them.
People who had not yet retired were equally eager to tell me about their future plans: one man shared that he was looking into opportunities with the Peace Corps, another was hoping to sell his paintings, and several other people said they wanted to transition into part-time jobs in their local communities. Interestingly, almost nobody said that they planned to just play golf all day (well, maybe one or two did). One woman in her mid-fifties said of her second-act career plans, "What else am I going to do with myself all day? I plan to live for at least thirty more years, and I need to feel like I have a purpose."
Of course, at the same time that people say they want to work, many baby boomers are struggling with the reality that they will _need_ to work. A 2010 Harris poll revealed that a staggering 25 percent of people age forty-six to sixty-four say they have no retirement savings. Even for those who have put money aside for retirement, the triple threat of dwindling pensions, insufficient personal savings, and the uncertainties surrounding Social Security—combined with record levels of personal debt, rising health care costs, and falling real estate values—are forcing many to rethink their retirement plans.
As I write this, my husband and I are rethinking our retirement plans too. We have always worked hard at professional jobs, put the maximum amount allowed into our 401(k)s, lived within our means, never carried credit card debt, and own a house that is thankfully valued at more than we originally paid. According to the experts, all of our efforts should have been more than sufficient to guarantee a comfortable retirement. But even after having done everything "right" and then some, we can't afford to be complacent. Neither of us is eligible for a pension or employer-subsidized health insurance, and the swings in the stock market combined with the meager returns on our investments are giving us cause for concern.
Bottom line? It is clear that we, along with millions of our fellow boomers, will need to find a way to work past the traditional retirement age. Of course, that doesn't mean that we plan to work in the same way, doing the same things, at the same frenetic pace, that we are "forced" to do while employed full-time. In fact, quite the opposite is true. We intend to work—but this time around, we want to be able to do so on our own terms, on our own timetable, and in our own way. This time, we plan to call the shots.
Whether out of necessity, desire, or a combination of the two, it is clear that millions of boomers will soon be looking for ways to reinvent their careers without a traditional 9-to-5 job. We will work during a phase known as "semi-retirement"—the stage that occurs after the big full-time job ends and before full retirement sets in.
I'm assuming that if you picked up this book, you want that too. But is it really possible? Can you find work options that are fun, fulfilling, and flexible—and also give you enough time (and money) for travel, leisure, learning, and other personal interests?
I believe that you can. In fact, I am sure of it. In doing the research for this book, I spoke at length with nearly forty people, most of whom were in their fifties and sixties, who are having the time of their lives working in their second acts. And even though they typically no longer earn what they once did, they are energized, engaged, and connected to their communities; they feel valued, are learning new skills, and know they are making a difference. When asked how long they planned to continue working, the vast majority said they have no intention of slowing down anytime soon; they are simply having too much fun. As Eve Young, a sixty-year-old woman who juggles two part-time jobs as an interfaith minister and acting extra, puts it, "When I'm too old to stand up, then I'll stop."
While it is true that the outlook for the traditional job market continues to appear bleak, I am convinced that the future for boomers who want to pursue flexible and entrepreneurial work options looks very promising indeed. Why? Consider the following:
• **Technology has completely revolutionized how, where, and when we work**. Thanks to wireless networks and mobile technologies, you can now work from just about anywhere: while sitting in your backyard, on a boat, in a coffee shop, or in your mobile home.
• **The options for flexible employment have improved and diversified**. Telecommuting has become increasingly commonplace, and a growing number of companies are offering work-from-home alternatives.
• **The costs of running your own business have decreased dramatically, and the global reach of the Internet has made it possible to sell to anyone, anytime, anywhere**. Gone are the days when you needed a storefront to sell products, a printer to produce a newsletter, or a classroom to teach your lessons. With so many inexpensive and sophisticated tools readily available on the Web, you can now sell products on your website, send out your newsletter electronically, and teach classes online. If you don't want to run your own website, you can sell your handicrafts on sites like Etsy.com, your informational products on Clickbank.com, or your collection of vintage clothing on eBay.com. Going from idea to income can take less than a day and cost less than one hundred dollars!
• **We are fast becoming a nation of freelance workers** , and although that is an arguably problematic trend for many people—especially younger workers—it is an opportunity for boomers who like project work and no longer want to deal with the demands of full-time employment.
• **The Internet provides us unlimited access to information and training twenty-four hours a day**. Thinking about starting a gift basket business? Google the term "gift basket business," and in a matter of seconds you'll find videos, courses, associations, and conferences designed to help you learn how to get this type of business off the ground. Need help after you get your business started? You can post a question to an industry group on LinkedIn or send out a query on Twitter. Interested in finding a seasonal job with the National Park Service? There are job boards where you can easily locate those openings. Looking for training to help you learn how to write grants or start a nonprofit? You can find multiple websites that will teach you all about those skills. I could go on and on, but suffice it to say there is no end to the amount of useful career and business information you'll find online.
Of course, the sheer volume of all this information can lead to information overload. It is hard to know where to begin your research, which sources to trust, and how to figure out what you want to do, especially if you've spent the bulk of your professional life working more or less in one career or industry.
That is why I wrote this book. It will help you sort through the options as you move away from the "big" career and begin to phase into this next stage of your life. This book is divided into two parts. The first highlights more than fifty different models for turning your passions into profits, your interests into income, and your hobbies into cash. The second offers a variety of exercises that will you help you better understand your motivating skills and interests, clarify your lifestyle goals, and help you begin to plan for your next act. After all, it's great to read inspirational stories and learn about new ideas and resources, but at some point you need to turn those dreams into actions that work for you. Here is a brief overview of the chapters:
## **Part One. 50+ Ways to Generate Income in Semi-Retirement**
**Chapter One: Build Multiple Streams of Expert Income**. All of us have special knowledge, experiences, and skills that can be monetized through a variety of "expert" income streams such as consulting, coaching, teaching, training, and speaking. In chapter one, you'll learn about the different models for turning your expertise into multiple streams of income. You'll get to meet a sixty-year-old woman who runs a highly successful coaching business, a lawyer turned mediator, and a former Microsoft executive who teaches marketing to magicians.
**Chapter Two: Create an Information Empire**. Chapter two explores the different avenues, and new models, for turning your expertise into informational products; it features interviews with a mom who runs a food blog, a woman who makes a healthy five-figure annual income selling digital downloads while enjoying life in Hawaii, and an interview with an expert on "Making Money in Your Jammies."
**Chapter Three: Start a Small Service Business**. Looking for a home-based business that is easy to start on a shoestring budget? Service businesses can be run from home, operated on a part-time basis, and require minimal start-up expenses—an enticing combination for boomers wanting a lifestyle-friendly income stream. In this chapter, you'll learn about dozens of different types of service businesses, including personal, business support, and pet care options.
**Chapter Four: Pursue a Business-in-a-Box Opportunity**. Not everyone wants to start a business from scratch. If the thought of being totally on your own makes you uneasy, you may instead want to consider a business-in-a-box opportunity, such as a franchise, direct sales, or licensing arrangement. Although many people have a negative impression of multilevel marketing companies and franchises, I think you'll be pleasantly surprised by what you'll learn about these options in chapter four. People you'll meet in this chapter include a woman who sells clothing as an independent fashion consultant with a direct sales company, a franchisee with a company that supports female entrepreneurs, and a disabled veteran who became a power seller on eBay.
**Chapter Five: Trade Your Time for a Paycheck**. This chapter explores the different ways you can earn income as a part-time employee, temporary worker, virtual employee, freelancer, or seasonal worker. It includes tips from a woman who runs a flexible jobs board, an interview with the president of an interim executive services firm, and advice from the founder of CoolWorks.com, a job board that features jobs in "cool places."
**Chapter Six: Make a Living While Making a Difference**. Many boomers are looking for an "encore career," a term that refers to career paths that combine passion, purpose, and income during the second half of life. Chapter six examines five different encore career paths and includes interviews with several inspirational boomers who are using their second-act careers to change the world for the better.
**Chapter Seven: Get Paid to Travel**. Chapter seven highlights nine different ways that you can get paid to travel (or at least paid enough to offset the costs of your travel), including tour director, tour guide, import-export businesses, temporary innkeeper, working on cruise ships, and ideas for volunteer vacations. But be warned, by the time you get done reading this chapter, you could be infected with a serious case of wanderlust!
**Chapter Eight: Ten Reinvention Lessons Learned**. In between part one and two, I discuss the ten key reinvention lessons learned from the people profiled in this book. We'll take a look at the factors that helped them be successful and consider ways that you can apply those same strategies to your own reinvention plans.
## **Part Two. Creating Your Second-Act Career**
**Chapter Nine: Envision the Life You Want**. Building a fulfilling second-act career revolves around both lifestyle and career decisions. The exercises in this chapter will help you to better understand the personal motivators, lifestyle goals, and financial objectives impacting your next act.
**Chapter Ten: Look to the Past for Clues to Your Future**. Introspection is a key step in the reinvention process. Chapter ten offers guidance on how to collect and organize your personal history into a format that will allow you to more easily complete this task.
**Chapter Eleven: Ask, Analyze, and Assess**. Although many of you have undoubtedly changed jobs many times, and some of you may have changed careers several times, the descriptor "second-act" refers to making a distinct shift from your prior career path during the second half of life. The exercises in this chapter will help you to better understand your strengths, values and skills so that you can navigate this transition with greater clarity, purpose and ease.
**Chapter Twelve: Research the World of Possibilities**. Once you know what you love to do, do well, and find meaningful, the next step in this process is to identify real-world opportunities that are a good match for your interests. Chapter twelve overviews the "best-of-the-best" from the world of career research: dozens of resources to help you explore interesting and unusual career possibilities.
**Chapter Thirteen: Try It Out!** No matter how intriguing a career idea sounds, you'll never know if it is truly a good match until you've had a chance to try it out in the real world. This chapter highlights a variety of low-risk ways to test out potential new directions.
**Conclusion: Some Final Tips on Creating Your Second-Act Career**. The conclusion offers strategies for ensuring lasting success as you move forward.
As you will soon learn, this book covers a diverse assortment of ideas for creating income on a flexible basis during semi-retirement. Not every idea will appeal to or be a good fit for every reader. But I do think that you will find plenty of surprising and attractive options for building a second-act career, so I encourage you to keep an open mind.
My hope is that this book will help expand your horizons, empower you with knowledge, and leave you feeling inspired, hopeful, and excited about your future. Welcome, in advance, to your second-act career. I think you'll be delighted by what you'll find here.
—Nancy Collamer
mylifestylecareer.com
#
One of my favorite childhood memories is of a restaurant called Sweden Towers, which back in the 1960s was known as _the_ smorgasbord restaurant on the south shore of Long Island. At the time, the concept of an all-you-can-eat restaurant was relatively new, and I can still remember my mouth watering as I walked around the buffet table surveying all the delectable choices: little Swedish meatballs swimming in gravy, butter cookies with chocolate sprinkles, and wiggly red Jell-O salads garnished with mini marshmallows. I must have asked my parents at least three times, "You mean I can take anything I want as many times as I want?" To which my parents would reply, "Yes, but don't just fill up your plate with spaghetti. Try a few new things for a change."
Reading the first part of this book is a bit like going to Sweden Towers; it offers a smorgasbord of possibilities designed to whet your appetite as you begin to ponder your second-act career. Some of the ideas—like consulting, working a part-time job, or teaching—will be quite familiar to you. Others—like creating your own informational products, training as a mediator, or working as an extra on a movie set—might seem a bit unusual. I've strived to present a well-balanced menu of options, although I must admit that deciding what to include made me feel a bit like that wide-eyed little girl in the restaurant all over again—it was difficult to limit myself! Nonetheless, the opportunities in part one all meet the following six criteria:
1. **Work-life flexibility**. These are work options that can realistically be done on a flexible schedule. You can decide to work them on a part-time or full-time basis, as you prefer. Knowing that many of you hope to be able to travel or work from home during your semi-retirement, I was also careful to include opportunities that can be done on a virtual basis and steered away from brick-and-mortar businesses like restaurants, bakeries, farms, and retail shops that typically require full-time attention (and a large upfront capital investment).
2. **Scalability**. These ideas can work as stand-alone income streams or you can combine several options together to generate multiple income streams (also known as a "portfolio career"). For example, whereas you might be happy teaching just one class a semester as an adjunct professor, another reader might want to teach _and/or_ write a book _and/or_ create a webinar, _and/or_ teach on a cruise ship. Many people start off with one income stream and then slowly add on other profit centers as their time and circumstances allow. You can mix-and-match the options to best meet your lifestyle and income goals.
3. **Range of income potential**. The careers in this book offer a wide range of earning potential. For example, there are bloggers who barely earn a few hundred dollars a year and others who generate a solid five-figure monthly income; temps who earn a few hundred each month and others who get paid the equivalent of a full-time professional salary; direct sales people who are happy making just a few thousand dollars a year and superstars who generate six-figure incomes. When possible, I have included income information with the profiles (current as of the time of this writing), but it's important to remember that, although traditional jobs have somewhat standard salary ranges, the amount you earn as a freelancer or entrepreneur is ultimately determined more by your individual effort, background, credentials, marketing abilities, and personal circumstances than by the restrictions of a specific job category.
4. **Low start-up costs**. The vast majority of the entrepreneurial ideas in this book are service-oriented options that require minimal start-up capital (often as little as a few hundred dollars and generally no more than one thousand).
5. **Limited additional training requirements**. Most of you will need to invest in some form of additional training (workshops, seminars, certificate programs, and the like) as part of your career transition. That said, I intentionally eliminated any options that would require you to go back to school for an advanced degree. If you want to pursue a bachelor's or an advanced degree, I applaud you, but I assume that most of you, if given the choice, would prefer to not have to invest in yet another expensive and time-consuming college degree.
6. **Age appropriate**. I hesitated to include this because almost any job can be done at any age, and I know of many people who are actually in better shape at age fifty-five than they were at age twenty. Nonetheless, I deliberately chose to avoid jobs that are physically demanding and could prove taxing as you age. Conversely, I favored jobs where age, experience, and maturity are perceived as a competitive advantage.
There are more than fifty different career and business ideas for you to learn about in part one. But you are certainly not limited to these choices; just like an apple can be baked into a pie, crushed into applesauce, or chopped into a cobbler with equally delicious results, each of these career ideas can be sliced, diced, and assembled in hundreds of different ways that satisfy your unique interests, goals, and income needs. As you read through this section, please remember that while the descriptions provided are designed to give you a "taste" of each career, they do not cover all the specifics (licensing requirements, income potential, zoning restrictions, and so on) that you'll need in order to make a truly informed decision. Every career and entrepreneurial option, no matter the focus or industry, comes with its own set of risks, regulations, and rewards; it is up to you to research and fully consider every aspect. I have included information about income potential and licensing requirements when possible, but the specifics change over time, and I encourage you to use the resources provided alongside these descriptions and profiles to help you continue to explore and learn more on your own.
And now, with that understanding in mind, I invite you to pull up a chair, take your seat at the table, and get ready to work up an appetite. It's time to sample the smorgasbord of semi-retirement careers. _Bon appétit!_
# **CHAPTER ONE**
# **Build Income from Your Expertise**
If you have invaluable information, expertise, and life lessons that you want to share with the world and get paid for (and who doesn't?), then this chapter is going to be of great interest to you. Each of you is an expert at something related to your professional experience, hobbies, or personal life. You may be a whiz at technology, a pro at planning events, a scholar on the Civil War, or an expert on the subject of getting into college. Whatever your specialty, it's important to remember that you do not need to be _the_ leading expert, practitioner, or guru in your field to make money from your expertise; if you know more than 90 percent of the population knows on any given topic, you can probably find a way to profit from it.
So how can you monetize that expertise?
In this chapter, you'll find a number of different ways to profit from your knowledge capital. You will meet people who have taken bits and pieces of their expertise, added new elements, and blended them all together to create income streams that take advantage of their special talents. Instead of relying on one employer for their livelihood, they generate their income through multiple income options, including coaching, teaching, speaking, and performing. Many of them also supplement their income with the sale of informational products—a subject that we will explore in more depth in the next chapter. But for now, let's kick things off by taking a closer look at consulting, one of the most popular of all semi-retirement careers.
## **CONSULTANT**
If you ask a group of boomers what they plan to do in retirement, you can bet that at least one of them is going to respond with "I'm thinking about doing some consulting." It is no wonder that consulting is often at the top of the semi-retirement careers wish list. Life as a consultant allows you to capitalize on your work experiences, contacts, and expertise, while enjoying the benefits of being your own boss. If you consult on a part-time basis, you'll still have the flexibility to do the things you want to do in retirement. And if, like many new consultants, you start your business by consulting to your former employer, it can prove to be a nice way to remain connected to your colleagues without the commitment of a full-time job.
What types of consulting can you do? Consultants advise companies, organizations, and entrepreneurs on a multitude of issues, including:
• **Management issues**. Management consultants advise companies on "big picture" topics like strategic planning, operations, and technology. These consulting assignments tend to be high-visibility, high-risk, and high-reward projects that are best for people willing to work long hours in sometimes stressful environments.
• **Industry-specific issues**. Companies hire consultants who have strong industry expertise to work on issues that cannot be adequately addressed by their own internal employees. For example, a former military officer might be asked to consult on security matters, or an insurance executive might be retained to consult on risk management policies.
• **Business processes**. Some consultants specialize in advising companies and organizations on better ways to handle specific tasks like fund-raising, social media outreach, or managing public relations campaigns. Consultants are also brought in to provide counsel in response to newly enacted regulations and laws.
• **Business development**. Companies of all sizes, from start-ups to large corporations, hire consultants who can help them find more clients, make more sales, and develop new sources of revenue.
• **Business advisory and forecasting services**. In every industry there are "gurus" who get paid handsomely to speak, consult, and write about the trends and technologies that impact the future direction and profitability of the industry.
Before you start work as a consultant, you will want to be very clear about your unique value proposition: what it is you bring to the table and how it will benefit your clients. Although many consultants launch their practices with a wide-ranging menu of services, most quickly discover that it is easier to offer a well-defined niche expertise than to try to be all things to all people. Like any entrepreneurial endeavor, consulting has its challenges. The unpredictable cash flow, feelings of isolation, and lack of support systems can make this a difficult choice if you are accustomed to the predictability and support of corporate life. In general, consultants to large companies earn the highest fees, but in exchange they are expected to work long hours and travel wherever and whenever the client needs them. As a result, many semi-retired people prefer to consult to smaller organizations, entrepreneurs, and nonprofits because they tend to offer a more lifestyle-friendly consulting alternative.
Because consulting is such a popular career choice, there is no shortage of resources available to help you learn about this option:
• Start your research by asking other people who are working as consultants in your field for their advice on best practices within your industry. If you don't personally know of anyone, you can always find consultants by asking colleagues for referrals or by doing a Google search using the name of your industry and the word "consultant" as search terms.
• Investigate the consulting workshops and programs offered through your local community colleges and continuing education programs. Check the offerings of SCORE (previously known as the Service Corps of Retired Executives), a nonprofit association with hundreds of local offices offering free business mentoring and low-cost workshops (www.score.org), or the US Small Business Administration (www.sba.gov) for listings of helpful workshops, webinars, and consulting services—many of which are provided free or for a low cost.
• Check with your professional industry association to learn about their training offerings for consultants.
Recommended reading: _Million Dollar Consulting: The Professional's Guide to Building Your Platform_ by Alan Weiss (McGraw-Hill, 2010). Weiss is widely regarded as _the_ authority on how to succeed as an independent management consultant and has authored many books on this subject. Although his books are geared toward people who want to be full-time consultants, his advice can easily be adapted to meet the needs of part-time consultants as well.
## **COACH**
At a time when people increasingly operate as "lone cowboys" in both their personal and professional lives, it is no surprise that the popularity of working with a coach—and _as_ a coach—is on the rise. As opposed to consultants who get paid primarily to give advice, coaches focus on both the mechanics and the mind-set of solving problems, helping their clients to overcome self-defeating behaviors and achieve greater success. There are coaches for just about every type of life situation imaginable including life, career, executive, and financial issues. And within those broader coaching categories there are subspecialties: executive coaches who coach only Hispanic women, life coaches who cater to divorced women, and financial coaches who specialize in retirement planning. You name it and there is a coach for it—and no matter what your area of expertise, it is possible to find a way to build a coaching service around it.
Coaching is a relatively new profession, and as such, the standards for licensing and credentialing are still being formulated. For the time being, virtually anyone can hang out a shingle and declare that she or he is a coach. The low barriers to becoming a coach, along with the misconception that anyone can earn a high hourly rate for "just talking with people on the phone," means that there are a lot of people who aspire to be coaches—but not everyone succeeds. Executive coach Douglas Campbell III warns that you need to be prepared to market your services very effectively in order to distinguish yourself from the crowd. "There are a lot of wannabe coaches out there," says Doug. "But I think less than 30 percent of the coaches are actually making a living from it."
One of the great appeals of coaching as a semi-retirement career is the lifestyle it allows: you can set your own hours, work from anywhere, and once you've established a strong following it is possible to earn an impressive income. Most coaches work with clients by telephone, although executive coaches often meet with their clients in person. Coaching rates range from $75 per hour for novice life coaches up to $1,000 per hour for top executive, small business, and celebrity coaches. However, even top coaches find that it can be hard to make a living from coaching sessions alone, so many coaches supplement their income with the sale of training programs, books, seminars, and other offerings that complement their coaching services. Established coaches also earn income by teaching and coaching other coaches in the "business of the business."
There are hundreds of training programs for aspiring coaches: from degree and certificate programs at major universities, to full-year programs run by coaching institutes, to online niche coaching programs developed by enterprising entrepreneurs. The quality and credibility of these programs vary widely, and different programs focus on different specialty areas, so do take the time to find a program that meets your specific goals and interests. Consult with other coaches to get their recommendations on the best programs for your unique needs.
Here are some resources for further exploration:
• **International Coaching Federation (ICF) (www.coachfederation.org)**. The world's leading coaching organization, ICF provides credentialing, certification programs, conferences, and research for the coaching profession. ICF members include life coaches, executive coaches, career coaches, and business coaches. The ICF has active local chapters around the globe.
• **Coaches Training Institute (CTI) (www.thecoaches.com)**. The world's oldest and largest in-person coach training organization, CTI offers a number of highly regarded training programs for both new and experienced coaches. The founders of CTI wrote an excellent book about coaching, _Co-Active Coaching: Changing Business, Transforming Lives_ (Nicholas Brealey Publishing, 2011), that is considered a classic on coaching techniques.
• **Peterson's (www.petersons.com)**. This site lists universities and colleges that offer coaching programs and classes.
**THREE TIPS FROM THE ENTREPRENEURIAL EXPERT**
**"Don't forget to have fun: part of the reason you start your own business is to enjoy life."**
—DOUGLASS CAMPBELL III, CEO, executive coach, and managing director of the Success Coach (www.thesuccesscoach.com)
Doug Campbell knows what it takes to run a successful business. An executive coach since 1996, Doug was the chief marketing officer of a $200-million-dollar division of a Fortune 100 firm, taught MBA programs for the Darden School at the University of Virginia, and has started five businesses. Here are his tips on how to be a successful entrepreneur:
1. **Surround yourself with good advisers and mentors**. There is tremendous value to be gained from actively seeking the advice of mentors as you build and grow your business. If you don't feel comfortable reaching out and asking for feedback on your own, Doug suggests that you consider participating in a mastermind group. Several times a year he invites a selected group of entrepreneurs to participate in his High-Talent Creatives Group, a brainstorming event where group members bounce around ideas, share suggestions, and learn from each other's experiences. One business is chosen to be the focus of the meeting (past participants have included the founders of Sobe beverage company and Edgar Online), but everyone is given time to speak, network, and benefit from the collective wisdom of the group.
2. **Know your risk profile**. There are different levels of risk associated with different types of businesses. The level of risk you are willing to assume will affect the level of comfort and confidence you are able to bring to your business, so choose a business that meshes well with your personal tolerance for risk and financial uncertainty.
3. **Stop worrying that someone will steal your idea**. Yes, there is a risk that someone will steal your idea, but the way you develop and refine ideas is by soliciting input from other people. "Let's be honest," says Doug. "If you see a need for something, chances are good that at least eight to ten other people around the country have had the same idea." Worry less about somebody stealing the idea; focus more on getting suggestions from other people that will make your idea better and stronger.
## **TEACHER/TRAINER**
Are you a natural teacher? Do you enjoy explaining concepts, theories, and the mechanics of how to do things? Would you like to share the wealth of experiences you've accumulated with others and pass on your knowledge to future generations?
If the prospect of empowering people with the skills, resources, and expertise needed for success in both their personal and professional lives excites you, then you might want to consider sharing your expertise either as a classroom teacher or a "how-to" trainer who instructs via webinars, workshops, or seminars. For people who are outgoing and enjoy an audience, teaching can be a great way to earn an income. Here are some interesting options to consider:
• **Adjunct professor**. Adjunct-level professors are hired on a contractual, nontenured basis to teach at universities, community colleges, vocational schools, and colleges. Some institutions require that their adjuncts meet the same degree requirements as their full-time faculty (meaning you may need a doctorate degree to be hired), whereas at other schools a bachelor's or master's degree is sufficient. Prior teaching experience is always advantageous, but the combination of an advanced degree plus work experience is often sufficient to make you an attractive teaching candidate, especially if you want to teach at a community college or smaller school. Adjuncts don't earn a lot (typically anywhere from a few hundred to a few thousand per course), but adding the word "professor" to your resume or bio can be a great way to enhance your reputation, reach, and marketability.
• **Online instructor**. The world of online education is rapidly gaining traction, credibility, and prestige. Although brick-and-mortar universities tend to use their in-house faculty for online assignments, online institutions hire outside applicants who offer strong subject-related work experience. A master's degree can make you more marketable, but schools will consider applicants who hold a bachelor's degree along with relevant work experience. To find an online teaching position, apply directly to the online institution, or search on one of the many online job boards—for example, Simplyhired.com, Indeed.com, or the jobs listed on the Chronicle of Higher Education site (chronicle.com), using keywords such as "online teacher" or "virtual instructor."
• **Corporate trainer**. Few companies still maintain in-house training departments, and as a result, many have increased their use of outside vendors to train their employees on topics ranging from sales to business etiquette to leadership. To learn more about these opportunities, and to find vendors who might be interested in contracting with you as a freelance trainer, consult the website of the American Society for Training and Development (www.astd.org).
• **Adult education instructor**. Continuing education programs are always in need of new programs, workshops, and classes to fill their catalogs. Although most programs will pay only a small stipend for your services, teaching in one of these programs is an easy and cost-effective way to market and advertise your services. In addition to teaching opportunities at local community colleges, vocational programs, or town continuing education programs, you can teach at privately run adult education programs such as the Learning Annex (www.learningannex.com) or the Gotham Writers' Workshop (www.writingclasses.com).
• **Online trainer**. Thousands of entrepreneurs are generating significant income by creating their own brand of online training programs, formatted as videos, webinars, and multisession "universities." Although many online courses focus on teaching business development and internet marketing, the possibilities for packaging your expertise into your own program to deliver a virtual learning experience are limited only by your imagination. And once you develop a course, you can sell it in multiple formats (downloadable manual, video, podcast, and so on) for as long as the information remains relevant and timely. You can learn more about this option in the next chapter.
• **School owner-director**. As a child, I attended a ballet school taught by one of the neighborhood moms in the attic of her home. It was a simple studio that catered to the needs of the local tutu-lovers while providing a steady income stream for my neighbor while she stayed home to raise her children. This spirit of homegrown entrepreneurship is still alive and well, in the form of home-based cooking schools, language programs for toddlers, and acting classes. Of course, before opening any school in your home, be sure to check with your town and state government for applicable zoning and licensing requirements, especially since your neighbors might protest if your business increases traffic in the neighborhood.
• **One-to-one tutor**. The demand for tutors is always strong, especially for people who can help children improve their grades, study habits, and SAT scores (tutors in affluent neighborhoods can command upward of $150 per hour for their services). If you'd prefer working with adults, consider offering your expertise as a computer and technology tutor. Although most tutors run their own businesses, you can opt to work for one of the big tutoring services, such as Kaplan or Kumon, if you don't want to go it alone.
• **Private teacher**. Would you like to teach people on a one-to-one basis or in a small group setting? The opportunities to profit as a private instructor are limited only by your imagination—people will gladly pay for personalized instruction in any number of interest areas, including yoga, painting, video-editing, and photography.
To learn more about teaching jobs and the training field, consult:
• **Chronicle of Higher Education (chronicle.com)**. An online resource for jobs and information related to colleges and universities.
• **American Society for Training and Development (www.astd.org)**. The professional organization for people involved in corporate and business-related training and development. Their website is an excellent resource for people interested in all aspects of the training world.
• **HigherEdJobs (www.higheredjobs.com)**. Lists openings in academia.
## **TEACH THE BUSINESS OF THE BUSINESS**
Have you ever built a business, turned a business around, or significantly improved the profitability of a business? Do you have strong expertise in marketing or business development? Are you knowledgeable about a specific business process, such as how to get a nonfiction book published, write a press release, design a website, or create a YouTube video? If so, you may be able profit handsomely (very handsomely!) from teaching other entrepreneurs what you know.
We are fast becoming a nation of independent entrepreneurs; according to the Kauffman Index of Entrepreneurial Activity, a leading indicator of new business creation, the share of new fifty-five- to sixty-four-year-old entrepreneurs increased from 14.3 percent in 1996 to 20.9 percent in 2011. This entrepreneurial trend is feeding a growing demand for people who can teach the "business of the business"—that is, all of the business skills needed to start, run, grow, and manage a profitable business.
This is an idea with tremendous income and growth potential. Although most entrepreneurs are great at their core business—they are wonderful photographers, talented jewelers, skilled coaches—they often lack the business skills and knowledge needed to turn their talents into a sustainable business. And even successful business people are not equally skilled at all aspects of running their business; they may be great at cold-calling, but lousy at copywriting; skilled at promotions, but weak at closing the sale; savvy at networking in person, but clueless when it comes to building relationships online. Sadly, no matter how good people are at their craft, if they don't know how to find clients and make the sale, they will eventually go out of business.
Needless to say, the mere threat of going out of business causes entrepreneurs a lot of sleepless nights, so they are more than willing to invest in learning proven techniques for avoiding this fate. Here are a few examples from my own entrepreneurial journey to demonstrate how you might be able to profit from teaching the business of the business:
• **Marketing and publicity**. Most people don't know how to write a press release, get publicity, or handle the publicity once they get it. I sure didn't when I was new to business, but I learned from Marcia Yudkin, who runs a business that teaches people the how-to of business writing and marketing. She sells a wide range of products and services, including books, courses, informational products, and consulting services that teach people how to create compelling content, attract publicity, and better market their services.
• **Business development**. There is no shortage of people eager to teach the basics of business development to new entrepreneurs. In the early stages of my business, I read a very helpful book by C. J. Hayden called _Get Clients Now!_ (Amacom, 2007), which helped me understand the principles and practices associated with building up a private practice. From there, I went on to take other courses to learn about different business development topics including pricing, marketing, and branding.
• **Publishing**. When I first thought about writing a book, I didn't have a clue as to how to find an agent or how to write a book proposal. I learned by reading several helpful books and by attending a few seminars (some free and some for a fee) that helped me better understand the book publishing business. There are people teaching every aspect of the publishing process, including how to run a book blog tour, how to write a book in a month (I probably should have signed up for that one!), and how to make money speaking about your book.
• **Technology**. Technology is constantly changing, and because of this, entrepreneurs have an ongoing need for people who can help them manage their technology issues. I have paid for classes on blogging, website design, and social media networking, and I am certain that I will invest in many more technology classes in the years ahead.
There are infinite ways you might be able to use your skills, industry knowledge, or technical expertise to help other entrepreneurs succeed. But if you do decide to "teach the business of the business," you may find it beneficial to tailor your offerings for a specific industry. For example, within my own industry there are people who specialize in teaching marketing to career coaches. This can be a particularly effective strategy for people who have an established track record of success working in their industry; their credibility tends to be far stronger than that of industry outsiders who sound good in theory but lack the practical experience to back up their theoretical expertise. To illustrate this point, let me pull a rabbit out of my hat and introduce you to Jack Turk of Redmond, Washington, who specializes in a very unique niche—teaching marketing to magicians.
### **Poof! From Microsoft to a Magical Marketer**
_"I'm a big multiple streams of income guy, and in this economy, that is not a bad thing."_
—Jack Turk, marketer and magician
On the day that Jack Turk turned fifty, he walked into his boss's office, sat down, and announced that he was quitting his job. After a fifteen-year career with Microsoft as a writer, program manager, and game designer, Jack didn't quit to ride off into the sunset—he chose to walk away from his six-figure income to pursue his lifelong passion for the magic business.
Jack first discovered the joy of magic when he was just five years old, and ever since, magic has played an important role in his life. Even when he was employed full-time, he kept up a side business as a magician, performing at family, civic, and corporate events whenever his schedule allowed. While working at his corporate job, Jack learned how to perfect his writing and marketing skills—and those skills enabled him to easily market and advertise his magic shows.
The more adept Jack became at his own marketing, the more he began to notice that his peers in the magic world seemed to struggle with that part of their business. They were skilled magicians, but they had difficulty getting enough work to support their passion. It was painful for Jack to watch. "The magic business is like every other business," says Jack. "Everyone is into what they do, and they think because they are really good at it, then the word will get out and then they will get really busy. But that is not the case. You've got to market yourself."
Jack knew that with his strong writing skills, business background, and firsthand experience as a magician, he could make money by teaching the "business of the business" to other magicians. But rather than starting his own business from scratch, he bought an established site that was run by a man named Dave Dee, who at the time was considered the "magician's marketing guru." Jack had studied with Dave and knew his materials were very helpful. Jack and Dave worked together for a year while they transitioned ownership of the site, and then Jack went from paying the guru all the money to being known as the guru himself.
Today on his website, www.magicmarketingcenter.com, Jack sells a variety of different products and services, ranging from free downloadable reports to live training events that cost thousands of dollars. His offerings include products with titles like "Success Strategies for the Restaurant Magician," "How to Create, Market, and Present Motivational School Assembly Programs for Big Profits," and "How to Make $25,000 Doing Birthday Parties Part-Time." His products and trainings are designed to alleviate the money fears that keep magicians awake at night: fears that revolve around not having enough business and not knowing what to do or say to attract more business. In addition to running his e-commerce site, Jack continues to earn income as a performing magician, working between two to three hundred events per year, the majority of which are birthday parties. And as if that wasn't enough to keep him busy, he also helps to organize technology conferences and takes on a limited number of freelance writing projects.
When asked what advice he has for others who want to build an expert income stream around their passion, Jack suggested the following.
#### **Jack's Top Three Tips for Creating a Successful Business-to-Business Service**
1. **Be an active contributor on key online sites**. Every group, every "band of brothers and sisters" has an online meeting place. Identify the popular forums in your niche and post helpful suggestions to these forums on a regular basis. People will learn to trust your recommendations, which will help them be more comfortable purchasing your products and services down the road.
2. **Know your income goals**. As an entrepreneur, it's easy to get diverted by all types of non-revenue-producing activities. Have a target for what you need to earn, and then ask yourself each day, "Am I focused on a task that supports that goal?"
3. **Get out of the house**. The notion that you can do all of your networking online is a fallacy—you have to get out and meet people. Most of Jack's income comes from people whom he has met in person, and over time they have developed strong friendships, co-branded events, and business alliances.
To learn more about how to teach the business of the business, look into the many online courses designed to teach entrepreneurs about how to create curriculum and develop classes, webinars, and training programs:
• Jen Louden and Michele Christensen have an online program called TeachNow (www.theteacherspath.com) for people who want to learn how to teach and put together their own courses.
• Pam Slim of Escape from Cubicle Nation offers an online training course called "Power Teaching" through her website at www.escapefromcubiclenation.com/power-teaching.
## **SPEAKER**
Many people fear public speaking. But even if the idea of being a public speaker scares the heck out of you, it may still be worthwhile to consider speaking as part of your income strategy. Why? Done well, speaking is the single most effective way to market your services and sell your products. People want to buy from vendors whom they know, like, and trust, and speaking gives you an opportunity to establish a personal, lively, and lasting connection with your potential customer base. And although speaking can be an intimidating prospect for certain personalities, it's helpful to remember that with a little bit of practice, speaking skills can be learned and nerves can be conquered.
If you've got industry expertise, an inspirational message, a keen sense of humor, or a unique perspective, trust that somebody, somewhere, is going to want to hear what you have to say. Speakers work in a variety of settings and presentation formats. Inexperienced speakers can try out their speaking skills at local community groups like the Lions Club, schools, churches, and synagogues. Of course, as a newbie speaker, it's unlikely that you will be paid much, if anything, for these local talks. But even if you don't earn more than a free dinner, you can leverage your talks as a marketing tool that leads to other speaking invitations. Over time, as you develop your reputation as a speaker, it will be much easier to ask to be paid for your talks.
Who will hire you to speak? You'd be surprised. There are more groups out there than you could ever imagine. Conferences, associations, corporations, colleges, the military, and even nonprofit organizations hire speakers to address a wide variety of topics. Although there is no one single topic that is _the_ golden ticket to speaking success, certain types of speakers definitely command higher fees than others: celebrities, professionals with strong technical expertise, people who can teach a "proven formula" for increasing sales or building a business, leadership experts, and motivational speakers are all in demand.
There are several different ways to generate revenues from your speaking engagements. First and most obvious is to get paid a speaker's fee, which could range from a few hundred dollars for a small group presentation to tens of thousands of dollars for prime-time keynote speeches. The exact amount you'll earn will depend on a variety of factors, but in general you'll command the highest fees from corporations and larger associations. In addition to speaking fees, you can earn income from "back of the room" sales of books, videos, and other informational products. Another possibility is to host your own speaking gigs—private presentations, workshops, and seminars—a potentially lucrative option because you get to pocket all the profits after expenses. Most speakers also generate indirect profits from their talks by using them as a platform to market their products and services. According to a survey conducted by the National Speakers Association (NSA) in 2007, the majority of professional speakers supplement their speaking income with higher-end offerings like consulting, coaching, and training services. Of course, the rewards of life as a speaker extend far beyond just the financial gains. The opportunity to speak in different places can be a very attractive perk for people who love to travel. For outgoing personalities who relish the thrill of a interacting with a live audience, speaking provides a fun way to make a living, much more so than the more solitary existence of being a writer. And for many speakers, particularly those who have a strong message to share, the opportunity to inspire, empower, and change people's lives for the better often proves to be the greatest reward of all.
**ADVICE FROM THE SPEAKING EXPERT**
**"I've always believed that work can be rewarding and fun** , **but being a speaker has confirmed it for me."**
—GILDA BONANNO, speaker, trainer, coach
Gilda Bonanno of Stamford, CT, runs her own public speaking coaching and training business and travels around the globe to places as diverse as China, Brazil, and Rome: she presents keynotes, delivers corporate training programs, and coaches individuals to be more effective public speakers. Her speaking topics range from leadership development to improvisational techniques to presentation skills. She started the business in 1996 following a career as a project manager for a pharmaceutical company and in just seven short years, she has gone from being a novice speaker to president of the Connecticut Speakers Association, past president of the Southern Connecticut Chapter of the American Society of Training and Development, and a contributing author to the National Speakers Association's flagship book _Paid to Speak: Best Practices for Building a Successful Speaking Business_ (Greenleaf Book Group Press, 2011). I asked Gilda, a former client of mine, to share her tips for people who want to break into the speaking profession, and she graciously agreed.
**What is the best way to get started in the speaking profession?**
G.B: Start by speaking about what you know. When you focus on an area where you know the issues and people, you avoid positioning yourself as a newbie speaker and instead establish yourself as an expert who also happens to speak.
**This seems like a profession where experience and age can be used to your advantage. Do you agree?**
G.B: I do! People who have proven experience in the trenches bring tremendous credibility to the table. Your audience knows that you "get it." Use your old career and established network as a bridge to new opportunities. Build on your experiences and connections and then branch out from there.
**What advice do you have for people who want to polish their speaking skills?**
G.B: The first goal is to speak as much as possible, for free if you need to. Getting experience in front of groups will allow you to refine your message and your skills. Every town has organizations and associations in need of speakers. Hone your skills by joining Toastmasters, videotaping yourself, and if needed, consider hiring a speaking coach.
**How did you learn about the business side of speaking and training?**
G.B: I joined my local chapters of the National Speakers Association and American Society for Training & Development to learn more about the business side of speaking. I also asked other speakers that I respected for their suggestions on the best resources for educating myself about the business. You need to be careful about what you buy; there is a lot of information out there that is gimmicky and only designed to make the seller money. One of my favorite books on the business of speaking is _Million Dollar Speaking_ by Alan Weiss.
**You have been very active in your professional associations. Do you recommend that to others?**
G.B: The opportunity to volunteer with professional associations is important, and it's a great way to make connections. But it's also important not to confuse going to meetings and serving on the board as [equivalent to] getting out there and being a speaker. Don't allow yourself to be pulled into that trap.
**What are some of the challenges of being a speaker?**
G.B: The travel can be tough, so be mindful of your lifestyle objectives when making your choices. Almost all of the speakers I know depend upon multiple streams of income (monthly coaching programs, seminars, membership sites, audio and video products, and so on). It enables you to weather the economic storms and generate income without the need to travel all the time.
A final note: Regardless of whether or not you want to pursue the speaking option, take seven minutes and watch Gilda's inspirational video, "28,000 Days," on her website (www.gildabonanno.com)—it will encourage you to stay focused and on task as you go through your own reinvention process.
To learn more about the speaking industry:
• American Society for Training & Development (www.astd.org)
• National Speakers Association (www.nsaspeaker.org)
• Toastmasters International (www.toastmasters.org)
• Speaker Net News (www.speakernetnews.com)
## **CREATE EVENTS AND HAPPENINGS** **FOR YOUR "TRIBE"**
People are social beings, and in a world that is increasingly connected by high-tech electronics, the need for in-person, high-touch interaction is stronger than ever. Many people want opportunities to get together, laugh, and enjoy face-to-face conversations. As you consider ways to earn money as an expert in your field, think about how you might be able to create special events, groups, and gatherings for your community. If you let your imagination go wild, you'll find that the opportunities to connect your community are almost endless. For example, you could:
• Sponsor a conference, expo, or lecture series.
_Revenue potential_ : vendor fees, admission fees, and sponsorships
• Organize a job fair, crafts fair, or gift expo.
_Revenue potential_ : vendor fees, sponsorships, and commissions from sales
• Create a support group that enables people who share a common need (for example, job seekers, entrepreneurs, caregivers) to come together to exchange resources, share leads, compare strategies, and enjoy a safe haven of like-minded peers.
_Revenue potential_ : membership fees, event fees, and sponsorship fees paid by affiliated service providers
• Organize a special trip or outing (or series of trips).
_Revenue potential_ : event fees and referral fees from participating merchants or vendors
• Plan a monthly social or learning event series.
_Revenue potential_ : event fees and referral fees from participating merchants or vendors
• Build an "online mall" where your tribe can easily sell their products and services.
_Revenue potential_ : listing fees, membership fees, and advertising revenues
• Compile essays and articles from your peers into a book.
_Revenue potential_ : income from sales of the book and partnership opportunities
• Start an association.
_Revenue potential_ : membership fees, product sales, advertising revenues, and the opportunity to earn revenues from add-on services like training programs, books, and special events
Of course, not everyone is well suited to lead a community or host group events. But for the right personality, this can be a really fun way to earn a living. Read on to learn how one business coach is generating multiple streams of income by continually innovating new events and services for her community.
### **From Artist to "Soul" Proprietor**
_"Network, network, network: sometimes you don't know where it will lead, but everything I have achieved in my business has come from a business relationship."_
—Jane Pollak, author of _Soul Proprietor_
Hard as it may be to believe, Jane Pollak used to earn her living painting eggs. Of course, these were no ordinary kitchen eggs; they were intricately painted Ukrainian Easter eggs that Jane made into jewelry and collectible pieces. They were so unique that she was even asked to make a special egg for the Easter egg roll at the White House, a contribution that is now housed in the Smithsonian Institution. Jane went on to write a book about her eggs, and her business was featured on NBC's _Today_ show.
But after spending thirty years being known as "the egg lady," Jane decided she was ready for a change. As she notes in her second book, _Soul Proprietor: 101 Lessons from a Lifestyle Entrepreneur_ (Roberts Press, 2010), "I felt that artistically I had already said everything in eggs that I needed to say." In a seeming wink from the universe, her decision to switch gears from being an artist to coaching artists was cemented when the week she was supposed to be on _The Martha Stewart Show_ turned out to be the same week that Martha went off to jail.
By the time she made the final decision to pack up her paintbrushes, clean out her studio, and shift her focus to coaching other entrepreneurs, Jane was carefully positioned for success. She had always invested heavily in her entrepreneurial education: making it a habit to listen to motivational tapes, attend seminars, and read everything she could about entrepreneurship. She served a term as president of the Entrepreneurial Woman's Network of Westport, Connecticut, a group dedicated to educating, supporting, and inspiring female entrepreneurs. As she gained confidence in her entrepreneurial expertise, Jane began to build up her speaking career: delivering motivational speeches focused on the message that if she could make a living out of painting eggs, surely others could earn their living pursuing a passion too.
Jane organized a group of local artists into the Artsy Girls, an informal networking group that continues to meet on a quarterly basis to socialize, talk about projects, and support one another in their professional and artistic endeavors. When several members of the Artsy Girls expressed interest in receiving more formal entrepreneurial education, Jane responded by creating Jane Pollak's Arts Forum, a monthly coaching group composed of ten artists eager to take their businesses to the next level. The Arts Forum proved so successful that Jane began offering group coaching to people outside her original network of artists. As she got more involved with the coaching arm of her business, Jane decided to invest in formal coach training with the Coaches Training Institute, and she earned her designation as a Certified Professional Co-Active Coach (CPCC). In addition to coaching individuals on a one-to-one basis, she offered multiday coaching retreats and she began to tour the country as a speaker, sharing her entrepreneurial lessons with both new and seasoned business owners.
Her business did extremely well until the financial downturn of 2008. But when tough times hit, Jane responded to the business challenges by revamping her offerings to be more in sync with the new economic climate. She created the Remarkable Women's networking evenings: a by-invitation-only event restricted to thirty women. (Jane often runs the events in the studios and stores of other entrepreneurs who offer their space in exchange for the free publicity and exposure.) "The energy in the room is always amazing," says Jane, noting that the events are characterized by purposeful networking and a generous spirit of sharing mixed with a large dose of fun. More recently, Jane added a webinar series to her mix of services, a lower-priced offering that has prompted long-time fans to finally become paying clients. Jane says, "I have people who I met six years ago who are now able to afford me. It's amazing how they come out of the woodwork when you are able to offer something that fits their needs."
In a field in which many coaches struggle to make a living, and at an age when most people plan to slow down, Jane, age sixty-four, is proud to say, "I earn six figures starting with the number one, working three days a week." As a new grandmother, that level of flexibility is especially precious to her—when her granddaughter Chloe was born, Jane happily promised her daughter that she would reserve one day a week for babysitting duties. But even while making more time for her personal life, she is determined to continue to "live life big," and her goals for the business remain as ambitious as ever. "My ultimate vision is to address thirty thousand business owners at Madison Square Garden," says Jane. "I don't know what the forum will be, but I see myself from the stage talking to them. Somehow that will happen."
### **Jane's Top Three Tips for Entrepreneurial Success**
1. **Don't go it alone**. Join a mastermind group, team up with an accountability buddy, hire a coach, and make it a point to always invest in education. Jane proudly admits to using all of these support systems as part of her ongoing career development. "I work very hard on myself all the time," she says. And, of course, make it a habit to network. Sometimes your networking won't yield immediate results, but over time your efforts will be handsomely rewarded.
2. **Take a measuring stick to your passion**. At this point in your life, you should choose to do work that you love. What they say is true—when you love what you do, what you do is not work.
3. **Be persistent**. Don't quit before the miracle. If you stay in the game, you're going to win.
## **RECRUITER**
Is your Rolodex bulging with business cards gathered from years of networking and business meetings? If so, you may be able to leverage those connections by working as a recruiter. This is a career option for which age can definitely play in your favor. As a veteran member of your industry, it is likely that you not only know a lot of people but also possess a real understanding of the technical expertise, personal characteristics, and skills needed to be a top performer in your field. That combination of networking connections and industry insights could help you be a very successful industry recruiter. There are several different ways you could potentially work as a recruiter:
• **Get hired by an executive search firm**. Executive search professionals help companies fill top-level management jobs and assist them throughout the hiring process—sourcing prospects, coaching candidates on interview skills, and running background checks. Successful recruiters tend to be good salespeople; they know how to bring parties together, negotiate through objections, and close deals. Executive search is the most highly compensated type of recruiting (fees can average up to 25 percent or more of a first-year salary). Be forewarned, however, that full-time recruiters with large firms tend to work long hours, including evening and weekends, so if you need flexibility, negotiate for a part-time role or work for a boutique recruitment agency instead.
• **Create your own niche recruitment agency**. You can hang out your shingle as an independent recruiter who specializes in filling jobs within a specific industry niche. For example, while researching this book, I learned of a man who had worked as a yacht club manager for many years and was starting a recruiting service that will specialize in sourcing yacht club staff. It is also possible to work as a contract researcher who does the behind-the-scenes research that helps agencies locate suitable candidates for their searches.
• **Work as a temporary recruiter**. Contract recruiters are used by companies to help staff-up for specific hiring needs, such as when a business is opening a new store or needs extra help for the holidays. You can find these opportunities advertised on the major job boards or by directly contacting temporary employment agencies.
To learn more, look into the Association of Executive Search Consultants (AESC; www.aesc.org), the professional body for the executive search industry. They offer a number of useful resources and training programs for search professionals.
## **MEDIATOR**
We live in a litigious society. But going to court is an expensive and painful process that often leaves everyone involved dissatisfied. In contrast, the mediation process allows people to come up with a solution that both parties find acceptable, without having to incur the astronomical fees and aggravation associated with filing a lawsuit. That is why more people are hiring mediators as an alternative for settling workplace disputes, divorces, and other types of contentious disagreements.
It might surprise you to learn that all that is required to become a mediator in the United States is to complete a forty-hour basic mediation training class. Of course, what is officially required and what is needed to launch a successful practice are two different matters; experienced mediators warn that completing the basic class is not nearly enough to prepare you to be an effective practitioner. If you want to be taken seriously, before you accept any paying clients you should plan to invest in further education by taking additional seminars, working at volunteer assignments, and interning—in other words, learning by doing.
There are many different ways to work as a mediator. Two of the more popular specializations are divorce and parent-child mediation, but mediators also help to resolve disputes in the workplace, religious institutions, schools, nursing homes, hospitals, and neighborhoods. If you think about your own industry, or life experience, you could probably come up with some interesting ways to specialize in dispute resolution in the field you know well. After all, you have far greater familiarity with the potential disputes common to your area of expertise than the average person, and that experience could make you a very effective mediator. To better understand how this works in practice, read on to learn how one enterprising woman from Armonk, New York, has built up a successful mediation practice resolving disputes in a most unusual specialty.
### **From Litigator to Mediator: A Heartwarming "Tail"**
_"Encouraging conversation often alleviates the need for litigation."_
—Debra Hamilton, Esq., owner of Hamilton Law and Mediation, PLLC
When you hear the term "pet business," you likely think about options like dog walker, groomer, or vet. But Debra Hamilton, age fifty-four, owner of Hamilton Law and Mediation, a firm that specializes in resolving animal disputes, has one of the most unique pet-oriented businesses you'll ever encounter. A lawyer by training, Debra worked as a litigator before taking time off to stay home with her children. But after her son entered first grade, Debra decided it was time to dust off her legal skills and return to paid employment. Reluctant to return to the stresses of life as a litigator, Debra decided instead to train as a mediator, and in 2010 she opened her mediation practice.
Why did she choose to specialize in animal-related disputes? As a lifelong dog lover and breeder of championship dogs, Debra had long been passionate about helping animals. But as a practicing lawyer, she discovered that the courts are required to treat animals like property, and as a result, the courts rarely resolve animal disputes in a way that anyone finds effective. Debra's experience with the court system convinced her that mediation is much better than litigation for resolving animal-related problems. As she notes on her website, "Treating an animal as a mere object when resolving a dispute in a confrontational litigious setting creates unnecessary contention and divisiveness." Using mediation as an alternative to litigation, Debra is able to help her clients, and their four-legged friends, find a mutually satisfactory resolution to their conflicts.
Debra helps to mediate all types of animal-related conflicts: from family-related pet issues (for example, who gets to keep the dog when a couple divorces), to conflicts involving animal trainers and veterinarians, to animal-related arguments that erupt between owners, breeders, and handlers. Using her trademark kind and gentle style, Debra guides the two feuding parties to an agreement that is a win-win for all involved. "Mediators create a venue where people can solve their own problems," says Debra. "I provide an environment where they can say what they have to say—with passion and with anger and with whatever they need to do to get the conversation to the next level."
Debra charges $500 an hour for her services (with a two-hour minimum), and most cases take about six hours to resolve. Both parties involved in the mediation assume equal responsibility for her fee, and payment is required regardless of whether or not an agreement is reached. If the conflict cannot be resolved, the parties can opt to proceed to litigation.
Having found a perfect way to blend her professional background, personal values, and passion for animals, Debra is unfailingly enthusiastic about her life as a mediator. "It is a phenomenally rewarding area to be involved with as a second career," she says, adding that it is a particularly strong fit for more mature adults who "know what they don't know." "As an older person, you bring a wealth of experience to the table," notes Debra. "That keeps you from being a know-it-all, because you know from your own experience that you don't know it all—and that helps you be an effective mediator."
#### **Debra's Top Three Tips for Potential Mediators**
1. **Mediation is a suitable career for people from many disciplines**. Debra was quick to point out that although it is very beneficial to be a lawyer in order to work as a mediator, you don't have to be, and she knows of therapists, psychologists, educators, and people from many different walks of life who work successfully as mediators.
2. **Find a niche**. Debra recommends that people interested in mediation find an area to specialize where they have a specific passion or expertise and then invest in quality training to enhance their skills. She chose to specialize in animal-related conflicts in part because her exposure to the professional dog show world gave her instant credibility as a mediator who understands the nature of the conflicts related to breeders and handlers.
3. **Be prepared to invest in training**. As previously noted, although a forty-hour training is the minimum requirement, you should expect to invest time and money in additional training to bring your skills up to par. Even as a trained and experienced lawyer, Debra completed two internships and multiple continuing education classes on top of the forty hours of required mediation training. In some jurisdictions, mediators may be limited with respect to the kinds of services they can provide, so it is imperative that you educate yourself about mediation regulations in the state where you plan to practice.
To learn more about mediation, consult:
• The Center for Understanding in Conflict
(www.understandinginconflict.org)
• Mediate.com (www.mediate.com)
• _Success as a Mediator for Dummies_ by Victoria Pynchon (Wiley, 2012)
## **PERFORMER**
Have you been keeping your "Inner Seinfeld" hidden under your lab coat or buttoned inside your blazer? If so, now might be the perfect time to finally loosen your tie, toss off your pearls, and let the world get a taste of your more creative side!
There are dozens of ways you can profit from sharing your creative spirit on stage. Jack Turk, whom you met earlier in this chapter (this page) does magic shows for a variety of audiences ranging from children to corporate audiences. Gilda Bonanno, whose advice was featured in the section on speakers (this page), is part of an improvisational comedy group that performs at corporations, charity events, and comedy clubs. But of all the interesting ways that I've seen people incorporate performing into their portfolio of activities, Bob Alper just might have the most unusual story of all. He is a rabbi who traded in his pulpit for a stage, and he now claims that he is "the world's only practicing clergyman doing stand-up comedy... intentionally." Read on and be prepared to smile—this is a fun one.
### **Profile of a Stand-Up Comic—and Practicing Rabbi (Really)**
_"I always used a lot of humor in my rabbinate, and there is a lot of rabbi in my comedy."_
—Rabbi Bob Alper
Growing up, Bob Alper found the decision to become a rabbi an easy one: the job was a good fit that allowed him to merge his desire to work with people with his strong commitment to Judaism. Bob served as a congregational rabbi for fourteen years, first in Buffalo, New York, and later in Philadelphia, Pennsylvania, while also earning a doctorate from Princeton Theological Seminary. But in 1986, after he and his wife decided that they wanted to have more time to spend at their vacation home in East Dorset, Vermont, Bob knew it was time for a change. After submitting his resignation ("I did it all properly," jokes Bob, "no scandals, same wife"), he opened an office with plans to work on a more flexible basis: officiating at lifecycle events and doing some pastoral counseling.
But less than a month after leaving his full-time position, Bob noticed an advertisement in a local paper for the Funniest Jewish Comic in Philadelphia contest. He entered the contest and came in third place behind a chiropractor and a lawyer. ("I was funnier. But who's bitter?" laughs Bob.) One of the contest judges was the host of the top-rated morning television show in Philadelphia, and she invited Bob to appear on her show. That appearance launched his career as a stand-up comedian, and within four years he was earning enough from his comedy work that he and his wife were able to move to Vermont full-time. Becoming a comic was a dream come true. "If someone had asked me what I would love to do when I was younger, I would have replied that I wanted to be a comedian," says Bob. "But the thought of making a living from doing comedy didn't seem like a possibility at the time I grew up. When the opportunity came, it was great."
Bob's training as a rabbi served him well in his development as a stand-up comic who always keeps his routines clean and appropriate. "I have this wonderful and precious title 'rabbi' that is attached to me," says Bob, "and it is always looming in the background in a very positive way. I am zealously protective of that title." His rabbinical training also comes in handy when he encounters the occasional heckler and Bob asks, "Excuse me, sir, but would you mind leading us in the silent prayer?"
Bob's brand of comedy doesn't just make his audiences laugh; it makes them think. As part of the Laugh in Peace tour, an act that has been featured on CNN and the CBS _Early Show_ , he performs with a Muslim and a Baptist minister who team up in a routine that gently pokes fun at our insecurities and prejudices. When he presents his act at colleges nationwide, Bob delights in seeing Jewish and Muslim students sitting side by side, laughing and enjoying a show together. Even when he is not busy performing, Bob is able to spread his humor through his media appearances, books, tapes, and CDs—and he still works as a rabbi conducting services for the Jewish High Holy Day services in the fall.
Bob believes that making people laugh is about much more than just comedy. In his book _Life Doesn't Get Any Better than This: The Holiness of Daily Dramas_ (Liguori Publications, 1996), Bob writes, "I nurture a mental treasure trove of special compliments that have followed my performances. Every entertainer does; it's a healthy way to emotionally balance the occasionally negative remarks. For example, I will never forget the woman who explained, 'Six months ago my husband died. Tonight is the first time I've laughed.' And I cherish the image passed on to me by a grateful husband about the way he and his wife smile during her chemotherapy treatments while they listen to my audio tape through headsets."
Bob is the first one to admit that his success as a comic is a bit of a rarity, especially for someone who is already well into his sixties. "Comedy is a tough business," says Bob. "A lot of really good people don't make it. Talent is not the only thing you need. I think I am a rare performer in that I like the business side of the business. I see it as a challenge."
Like every performer, Bob still has big dreams yet unfulfilled. He'd love to get on late night television. "I think I'm ready, although maybe I am too old or too Jewish," he says.
But no matter what, he just wants to do more of the same, whether it is making sad people laugh, making happy people happier, or bringing Muslim and Jewish college students together, if only for a few hours. "I'm sixty-six years old and doing well on college campuses," marvels Bob. "That's amazing, considering I am two generations older than most performers on college campuses. I mean, besides Cosby, who else is doing that? If I end up doing the same types of venues I'm currently doing for the remainder of my years, I'll be very happy."
#### **Bob's Top Three Tips for Aspiring Comedians**
1. **Find a hook**. It's helpful if you have an interesting angle to sell. Bob's dual billing as both a rabbi and a stand-up comic helps him to both attract media attention and fill his performances. "Four years in college, six years in seminary, three years in a doctoral program, and fourteen years serving a congregation—it was all because I wanted to be a comedian and I needed a hook," jokes Bob.
2. **Be persistent**. The best way to hone your craft is to just find as many audiences as you can. Offer to perform for free, and keep at it.
3. **Keep the faith**. Recognize that you will fail miserably. A lot. Everyone does.
**THREE FINAL TIPS FOR CREATING INCOME FROM YOUR EXPERTISE**
1. **Focus on lifestyle-friendly niches**. Think about tailoring your services to an audience whose business needs complement your lifestyle needs. For example, if you want to enjoy having your summers off, you may want to offer a service that is most in demand during the school year (for example, tutoring or piano lessons). I used this strategy early on in my coaching practice when as a young mom I wanted to be available for my children when they were home from school, and by restricting my practice to other moms, it was easier to schedule my work hours around "mommy time."
2. **Partner**. Find complementary business partners who can feed you business leads and work with you to provide services. This will reduce the amount of time you need to spend on marketing, increase your base of clients, and provide you with a network of reliable colleagues who can cover for you when you want time away from your business.
3. **Leverage your expertise with informational products**. If you are selling your expertise as a consultant, coach, or teacher, your income will be limited by your billable service hours. However, you can multiply that income by adding informational products to your line of products and services. It takes work to develop those products, but once you have created them, the opportunities for marketing them on the Internet are virtually limitless.
# **CHAPTER TWO**
# **Create an Information Empire**
How would you like to turn all the information you carry around inside your head into income? You can—and you don't need to be a recognized expert to do it. Thanks to an explosion in the affordability and variety of easy-to-use web-based tools and publishing platforms, there truly has never been a better time to turn your expertise into an informational product income stream. If you've ever thought about publishing a book, writing articles, making money from a blog, or selling informational products, this is the chapter for you. And even if you have never previously considered those options, this chapter will open your eyes to the growing possibilities for generating income from creating your own informational products. As you'll soon learn from the examples in this section, not everyone who produces informational products has strong writing skills. We are living at a time when people are increasingly getting their information via videos, podcasts, and webinars, and that shift has opened up opportunities for both literary types _and_ nonwriters to productize their expertise into multimedia products.
I invite you to use this chapter to explore the different ways to take advantage of this monetization option, starting with the relatively new world of blogging.
## **BLOGGING**
It wasn't all that long ago that if you wanted to create a website, you needed to pay a lot of money and hire a website designer to help do it for you. But those days are a distant memory. The new blogging platforms, such as WordPress, Blogger, and TypePad, have dramatically simplified the process of bringing a blog online; you can set up an impressive-looking and multifunctional blog in under an hour with little or no expense. That's good news, because if you plan on launching any sort of business in the near future, you will likely be building a blog as part of that venture.
Of course, launching a blog is relatively easy compared to building a blog that actually makes money. So how exactly do people make money with their blogs?
There are two ways to generate revenues from blogging: you can earn income _directly_ from advertising, affiliate marketing, or sponsorships revenues, or you can create income _indirectly_ , using your blog as a platform to build your brand, which in turn leads to greater interest in your products and services. Certain types of blogs tend to be better suited to the advertising model than others: sites that feature reviews of high-value products and services; sites that consistently attract repeat traffic, such as news, sports, gossip, coupon, cooking, or weather sites; and sites that cater to affluent audiences all can be good candidates for monetization.
One of the most effective ways to earn money from your blog, regardless of topic, is with affiliate advertising: a monetization model that results in referral or "thank-you" fees for recommending other people's products and services to your audience. If you've ever read a book review online, clicked on a link, and ended up purchasing the book on Amazon's sales page, there is a good possibility that the originating site earned a small affiliate fee off of your purchase. Affiliate advertising is a win-win for both you and your audience: your reader learns about valuable products and services that they might not have known about otherwise (without paying anything more in the process) and you get compensated for sharing your virtual real estate. Under the right circumstances, affiliate commissions can add up to significant income, particularly when your readers have a strong interest in the types of products you recommend. Programs that sell higher-priced digital products (webinars, training programs, and so on) can be especially attractive because many offer a 50- to 75-percent commission rate to affiliates, and those payouts can add up to hundreds or thousands of dollars in monthly commission payments for bloggers with a loyal following. Once you've built up your audience, you may be able to also secure private sponsorship deals for your blog. For example, if you write a travel blog, a cruise line or hotel may be interested in sponsoring a contest or special promotion on your site. Most experts advise that you'll need a proven track record before you can attract sizeable deals, but once you have one, those can be an attractive source of additional revenues. Of course, as with any business venture, it's not enough to just post the ads and then expect the money to roll in. It takes time to build trust with your readers. You will want to be extremely careful about who, what, and how often you choose to promote—the last thing you want to do is damage the trust of your readers by making an ill-advised recommendation.
As you can see, there are lots of different ways you might be able to create income from sponsorships and advertising on your blog. The challenge is to generate enough traffic to make that advertising worthwhile; it is a time-consuming process that takes work, dedication, and patience. It absolutely can be done, but most of you will probably find it easier to monetize your blog through these nonadvertising related methods instead:
• **Sale of informational products**. You can sell either your own products or products (webinars, e-books, and so on) from other vendors that you handpick for your audience.
• **Membership sites**. You can charge a monthly subscription fee to access a section of your site where you offer premium content to your members.
• **Speaking, consulting, coaching, and teaching offers**. Many people use their blogs as a marketing vehicle that helps to attract consulting, coaching, and teaching offers.
• **Book deals**. Did you know that the hit movie _Julie and Julia_ evolved from a blog? Blogger Julie Powell's posts about her attempt to prepare all of the recipes in Julia Child's _Mastering the Art of French Cooking_ caught the attention of a _New York Times_ reporter, which led to a book deal that ultimately led to the movie. Although movie deals are admittedly rare, Julie Powell's book deal is not a novelty; other writers have successfully leveraged their blogs to secure book deals from major publishers. (And if you can't get a book deal, you can always compile your blog posts into a self-published book, otherwise known as a "blook.")
Whichever methods you chose for monetizing your blog, be sure to focus on a topic you really care about—and one that others care about as well. Once you've settled on your topic, you'll discover that there is no shortage of different ways you can slice and dice the type of information you share: how-to instructions, commentary, musings, links to helpful resources, product reviews, listings of events and seminars, templates, recipes, or time-sensitive offers.
**THE THREE P'S OF PROFITABLE BLOG TOPICS**
If you're eager to create a blog that has the potential to generate income, you'll want to give serious consideration to choosing the right focus for your site. Here are three important elements to consider:
1. **Passion**. Passion is important for two reasons. First, it is critical to pick a topic that excites you. I know that sounds painfully obvious, but you'd be amazed at the number of people who choose to write about something simply because they think it will make them rich. The allure of "easy income" may be sufficient fuel to get you started with a blog, but blogging is a marathon, not a sprint; successful bloggers post week after week, month after month, year after year. If you can't picture yourself writing about this same topic three years from now, find something else to blog about. Second, it is helpful to choose a topic that other people are really, really passionate about. Some of the most profitable blogs revolve around people's favorite indulgences, like cars, wine, chocolate, and designer fashion. Passion-driven blogs are relatively easy to monetize with advertising because their readers are likely to buy products, accessories, and experiences related to their passions (whether they really need them or not!).
2. **Problems**. People read blogs for information, advice, and entertainment. But they _pay_ bloggers to solve their problems. Once people view you as a trusted problem solver, you'll be in a better position to monetize your site through the sale of coaching and consulting services, how-to guides, and training programs that help your readers figure out how to solve their problems more effectively.
3. **Pain**. People with problems want solutions. But people in dire pain—pending divorces, looming foreclosures, serious health issues, and the like— _need_ solutions, _fast_! If you can develop products and services that provide proven and practical strategies for getting out of pain quickly, you will have a much easier time generating sales than if you focus more on preventing pain.
Remember, if you just want to blog as a means of expression, blog away. But if you eventually want to earn income from your writing, build a blog that features a mix of the three P's—passion, problems, and pain—to create a strong foundation for profitability.
### Profile of a Food Blogger
_"My head never stops thinking about food. I dream about food. I'll go to bed and a recipe will come to me and I'll write it down."_
—Diane Eblin, health coach and blogger at www.thewholegang.org
Herndon, Virginia, resident Diane Eblin created her gluten-free food blog in 2007, shortly after her doctor informed her that she would need to switch to a gluten-free diet. She initially started the blog as a way to keep her recipes and gluten-free resources organized for her own use, but over time the blog grew into an integral component of her health coaching business. Thanks to her active online presence (her blog averages eighteen thousand views per month), Diane has been able to establish herself as an authority on gluten-free living and has enhanced her reputation as a resource for other health coaches who have clients with gluten issues. While Diane uses her blog primarily as a platform for her coaching practice, she generates some revenues from the sale of an e-cookbook and from a limited number of sponsorship arrangements with food companies. When not blogging, Diane helps her husband, Scott, run his executive coaching business, cooks, goes to yoga class, and is finishing up her studies at the Institute for Integrative Nutrition.
#### **Diane's Eight Ingredients for Successful Blogging**
1. **Learn from other bloggers**. Identify five good blogs in your niche and follow them religiously. Attract their attention by commenting on their posts. Observe the methods they use to create and maintain their audience of devoted fans.
2. **Attend blogging conferences**. Diane is a big advocate of going to blogging conferences held by organizations like BlogHer.com. She especially enjoys food blogging conferences, where she networks with other bloggers, cookbook authors, and food industry insiders. The blogging community isn't just good for business; the friends she has made at conferences have also become part of Diane's social network.
3. **Create a network of like-minded bloggers**. Diane attributes much of her success to her ever-growing network of food-related bloggers. They share information and cosponsor online blogging events that result in more traffic for all involved.
4. **Blog consistently, for search engine optimization (SEO) success**. Google rewards sites that consistently have new content; be prepared to post on a regular basis to maintain a favorable search engine ranking. Diane generally posts at least three times a week.
5. **Read for inspiration**. Coming up with new topics to blog about can get tedious, but you can gain a steady diet of inspiration from reading books, blogs, newspapers, magazines, and Twitter posts related to your field. Diane always keeps a notepad and pen by her side to capture blog inspiration when it hits.
6. **Select your blogging platform carefully**. Although it's tempting to build your blog on a free service like Blogger.com, Diane warns that you could face logistical problems if you later decide to move the blog to a platform with more robust and flexible capabilities. She is a big fan of the versatility and affordability of the WordPress publishing platform.
7. **Practice good blogging etiquette**. Bloggers share generously, but they don't take kindly to people who fail to follow good blogging etiquette (like linking back to people who link to you and giving credit where credit is due).
8. **Understand your monetization objectives**. Diane uses her blog primarily as a way to stay connected to the gluten-free community and as a means of attracting people to her coaching services. She earns some revenue from her e-cookbook and through agreements with a few select food companies. She is not a big fan of posting ads; she notes, "You need a lot of traffic to make that worthwhile."
Finally, Diane advises, "Don't be afraid to fail, and don't wait to be perfect—just start doing it!"
To learn more about blogging: There is no shortage of information about the business of blogging, but there is also no shortage of scams and unsavory operators in this space, so be careful about vetting the vendors before purchasing any of their products or advice. The more reputable vendors give away their information in abundance, so I recommend that you sign up for their free reports and teleseminars before investing in their more expensive programs. Here are three resources I have found to be especially useful:
• **Problogger.net**. Darren Rowse's book, _Problogger: Secrets for Blogging Your Way to a Six-Figure Income_ (Wiley, 2010), should be required reading for anyone interested in this topic. His website is also an outstanding resource for bloggers.
• **Copyblogger.com**. This blog features useful advice about how to write clear and compelling content, along with helpful information about the business of blogs. Lots of free information on this site!
• **ThinkTraffic.net**. This site is run by Corbett Barr, who runs a number of useful sites for people who want to learn how to run a profitable blog.
## **DIGITAL INFORMATIONAL PRODUCTS**
Constantly trading your time for money as a blogger, speaker, consultant, teacher, or coach can get tiring. And because there are only twenty-four hours in a day, there is only so much you can earn using a billable-hour model. To get yourself out of that time-for-money trap, consider turning what you know into an informational product that others can benefit from without your needing to be there. You create the product once and then continue to reap profits from the sale for as long as the market demands. That is why informational products are often referred to as passive income—although that is a bit of a misnomer, because in practice you will need to actively and consistently market the product if you want to enjoy continual sales.
There are dozens of ways to format your information into products, including audio products, mobile apps, forms and templates, bundled multiproduct programs, DVDs and videos, e-books, telecourses, workbooks, webinars, and tips booklets. Almost every day I read about another interesting informational product or package that is being sold on the Web. It never ceases to amaze me how enterprising people have become in finding novel ways to productize their expertise. Here are just three examples of ways savvy entrepreneurs are turning their knowledge into product income streams:
• The Girls' Guide to Paris (girlsguidetoparis.com) sells both mobile apps and downloadable PDFs of customized walking tours of Paris. (I couldn't resist downloading their chocolate lover's tour!) You can download one PDF for $1.98 or you can buy all ten at a significant discount. You can also sign up to be a member of their Girls' Guide to Paris Travel Club, which offers a three-tiered membership plan that ranges from a free basic service up to $575 per month for a multiservice offering.
• Nutritionist and chef Lisa Corrado (www.lisacorradonutrition.com) offers a downloadable four-week program, Ready-Set-Go! A Jump Start to Healthy Eating, for $325. The package includes four weeks of program manuals, a recipe book, daily diaries where participants can track their progress, and access to an online support community.
• Bizstarters.com, a site that provides start-up coaching, training, and resources for entrepreneurs over fifty, sells a marketing plan service ($399) that includes a downloadable marketing plan template, a one-hour telephone consultation to learn ways to improve your plan, and a final review of your revised document.
As you can see from these examples, the price point for digital products tends to be considerably higher than for paper books, especially when you start to sell bundled programs that include CDs, manuals, and audio files for several hundred dollars per package. And speaking of price points, although the prices just noted were in effect at the time this book was written, it is entirely possible that when you go to look for them the prices, or the products themselves, will have changed or even disappeared from the sites! That is one of the other benefits of creating digital products—you can alter the packaging, pricing, and product mix as often as you wish. It is a far more dynamic way to sell information than through printed products.
But as attractive as this business option appears, you can't expect to command top dollar for your products without first paying your dues; it takes time, energy, and consistent effort to build credibility with your customers. Jack Turk, the magician's marketer who you met in chapter one, says, "The dream is that you'll create a product that will sell for $200 and then you can sell a gazillion copies and the money will roll in on automatic pilot. That is not how it works. You need to create a funnel that woos the customers into buying bigger and bigger products. You want to lead the customers from a $10 report, to a $99 dollar manual, to a $500 detailed multimedia product, to a $1,000 weekend seminar, to a $5,000 ongoing coaching program. That is the real way the informational product business works."
Jack is right. And that is why most people start building their information empires in small steps. First they establish a blog, and then once they have started to build their list of interested readers, they post a simple product, like an e-book or audio file for sale. Digital downloads are the easiest informational products to create because all you need is an idea, the ability to turn a document into a PDF file, and a shopping cart service to sell the document on the web. To illustrate this point in action, let me introduce you to Pat Katepoo, a fifty-five-year-old Kaneohe, Hawaii–based woman who has been selling informational products on the Internet since the mid-1990s.
### **Helping People Create Flexibility, One Download at a Time**
_"If your informational product is born of your own experience and comes with a compelling story besides, marketing angles and media coverage will come easier."_
—Pat Katepoo, founder of WorkOptions.com
Pat Katepoo runs her flexible work options advisory service, which helps professionals carve out more time for personal priorities, from her home in Hawaii. Through the widespread sales of her downloadable flexible schedule proposal packages, she has guided thousands of working mothers, boomers, and others through the successful negotiation of a flexible work arrangement. A dietitian by training, Pat never imagined that one day she would earn her living on the Internet, selling proposal packages to people around the globe. But since 1997, she has been doing just that—consistently earning a five-figure income—while selling her products to customers mainly in North America, but also in countries as far away as Australia, the United Kingdom, South Africa, and Singapore.
Of course, like most entrepreneurs, it took Pat some time to come up with her "aha!" moment. Until age thirty-one, Pat was a single working woman with a number of married friends and coworkers. When speaking with those women, Pat couldn't help but notice how hard it was on them as they tried to juggle work and family. So when Pat got married and became both a spouse and a stepparent at the same time, she was very grateful to secure a flexible professional job working just three days a week.
One day, while enjoying one of her days off, she stopped to wonder: "Why can't all my friends do this?" That question started Pat on a journey to learn everything she could about flexible work arrangements. The more she researched, the clearer it became that although there was plenty of information on the workings and value of job flexibility, there was little how-to help for people who wanted to present their case for flexibility to their employers. Interestingly, everything Pat read emphasized that the single best way to get a manager's agreement of a flexible work arrangement was to make a strong business case in a written proposal, but nobody said, "and here is _what_ to say." Sensing a market need that was strongly aligned with her values, strong writing skills, and background in sales, Pat set out to create a user-friendly, flexible work proposal template. Initially she produced the template and planning tool as a small booklet that she sold locally, but as the Internet took hold in the late 1990s, she turned the booklet into a series of downloadable proposal packages and sold them on her website.
Online sales were slow at the beginning. It took a while before Pat figured out the best way to market her products, but she began to gain traction after sharing helpful articles with sites targeted to working mothers and other people interested in flexible work arrangements. Her website received favorable coverage from several media outlets including the _Wall Street Journal, Chicago Sun-Times_ , and National Public Radio, and that media exposure, combined with the powerful testimonials from her grateful tribe of satisfied customers, has helped Pat maintain a healthy level of sales over time.
#### **Pat's Top Three Tips for Informational Product Success**
1. **Pick a nonfiction topic that solves a painful problem among a well-defined category of people**. Ideally your topic choice will reflect not only your knowledge, but also a passion. Otherwise, you'll quickly tire of both writing about it in the short term and marketing it in the long term.
2. **Be persistent**. A quality informational product takes time to write well. Expect to go through repeated cycles of rewriting and editing. Get early draft reviews from friends. Have the final draft edited by a professional copywriter or editor. Refine it yearly based on customer input. Pat's favorite guide to clearer, crisper writing is _On Writing Well_ by William Zinsser (Harper Perennial, 2006).
3. **Share your positive feedback**. Ask for testimonials from early customers and get permission to post these—with their full names—on your new website. Displaying a page of success stories like these builds trust and helps promote future sales for years to come.
To learn more, look into reputable vendors of informational products like these:
• Copywriter and internet marketer Bob Bly's books, blogs, and informational products are filled with helpful information for anyone eager to learn more about blogging, info products, and effective writing (www.bly.com).
• Fred Gleek offers classes, products, and other useful information on the how-to of creating and marketing informational products (www.fredgleek.com).
• Rebecca Morgan's site, makingmoneyinjammies.com (see below), offers a good resource for learning more about creating informational products.
**FIVE TIPS FROM THE MAKE MONEY IN YOUR JAMMIES EXPERT**
Selling informational products can be a very lucrative endeavor. But as Rebecca Morgan, founder of the Make Money in Your Jammies e-course, says, "This is not a get-rich-quick scheme, and if anyone tells you that it is, run the other way." Morgan advises people interested in creating informational products to take these steps:
1. **Do your research before creating a product**. Consult your target market to determine whether there is a demand for your expertise before you spend a moment of time actually developing the product. Learn to use the Google AdWords tool (www.google.com/AdWords), where you can search for phrases, evaluate the market, and determine whether there is ample interest in your topic.
2. **Develop a unique spin on your topic**. Sell information that is different from all the free stuff already out there and that leverages your unique credentials and experiences.
3. **Choose a product format that is compatible with your skills**. There are lots of ways to create informational products. If you're comfortable leading a seminar, consider producing a webinar. If you're better at writing, go with e-books or print-centric products. If you hate to write, you can produce audio or video products. Don't cram yourself into a methodology that isn't a good fit with your talents and skills.
4. **Be prepared to sell**. No matter how good your product is, you need to be prepared to market it effectively.
5. **Think long term**. Although it takes a lot of up-front energy to research, write, and produce informational products, once the information is compiled, over time you'll find new ways to package and repackage it into multimedia formats.
## **PRINT PRODUCTS**
In this chapter, I focus on downloadable products because they are relatively inexpensive and easy to produce compared to printed items. But, of course, not every informational product should be sold as a download. Lots of people prefer to read their information the "old-fashioned" way, and certain types of informational products—like posters, journals, and magnets—are, by definition, intended to be printed products. Consequently there may be times when you will need to turn to a print shop to help you bring your ideas to market.
That proved to be the case for Aileen Zsenyuk of Las Vegas, Nevada, a seventy-five-year-old great-grandmother and retired business manager for a group of physicians, who developed a product called KIT (KeepItTogether) that helps people to organize and maintain their own set of personal medical records. Aileen came up with the idea for the KIT after she experienced a medical emergency that resulted in a sudden and unexpected hospital stay. Thanks to her experience working in a doctor's office, Aileen knew the importance of having her medical history readily available in case of an emergency, and the fact that she was able to share that information when she was hospitalized helped the doctors to quickly diagnose her condition.
After she recovered, Aileen made it her mission to share her potentially life-saving KIT with others. She spent a full year researching and designing the KIT, and along the way, consulted with her local SCORE office for advice on marketing, production, and other business-related issues. From the start, the KIT was conceived as a product intended for seniors, many of whom don't own a computer. "The seniors I know aren't really into computers that much," notes Aileen, who lives in a retirement community. The KIT comes packaged in a compartmentalized portfolio and includes a wallet-sized medical ID card, an incase-of-emergency medical record form designed to be posted on the refrigerator, and a fill-in-the-blank booklet where people can record their personal and family medical histories. (The KIT is sold online at www.medicalrecordorganizer.com.)
Aileen used a local printer to produce the kits. "They were so helpful all along the way," said Aileen, clearly grateful to have worked with a local vendor who took a personal interest in her product. Aileen recommends that if you want to sell your product in a printed format, it pays to get price quotes from several sources. Although online print vendors might be less expensive, price is only one factor to consider. An experienced local printer, particularly one with significant design experience, can be a critical ally in helping you develop a winning product. They may be able to both suggest ways to cut costs and help you improve the product design, and they also may work with you to market the product locally.
## BOOK PUBLISHING
Even as recently as five years ago, I might not have chosen to include book publishing as a realistic income option for semi-retirement; landing a publisher was simply too tough a hurdle for most people to clear. But times have changed, and now—as a result of the proliferation of self-publishing tools, print-on-demand technologies, and inexpensive author support services—the playing field is open for anyone willing to put in the time and effort to produce a book for sale. Given all the publishing options, selecting the best method for publishing your book—traditional publisher, e-publisher, or printing services—can be a project in and of itself. Each of the publishing models offers advantages and drawbacks, and what appears to be the best option today may be different by next year. Here is a brief comparison of the relative merits of traditional publishing versus self-publishing:
### **Traditional Publishing**
**Benefits:**
• The publisher oversees the book from concept to market (editing, design, distribution, marketing, and so on).
• The publisher absorbs all costs of publication and arranges to get the book into all the appropriate distribution channels and retail outlets. The author is paid an advance against royalties prior to the book's publication (the author keeps the advance regardless of sales).
• The author enjoys the prestige and credibility associated with being an author "accepted" by a traditional publisher—a stamp of approval that can be used to attract more lucrative business opportunities.
• Publishing companies, particularly the larger ones, have greater clout when it comes to the distribution and marketing of the book.
**Challenges:**
• The author needs to secure a book agent and write a book proposal in order to even be considered by most traditional publishers. (Some smaller publishers will accept proposals submitted directly by an author, though.)
• Publishers want to work with authors who already have an established platform and media presence; simply having a great idea is not enough to secure a contract.
• The time lapse between submitting a manuscript and actual publication can be significantly longer than with digital publishing, which can be a liability for authors writing about time-sensitive topics.
• The publishing company retains the majority of the revenues associated with the sale of your book.
### **Self-Publishing**
**Benefits:**
• The author maintains complete editorial control over the finished product (and there is no need to prepare a proposal or secure a book agent).
• The time it takes to bring a book from manuscript to market is much shorter than traditional publishing; print-on-demand technology allows authors to literally publish overnight.
• There are a growing number of "one-stop-shop" services available to help authors with every aspect of the book publishing process: from editing to layout to cover design to proofreading.
• The author retains all profits from the book (after absorbing the costs of editing, design, production, printing, fulfillment, and marketing).
**Challenges:**
• Because the author is responsible for every aspect of the book—from writing to marketing—this can be an overwhelming do-it-yourself project, particularly for first-time authors.
• This project could result in a negative cash flow (and a garage full of unsold books).
• Self-publishing still lacks some of the cachet and credibility associated with books published by a major publisher. This can be an issue if you want to use the book to attract attention in academia and/or corporate markets, although this tends to be less of a problem in other markets.
Whichever method of publishing you choose, be aware that publishing is not a get-rich-quick scheme. As much as I'd love to say otherwise, very few authors make serious money directly from the sale of their books. Although it is difficult to find firm statistics, it appears that most earn less than $5,000 per book _before_ expenses. Sadly, many great writers are not great marketers, and successful publishing often comes down to effective marketing. Of course, there are authors who make a solid living pumping out one or two books a year, or by selling in bulk to companies and associations, but for most people, especially nonfiction authors, the financial benefits of publishing come primarily from lucrative speaking engagements, consulting assignments, and higher coaching fees that the author commands as a result of the book.
In spite of the challenges, there are still many compelling reasons to publish a book. Even with all the other media out there, or perhaps because of it, the prestige associated with "being the author of" is hard to replicate with other informational product formats. Publishing a book, especially in business circles, can open doors to opportunities that might have previously been out of reach. The process of researching and writing the book can increase your knowledge base and make you an expert in your field. And on a personal level, most authors find tremendous satisfaction in publishing a book: it can be a meaningful way to leave a legacy, share new ideas, or contribute to the greater good.
To learn more: Not surprisingly, there are numerous books, websites, and informational products available to help people learn about all aspects of the publishing world. Here are some of the resources I have found helpful in my own publishing endeavors:
• **Websites for writers**. There are lots of websites for people interested in writing books, but I think the best place to start is with a visit to WritersDigest.com. _Writers Digest_ has been around for over ninety years (originally in print format), and they are considered the destination site for writers who want to hone their craft and learn the business. Here are a few more helpful sites:
Gotham Writers Workshops (www.writingclasses.com) and Media Bistro (www.mediabistro.com) both host reputable training programs for writers.
Self-Publishing Resources (www.selfpublishingresources.com) was created by Marilyn and Tom Ross, whose books about self-publishing are industry classics.
• **Print-on-demand services**. It's amazing what you can learn about print-on-demand simply by visiting the websites of the major print-on-demand services, including Amazon's CreateSpace (www.createspace.com), Lulu (www.lulu.com), and Lightning Source (www1.lightningsource.com). They are great resources for educating yourself about the features, benefits, and costs associated with this publishing platform.
• **Local resources**. Your local library or community college may offer introductory classes about book publishing and book marketing. Explore the possibility of joining a writers' group to hone your writing skills.
## FREELANCE WRITING
Finally, if you love to write but don't want to get involved with publishing products, then you might want to explore freelance writing. Possibilities for freelance writing include the following:
• **Writing "ghost" blog posts**. Many business owners want to have a blog, but they have neither the time nor the inclination to write their own blog posts. As a result, there is a market for freelance blog writers. Newbie bloggers typically start at the low end of the pay scale (under $50 per post), but seasoned bloggers and people with a strong technical or industry expertise can command several hundred dollars per post. Sites that post blogging jobs include ProBlogger (jobs.problogger.net), BloggingPro (bloggingpro.com/jobs), and Blogger Jobs (www.bloggerjobs.biz). In addition, you can find such positions listed on major job boards like Indeed (www.indeed.com) and Career Builder (www.careerbuilder.com).
• **Business writing**. Companies, associations, and nonprofits utilize freelance writers to produce content for their newsletters, websites, and other publications. They also hire writers to craft speeches, write position papers, issue press releases, and develop marketing collateral. These jobs are especially well suited for people who have a combination of strong industry expertise and good writing skills.
• **Technical writing**. Whenever any new product involving technology is released to the market, there is a need for some type of brochure or material to explain it. Technical writers who possess the combination of strong writing skills and the ability to explain complicated concepts in easy-to-understand language—along with strong technical, scientific, or financial expertise—can command a high rate for their in-demand talents.
• **Magazines and newspapers**. Freelance writers get paid to write articles for popular magazines, trade journals, and newspapers. Newspapers and websites hire subject matter experts to write columns, provide commentary, and respond to readers' questions.
As you review this list, think about ways you might be able to use your unique industry expertise and insider knowledge to your competitive advantage. Then spend some time exploring the many resources and courses available to help you learn about the world of freelance writing.
To learn more, in addition to the resources already mentioned in this section, here are some of my favorites:
• The Well-Fed Writer (www.wellfedwriter.com) is a site targeted for business writers.
• The American Medical Writers Association (www.amwa.org) and the Society for Technical Communication (www.stc.org) are appropriate for technical writers.
• Freelance Writing Jobs (www.freelancewritinggigs.com) is a useful site for finding freelance job leads, writing tips, and business advice.
**THREE FINAL TIPS ON CREATING AN INFORMATION EMPIRE**
1. **Focus on producing "how-to" information**. There is an almost limitless appetite for "how-to" information, and as long as you can explain things in a clear, organized, and practical style, you don't need to be an exceptionally great writer to make money from your informational products. Your buyers will be more interested in your expertise than in your literary talents.
2. **Try things out with a blog first**. Writing a blog is an easy way to test out your writing chops; you can blog in small increments, change things up depending on your mood, and use the blog as a way to gauge reader's interest in your expertise.
3. **Take advantage of free teleclasses, downloadable reports, and seminars**. I have been amazed by the high quality of the free introductory teleclasses, downloads, and seminars presented online by the different sites that are selling services in the informational product and blogging space. Granted, there are some that are little more than thinly-veiled sales pitches, but in general, you can learn a surprising amount about a number of business-related topics without ever paying a dime. These classes are filled with useful information and provide a helpful way to vet vendors before you invest in their more expensive educational products or services.
# CHAPTER THREE
# **Start a Small Service Business**
This next chapter is for all of you who would prefer to find a way to make money that doesn't require you to make speeches, write books, or teach. Clearly not everyone is cut out for life as an "expert," and fortunately there is plenty of demand for people who want to run other types of businesses. One of the easiest ways to do this is with a service-based business that helps companies and people with the day-to-day demands of their lives. For lack of a more technical term, I refer to these as the let-me-help-make-your-life-easier category of businesses: a variety of services that alleviate the pain, drudgery, and worry associated with the endless chores we all juggle on a daily basis.
Here are five reasons why service businesses are a particularly good fit for people looking for a lifestyle-friendly career during semi-retirement:
1. **Low start-up expenses**. Small service businesses require little start-up capital compared to brick-and-mortar businesses; you probably already own the basic equipment and tools you'll need, your marketing expenses should be minimal, and in most cases you won't require much additional training to do your job well.
2. **Built-in repeat business**. There will likely be an ongoing demand for your services—dogs must be walked every day, the elderly need rides to appointments several times a week, and self-employment taxes need to be filed on a quarterly basis. As a result, after you have secured a steady stream of customers, you can reduce the time you spend on marketing efforts and increase your billable working hours. Spreading the word about your services will happen organically. Once people find a reliable provider, they are more than happy to share your name with friends—Glen tells Lindsey, who tells Bruce, who tells Grace—and before you know it, you've got a full roster of satisfied clients.
3. **Life experience—a valued asset**. Local services businesses are a natural fit for "older" people who bring a lifetime of experiences—raising children, caring for pets, running homes, and dealing with aging parents—to their work. Personal qualities that tend to come easily to people over fifty, like maturity, a strong work ethic, and empathy are also highly valued and appreciated.
4. **A lifestyle-friendly pursuit**. Although not all service businesses can be run on a flexible basis, the ones highlighted in this chapter can largely be operated on a more part-time schedule.
5. **A scalable business**. Service businesses are relatively easy to scale up or down; you can start your business with a handful of customers and then choose to grow the business as time and resources allow.
All of these features combine to make service businesses an appealing, albeit not always terribly glamorous, income option. Please be aware that many of these opportunities are subject to zoning, licensing, and insurance restrictions, so always do your homework and file the needed paperwork before opening for business.
**THREE OUTSTANDING FREE RESOURCES FOR ENTREPRENEURS**
Making the decision to start a business, even as a part-time entrepreneur, means you will have to learn the basic financial, planning, marketing, and administrative skills necessary to run a successful business. Here are three outstanding resources that can help you through every step of your entrepreneurial journey:
1. **Small Business Administration (www.sba.gov)**. The SBA is a goldmine of information for new entrepreneurs—a must-visit for anyone starting a new venture.
2. **Small Business Development Centers (SBDCs) (www.sba.gov/content/small-business-development-centers-sbdcs)**. The SBDCs are located in all fifty states, as well as the District of Columbia, Puerto Rico, and the US territories. They offer free and low-cost workshops on dozens of topics including pricing, marketing, and leadership.
3. **SCORE (www.score.org)**. SCORE provides free one-to-one mentoring services and educational workshops for people who need assistance with starting, managing, and growing their businesses.
## HANDYMAN OR HANDYWOMAN SERVICES
If you have a knack for fixing, repairing, or sprucing things up around the house, you can build a business around your fix-it talents. In most communities, there is an inexhaustible demand for people to complete basic repair jobs, small painting projects, and other tasks on the "Honey-do!" list. Although it might seem like people should be able to do these jobs themselves, the reality is that lots of people—the elderly, two-career couples, and people with two left thumbs—simply lack the time, tools, and desire to take care of these tasks on their own. You can offer your services on an as-needed basis, or you can sell packaged services to maximize your profits. For instance, if you live in an area where winters are harsh, you could offer snowbird services for absentee homeowners; if you live near a retirement community, you could market a "move-in" service helping people to install computers, hang pictures, and assemble furniture; and during December you could sell a holiday package that includes the delivery and disposal of Christmas trees, hanging of holiday lights, and display of holiday decorations.
In general, marketing this line of work tends to be a low-budget affair; you don't need to invest in a fancy website or a big advertising campaign to attract clients. This is a business that depends heavily on word of mouth and personal referrals, so the best marketing technique of all is to consistently deliver a quality service at a fair price. It also helps to spend time at networking events where people can meet you and see that you are the type of person they would be comfortable inviting into their homes.
## **PERSONAL SUPPORT SERVICES**
Life is hectic, especially for time-starved working parents and busy executives, and there never seem to be enough hours in the day to handle all the chores that need attention. As a result, there is a need for outside vendors to do the many things people don't have time to do themselves: tasks like grocery shopping, paying bills, waiting for delivery people, and picking up prescriptions. If you are the type of person who loves to run errands, organize clutter, or assist people in need, here are some variations of personal support services you could offer:
• **Concierge services**. Hotels have long provided concierge services to their guests, but in recent years this service has expanded to hospitals, office complexes, and residential living communities. Concierge literally means "keeper of the keys," and as a concierge you'll help your clients locate tickets to sold-out shows, arrange for limousines, make last-minute dinner reservations, and otherwise make the impossible, possible. People who work as concierges for companies or residence centers may also plan day trips, golf outings, and holiday events. Although many concierges do work on a full-time basis, people who run their own concierge services tend to work on a more flexible schedule. To learn more about this career, consult the National Concierge Association at www.ncakey.com or _Entrepreneur_ magazine's start-up business guide for people interested in creating their own concierge service, www.entrepreneur.com.
• **Postpartum doula**. The first few weeks following childbirth can be a stressful time for new parents. For past generations, family was almost always on hand to help out, but in today's world, many new parents don't have family living nearby. This has created the need for postpartum doulas—trained helpers who provide assistance with breastfeeding support, cooking, light housekeeping, and other household-related chores. Doulas may work independently or through an agency, and assignments last anywhere from a few days to a few weeks. To learn more about this profession and options for certification, consult DONA International, the world's oldest and largest doula association at www.dona.org.
• **Personal chef**. Busy people don't have the energy or time to cook dinner every night, but they still want to enjoy nutritious and tasty home-cooked meals. If you love to cook, consider investing in a career as a personal chef who plans menus, shops, and prepares customized meals for one or more client households. In addition to providing in-home personal chef services, you could also cater small dinner parties, office luncheons, or small charity events. Keep in mind that because you will be working with food, it is imperative that you check out licensing and zoning requirements before you hang out your shingle for business. To learn more, consult the United States Personal Chef Association at www.uspca.com.
• **Personal shopper**. Shopping is a favorite leisure activity for many of us. But did you know that some people actually get paid to shop for busy families, wealthy people, and companies? Personal shoppers help people who either don't have time to shop or lack confidence in their ability to select the "perfect" gift or outfit. If you love to shop and have impeccable taste, this could be a really fun way to profit from your passion. To learn more, look into the Association of Image Consultants International at www.aici.org or take a look at the _How to Become a Personal Shopper_ guides sold at Fabjob.com or Entrepreneur.com.
• **Driving services**. People hire drivers for all different reasons: executives need transportation to the airport, parents need children shuttled to after-school activities, and seniors need help getting to and from doctor's appointments. If you have a comfortable car, a friendly disposition, appropriate insurance coverage, and a clean driving record, you could offer your driving services as a budget-friendly alternative to the pricier commercial limousine and town car companies. Or if you own a truck, you could do dump runs or assist with small local moving jobs. Most people advertise this type of business using inexpensive marketing strategies like posting flyers on local bulletin boards and word-of-mouth referrals.
• **Professional organizer**. If you have a flair for organizing data, cleaning clutter, or making order out of chaos, a career as a professional organizer might be a smart match for you. Organizers help people clean out cluttered garages, organize files, and set up more efficient billing systems. Many professional organizers have a recurring schedule of services that they bill their clients for on a monthly basis. To learn more, consult the National Association of Professional Organizers at www.napo.net; they offer a number of helpful training programs and resources.
## SENIOR CARE SERVICES
More people are living longer than ever before, and with over seventy-six million baby boomers approaching retirement, the demand for eldercare services is certain to explode. Many seniors need help with both the basic tasks of daily living and the administrative needs connected to estate planning, medical claims filing, and bill paying. If you enjoy working with people in the same age group as yourself (give or take a few years), here are three ways you can turn that interest into a business:
• **Senior move managers**. Senior move managers help people juggle all the issues involved with cleaning out their homes and relocating to a new residence. Additionally, they work with individuals who choose to stay in their own homes but need help streamlining their possessions and organizing their space. This is a business where your older age will work in your favor; according to a survey conducted by the National Association of Senior Move Managers (NASMM) in 2010, 75 percent of their members are age fifty or older. To learn more, visit www.nasmm.org.
• **Medical claims assistance professional**. As most of us know from personal experience, dealing with medical insurance claims can be a massive headache, and if handled incorrectly, you can lose a lot of money needlessly. Medical claims assistance professionals help people negotiate through the medical insurance system: they file and track claims, check the accuracy of bills, and advocate on their clients' behalf when negotiating claims with insurance companies. Although there is currently no certification needed in this field, most claims assistance professionals have previously worked for insurance providers or in a doctor's office and/or have extensive personal experience in this arena. To learn more, consult the Alliance of Claims Assistance Professionals at www.claims.org.
• **Geriatric care managers**. If you have a background as a nurse, social worker, gerontologist, or other professional involved with eldercare, you might want to explore options to become a geriatric care manager who assists seniors (or their family members) with making decisions regarding long-term healthcare and living arrangements. Care managers visit their clients in their homes, assess their needs, arrange for care services, and monitor ongoing care. In addition, they can be a resource for families of older adults and others with chronic needs, including those suffering from Alzheimer's and other dementia conditions or Parkinson's disease. Care managers can work independently, freelance through an agency, or be employed by a larger senior care or residential institution. For more information about this career, including certification options, consult the National Association of Professional Geriatric Care Managers at www.caremanager.org.
### **Turning Clutter Into Cash: Profile of a Senior Move Manager**
_"At age sixty-eight, I am a comfort to other people precisely because I am not a kid."_
—Beth Chapman, senior move manager
For nearly twenty years, Beth Chapman worked as a public relations consultant to the financial services industry, helping to develop public relations and marketing programs. But when the 2008 financial crisis took a heavy toll on her clients, she began to look for other opportunities outside of the financial services world. A friend who knew Beth was exploring new careers sent her a newspaper article about senior move managers who help people manage the daunting process of downsizing and moving to a new residence.
Beth was intrigued by the idea for several reasons. She had been wanting to start a business that would serve the large population of retirees where she lived in Cape Cod, Massachusetts; she liked the fact that it wouldn't take much capital to get a business like this started; and because she had personally moved homes eighteen times, settled five estates, and served as the chairperson of her church's white elephant sale, she knew she had the experience needed to succeed as a move manager. After going online and reading about the annual conference of the National Association of Senior Move Managers (NASMM), Beth was sold on the concept. "I wanted to attend every seminar they were offering," recalls Beth. "That for me was the key deciding factor."
She flew out to the conference and, as anticipated, had a wonderful time meeting people and learning about the industry. The people she met came from a wide variety of backgrounds as social workers, home stagers, and movers. They had more years than Beth in the moving industry, but few of them had much experience with public relations. The more she networked, the more Beth began to realize that there could be an opportunity to both start her own senior move manager business _and_ help other senior move managers publicize their businesses too.
While mulling over the possibilities for teaching PR to her peers, Beth set about building her own senior move business, Extra Daughters (www.extradaughters.com), a service to help people in her community declutter, organize, and relocate. As part of her offerings, she developed a Life Legacy Party, a system that helps clients to inventory their "treasures" and then distribute them in an orderly, fair, and meaningful way to family and friends. As she built her business, Beth tried out different types of marketing and advertising strategies and kept notes on which strategies worked best. She discovered that some of her most effective advertising tools were decidedly low-tech techniques, such as posting flyers on bulletin boards. The homespun feel of her local community outreach seems to resonate with this demographic more effectively than a glitzier marketing campaign. "Bulletin boards are big," says Beth, noting that more than three-quarters of her inquiries come from bulletin boards. She also bought vinyl letters for her car, registered it as a commercial vehicle, and turned it into a moving billboard. "I get comments all the time," laughs Beth. "It is a low-budget way to market."
Beth is already looking forward to attending her next NASMM conference, but at that event she will do double-duty as both an attendee and a presenter speaking about public relations strategies. By that time, she will have tested out many of her suggestions in her own business, and she thinks that real-world experience will boost her credibility with her audience. Beth hopes that the conference will serve as a launch pad for what she terms a "new branch" of her public relations services. "I am focusing on the Big M's: money and moving," says Beth, who plans to continue to work with her financial service clients along with her new senior move manager clients.
Assuming that this new branch of her business takes off, Beth plans to hire people to assist with the hands-on tasks of Extra Daughters—a task she anticipates should prove easy, given all the retirees in her town. She readily admits that she has a lot on her plate, but she insists she would not do it any other way. "My bottom line is that if you've got the energy and you're not done yet, then do something you'll really enjoy. You probably have already paid your dues doing jobs you don't really like much," says Beth. "At this stage in your life, you don't have time to do that again."
#### **Beth's Top Three Tips for Potential Senior Move Managers**
1. **Attend the NASMM national conference**. The conference is a wonderful way to learn and meet your industry peers.
2. **Partner with complementary service providers**. Go to the local senior living facilities in your area and speak with them to see if you can help their residents with their relocations. (Some facilities offer this service as a "gift" to entice prospects to become new residents.)
3. **Use your age to your advantage**. "I had no qualms age-wise about doing this; I relate well to this population," says Beth.
## PERSONAL/HOME IMPROVEMENT SERVICES
For better or worse, we live in a world where appearances matter. It can make the difference between success and failure in many different situations, whether it is a job interview, a first date, or an important business meeting. And because image is so important, people are willing to pay good money for assistance in this area. If you are someone with impeccable taste, savvy style, flawless manners, or a great eye for design, here are some ways you could turn your personal panache into profits:
• **Image consultant**. Image consultants teach people how to present themselves in the best light possible. They help people choose the most flattering clothing, show them how to apply make-up, and advise them on selecting attractive accessories. Many image consultants also offer personal shopping and wardrobe consultation services. Some image consultants specialize in meeting the needs of specific niche populations such as business executives, celebrities, or politicians—or people who have special wardrobe challenges because they are full-figured, petite, or tall. Image consultants are hired by both individuals and organizations to provide seminars and coaching services. To learn more about how to train as an image consultant, consult the Association of Image Consultants International at www.aici.org.
• **Etiquette or protocol consultant**. Are you a fan of Emily Post? If so, you may be able to turn your passion for etiquette into profits. Companies hire protocol consultants to teach their executives about the norms and customs of other cultures; parents pay to have their children schooled in the social graces of everyday table manners, proper telephone etiquette, and other social niceties; and universities hire consultants to teach business etiquette to their graduating students. To learn more, consult the International Association of Protocol Consultants and Officers at www.protocolconsultants.org, or explore the different etiquette classes offered by the Emily Post Institute at www.emilypost.com.
• **Home staging services**. Home stylists and staging professionals help people beautify their homes by rearranging furniture, adding accessories, and making other small changes that enhance the visual appeal of the house in a budget-friendly way. This is an especially useful service for people who are trying to sell their homes since stagers know how to "neutralize" a home's appearance in order to improve the likelihood of a sale. No advanced degree is necessary for this occupation; people with a flair for design can become stylists without any training or certifications. If you want to get training, there are a number of workshops and products to help you learn about this business. For more information, consult www.redecorate.com or www.stagedhomes.com.
## BUSINESS SUPPORT SERVICES
Most small companies these days run "lean and mean"; consequently they tend to outsource their administrative, technical, and bookkeeping tasks to freelance service providers. If you have strong business, financial, or technical support skills, this can be a good way to use your skills without having to drag yourself into an office every day. Here are several ways to potentially earn a living in the business services field:
• **Virtual assistant (VA)**. Virtual assistants support business people with their administrative, creative, and technical needs. They provide a convenient solution for the growing population of home-based entrepreneurs who have periodic needs for assistance, but can't justify the cost of hiring a full-time support person. If you have a background as an administrative assistant or strong office skills, life as a VA is an attractive option to consider. Unlike traditional administrative workers who must commute to an office, most VAs work remotely from their own home office locations, handling tasks including correspondence, data entry, billing, and making travel arrangements. For more information, consult the International Virtual Assistants Association at www.ivaa.org.
• **Bookkeeper**. Many entrepreneurs lack the inclination and time to keep their own financial records. But like it or not, bookkeeping is one of those tasks that has to be done, and that drives a strong demand for freelance bookkeepers. Bookkeepers' duties can range from minimal record-keeping responsibilities to handling all tasks leading up to the preparation of financial statements and tax forms. Even if you have no prior experience as a bookkeeper, you can learn these skills fairly quickly; many community colleges and distance learning programs offer basic bookkeeping classes that prepare you to take the National Certified Bookkeeping Exam. Although certification is not required, this credential is very helpful to distinguish you from the competition. To learn more, consult the American Institute of Professional Bookkeepers at www.aipb.org or the National Association of Certified Professional Bookkeepers at www.nacpb.org.
• **Editor or Proofreader**. As more of our communication takes place via e-mail and the Internet, there will be a continuing need for people with strong editing and proofreading skills. Anyone who publishes content, maintains a web presence, or sends correspondence is a potential client, but the demand is especially strong among professionals who routinely produce a large volume of content, such as bloggers, lawyers, and publishers. To learn more about this career, consult the Editorial Freelancers Association at www.the-efa.org and the National Association of Independent Writers and Editors at naiwe.com.
• **Translator**. As the United States becomes an increasingly multilingual nation, the need for qualified translators will continue to grow. Doctors, lawyers, insurance agents, and other professionals who routinely deal with the public need help translating correspondence and documents for their multicultural customer base. Although the market is currently strongest for Spanish-speaking translators, there is also a demand for people who can translate other languages including Chinese and Arabic. You can learn more at the American Translators Association website, www.atanet.org, and you'll also find translation opportunities posted on many of the major job boards.
## PET CARE SERVICES
People love their pets, sometimes as much as or more than they love their own children! According to the National Pet Owners Survey sponsored by the American Pet Products Association, Americans spent over $50 _billion_ on their beloved pets in 2011. Although much of that money was spent on food and healthcare, there is still plenty being spent on pet pampering and pet care services. If you're a die-hard pet lover, here are some lifestyle-friendly career choices to explore:
• **Doggie daycare**. At a time when so many people are working long hours, the demand for doggie daycare services is on the rise. As a daycare provider, you will be responsible for feeding, walking, and playing with the dogs while their owners are busy at work. Whether you choose to run a daycare service out of your home, through a franchise, or at a leased business location, you'll likely find plenty of customers eager to use your services, although you should be aware that the demand for your services is likely to be greatest during the summer months and peak vacation times, so this could put a crimp in your personal travel plans. For more information about careers in doggie daycare, consult Pet Sitters International at www.petsit.com.
• **Dog walking**. Dog walking is an easy business to start, a great excuse to get exercise, and a surprisingly lucrative enterprise for people who work in major cities (some New York City–based dog walkers earn in excess of six figures annually, although they are admittedly a rarity). Start-up costs are minimal, and it can be relatively easy to build up a steady stream of clients after you establish yourself as a caring, trustworthy, and reliable provider. Believe it or not, you can even get certified in this line of work by attending the Dog Walking Academy, a four-day intensive training workshop designed to equip you to start your own dog walking business. You can learn more about the Academy and other dog-related business opportunities at www.dogtec.org.
• **Pet photography**. Pets are an integral part of the family, so it's no surprise that an increasing number of people are willing to pay for professional portraits of their four-legged friends. And it's not just dogs and cats who are posing for portraits. Equine photography is a growing subset of the pet photography business, with opportunities to find business at horse shows, race tracks, and equestrian centers. To learn more about business opportunities as a photographer, check out Virtual Photography Studio at virtualphotographystudio.com.
• **Pet paraphernalia**. From Halloween outfits to gourmet biscuits to eco-friendly bath products, pet owners are eager to indulge their furry friends with special toys and treats. You can sell your goodies at craft shows and local pet stores or on the Internet. If you don't want to create your own products, consider becoming an independent sales rep for one of the direct sales/home party companies that specialize in pet-related products (check the Direct Selling Association at www.dsa.org for listings).
• **Grooming services**. Nothing spruces up a pet's appearance quite like a good shower and shave—so to speak. Pet grooming services can be operated in stores, private homes, salons, and in mobile pet grooming vans. If you are leery about creating a pet grooming business of your own, investigate the options for buying into a pet grooming franchise (for listings, check www.entrepreneur.com).
To learn more about careers and business opportunities in the pet arena, consult these websites:
• The American Society for the Prevention of Cruelty to Animals offers a wealth of information at www.aspca.org/about-us/faq/animal-careers.aspx.
• DogTec.org: This site has a number of excellent articles and training resources for people interested in starting a pet business.
As you can see, the options for turning your passion for animals into profits are many and varied. And if this niche intrigues you, I can think of no better way to demonstrate how you can turn your love of pets into a full-fledged business than to introduce you to Sharon Sakson. I spoke with Sharon right before Thanksgiving 2011 and was delighted to discover that among her many different income streams, she helps coproduce the televised broadcast of the Kennel Club of Philadelphia dog show on Thanksgiving Day, the most viewed dog show of the year. As you'll soon learn, Sharon has turned her lifelong passion for dogs into a robust and multifaceted income portfolio.
### **Portrait of a Dog Lover Extraordinaire**
_"I absolutely love my work. It is the most wonderful thing in the world."_
—Sharon Sakson
Many of us love our dogs. But Sharon Sakson doesn't just love dogs; she has built an impressive career around that passion. As was the case for many of the second-act stories featured in this book, it took a while before Sharon was able to craft a career around her passion. After graduating from college, she settled into the broadcast news world with jobs that included a field production assignment with _ABC Nightly News_ anchor Peter Jennings. Life in the news world was hectic, but even with her packed schedule, Sharon always found a way to spend time with her dogs. In addition to keeping dogs as pets, she worked as a breeder, participated in dog shows, and studied to become an accredited American Kennel Club (AKC) dog show judge.
All went well until the economic downturn of 2008 when Sharon lost her job. At the time, she was just fifty-six years old, and at a point when she was neither financially nor emotionally ready to retire. Fortunately it didn't take Sharon long to reconfigure her dog-related hobbies into work that generated a full-time income—a multipronged career that takes advantage of her passion in a variety of interesting ways. Although the transition was a difficult one, Sharon says she now finds herself busier and happier then ever.
Today she travels the world as an AKC international dog show judge and has visited numerous countries including Canada, England, France, Italy, Switzerland, Germany, Russia, Finland, and Taiwan. She also works as a breeder of champion whippets and Brussels griffons, and although the income she earns as a breeder is relatively low, it helps to offset the considerable costs of caring for and showing her dogs in competitions. While at those competitions, she is able to network with other judges and handlers, and just as with any other profession, the more people she meets, the more opportunities for judging come her way.
In addition to her breeding and judging activities, Sharon writes about dogs. She is a contributing columnist to _Dog News_ magazine and the author of several books about dogs, including: _Paws & Effect: The Healing Power of Dogs_ (Spiegel & Grau, 2009), _Paws to Protect: Dogs Saving Lives and Restoring Hope_ (Alyson Publications, 2008) and _Paws & Reflect: The Special Bond Between Man and Dog_ (Alyson Publications, 2008). Her books feature heartwarming stories about dogs as healers, rescuers, and faithful companions. But unlike so many other books in this genre, hers are more than just feel-good stories; Sharon includes scientific studies and research to substantiate her claims about the human-like qualities of the featured dogs. Sharon also earns income from speaking engagements and offering private consulting services to help dog owners with their dog-related behavioral issues and questions.
In between juggling her many income-generating activities, Sharon always makes time to relax and enjoy her household full of dogs. At the time we spoke, she was caring for eight dogs and a litter of six puppies, a task that some would consider a full-time job all its own. (Not surprisingly, our interview was interrupted several times by the sound of dogs barking in the background!) She is also involved with Xolos for Chronic Pain Relief, a nonprofit organization that matches Xolo puppies, a unique therapeutic dog breed, with patients suffering from chronic pain conditions. And finally, as if that was not enough to keep her busy, Sharon continues to do television production work on a freelance basis whenever time allows.
#### **Sharon's Top Three Tips to Profit from Your Pet Passions**
1. **Familiarize yourself with the American Kennel Club's offerings**. The AKC website www.akc.org, is an outstanding resource for breeders and dog lovers.
2. **Be prepared to work hard (and long) to train as an AKC judge**. Although dog judging may seem simple to the untrained eye, judges have to meet the exceedingly rigorous standards set by the American Kennel Club. These include a minimum of twelve years' involvement in the diverse field of dog competitions, breeding of at least five litters of champion dogs, and successful completion of a series of examinations. To learn more, consult www.akc.org.
3. **Network**. Networking is as important in the dog world as it is in the business world. Sharon's diverse income streams provide her with opportunities to attend different events where she can continually make new acquaintances, and that, in turn, has helped expand her income potential.
**THREE FINAL TIPS FOR PEOPLE INTERESTED IN PURSUING A SERVICE BUSINESS**
1. **Don't underestimate the value of your talents**. Most of us have a tendency to underestimate the true worth of our skills and experiences. But keep in mind that what may come naturally to you may not come so naturally to others. You might think nothing of your ability to easily cook nutritious and tasty meals, but to the person who eats on the run and is craving a healthy alternative, that skill can be invaluable.
2. **Be honest about your lifestyle objectives**. Define what a good work-life balance means to you before investing money in a business. If you really want to work only ten hours a week, you don't want to work weekends, and you have no interest in doing much marketing, you need to focus on service businesses where those time constraints won't be a major problem. This doesn't mean you lack ambition; it simply means you're being honest about how much work you can comfortably handle. Some of these businesses require you to be on call and respond to emergencies, whereas others can be done on a by-appointment-only basis. Pick and choose accordingly.
3. **Write a basic business plan**. No matter how big or small your potential business, it's a good idea to write a basic business plan. It doesn't have to be anything lengthy or fancy; think of a business plan as a roadmap that outlines what your business is, where you plan to go with it, and how you plan to get there. It is a fluid document that can (and should) be amended as time goes on. For help with the basics of writing a business plan, consult your local SBA or SCORE office.
# CHAPTER FOUR
# **Pursue a Business-in-a-Box Opportunity**
If the thought of creating your own business from scratch makes you uncomfortable, you may instead want to consider a business-in-a-box opportunity, such as a franchise, direct sales, or licensing arrangement. When you invest in a business-in-a-box, you eliminate many of the headaches associated with starting your own company. Instead of having to create your business from the ground up, you get to take advantage of a proven and successful business model; they've already worked out the kinks, developed best practices, and built the infrastructure for you. Of course, there is a price tag associated with this level of convenience. The cost of buying into a business-in-a-box model ranges from a few hundred dollars for a simple starter kit to hundreds of thousands of dollars for a more elaborate franchise.
In this chapter, you'll learn about four different types of business-in-a-box opportunities: direct sales, franchises, licensing agreements, and business start-up kits. I've also included a fifth option—selling through online marketplaces such as eBay—because, although technically not a business-in-a-box model, it offers you much of the same support, community, and infrastructure as a business-in-a-box system. You'll be pleasantly surprised by the range of possibilities in our global economy—the options available today are far greater than just McDonald's or Amway.
## DIRECT SALES COMPANIES
I suspect more than one of you will read this title, roll your eyes, and think, "Really, Nancy? You are going to try to convince me to become an Avon salesperson? C'mon now!" I hear you. Like many people, I used to think direct sales was a career best suited for stay-at-home moms or for people who couldn't find a "real" job. I equated direct sales with one of two things: unscrupulous pyramid schemes and unwanted invitations to home parties where I'd be pressured to buy products I didn't want, like, or need. Even worse, once I was at the party, I would be asked to sit through a sales pitch to learn about "an opportunity of a lifetime" guaranteed to make me millions. Ugh!
But over time I've met too many impressive people who are successfully working in direct sales to continue to dismiss this business model as a second-rate alternative. Most direct sales people aren't misinformed zealots; they are professionals who are genuinely enthused about their careers and earning potential (much more so than many of my corporate clients). A career in direct sales is not for everyone. But for the right person, with the right set of skills, working for the right company, this can be a good flexible work solution. Here are some of the reasons why:
• **Low barriers to entry**. Direct sales companies provide you with the inventory, marketing materials, and forms you need to begin selling from the day you purchase a starter kit. This "instant infrastructure" helps to eliminate many of the stumbling blocks you face when you build your own business from scratch.
• **Variety of selling opportunities**. Gone are the days when direct selling was limited to working for Avon or Tupperware. Today you can represent companies that sell all types of products and wares, ranging from spa products to wine, gourmet food, or clothing. It's a large and diverse industry that boasts nearly $30 billion per year in US sales.
• **Flexibility**. You can exercise complete control over where, when, and how you work (the majority of direct sellers work less than ten hours per week). This is a very portable business that can work wherever you are—an especially nice benefit if you want to travel or take time off for visits with the grandkids.
• **Minimal start-up costs**. You can open a direct sales business for a fraction of what it would cost to start a conventional business. Most direct sales companies charge less than $200 for their initial starter packages.
• **Social benefits**. Entrepreneurs often complain of feeling isolated. But when you work for a direct sales company, you get to be part of a larger team. Many companies host online training sessions and conferences where you can learn, network, exchange ideas, and socialize as part of your job.
• **Income potential**. Most people in direct sales earn less than $3,000 per year, but most people also work their businesses on a very part-time basis. If you are willing to invest the effort, you can turn this into a more serious part- or full-time income stream. In addition to sales commissions, some companies offer miscellaneous incentives, such as free trips or gift certificates as bonuses for high performers. If your company has a multilevel marketing compensation plan, you could also receive payment for recruiting other sellers into the organization (and earn a commission off a percentage of their sales as well).
Like any career in sales, the direct sales option is best for people who are relatively outgoing. It is not the best choice if you are shy or uncomfortable with the thought of asking your friends or relatives to purchase your products. Unfortunately this is also an industry that has been plagued by scams, pyramid schemes, and less-than-ethical operators, so please don't be fooled by promises of "instant riches" or let yourself be pressured into buying large amounts of product that might be difficult to unload. Remember, if it sounds too good to be true, it probably is. It takes consistent effort and commitment to build up a direct sales income, just as it does in any other type of business. Do your homework, find a company you like, make sure both the products and the company are legitimate, and choose a compensation plan that rewards you fairly and generously for your efforts. As this next profile illustrates, if you put the effort into finding the right company, a career in direct sales can provide a welcome combination of flexibility, personal fulfillment, and income during your semi-retirement years.
### **From Nurse to Direct Sales Superstar**
_"I look for someone who has confidence and who conveys to me that they want to be successful."_
—Karen Pagliurolo, regional manager and sales consultant for Etcetera
Growing up, Karen Pagliurolo always enjoyed fashion, but she never expected that one day she would get to make a living from working in the fashion industry. A registered nurse by training, she became a stay-at-home mom in order to accommodate the demands of her husband's career as a major league baseball player. During her early parenting years, she kept busy raising children, running the household, and doing a "ton" of volunteering. But when she received a phone call from a recruiter for the women's clothing company Etcetera, asking if she would be interested in working with them as a home-based direct sales consultant, Karen, then age forty-one, decided she was ready for a new challenge.
Etcetera (www.etcetera.com) is a high-end direct sales fashion company that sells chic everyday clothing via appointment-only trunk shows. Karen paid a small fee to get started with Etcetera, which she quickly recouped with the sales from her first show, and under the tutelage of her area sales manager, a Harvard MBA, she soon built up a loyal following of clients. Karen hosts trunk shows four times a year in the basement of her home in Winchester, Massachusetts, where her clients get to enjoy a personal shopping experience that is a welcome change from the hassles of shopping at department stores. She is paid a commission on all her sales, and in addition receives steep discounts on Etcetera's clothing. Although her life is admittedly hectic during the weeks leading up to and immediately following the shows, this is a business that allows Karen to have considerable flexibility during most of the year. In fact, for several years she successfully balanced her Etcetera business with a second home-based job as a recruiter for a healthcare company.
In 2011, she was promoted to a position as a regional sales manager, helping to recruit and train new consultants. Karen actively recruits women of all ages, but believes that the job of independent sales consultant is an especially good fit for older women. "In fact," Karen says, "I think women in their fifties are probably the best candidates I see. They are educated, they've been active volunteers, and they are the CEOs of their households."
Working as an independent sales consultant has enriched Karen's life in a myriad of unexpected ways; it allows her to control her own destiny and earn a good income, while having fun and flexibility on the job. The benefits of being affiliated with a larger company are not lost on Karen. "It allows me to work on my terms and yet I have the support of my manager to help me grow as a person," says Karen. "I get compensated well and feel like I am part of something bigger." That blend of teamwork and independence proved to be a winning formula for Karen, and now, as a regional manager, she helps empower other women to enjoy the same success, fulfillment, and satisfaction in their own home-based businesses.
#### **Karen's Top Three Tips for Direct Sales Success**
1. **Pick a company with a strong management team**. Karen says she has felt supported by management at Etcetera during every step of her professional career. Her first manager was an inspirational role model whose training and support were invaluable to Karen's development and success.
2. **Value your volunteer and life skills (even if you never got paid for them)**. Women are rarely given enough credit for all their accomplishments. If you are motivated and organized and have strong networking skills, you can be very successful at this type of business.
3. **Do work only if it is personally satisfying**. Karen has always viewed her job with Etcetera as being about more than just selling clothes. She derives great satisfaction from helping her customers look and feel terrific, and she is passionate about empowering her consultants to be successful businesswomen in their own right.
To learn more: The Direct Selling Association (www.dsa.org) is the single best resource on the Web for learning about direct selling (including the differences between direct sales and multilevel marketing companies) and for finding links to approved direct sales companies.
## FRANCHISES
If the word "franchise" brings to mind businesses like Dunkin' Donuts and Starbucks, it's time to update your thinking. The world of franchising has expanded way beyond fast-food chains and retail stores to include smaller service businesses that can be run on a flexible schedule. Franchises are a potentially attractive semi-retirement option for several reasons:
• Franchises boast a lower failure rate than businesses started from scratch; consequently loans are generally easier to obtain for these types of businesses.
• As a franchisee, you can take advantage of a recognized brand and a tested business plan, which can ease the risks associated with being out on your own.
• Franchises provide ongoing marketing, training, and other support to help keep your business running smoothly.
Of course, there are also considerable risks and challenges associated with the franchising model. This is typically the most costly business-in-a-box alternative. Even part-time and small franchises can be expensive to purchase, and in addition to the normal costs of doing business, there are licensing requirements, long-term obligations, and ongoing royalty fees that may be required. As a franchisee, you compromise your ability to fully control your business. Not only must you follow the franchisor's policies and procedures, but your success is tied to their performance; if the company enjoys great press, you benefit, and if they are embroiled in a scandal or file for bankruptcy, you will be negatively impacted as well.
It goes without saying that the decision to open a franchise should not be taken lightly; it requires careful thought, planning, and evaluation of the risks. Take the time to clarify your personal objectives, lifestyle goals, and willingness to accept financial risk before starting your franchise search. If work-life flexibility is paramount, avoid brick-and-mortar franchises. Be prepared to spend time on research, ask tough questions, talk to other franchisees, and meet with an attorney and accountant prior to entering into any franchise agreement.
Franchises can work well for both novice and seasoned entrepreneurs. As you'll learn in this next story, the benefits of having access to an instant infrastructure and proven business methodology can offer a very attractive combination for people who want to avoid the headaches typically associated with independent start-up ventures.
### **From Solopreneur to Franchisee**
_"Do your homework, do your homework, do your homework."_
—Kathy McShane, Ladies Who Launch Franchisee of Southwestern Connecticut
For eighteen years, Kathy McShane, age sixty, of New Canaan, Connecticut, ran a highly successful multimillion-dollar promotions company. But after the business hit tough times in 2008, Kathy decided it was time to close the agency and shift gears. She returned to school and earned both a certification in coaching from NYU and a certification in positive psychology from the University of Pennsylvania, with plans to teach positive psychology as part of her next career. Around that time, a friend introduced her to the business incubator groups run by Ladies Who Launch, a company that helps women entrepreneurs build their new business ventures. Even though she already had significant experience as an entrepreneur, Kathy decided to sign up for the incubator sessions—and quickly fell in love with the program's methodology and protocol.
From the beginning of her second-act journey, Kathy's objective was very clear: she wanted to help women build and grow successful businesses. But she was reluctant to go through the laborious process of building a new business from the ground up again. "That is why I found the business-in-a-box model so attractive," says Kathy. "It helped simplify the start-up process." After consulting with an attorney, she purchased a Ladies Who Launch franchise for $15,000. "The technology and the training alone were worth the cost of the entry," remarks Kathy. In addition to the initial payment, Kathy pays the franchise a percentage of the fees she charges for the different events she offers. "I don't mind it," she says, pointing out that the fees help to pay for things like website costs that she would pay for as a normal part of doing business.
Although Kathy was confident about the franchise idea from the start, she admits that her husband and friends expressed concern that she would feel encumbered by the franchise's rules and restrictions. Although not everything has always worked perfectly, Kathy maintains that the franchise route has proven to be a good fit for her needs. That said, there are some things she would do differently if she were going through the selection process again.
#### **Kathy's Top Three Tips for Franchisees**
1. **Remain objective**. Try not to fall in love with one franchise; even if you think you've found the perfect fit, take your time and look at other options. It is always helpful to research your full range of possibilities thoroughly before purchasing a franchise.
2. **Ask a lot of questions**. Develop a questionnaire ahead of time and get answers to every question you have on the list.
3. **Know what you are buying**. Talk with other people who already own the same franchise to solicit their views and input. Drill down far enough to ensure that you get to know the management team, their commitment to people in the field, and their marketing plans. Don't hesitate to use social media and other networking tools to better understand what specifically you are buying for your dollars.
To learn more about franchise opportunities, look into these resources:
• _Entrepreneur_ magazine offers a wealth of information about franchises through their website, books, and magazine at www.entrepreneur.com. You'll find lists of franchises including "10 Franchises for $20K (or Less)" and "The Best Home-Based Franchises," which include franchises that can be purchased for less than a $5,000 initial investment.
• International Franchise Association (www.franchise.org) is the world's oldest and largest organization representing franchising worldwide.
## LICENSEE
Successful service professionals (coaches, consultants, speakers) sometimes package their proven systems into off-the-shelf programs that they sell to colleagues for use in their own practices. In addition to offering content and materials, they train you on their systems and grant you a license to deliver their turnkey programs to your clients.
To better understand how this works in real life, let's take a look at the train-the-trainer business etiquette programs offered by the Emily Post Institute (www.emilypost.com). Imagine that you are an independent consultant who has noticed a need among your clients for coaching on business etiquette. You could spend months developing and testing your own programs, or you could invest in a one-week class with the Emily Post Institute and quickly leverage their years of experience and brand name recognition into a training program of your own. Upon completing the course and paying a small licensing fee, you have the right to use their training materials (PowerPoint slides, worksheets, and so on) and can promote yourself as having trained with the Institute and use their "Trained by Emily Post" seal on your website. Graduates of their programs are also entitled to additional coaching with the staff at the Post Institute and can purchase their etiquette books at a steep discount for use in their own workshops.
I've taken advantage of these off-the-shelf programs in my own coaching practice and found them to be an efficient way to expand my offerings without having to invest energy in developing my own content. It has saved me money and time (and angst) that I can apply to other parts of my business. In my case, I decided to become a licensed facilitator of Laura Berman Fortgang's Now What? coaching program, a twelve-week system that provides my clients with an alternative to my regular à la carte coaching services. To qualify as a facilitator, I paid a one-time fee, attended a training course, and passed a final exam. As a certified facilitator, not only do I have the right to use the Now What? program and materials in my own practice, but I also get to take advantage of special facilitator-only conference calls, newsletters, and follow-up trainings that Laura provides at no additional cost.
How do you learn about these types of packages in your own industry? Conferences, industry meetings, and associations can be good places to discover these opportunities within your own industry (the vendor areas are often rich with industry experts selling their programs). The terms, benefits, and fees involved with being a licensed facilitator vary from provider to provider, so be sure to shop around, check references, and compare your options before investing your time or money.
## BUY A BUSINESS STARTER KIT
Have you ever read about a business and thought, "That sounds like a cool idea!" but you lacked the know-how to turn your interest into action? Next time you have one of those "hmmm..." moments, do some research to see whether you can find a business starter kit that you can use as a blueprint. Starter kits are typically created by people who have years of experience running their businesses; they include the step-by-step instructions, templates, forms, and other resources that you need to get your own business launched. More expensive starter kits might also provide one-to-one consulting services, access to specialized databases, and/or website hosting services. These kits can save you considerable time, money, and aggravation. But like other forms of unregulated training (certification programs, webinars, and so on), the value and practicality of these kits varies tremendously, so once again, be sure to do your homework before investing your money.
Purchasing a high quality starter kit can be an economical alternative to the pricier and more restrictive franchise model. Take a look at this next story to learn how one California woman used a starter kit as a way to launch a successful home-based business.
### **Profile of a Starter Kit Success Story**
_"There are so many scams on the Internet and you cannot be too careful."_
—Penny Spark, owner of Southern California Home Improvement Referral Service
It's funny how sometimes our best business ideas happen when we least expect them. Penny Spark's lightbulb moment came as a result of the frustrations she experienced while renovating her home. After spending months dealing with unreliable contractors and wanting "to tear my hair out," Penny read an article about the Homeowners Referral Network (HRN), a service that helps people find reliable home contractors. The article mentioned that HRN sold business starter packages for people interested in starting their own referral businesses. Penny was instantly intrigued by the HRN concept, especially because she had recently sold her old business and was actively looking for her next venture. She called the company, asked for information, and ran the numbers. Then after reviewing the business model, she called the founder of HRN, Debra Cohen, and "bombarded" her with questions. "I really put the poor woman through the wringer," recalls Penny with a laugh.
It was time well spent; the more they talked, the more comfortable Penny felt. The fact that HRN was _not_ a franchise was a big plus for Penny, who worried that the restrictions associated with the franchise model could be suffocating. "I am an entrepreneur, and I needed to be free to take my ideas and run with them," she says. After careful consideration, Penny purchased the HRN manual, along with eight hours of one-to-one consulting time with Debra, and barely two months later she opened for business. Today her concierge-style service (based out of her home in Sierra Madre, California) helps clients find contractors for their commercial, residential, and industrial projects.
Thirteen years after purchasing a manual and consulting services that enabled her to open a business in an arena where she had little prior experience, Penny, now age fifty-five, is certain that she made a wise choice by choosing to work with both Debra and HRN. "Debra understands that making the sale is only the first step," says Penny. "She knew my success would be her success. And here we both are, thirteen years later."
#### Penny's Top Three Tips for Entrepreneurs
1. **Find a business that suits your lifestyle**. It's not easy to balance starting a business and running a business. For some people the franchise model is ideal—it can teach you what you need to do every step of the way. For others, it is too restrictive. Know what is right for you.
2. **Ask for references**. You have to make sure not only that what you are buying is a viable business, but that the person you're buying from is ethical and telling you the truth. Call other licensees, ask lots of questions, and don't hesitate to ask for multiple references.
3. **Invest time in building relationships**. Penny's business operates on a small budget, so she relies on business networking, repeat business, referrals, and the Internet to secure her clients.
For more information: Industry magazines and trade associations can be good resources for locating information about starter kits. If you aren't ready to invest in a full-service kit, you might want to purchase a less expensive business starter guide or manual. Two websites, Fabjob.com and Entrepreneur.com, sell basic starter guides covering a wide variety of entrepreneurial businesses.
## SELL ON eBAY (AND OTHER ONLINE MARKETPLACES)
The Internet has simplified the process of turning your trash into treasures and collectibles into cash. And while most people use online marketplace sites primarily to earn just a little extra cash, if you take the time to learn how to buy, sell, and market smartly, you can actually earn real money—sometimes even the equivalent of a modest full-time income—selling goods online. The economic impact of eBay is enormous: in 2011, the total value of goods sold on eBay was $68.6 billion—more than $2,100 _every second_. It is the world's largest online marketplace, where people around the globe can buy and sell practically anything including cookie jars, antique paintings, or a bag full of children's socks. Although it is the biggest online marketplace, eBay is not the only player in this space, and there are many other online marketplaces where you can potentially sell your goods. Here are three of the bigger sites:
• **Bonanza.com**. A rising star in the online marketplace galaxy, Bonanza specializes in items that you can't find mass-produced in stores, like purses, vintage clothing, antiques, jewelry, memorabilia, and collectibles. Their tagline, "Everything but the ordinary," sums it up well.
• **Etsy.com**. Etsy is the online marketplace for handmade items and crafts, including art, furniture, glass, clothing, candles, and more. Etsy has a very vibrant online community where you can exchange ideas, access online training and learn about educational and networking events.
• **Amazon.com**. Merchants can sell a wide variety of products and inventory on Amazon.com. You can download a guide from their site that explains how to get started selling as a merchant on Amazon.
Earning a living as an online merchant is not unlike every other business; if you want to succeed, you need to learn the rules of the road, be realistic about your expectations, and be willing to adapt when necessary. As you'll learn from the tips offered in this next profile, success selling online is more about being a savvy businessperson than it is about just being a smart shopper.
### From Disabled Executive to eBay Hall of Fame
_"I had no interest in collectibles—my interest was in being busy and productive."_
—"Uncle" Joe Adamson, eBay Hall of Fame
Joe Adamson was a technology executive in his thirties when he became seriously ill—so ill that his doctor told him that it was unlikely that he could ever return to work. Overnight Joe went from climbing the corporate ladder to staring at the television for hours on end. "I watched my brain cells marching out the door," recalls Joe. "I was no longer useful. I was no longer desirable. I was no longer needed. If they had rolled tanks up in front of my house, it couldn't have been any worse. It was quite a shock." As the months wore on and Joe began to acclimate to his new normal, he focused on the difficult process of pulling his life together and moving forward.
Fortunately he was familiar with the online world, and because he had friends who owned a local surplus store, he decided to try his hand selling their secondhand items on eBay, figuring it would be a relatively easy way to supplement his income. He began by selling rosin animal head statues, collector pocketknives, tools, and other items that he could physically handle. He figured out the best ways to market the items online, and with time, he started to increase sales.
Joe acknowledges that his background was tailor-made for online success: he has strong communication skills, he had designed IT networks, and he knows how to sell, how to write, how to take pictures, and how to make videos. As he notes on his website, "It's been said that I was raised in a laboratory, created in a petri dish, with e-commerce skills gene-spliced into my DNA." With that winning combination of personality, determination, and skills, it wasn't long before Joe's business flourished. "I got really good at it, really fast," says Joe. "I was in the right place, at the right time, with the right mix of products."
Today Joe still sells on eBay, but his main income now comes from teaching and mentoring other people interested in learning how to create their own eBay success. He is a certified eBay education specialist who shares his expertise through his training programs, meet-up groups, and the informational offerings on his website at www.unclejoeradio.com. Joe also helps to run the eBay meet-up group where he lives in Oklahoma City, Oklahoma.
His work these days is as much about giving back as it is about earning his own livelihood. Joe knows all too well what it feels like to be down on your luck. He frequently offers his time to people in need, but they in turn must be willing to make the effort to change. "It is my one-man mission to help fight unnecessary poverty," shares Joe. "I know that some of the people I work with are fifty bucks away from having their lights turned off." Helping these people learn how to sell on eBay starts them on a path that enables them to be productive and valued and to have a sense of worth. Joe believes that if he can impart that knowledge to people, he can imbue them with the skills to "go out there and get it done" and, in the process, help to turn their lives around.
#### **Joe's Top Six Tips for eBay Selling Success**
1. **It's more about the selling than the buying**. People have a great time shopping and treasure hunting. It can be wonderful fun. But at some point, you need to do the work and sell. "Selling" doesn't just mean posting items online; you need to write compelling content, post attractive photos, and be realistic and competitive about pricing.
2. **Remember the Golden Rule**. eBay operates on a rating system, and bad feedback is ruinous for sellers. The sellers who go above and beyond in their customer service tend to be very successful. They always pay attention to detail and have a dogged determination to be "white-glove honest."
3. **Be a smart shopper**. The two ways to make money on eBay are by buying right and by buying with efficiency. It takes as much effort to sell something for a fifty-dollar profit as it does to make a five-dollar profit, so it's important to concentrate your buying on items that have the best markup potential. Don't allow yourself to become emotionally connected to your purchases.
4. **Invest in education**. eBay.com offers online training that takes people through all the steps necessary to start selling on eBay. Once you know the basics, it can be very helpful to learn more from certified training specialists. Certified specialists, like Joe, have been teaching for some time and generally have their own successful businesses. Specialists can also provide ongoing mentoring for people who want to take their business to the next level.
5. **Participate in the eBay community**. This is a warm group of people with a helpful spirit. There are numerous online spaces where people exchange shoptalk, resources, and tips. As Joe says, "We don't have a union hall or meeting place, so we meet online." There are also groups that meet in person (you can locate them on www.meetup.com), discussion boards, and groups you can find listed under the community tab on eBay and on Facebook. eBay hosts several "on location" seminars and conferences that are terrific events for networking and learning; people who pay to attend these conferences tend to be a good group of people to know, because they are either already very successful or "up-and-comers" in the business.
6. **Don't trust everything you read online**. New sellers should be aware that the online groups and message boards can sometimes be simmering kettles of negativity. You need to interpret their comments carefully and remember that people generally don't go online to celebrate—they go online to kvetch, vent, and let off steam.
The growth of online marketplaces has created a whole new industry designed to support, educate, and unite people involved in this profession. To learn more, start with a basic Google search; you'll find conferences, meet-up groups, online forums, training programs, and books to help you succeed and thrive in this world.
• Two books of note are _Starting an eBay Business for Dummies_ by Marsha Collier (For Dummies, 2011) and _The Handmade Marketplace: How to Sell Your Crafts Locally, Globally, and Online_ by Kari Chapin (Storey Publishing, 2010).
• eBay offers a helpful learning center at http://pages.ebay.com/education/index.html.
**THREE FINAL TIPS FOR PEOPLE INTERESTED IN PURSUING A BUSINESS-IN-A-BOX OPPORTUNITY**
1. **Do your homework**. You've read this advice several times already, but it bears repeating. There are many questionable opportunities out there, and you can't be too careful. Ask lots of questions, call other people who are involved with the business, and, when needed, consult with an attorney or accountant before investing money.
2. **Beware of scams**. Here are some of the warning signs to look for:
• The ad uses phrases like "No experience needed," "Unlimited earning potential," or "Make hundreds a week."
• The ad is vague, and job responsibilities are not clearly defined. No company address is listed.
• For a fee, the business will send you a list of companies interested in home-based workers or a kit of products to assemble.
If your gut tells you something is amiss, pay attention to it. Don't hesitate to check out your suspicions by calling the Better Business Bureau (in the state where the company is based) to check for complaints filed against the company. You can also contact the attorney general's office in your state or the state where the company is located. A well-placed phone call may save you considerable aggravation and money.
3. **Decide whether you're comfortable with having to "color inside the lines"—whether you're a leader or a follower**. Business-in-a-box models take a lot of the guesswork out of creating a business, but for some people, the restrictions and formulas are suffocating. Find a model that works with _your_ goals and _your_ personality. If you want something that you can shape, mold, and tailor from scratch, you will probably be better off striking out on your own.
# CHAPTER FIVE
# Trade Your Time for a Paycheck
Up until now, we have been exploring entrepreneurial options. But not everyone is eager to start their own business. Some people are far more comfortable with the structure, camaraderie, and support offered by being employed by, or associated with, a larger entity. If you think you might prefer to find a job, or work on a freelance or project basis, then this is the chapter for you. In this section, we will examine different ways you can trade your time for a paycheck: either as a part-time or seasonal employee, by securing a freelance assignment, or as a temporary worker affiliated with a temporary agency or interim executive services firm. Let's begin by discussing the traditional option of part-time jobs.
## PART-TIME JOBS
If I had a dollar for every person who came into my office and said, "I'd love a job, but I really only want to work part-time," I'd be a wealthy woman. I understand that desire. Part-time work is attractive; it offers the familiarity of a set schedule, a predictable paycheck, and the support provided by a traditional work setting, all without the demands of a full-time job. Some part-time jobs, like working at a neighborhood bookstore or at the local library, can be an especially pleasant alternative for people in semi-retirement. And it is not just "easy" jobs that are now being done on a part-time basis; quality part-time professional jobs are on the rise as more employers are increasingly willing to consider creative alternatives to full-time schedules.
Finding those quality part-time openings can still be a challenge though, and if working as a part-time professional is your goal, you'll need to employ slightly different strategies than you would if searching for a full-time job. But if you are willing to invest the energy, interesting part-time jobs can be found. Here are some of the best tactics for part-time job-search success:
• **Talk to your former employers**. They know your value, and under the right circumstances they may welcome having you back on payroll. Even if they can't give you a regular part-time position, they may be willing to offer you project or temporary work assignments, and over time those assignments could lead to a more permanent arrangement. (One note of caution: retirees who work for the same employer from which they retired should check with the benefits department to see whether their reemployment status will affect their pension benefits.)
• **Target small businesses**. My clients are most successful at finding part-time jobs when they target small businesses and entrepreneurial firms. Why? Many small-business owners have learned that by offering flexibility they can attract and retain top-level talent who might not work for them otherwise. Small-business owners also appreciate the value offered by part-time workers who often prove to be as productive as their more costly full-time counterparts. Of course, not every small business is a good fit for this; companies that operate under tight deadlines or are heavily involved in client services will not be as accommodating as companies where the work can be completed on a more flexible timetable.
• **Explore opportunities with entrepreneurs**. Working for a successful entrepreneur offers several of the advantages of being in your own business—flexible hours, work-from-home options, and varied job responsibilities—with none of the risks associated with running your own show. If you want to find opportunities working with entrepreneurs, plan to attend meetings of small-business groups, such as your local chamber of commerce, to increase your network of entrepreneurial contacts. Venture capital (VC) firms can also be a good source of leads about part-time openings with start-up companies. Check with colleagues for recommendations of VCs (this can be a clubby world, so it helps to network your way into a conversation). Gust.com is a good site for information about angel investors and VC firms.
• **Consider local cultural, religious, and community-based institutions**. Museums, theaters, arts agencies, churches, temples, and libraries all rely heavily on part-time workers to meet their staffing needs. Although the compensation packages at these institutions are not as rich as those offered by corporate employers, their social, cultural, and educational benefits and perks can be very appealing.
## THE POWER TRIO OF FLEXIBILITY: EDUCATION, HEALTHCARE, AND SALES
Part-time and flexible jobs have long been a staple in education, healthcare, and sales-related occupations. Here is some helpful background on each of these three industries:
### Education
Teaching can be an appealing option for midlife career changers who want an opportunity to share their knowledge and make a difference in the lives of future generations. According to the 2012–13 online version of the _Occupational Outlook Handbook_ , the hiring outlook for teachers is looking strong for the foreseeable future, although hiring conditions are, of course, impacted by budgets, legislation, and the general health of the economy. Employment prospects for teachers tend to be better in inner cities and rural areas than in suburban districts, and are expected to be strongest for math, science, bilingual, and special education teachers.
Attaining a teaching certification has become easier in recent years, with nearly all fifty states offering some form of alternative teaching certification for people who have either a bachelor's degree or significant work experience in the subject they will teach, but who lack the educational courses needed for credentialing. The cost of training may run from a few thousand dollars to more than $15,000, but you might be able to reduce those costs if you qualify for grants or loan forgiveness programs. Former military personnel who want to retrain as teachers may qualify for financial assistance and counseling through the Troops to Teachers program (www.proudtoserveagain.com). Teachers in private schools do not have to be licensed but typically still need a bachelor's degree to be considered for employment (and some private schools will expect you to become certified within a year or so after employment).
Life as a teacher is both rewarding and challenging. And although you will get to enjoy having summers off and plentiful school holidays and break periods, the day-to-day demands of the classroom can be considerable, especially for new teachers. One of the best ways to determine if you'll enjoy life in the classroom is to test it out as a substitute teacher (contact your local school system for details on how to apply as a sub). Alternatively, you could volunteer to work in the classroom, but if you do, remember that teaching in a suburban elementary school will likely be a very different experience from teaching in an urban high school, so be sure to give preference to volunteer settings that match your longer-term career objectives.
To learn more about teaching careers:
• Look into alternative certification programs from the National Center for Alternative Certification (www.teach-now.org).
• Find information on loan forgiveness programs from the American Federation of Teachers at www.aft.org/yourwork/tools4teachers/fundingdatabase.
• Consult your local colleges to find out about their teacher training programs.
### Healthcare
Healthcare employment opportunities are expanding, and as baby boomers grow older and live longer, the demand for healthcare workers should continue to be exceptionally strong. According to the US Bureau of Labor Statistics, approximately 26 percent of all new jobs created between 2008 and 2018 will be in the healthcare and social assistance industries. Healthcare careers are an excellent option for semi-retired people looking for meaningful work outside the corporate box. It is an industry in which maturity is valued and opportunities for flexible scheduling are robust. A career in healthcare usually requires some type of certification or training, although the majority of jobs require less than a four-year degree. Here are some options to explore if you want to pursue a part-time or flexible healthcare career:
• **Holistic/alternative practitioner**. There is a growing acceptance of holistic healing alternatives including hypnosis, reflexology, acupuncture, and naturopathy—even within the traditional world of mainstream medicine. Although you could be employed by a hospital, most practitioners in these disciplines usually work independently or affiliate with small private practices. To find more information about careers in holistic medicine, consult www.alternativemedicine.net.
• **Diet and nutrition counselor**. The obesity epidemic is driving a growing need for professionals who can provide nutritional counseling, behavioral therapies, and exercise advice to help people gain better control over their weight. If you're interested in this field but don't want to go back to school for an advanced degree, you may want to explore a career as a health coach. The Institute for Integrative Nutrition has a one-year training program (www.integrativenutrition.com), run in partnership with the State University of New York at Purchase College, for people interested in becoming health and nutrition coaches.
• **Fitness instructors**. The boomer generation grew up with Jane Fonda, aerobics, and Jazzercise. But as they age, they will be looking for fitness teachers who can help them stay in shape without placing undue stress on their aging bodies, joint replacements, or fragile bones. As a fitness instructor, you can work at senior centers, gyms, and in private homes. To learn more about becoming a fitness professional, consult the American Council on Exercise at www.acefitness.org. For information about Pilates certification, contact the Pilates Method Alliance at www.pilatesmethodalliance.org; for information about yoga training, check with the Yoga Alliance at yogaalliance.org.
• **Physical therapist aide or assistant**. Physical therapist aides and assistants help physical therapists provide therapeutic services to their patients. This field offers many good opportunities for part-time and flexible working hours. According to the _Occupational Outlook Handbook_ , 72 percent of physical therapy employees work in offices of other health practitioners and in hospitals; the remainder work in nursing care facilities, home healthcare services, and outpatient care centers. For more information, consult the American Physical Therapy Association at www.apta.org.
• **Medical assistants**. Medical assistants perform medical and clerical tasks that help keep the offices of a doctor or healthcare practitioner running smoothly. Formal training in medical assisting is not required, but there are one-year certificate and two-year associate programs for those wishing to get advanced training. For more information, consult the American Association of Medical Assistants at www.aama-ntl.org or consult your community college catalog for their class listings.
• **Phlebotomy technician specialist**. Phlebotomists help to draw and collect blood samples. Upon successful completion of forty-five hours of classroom instruction and an additional thirty hours of hands-on phlebotomy training, students are eligible to take an examination offered by the National Health Career Association (www.nhanow.com) to become a certified phlebotomist.
• **EKG technician**. Trained EKG technicians run the heart monitoring equipment in cardiologist offices, rehabilitation programs, and hospital cardiac catheterization laboratories. Training typically consists of approximately twenty hours of classroom instruction and an additional twenty-plus hours of hands-on training. Students who successfully complete the training are eligible to take an exam administered by the National Health Career Association for certification.
• **Dental assistant**. Dental assistants educate patients on dental care, take X-rays, and perform other functions in a dental office. Many assistants learn their skills on the job, although an increasing number are trained in dental-assisting programs that take one year or less to complete. For more information, consult the American Dental Assistants Association at www.dentalassistant.org.
### Sales
Talented salespeople are always in demand. During weak economic times, strong salespeople keep companies afloat, and during prosperous times they help companies tap into new markets and increase profit margins. Compensation for sales jobs is directly linked to performance, and results matter far more than how, when, or where you spend your time. If you meet or exceed your goals, you'll be rewarded, even if your "face time" is not as high as that of your full-time colleagues. As a result, top salespeople can earn impressive incomes, irrespective of the number of hours they work. This is in sharp contrast to many other lifestyle-friendly jobs, for which flexible schedules all too often result in reduced earning potential.
Real estate sales is one of the more popular options for semi-retirees, and if you enjoy working in sales and live in an area with a strong real estate market, it can be a good second-act career. But as any successful real estate agent will attest, life as a real estate agent isn't quite as flexible as some think; although you can work as much or as little as you want (within reason), successful agents tend to work quite hard, and you should expect to work some evenings and weekends. This is also an industry that has been negatively impacted by both the Internet and the sluggish housing market, so be sure to research the outlook for real estate agents in your local area before you invest in training. Real estate brokers and sales agents must be licensed and people who want to earn a broker's license need both formal training and experience selling real estate, usually one to three years. To learn more, consult the National Association of Realtors at www.realtor.org.
**JOBS "WITH BENEFITS"**
A surprising number of part-time jobs include special benefits, perks, and unique experiences that could add extra incentive to your official compensation package. Here are some of the benefits that might be included as part of your job:
• Crazy about travel? Careers in the travel industry don't always pay top salaries, but the perks are priceless. Employees of travel-related companies like airlines, hotels, travel agencies, and cruise ships can enjoy significant travel discounts. In some situations, they may also be entitled to discounts from affiliated travel providers (for example, an employee with a cruise ship might be entitled to discounts at select hotels).
• Love to learn? Employees of colleges and universities are often entitled to tuition discounts—a valuable benefit that can apply to family members as well. Even if you have no interest in earning another degree (or if your college's tuition benefits don't extend to part-timers), working on a college campus gives you easy access to symposiums, lectures, book readings, and special exhibits. On larger campuses, you may also be entitled to free use of the university gym or complimentary tickets to college sporting events.
• Fan of fashion? Department stores and clothing manufacturers normally give their employees a significant discount on their in-house purchases. Some employers also invite their employees to special trunk shows, sample sales, and end-of-the-season clearance events, where they can buy clothing and accessories at a steep savings.
• Are you a sports fan? If spending a day at a sporting event is your idea of sheer bliss, consider working for a company that is connected to the sports industry. Jobs with a sports-related venue, media company, professional association, or team can give you access to free or discounted tickets to major sporting events. You don't need to be an athlete to get hired in this industry; there are opportunities for people with sales, public relations, management, human resources, financial, and accounting skills.
Remember that these little perks can add up and make a real difference in both your compensation package and the fun factor associated with your job.
You never know where, when, or how you might find that perfect part-time job. As this next story illustrates, sometimes the best opportunities surface when you least expect them.
### From Retired to Rehired: A VP with Flex Hours
_"It's very refreshing to not worry about climbing the ladder after doing that for so many years."_
—Joanne Schumacher, VP with flex hours
After enjoying a long career in recruiting and staffing management for high-tech firms in Silicon Valley, California, Joanne Schumacher and her husband looked forward to a retirement filled with leisure and travel. They moved to a retirement community in Northern California and quickly settled into a routine filled with golf, social outings, and community activities. All went according to plan, until one morning while browsing an e-mail newsletter, Joanne read about a job with a start-up called Staffingbook, an online service that connects third-party recruiters representing passive candidates to employers. Although she wasn't actively looking for work, Joanne was so intrigued by the job description that on a whim she decided to apply.
From her first conversation with the company's owner, Joanne knew she had found a good fit. "The owner is an expert at building companies, I am an expert in recruiting, and the third employee is an expert in building software," Joanne said. "We all complement each other—it is just a really nice combination of skills." Although she was officially hired as the vice president in charge of subscriber services, like most employees in small start-up situations, Joanne wears many hats and juggles a variety of tasks each day. Nonetheless, she finds the fast pace of the job exhilarating. "I thrive on change," she says. Given that it is a start-up situation, she works for a "very modest salary" that is significantly lower than her old compensation as a recruiter, but she holds an equity stake in the company that she hopes will prove lucrative in the not-too-distant future.
Joanne spends about thirty hours a week on the job. Most days she commutes to the office, but she can work from home when it is convenient to do so. Her schedule leaves her with "enough" time to enjoy life in her retirement community, albeit not as many hours as she originally planned. It is an arrangement that seems to work for both Joanne and her husband, who has been retired for several years. "I thought maybe I'd resent working knowing he is home, but I don't," observes Joanne. "I love working, and I think it is healthy for each of us to have our own time to do what we want to do."
How long she will remain working depends on the success of Staffingbook, her health, and her desire to continue with the job. Noting that her own parents worked well into their seventies, Joanne, now sixty-seven, anticipates working for many years to come. But in the meantime, she is enjoying the chance to build a new company without feeling the pressures she would have when she was just starting out in her career. Looking back on her unexpected second-act career, she is still amazed at how easily things fell into place. "I guess sometimes I say I believe in fate," Joanne observes. "When it is the right thing, it just works well."
#### Joanne's Top Three Tips for Working Part-Time in Retirement
1. **Keep an open mind**. You never know what type of job might prove to be a great fit, so be open to new ideas and new ways of working.
2. **Do something you enjoy**. Life is too short to make sacrifices. Remember, you aren't climbing the corporate ladder anymore.
3. **Don't be afraid to negotiate**. What do you have to lose? Ask for what you want, and you just might get it—more flexible hours, time off for travel and volunteering, work-from-home options, company equity instead of salary, and so on.
**ADVICE FROM THE FLEXJOBS EXPERT**
**"Have hope! There are many more professional part-time and flexible jobs available than you might expect."**
—SARA FELL, CEO and founder, FlexJobs.com
Sara Fell manages a job board that specializes in flexible job listings. Her team of trained researchers has found flexible jobs in virtually all industries and at all levels, including managerial and executive roles. Here is a sampling of recent professional part-time jobs listed at www.flexjobs.com:
• Ombudsman
• Chief financial officer
• Aquarist/Zookeeper
• Senior systems engineer
• Master schedule consultant
• Website Coeditor and writer for a chronic pain website
• Associate professor, Child Studies
• Psychologist
• Associate general counsel
• Executive director
The jobs on FlexJobs.com offer a range of flexible benefits, including telecommuting, flexible schedules, and alternative schedules. Sara cautions that you should be aware that there are often degrees of flexibility with these work options—a job might offer telecommuting three days a week but not every day, or a flexible schedule but one that is not completely in your control.
Sara also warns that professional part-time and flexible jobs can be difficult to find among the piles of less-skilled jobs, ads, and scams. A keyword search for "part-time jobs" will generally yield an abundance of retail, restaurant, and student jobs, but fewer higher-level positions. Similarly, if you're interested in finding a job that allows you to work from home, you'll likely find yourself neck-deep in a pile of too-good-to-be-true business opportunities and suspicious-sounding ads.
**Sara's Top Three Keyword Search Terms**
1. **Part-time jobs:** Be specific, and use "part-time" plus the job title and location you're looking for, such as "part-time engineer in Colorado."
2. **Work-from-home jobs:** Try using "telecommute," "telecommuting," or "remote job" paired with related career words, such as "telecommute marketing jobs." Stay away from "work from home" or "work at home."
3. **Consulting jobs:** It's fine to use "consulting," and be sure to try the variation "consultant" as well as search terms such as "freelance" and "contract" plus your industry.
### How to Find Part-Time Job Openings
Now that you know the types of industries and situations most likely to have part-time jobs, the next challenge is figuring out how to find those elusive opportunities:
• **Network, network, network**. As in any job search, the best way to find part-time opportunities is through a process of active networking. Tell everyone you know that you are interested in working part-time; reach out to former colleagues, employers, and personal friends through both in-person initiatives and social media channels.
• **Approach companies directly**. If you don't have a way to network into a company, contact the hiring manager in the department where you would like to work and pitch your part-time services as a solution to their business challenge. For example, if you want to work as a part-time employment interviewer, analyze the classifieds to identify employers who are in an active hiring mode and then contact them about your recruiting services.
• **Temp your way into a part-time job**. Companies like to offer jobs to people who have worked for them on a temporary basis (and it is often easier to sell the company on a part-time schedule if they already know and like you). Some companies maintain a list of on-call temps and others hire contractors through temporary agencies. There are also a growing number of employment services that place people into companies on a flexible basis, such as www.tentiltwo.com, www.flexibleresources.com, and for lawyers, www.flextimelawyers.com.
• **Use the job boards**. Most of the larger online job boards—like Indeed.com, Careerbuilder.com, and SimplyHired.com—provide a filter that allows you to restrict your search results to jobs with flexible or part-time hours. Craigslist.org has become a favorite place for small businesses to post their jobs. You'll find many local positions listed that are difficult to find elsewhere.
• **Look on bulletin boards**. Seriously, you'll be amazed by the number of interesting local listings you'll find advertised on community bulletin boards in libraries, town halls, schools, and recreation centers.
Most important, be patient. Finding a good part-time situation takes perseverance, but the payoff of a less stressful lifestyle, improved flexibility, and a steady part-time paycheck makes it a challenge worth pursuing.
## SEASONAL JOBS
Working a seasonal job can be a good solution for people who want to work but don't want to be tied to a job year-round. Although most people equate seasonal work with college students in need of summer jobs, it can also be a good fit for retirees who alternate their time between two residences or who want blocks of time to enjoy their personal interests. That certainly was the case for Penny Frederickson, age fifty-four, from Minneapolis, Minnesota, who sold her daycare center eight years ago and now has two seasonal jobs, one working in sales for a garden center in the summer and a second working for a design firm helping to decorate at Christmastime. "It's lots of fun," she says. "I love plants, I love to garden, I love to decorate, and I get to do all three." The jobs give her a chance to get out of the house, talk to people, and do work she enjoys, while still having plenty of time to travel and relax in between her seasonal jobs.
Here are several examples of seasonal jobs you could pursue:
• **Tax preparation services**. You don't need to be an accountant to prepare tax returns. Large companies like H&R Block offer their own training program for people interested in working for the firm as tax preparers.
• **Summer camps**. Camps hire college students to be counselors, but they also hire more "mature" adults for jobs as camp nurses, cooks, and office workers.
• **Delivery services**. Package delivery services like UPS and FedEx hire extra workers during the peak holiday seasons.
• **Retailers**. Stores hire extra staff to work during the holiday season (and many offer seasonal workers an employee discount—a nice way to offset your holiday shopping expenses).
• **Local government agencies**. Tourist agencies, parks, and recreation departments all need extra assistance during the busy summer and tourist seasons.
The options for working on a seasonal basis are more varied than you may realize. And, as the next expert explains, working a seasonal job could even give you a chance to spend time in some very cool vacation destinations.
**ADVICE FROM THECOOLWORKS.COM EXPERT**
**"Seasonal work is a pretty risk-free way to shake up your life or try something different. You go and do it for a few months. If you don't like it, there is no expectation that you signed on for the long haul."**
—BILL BERG, CEO of CoolWorks.com
It was a cold, bleak day in Connecticut when I interviewed Bill Berg, whose website, CoolWorks.com, specializes in "jobs in great places." When I commented on our weather, Bill invited me to take a peek at the webcam on his site so I could enjoy the view outside his office in Gardiner, Montana—an idyllic picture of freshly fallen snow glistening along the Yellowstone River. All it took was one look, and I instantly knew why Bill is so passionate about living and working in our national parks.
Bill first discovered the national parks many years ago when he was a college student looking for a fun job for the summer. A friend suggested that he apply for work in the parks, and Bill ended up spending the summer pumping gas at the service station in Yellowstone. That job turned out to be the first of a series of jobs in the parks for Bill, and he ultimately decided to permanently settle in Yellowstone, where he and his wife have now lived for the better part of their adult lives.
Recognizing that he was not the only one who would love the chance to work in "cool places," Bill created CoolWorks.com in 1995 as an online employment resource for people who want to work seasonal jobs in nice places. The site was originally designed for college students, but it didn't take long before he realized that the site was equally appropriate for the "older and bolder" crowd. According to Bill, boomers have become an increasingly attractive labor force for summer seasonal employers. "The boomers often come in pairs, bring their own housing (mobile homes), have a wealth of experience, and offer a fantastic work ethic," he says. Boomers also have greater scheduling flexibility than college students—a selling point that is much appreciated by employers who are frequently left short-staffed by college students who must quit their jobs to return to school before the summer season officially ends.
Working in the national parks provides an experience that is more than just a job. "As gorgeous as it is in the parks, what makes them so special is the community spirit," says Bill. "People who work here tend to self-select. They share the same passions and values, and that makes for a strong community." In an environment where people eat, sleep, work, and socialize together, it's no surprise that strong bonds form. And it is not just couples that find it a welcome social scene. Singles, divorcees, and widows and widowers also enjoy the communal spirit, and Bill divulges that more than one late-life romance has flourished amid the forests and meadows.
Over the years, Bill has met many people whose lives were permanently changed by their time spent in the parks. Although their jobs lasted just a few short months, the experience left them with a lasting appreciation for nature, new places, and a different way of life. The fact that Bill gets to play a role in such a life-changing experience is one of the main reasons he derives such great joy from his work. He loves it when people meet him and say, "CoolWorks? CoolWorks changed my life!" Bill says that he keeps a fairy wand on his desk as a reminder that he gets to sprinkle magic into people's lives. "If someone comes out and is touched by nature, even if it is just for one summer, I like to think that the way they look at our planet will change," said Bill. "And that," he adds, "is crazy cool."
**Bill's Top Three Tips on Seasonal Employment**
1. **Acquaint yourself with the full range of employment possibilities**. The parks aren't the only seasonal employers looking to staff their positions. CoolWorks.com posts job openings at fly-fishing lodges, dude ranches, adventure tour companies, the Nature Conservancy, and even the research stations in Antarctica.
2. **Don't assume all seasonal jobs are lower-level positions**. Most seasonal openings tend to be for positions like cooks, housekeeping staff, skilled-trades people, and maintenance workers. But employers also need people with professional backgrounds to work as hotel managers, food and beverage managers, bookkeepers, and accountants. Bill says that people with strong "management chops" may be able to find seasonal management jobs, especially if they have prior experience in the hospitality industry.
3. **Carefully research your housing options**. Many parks provide subsidized housing for their employees and try "within reason" to house older workers away from the "hormone-crazed twenty-something college students." Couples housing is available at many parks, but that tends to be limited, so many people opt to live in mobile homes, especially if they want to bring their pets along for the trip. You can find answers to your housing-related questions on the discussion forums and social networks hosted on CoolWorks.com.
In addition to the major job search boards and CoolWorks.com, here are some other useful seasonal-employment resources:
• American Camp Association (www.acacamps.org/jobs) maintains listings of both full-time and seasonal positions with summer camps.
• National Parks Association (www.nps.gov/personnel/index.htm)—the National Park Service hires up to ten thousand temporary and seasonal employees each year.
• SnagaJob.com and Seasonalemployment.com both specialize in seasonal job listings.
## FIND A FREELANCE GIG
Earlier in this chapter, I emphasized that it is not always easy to find quality part-time and seasonal jobs. That is why many people chose to bypass the employee route in favor of work as independent contractors. The percentage of freelance workers is steadily growing as companies continue to outsource their noncore functions, and it is likely that many of you will work in a freelance capacity at some point in the future. A 2006 US government report issued by the Government Accountability Office (GAO) said that 31 percent of the workforce was independent or contingent workers, and by some estimates nearly half of the US job market will consist of freelance and temporary workers by 2020.
So who is using freelance workers? According to a 2011 survey conducted by the International Freelancers Academy, the majority of freelancers make their living providing business-to-business services with the remainder servicing individual consumers, nonprofits, government work, and associations. Your earning potential as an independent will vary tremendously depending upon your location, expertise, field, and specialty. The survey indicates that 45 percent of respondents earn between $20 and $59 per hour, and 26 percent earn anywhere from $80 to $200-plus per hour.
Many freelancers focus on a niche area as a way to distinguish their services from their competitors. For example, instead of offering generic writing services, you could specialize in writing website copy for recruiters. Or instead of working as a portrait photographer, you might specialize as a photographer who takes photos of homes for realtors or interior designers. When determining your niche, consider the following questions:
• Who would you most enjoy having as clients?
• What types of services or projects could you reasonably and effectively provide on a flexible basis?
• What is a niche that is not being adequately addressed by your competitors?
• Do you want to work for corporate clients or do you prefer small businesses?
• Are you willing to travel?
Life as a free agent can be a bit like a ride on a roller coaster, as you roll from high point to low point and back up again. On the upside, you can arrange your own schedule and be selective about the clients and projects that you choose. That level of freedom can be quite attractive to people who want to continue to use their professional or technical skills but don't want the restrictions associated with regular employment. On the downside, it can be challenging to find steady work, so you'll need to budget for the peaks and valleys associated with the freelance life. The constant need for marketing your services can get tiring (and frustrating), so if you're concerned about generating a sufficient stream of business on your own, you might consider teaming up with other freelancers to share projects and marketing responsibilities. As an independent contractor, you'll be responsible for paying your own taxes, tracking your business-related expenses, and handling all the administrative and marketing tasks needed to keep your business healthy—a juggling act that can sometimes prove challenging for people accustomed to the predictability of life as an employee of a larger organization.
But challenges aside, working on a freelance basis can also give you the freedom to try fun and unusual jobs that you might not have previously considered. In the following profile, you'll meet a woman who has created a whole new life for herself in her sixties, while juggling two very creative and enjoyable roles.
### Profile of a Creative Free Agent
_"I used to tell myself that I could never act or be in front of a camera. But I finally realized I was the only person saying 'I couldn't.' Why would I want to limit myself now?"_
—Eve Young, celebrant and acting extra
For most of her adult life, Eve Young devoted herself to raising her children and being an active community volunteer, while also working as a part-time bookkeeper. But when her children grew up and left their home in Glen Ridge, New Jersey, Eve decided it was time for something new. For a while, she entertained thoughts of using her volunteer experience as a launching pad for a career in public service, but after serious consideration, she chose to explore other avenues instead.
One day, while reading her local paper, she learned about the Celebrant USA Foundation and Institute, a nonprofit organization that trains people to conduct ceremonies and officiate at life-cycle events. Eve was instantly drawn to the idea. As a woman who is part Native American, she had grown up around rituals and ceremonies, and the thought of helping other people commemorate milestone moments spoke to her in a very powerful way. She not only liked the idea but was confident that with her well-developed public speaking, interpersonal, and writing skills she could do the job well. "It all dovetailed so perfectly with my background," says Eve. She enrolled in the institute, and within a year's time had completed her training and was ordained as an interfaith minister.
Eve's clients come from all faiths and backgrounds and although some hire her simply to officiate and "make things legal," most want her to create one-of-a-kind ceremonies that reflect their unique heritage, vision, and value systems. As an example, Eve designed a wedding ceremony for a bride who was a single mom of Polish heritage and a groom who was African-American. The service included a traditional Polish blessing offered by the bride's grandmother, the groom's gifting the bride's daughter a charm bracelet as a token of his promise to care for her, and the reading of traditional African prayers. "I try to find readings for couples that are very personal so they are saying things that really mean something to them," says Eve, emphasizing that she never allows her own beliefs or values to influence the process. "The ceremony is all about them."
Eve's fee starts at $350 for a basic ceremony and goes up from there for more customized services. The initial meeting with clients typically lasts ninety minutes, but the actual writing of the ceremonies can require significantly more time. She officiates at an average of two events per month, a schedule that gives her plenty of time to write the ceremonies without feeling rushed—and allows her flexibility to pursue her other weekday job, working as a background actor.
Just as discovering the Celebrant USA Foundation was a serendipitous find, Eve's entry into acting was also a bit of a fluke. "I really wasn't interested in acting at all," she says, "but I needed to find a way to make some extra money to supplement the celebrant work." Once again, she discovered an opportunity through the newspaper—this time as the result of a classified advertising for acting extras. Despite having no prior acting experience, Eve went in for the interview and was hired as an extra on the set of the television show _Ugly Betty_. One assignment led to the next, and over time she has built up a steady flow of freelance work, finding opportunities through her agents and by responding to casting calls advertised online. Eve typically works anywhere from one to three days a week, although she says she could work more if she wanted to. She gets paid $75 to $125 per day for jobs on movie sets and at least $250 per day for jobs working as a model for print publications. If her jobs are secured through an agency, she pays the agency 10 to 15 percent of her fee. "I'm not getting rich and famous," she says, "but I'm meeting really interesting people and going places I wouldn't have otherwise."
Eve hopes one day to land a small recurring role on a television show. But whether or not she realizes that goal is secondary to the delight she feels at having found such a fun way to earn an income. "I'm working with really fascinating people," she says. "Doing this allows me to meet interesting people who don't always travel life in a straight line." Working in the creative world has given her other benefits as well, as she has learned to relax more, loosen up, and let go of her concerns about "what's dignified and the image I'm expected to portray." When I asked Eve, who is sixty, how long she intended to continue working, she said she sees no end in sight, noting that she had recently worked on set with a woman who was seventy-five years old. "When I'm too old to stand up, I'll stop," laughs Eve, "but until then I plan to keep right on going."
#### Eve's Top Three Tips for Aspiring Acting Extras
1. **Be patient, but persistent**. It takes time to build up relationships with casting agencies and directors. Rejection is a big part of the acting profession—Eve says that she typically gets only one callback for every ten applications she submits.
2. **Use your age to your advantage**. Eve gets hired to play characters in the over-fifty age group. In an industry that is dominated by young starlets, her age gives her a marketing advantage. She has been advised by casting directors that she should leave her distinctive salt and pepper hair untouched; when they need an older person, they know to call Eve.
3. **Look for jobs online**. Eve finds jobs through sites like www.actorsaccess.com, www.nycastings.com, and www.castingnetworks.com, but she warns that you do need to be careful to choose your sites carefully. Although it is easiest to pursue this option if you live in New York or Los Angeles, other cities—such as Philadelphia, Miami, and Chicago, among others—have opportunities as well.
To learn more about the celebrant profession, visit the website of the Celebrant Institute and Foundation at www.celebrantinstitute.org. You can also read more about Eve's services at www.yourcelebrantceremony.com.
## WORK-FROM-HOME GIGS
How nice would it be to collect a paycheck without having to leave the comfort of your own home? In our service-based global economy, almost any job that can be handled using a telephone and a computer can potentially be outsourced to a home-based worker. There was a time when "outsourcing" meant shipping jobs overseas, but these days many companies are shying away from the cultural and management challenges of offshoring, in favor of "homeshoring" jobs to home-based workers in the States. That's good news if you want to enjoy a paycheck that comes with the flexibility and portability of a work-from-home (or work-while-you-travel) arrangement.
At one time the domain of customer service representatives and telemarketers, the world of work-from-home jobs has expanded to include many professional level opportunities, including nurses who work for insurance companies, software designers, tax preparers, and others. Here is a small sampling of the types of virtual jobs you'll find advertised on the Internet:
• **Customer service and sales:** customer service agent, concierge services, sales representative, employment recruiter
• **Counseling and coaching services:** relocation counselor, camp or college adviser, job-search coach, employee assistance counselor, health coach
• **Computer-based work:** researcher, web designer, programmer, online tech support, translator, graphic designer, data entry operator, medical transcription/coding, legal researcher, online instructor, bookkeeper
• **Writing and editorial services:** copywriter, proofreader, editor, virtual assistant, online content provider, freelance writer
A small number of these jobs will provide you with company-sponsored benefits and/or office equipment, but those opportunities are limited. Be aware that the majority of the virtual jobs advertised are for people willing to work as independent contractors, not for people interested in full employment situations.
### How to Find Virtual Jobs
• **Network**. Just like when you look for a "real" job, the best way to find work-at-home jobs is through your contacts. Make it a point to reach out to people you know who run their own businesses. Home-based entrepreneurs often lack the office space to house staff, so they are eager to outsource tasks like bookkeeping, telemarketing, and web design to home-based professionals. In general, assignments you find on your own through networking pay more than jobs advertised to the public.
• **Contact companies directly**. Most companies post their current job openings on their websites. But often the best opportunities go unadvertised, and as a result, it pays to approach companies directly as a way to find those hidden jobs before the competition arrives. You can do this one of two ways: either by networking your way into a personal introduction with a decision maker at the target company or by sending an e-mail and resume directly to the appropriate hiring department.
• **Find opportunities online**. Michael Haaren, cofounder of Ratracerebellion.com—an excellent source of virtual job listings, and publishers of a very useful free e-newsletter—recommends job aggregator sites such as Indeed.com and Simplyhired.com as legitimate sources of home-based jobs of all kinds. Haaren cautions that scams abound, so beware of promises of high income for little work, "no experience necessary," and "testiphonyals" (bogus testimonials), which often feature pirated photos. Again, remember the old adage, "If it sounds too good to be true, it probably is," and be very skeptical about paying money to sites promising online job listings.*
Sites that specialize in telecommuting and virtual jobs:
• Rat Race Rebellion (www.ratracerebellion.com)
• Telework Recruiting (www.teleworkrecruiting.com)
• FlexJobs (www.flexjobs.com)
## TEMPORARY AGENCIES
Many of you are probably familiar with the concept of working as a "temp," either because you worked as a temp at some point in your career or because you've hired a temp to help out in your own office. Temps have been used for years to fill administrative, clerical, and manual labor assignments, but companies now use temporary workers to fill professional jobs as well. Either way, it is a big business. According to statistics released in March 2012 by the American Staffing Association, in 2011 US staffing companies employed an average of nearly three million people per day.
Applying for work with a temporary agency is relatively easy. At many of the larger agencies, such as Manpower and Office Team, you can register and search for jobs online. If you opt to apply at an agency in person, you will probably be asked to fill out an application, take a skills test, and complete a brief intake interview. Your information will then be entered into a database and the agency will contact you when they have suitable openings. Some agencies provide benefits and many offer computer skills training.
To learn more: consult the classifieds section of your newspaper, search the online job boards, and take a look at the American Staffing Association (www.americanstaffing.net), which has a searchable database of agencies and an excellent collection of articles for temporary workers. Another useful site for finding temporary work opportunities is Net-Temps (www.net-temps.com).
## INTERIM EXECUTIVE FIRMS
If you are a professional who still craves the challenges of executive life, you'll be interested to know that during the past decade a new and more elite model of talent-on-demand services, known as "interim executive firms," has gained hold in the United States. Interim executive firms contract with senior-level executives to assist companies in need of "leadership on demand." Interim executives handle a variety of assignments: filling in for an executive on leave, managing projects that can't be handled by in-house staff, or helping less experienced leaders with navigating through a transition or merger. Companies use interim executive firms for part-time assistance when they can't afford to hire an executive on a full-time basis; private equity firms also use interim executives to help manage and restructure their start-up ventures.
If your resume includes experience as a senior-level executive, consultant, or business owner, you may be well positioned to work with an interim executive services firm. Life as an interim executive gives you the opportunity to work on interesting assignments, earn a professional salary, and participate in high-level projects while enjoying time off in between assignments. It is an intriguing option for people who still want to enjoy the adrenaline, excitement, and challenges of the executive life after leaving their full-time jobs.
To help you gain a better understanding of what interim executive services firms look for in their employees and contractors, I turned to Karen MacLeod, a pioneer in the executive services industry who is currently president of Tatum LLC, a US-based executive services firm.
**ADVICE FROM THE INTERIM EXECUTIVE EXPERT**
**"This is a growing trend; companies are much more comfortable now hiring high-level variable workers. You can make a good permanent living being a variable worker."**
—KAREN MACLEOD, president, Tatum LLC
**What type of employees does your firm hire?**
K.M: We seek executives with broad-based accounting and finance experience. We like interesting personalities who can learn, adapt quickly to a number of different types of client environments, and easily build relationships with new clients.
**Are your interim executives considered employees or independent contractors?**
K.M: They are considered employees who work for Tatum on a project-to-project basis. Compensation is competitive with the market standard for full-time employment. Health insurance is offered after a sixty-day waiting period.
**Why are executive services firms a good fit for people over fifty who want flexibility?**
K.M: We only hire seasoned talent, and as a result, almost all of our employees are at least forty years old. In truth, because our business flow is subject to fluctuations, we prefer employees who aren't looking for a full-time schedule year round; it is more stressful for us to work with people who have a mortgage to pay and need a guarantee of a full-time salary. Interestingly many of our older workers tell us that now that they are empty nesters, they actually enjoy the opportunity to travel to different parts of the country. It can be a nice way to get to live in different cities without having to pay for travel out of your own pocket.
**Do all assignments require travel?**
K.M: There is a lot of travel with this type of work, but you don't have to travel all the time. Increasingly we have opportunities for employees to work from home, at least part of the time.
**What advice do you have for people who want to work as interim executives?**
K.M: We look for talented and experienced people who embrace change and strive to remain relevant, valuable, vibrant, and creative. If you are that type of person, we will work hard to keep you on assignments.
**How much flexibility can you realistically offer employees?**
K.M: When our employees are on assignment, we expect them to work the same hours they would as if they were permanent staff. We are fond of saying, "Don't look at it as if you are an interim; look at it as you are the CFO." But in between assignments, the employee is free to pursue other interests. It's a great fit for people who want to take blocks of time off between projects. Obviously the more parameters someone places around when they can work, the more challenging it can be to place them on assignment, but we try hard to accommodate the needs of our top talent. Our people are our business; retaining our best people is a key priority for us.
**Karen's Top Three Tips for Working as an Interim Executive**
1. **Spend time tweaking your resume to showcase your full range of experience**. Your skills are important, but we are even more interested in your ability to adapt to a number of different types of situations, personalities, and work environments.
2. **Invest in your professional presence**. It's important to look and act current. Be willing to update your wardrobe and invest in learning new technologies—texting is no longer just for your kids or grandkids!
3. **Realize that attitude trumps ability**. A good attitude is the single most important thing. We look for people who are flexible, open-minded, and happy to work with a diverse group of people.
To find interim executive services firms in your area of expertise, start with a Google search and by asking colleagues for recommendations of reputable firms. Most firms advertise their services on the major job boards.
**THREE KEY CONSIDERATIONS ON TRADING YOUR TIME FOR A PAYCHECK**
1. **Benefits**. Part-time jobs can sometimes provide a useful way to secure benefits after leaving a full-time employer. Although the number of companies that offer part-time benefits is limited, and in most cases you will need to work at least thirty hours per week to qualify for them, part-time benefit packages can include health insurance, paid holidays, vacations, 401(k) plans, and company discounts. Large retailers like Costco, chains like Starbucks, and many hospitals offer good part-time benefit packages. Be sure to check the websites of companies you like for more information.
2. **Hours**. Working part-time can be wonderful, but be careful to avoid situations in which employers try to squeeze full-time responsibilities into part-time hours. Ask questions that give you a good understanding about your expected job duties and responsibilities before you accept any position.
3. **Lifestyle objectives**. There are always tradeoffs involved in every work situation. A part-time job provides the security of a paycheck but doesn't provide the freedom associated with being on your own; a temp job gives you needed income, but you have to continually adjust to new work environments; and seasonal employment provides variety but also includes periods of time when you will earn no income. Be clear in your own mind about what is most important to you—and your lifestyle objectives—before you go looking for part-time income solutions.
* Both Telework Recruiting and FlexJobs charge a small fee for access to their sites, but in their case, I believe it is money well spent.
# CHAPTER SIX
# **Make a Living While
Making a Difference**
For many people approaching retirement, earning income may now be a secondary goal compared to the desire to make a difference in the world. They don't want to just leave a legacy; they want to live one! If that is true for you, consider yourself in very good company. According to a 2011 study by Civic Ventures, a nonprofit think tank on boomers, work, and social purpose, as many as nine million people aged forty-four to seventy are already working in "encore careers" that combine personal meaning, social impact, and continued income; and an additional thirty-one million people in the same age group say they are interested in finding encore career–related work. That means roughly 40 percent of all boomers hope to be able to find a way to give back through their second-act careers. As a career coach who specializes in working with older adults, I find these statistics to be in line with my own client experience. Indeed, the majority of my second-act clients express a strong desire to find work that will enable them to leave a more meaningful mark on the world.
In this chapter, we will examine different ways you can use your second act to create your own encore career. But before we get into the specifics, I want to emphasize that doing "good" work doesn't mean you are restricted to working for a nonprofit or in the public sector. Not everyone can, or should, go to work for a nonprofit, and if you consider only nonprofit paths, you may end up shortchanging both yourself and the greater world around you. As I am fond of saying to my clients: "You don't need to be Mother Teresa to a make a difference in the world. Mother Teresa needed to be Mother Teresa. You need to make a difference by honoring _your_ unique gifts."
Thankfully no single industry, organization, or profession offers the one right path to making a difference in our world; every endeavor holds the potential to make the world a better place. A fashion designer makes a difference when she donates her dresses to students who otherwise wouldn't be able to attend the prom. An architect who designs a cancer center that fosters emotional, spiritual, and physical healing makes a difference to people dealing with life-threatening illness. And a successful entrepreneur who creates new jobs makes a difference by giving people a way to support themselves and their families.
Each of these professionals makes a significant contribution to the world through her or his respective talents—and you can too. At a time when there are so many problems to be solved in our world, our nation, and in our local communities, there has never been a better moment to put your experiences and wisdom to good use.
## WORK FOR A NONPROFIT ORGANIZATION
Having just insisted that you don't need to work for a nonprofit organization in order to make a difference, I present this option first because it is the one most people think of when they consider doing good works. The nonprofit world is vast and diverse; it includes charities, advocacy groups, foundations, religious institutions, arts groups, universities, hospitals, associations, and unions. According to Independent Sector, a leadership network for the nonprofit and philanthropic communities, nonprofits and foundations play a major role in our economy; they employ 9 percent of the American workforce and account for 5 percent of our gross domestic product.
Whether you want to work for a museum, a charity, or an advocacy group, it is likely you will find the experience of working at a nonprofit somewhat different from your experience in the for-profit sector. On the positive side, nonprofits are generally regarded as nice places to work: kindness, passion, and purpose are more highly valued than in profit-driven companies, work schedules tend be more flexible, and the joy of working for a mission-driven organization is a welcome change for people accustomed to putting profits before people. That said, working at a nonprofit is not always an ideal situation. Most organizations still have their share of office politics (people are people, after all), and the realities of working with a limited budget, a volunteer staff, and a dependency on erratic funding sources can prove problematic and stressful.
Consequently, if you think you want to work for a nonprofit, take the time to consider your options before applying for work. Carefully assess your skills, experience, and interests, and then begin to explore ways you can best use your skills in organizations that appeal to you. It can be helpful to first volunteer or serve on a nonprofit board as a way to become familiar with an organization and its culture before committing to a more permanent employment relationship.
To help you gain a better understanding of what your transition into the nonprofit world might involve, I interviewed Barbara Salop, age fifty-eight, a career IBM executive who recently made her own transition into the nonprofit world.
### From IBM Executive to Nonprofit Consultant
_"People think there aren't many good business people in the nonprofit world, but there are wonderful people—they just have a whole lot less to work with than people in the corporate world."_
—Barbara Salop, nonprofit consultant
Barbara Salop, a former client of mine from Riverside, Connecticut, has long been a strong supporter of organizations that benefit people with developmental disabilities. But because she was a full-time working mother of two, the number of hours Barbara was able to devote to volunteer activities was restricted by the demands of work and family. So in 2010, when she was able to retire with full benefits from IBM, Barbara decided to take her executive expertise and apply it to the nonprofit sector. Recognizing that she needed to get some serious nonprofit experience in order to strengthen her credentials and her familiarity with the nonprofit world, Barbara spent eighteen months working as a pro bono consultant for several local nonprofits. She then applied for and was accepted into the Hartford Encore Fellows program, a workforce development program that helps seasoned professionals transition into the nonprofit sector. That program gave her an opportunity to immerse herself in the nonprofit world through classroom training, job shadowing, and a two-month internship experience. It also gave her a chance to get to know people actively working in the sector, as well as build a peer group of other executives who were also actively transitioning into the nonprofit sector. At the time I interviewed Barbara, she was starting her first paid consulting assignment with an organization she had originally worked for as a volunteer. I asked Barbara for her impressions of the nonprofit arena:
#### **What are the most striking differences between life at IBM and the nonprofit world?**
B.S: There are lots of similarities, but also plenty of differences. In corporate, it is all about making money, but in nonprofits, the focus is on the mission. Nonprofits sometimes make decisions that seem nonbusiness-like to the rest of us, but they represent tradeoffs that reflect their determination to put the mission before the money. It takes great discipline to make those tough choices, especially when funding is scarce. I have the deepest admiration for that level of commitment to a cause.
#### **Did you notice a difference in the types of people who work for profit versus nonprofit?**
B.S: I was very impressed by how happy most of the nonprofit executives seem to be. I don't mean to make it sound like it is always perfect in a Pollyanna-like way, but there was a real sense of mission, purpose, and fulfillment among the people I met. Even when they were having a tough day, it was clear that they have an underlying sense of happiness about what they are doing. Although I had many good days at IBM, and was proud of what my team accomplished, I rarely experienced that same sense of deep fulfillment from my corporate work.
#### **How did the nonprofits where you volunteered react to you being a "corporate" person?**
B.S: That was interesting. On one hand, there seemed to be some trepidation about a corporate person walking into a nonprofit. Their perception is that corporate types are only about the numbers, and we make decisions based on measurements and profits alone. On the other hand, some people are almost awestruck by people from corporate and [practically] treat us like we are from a different planet. I found it to be so important to take the time to listen to what they had to say, learn from them, and respect their expertise.
#### **There are so many ways to volunteer. How did you decide which organizations to approach about volunteering?**
B.S: I knew that I wanted to focus on working with organizations that support people with developmental disabilities, so I targeted those types of opportunities. In terms of what you choose to do for them, there are essentially two ways to help. One is to do the easy, hands-on things like stuffing envelopes or serving at a soup kitchen. It is needed work, and they will appreciate your time. But if you are an experienced businessperson, I think you owe it to the nonprofit to find a way to leverage your professional expertise. They are so grateful when you can help them do the things they can't do or don't have the time to do, like project management, facilitation, or strategic planning.
#### **After being a long-term volunteer, how did you broach the subject of getting paid for your work?**
B.S: I hung around long enough for them to really value my business expertise! When you can get them to see your value proposition and understand the business case for your fees, it is a much easier sell. Even once I was done with projects, I checked in with my volunteer sites to follow up with them about their implementation plans. Over time they realized that it would pay to keep me around. I think it also is helpful to offer your services as an independent contractor instead of expecting the organization to hire you. In this economy, if they have the option of bringing in a variable worker, it makes sense for them to do that. It may cost them a bit more in the short term, but it gives them greater long-term flexibility.
#### **How did you know what to charge?**
B.S: Quite honestly, it was difficult to know what to charge. I asked my friends in nonprofits who had previously hired consultants for their suggestions. I was willing to start with a low rate because I knew I still had a lot to learn and I needed to get some more experience in the sector. I suspect that as I continue to contribute and add value, there will be opportunities for me to raise my rates.
#### **What suggestions do you have regarding the nonprofit job search?**
B.S: Like any job search, networking is critically important, and I spent a lot of time on that. Sometimes I felt like I was just going for endless cups of coffee, but it paid off in the end. In terms of resources, LinkedIn is an invaluable tool that I used to identify board members and volunteers at organizations that appealed to me.
#### **Do you have any additional thoughts for people considering making a switch to nonprofits?**
B.S: Take your time in determining the types of organizations you want to work for. You are going to get paid a lot less than you earned in corporate, so find a sector that really speaks to you. This transition can take longer than you anticipate, but have faith that it will be worth the effort.
Here are five excellent resources to help you make the transition into the nonprofit sector:
1. **Encore.org (www.encore.org)**. If you are over forty and want to get involved in helping to make the world a better place, you owe it to yourself to get familiar with both Civic Ventures and Encore.org. Civic Ventures funds a number of initiatives, fellowships, and programs designed to help boomers solve serious social problems (including the fellowship program Barbara attended). The Encore.org website, published by Civic Ventures, is the single most comprehensive resource for boomers interested in careers that combine personal meaning, social impact, and continued income. Their outstanding guide to encore careers can be downloaded for free at www.encore.org/files/PDFs/guide/encore_guide.pdf. Marc Freedman, the CEO and founder of Civic Ventures, wrote the book _Encore: Finding Work That Matters in the Second Half of Life_ (PublicAffairs, 2008)—it is a compelling read for anyone interested in this subject.
2. **Bridgestar (www.bridgestar.org)**. Bridgestar.org is a site for seasoned executives who want to transition from the for-profit sector into nonprofits. They have an extensive career center and a job board that lists both staff jobs and nonprofit board positions.
3. **Idealist (www.idealist.org)**. Idealist.org is a must-visit for anyone interested in exploring the world of nonprofits. The site features career advice, a job board, and information about events, fellowships, internships, volunteer opportunities, and educational programs in the nonprofit world.
4. **The Foundation Center (www.foundationcenter.org)**. Whether you want to establish a foundation, learn how to write a grant, or secure funds for research, this is the right site for you. The Foundation Center is the leading source of information about philanthropy worldwide, with a site that lists training programs, job openings, and other useful resources.
5. **National Council of Nonprofit Associations (www.councilofnonprofits.org)**. The National Council of Nonprofit Associations is the network of state and regional nonprofit associations serving more than twenty thousand member organizations. Although this site is geared toward nonprofit administrators, their resources will help educate you about key issues relevant to smaller nonprofit organizations.
Finally, if you want to stay up-to-date on the latest news in the world of philanthropy, a great resource is the _Chronicle of Philanthropy_ (philanthropy.com). It is both in print and online, and it is like the _New York Times_ of the philanthropy world.
## SERVE IN THE PEACE CORPS
Have you ever thought about serving in the Peace Corps but assumed you'd missed your chance when you didn't enroll right after college? Well, think again! Now might be the perfect time to recapture that long-lost dream. Contrary to what most people think, the Peace Corps is not just for recent college graduates. More than 5 percent of Peace Corps volunteers are over age fifty, and at the time this book was written, the oldest serving Peace Corps volunteer was eighty years old! (You may remember reading about the Peace Corps's most famous older volunteer, Miss Lillian, President Jimmy Carter's mother, who served in India at age sixty-eight.)
The use of the word "volunteer" is a bit misleading, because the Peace Corps does pay volunteers a monthly stipend and a readjustment allowance. They also provide comprehensive health insurance and round-trip transportation to and from the destination country. After you complete your service, if you later apply for federal jobs you will receive preferential treatment; there are also opportunities for graduate school scholarships, fellowships, and internships.
Life in the Peace Corps isn't known for being easy, but it can be a highly rewarding, deeply meaningful, and life-changing experience. Volunteers are needed with expertise in a number of different areas, including education, youth and community development, information technology, agriculture, environment, business development, and health-related issues. Following a careful vetting process, the Peace Corps will determine where you will serve and what you will be asked to do; you will be placed with the host country that can best use your skills. Volunteers commit to a twenty-seven-month service term, which includes a three-month immersion-training program to learn a new language, technical skills, and cultural considerations. Upon completing your training, you'll live in the community you serve, which could be a small village, a medium-size town, or a bustling urban environment.
People who are interested in pursuing this option need to plan ahead. The application process can take nine months to a year, and not all applicants are accepted (note that 90 percent of applicants have a college degree). All applicants undergo a thorough and rigorous medical and dental assessment to determine whether they are medically qualified to serve—an evaluation that, if you have preexisting conditions or a complicated medical history, can take longer and require additional medical testing. The Peace Corps does accept married couples, but the placement process will likely take longer, and there must be a suitable assignment for each applicant in the same location.
To learn more, visit the special section on the Peace Corps website specifically for applicants over fifty: www.peacecorps.gov/50plus. Another helpful resource is _The Insider's Guide to the Peace Corps_ by Dillon Banerjee (Ten Speed Press, 2009).
## CREATE YOUR OWN NONPROFIT
Have you been frustrated in your efforts to locate the perfect nonprofit employer? It can be harder than you expect to find the right match. That is why for some people the best way to give back is to create their own nonprofit organization, foundation, or charity. Starting your own nonprofit can be a wonderful way to support initiatives that you really care about, especially when they are not being adequately addressed by existing foundations or charities. But as with any start-up venture, the effort involved with getting your new nonprofit organization up and running is considerable, and with over one and a half million nonprofits already vying for funding, attention, and volunteers, you'll want to ensure that the one you start is unique enough to thrive in a competitive marketplace. It can take several years before you're able to fund salaries, especially your own, so this is an option that works best when you have an alternate source of income to sustain you during the start-up phase. It can be a challenge to run these organizations, so plan on working long hours, at least until you are able to get the organization on a solid footing.
To help you gain a better understanding of what it might be like to run your own nonprofit, I interviewed two women who created their own nonprofit endeavors. They represent two very different types of organizations, but in each case, the woman is having a wonderful time working hard on a cause she cares passionately about. Their energy, dedication, and creativity are truly remarkable.
### **From Artist to Activist: A "Hag" on a Mission**
_"It's amazing to live a life that is aligned with one's purpose. My purpose is to make art and promote artists who would otherwise not be seen. It's been a fast and fun ride, with each day getting better and better."_
—Terri Lloyd, cofounder of the Haggus Society, Highland Park, California
Since she was a little girl, Terri Lloyd loved creating art. But as is true for so many women of her generation, the need to balance her roles as a mom, wife, and full-time worker (in Terri's case, as a marketing professional) left her little free time to devote to her fine art. As she approached her fiftieth birthday, Terri felt a strong desire to pursue her art on a more full-time basis. With her husband's blessing and support, she made the decision to leave the traditional nine-to-five workplace behind.
While transitioning into life as a working artist, Terri began to wonder whether there was funding available to help support older women artists like herself. But the more she explored, the more discouraged she became. Instead of discovering exciting scholarships and grants, her research revealed that there was surprisingly little institutional support for women who had put their artistic pursuits on hold for families and career. Terri knew she was not the only reemerging artist struggling with the lack of funding. Indeed, most of her women artist friends had taken time away from their creative pursuits to raise families. Once she realized the full scope of the funding problem, Terri was angered—and motivated—enough to put aside her desire to immerse herself in her own art and instead refocused her energies on creating a better support net for her fellow female artists.
Working together with her best friend, artist Monica Marsh, Terri formed the Haggus Society, a membership-based organization for older women artists "with an edge," whose creative endeavors don't necessarily fit into the "hygienic mold of what is perceived to be feminine." The name Haggus is a play on words that resulted from a conversation between the two founders when one of them noted, "We need something for 'old hags like us'!" Thanks to her prior experience working for a nonprofit arts group, Terri was able to get the society organized and off the ground quickly. She knew how to approach sponsors and apply for grants, and as a skilled marketer she also was able to quickly attract publicity and media attention.
By the end of their first year of operation, the group had secured a fiscal sponsor, enrolled their first forty members, and launched several exhibitions. Membership dues in the Haggus Society range from $50 for low and limited income members up to $500 for lifetime membership. Benefits of membership include opportunities to participate in juried shows, peer reviews, marketing services, and educational programs. Initially envisioned as strictly for midlife and older women, the makeup of the organization has evolved over time. "We have attracted attention from some younger women and some men as well," says Terri. "It's interesting to see where it goes. I am open to whoever wants to jump on board."
Terri is not currently earning an income from her nonprofit, but she anticipates drawing a salary within three years. According to Terri, it takes about three years to build up enough of a track record to qualify for the big funding sources. In the meantime, she helps support herself through the sale of her art (and her husband's financial backing). When the organization does apply for the more significant grants, they will be required to have a paid executive director on staff, and Terri anticipates that she will fill that role.
As exciting as this new venture is, Terri is already thinking about her exit plan, determined not to overstay her welcome and hoping to eventually have more time to devote to her own art. "I want the organization to stay fresh and current," says Terri, noting that five years from now she wants to cede her leadership role to someone who can keep the organization robust and vibrant. But until that happens, she is energized and enthusiastic about continuing to work to develop the organization. "I am having the time of my life. I really am," she says. "It's amazing to be doing this thing that is all about my passion for the arts and my desire to give women, particularly women over forty, a voice in the arts."
#### **Terri's Top Three Tips for Creating a Nonprofit**
1. **Develop a plan and a strategy**. You need a plan, even if it is a loose one. Terri has what she calls "a living document" posted on her wall: a month-to-month guide to her goals and action plan. She continuously evaluates what is working and what is not, and she adjusts as she goes along.
2. **Do your homework**. Learn what it takes to put together a nonprofit, and educate yourself about what it takes to write a grant.
3. **Be patient**. Terri says, "Success isn't one big shebang; it is many small steps, lots of failures, and the accumulation of the learning along the way. All roads lead to someplace. Everything I've learned in my life has contributed to this moment."
### **A Recipe for Nonprofit Success**
_"If you had told me in 2005, when I rolled into my first classroom to give a cooking class, that only six years later I would be designing an e-learning website, have dozens of employees, and be taking our program to a national scale, I would never have dreamed it."_
—Gracie Cavnar, founder and president, Recipe for Success
Obesity is a serious and growing epidemic that threatens our nation's future. The latest statistics indicate that more than 30 percent of American children are overweight and at risk of developing obesity. In Texas, where Gracie Cavnar lives, nearly 50 percent of fourth graders fall into an at-risk weight category. But while most of us simply worry about the impact of this epidemic, Gracie decided that talk alone wasn't going to solve anything. A vibrant woman, with significant professional and volunteer experience, she knew that she had the resources, connections, and personal determination needed to make a difference—she just needed to figure out the best way to make it happen.
Gracie set out to learn everything she could about the obesity problem, a research project that took nearly ten years to complete. Initially she planned to use funds from her family foundation to help finance other people's foundations and initiatives. But the more she learned, the more determined she became to play a bigger role in the solution. That determination, along with funding from Gracie's family foundation, led to the establishment of the Recipe for Success (RFS) Foundation, a 501(c)(3) organization dedicated to combating childhood obesity by changing the way our children understand, appreciate, and eat their food.
Using a curriculum designed to make learning about good food fun, RFS focuses on preventing obesity by teaching children healthy eating habits before obesity sets in. The concept behind RFS is a simple one: when children become familiar with food from "seed to table"—planting the seeds, harvesting the crops, and cooking the food—it can change the way they eat for the rest of their lives. As children experience the difference between how processed food and real food tastes, they start paying more attention to what and how they are eating, and that results in healthier lifelong eating patterns. According to the RFS website, "children need to learn that food doesn't grow in drive-through windows and plastic wrapping; that a Twinkie is not a vegetable."
The RFS foundation launched with a pilot program in five Houston elementary schools. One of their first offerings was Chefs in Schools, a monthly cooking class taught with the assistance of twenty-four volunteer professional chefs from the Houston area. Using tools, ingredients, and lessons provided by RFS, the children worked together with the chefs to blend pesto, bake muffins, and cook ratatouille. (The food was harvested by the students from gardens that were built in each of the pilot schools.) For some of the students, it was the first time they had ever eaten meals prepared with entirely fresh food, and for all the students it proved to be a memorable culinary experience.
What started as a pilot program run by Gracie, her assistant, and a group of dedicated volunteers quickly extended to many more Houston area schools. In their second year, RFS also began to offer monthlong summer camps for third to fifth graders and special nutrition classes for parents of infants and toddlers. Today Gracie oversees a paid staff of over twenty-five employees, and, working in collaboration with the Presidential Task Force on Childhood Obesity, RFS is developing an e-learning website that will provide remote teacher training and certification of their Seed-to-Plate Nutrition Education programs in affiliate locations across the United States. Future plans on the drawing board include a national television program and a companion series of cookbooks.
Not surprisingly Gracie and her foundation have attracted attention and accolades from a distinguished group of admirers, including the mayor of Houston, Dr. Mehmet Oz, and even President Obama. In 2011, _Self_ magazine honored Gracie as a recipient of their Women Doing Good award. Gracie is both flattered and humbled by the recognition, but she stressed that the press is most important because it brings attention to the work of the foundation and the problems of obesity. "I am always deeply thankful when somebody notices," she says. "If I can inspire someone else who has the time and ability to help, that is a big deal because there is so much that needs to be done." The success of RFS can be credited to many different factors, but the fact that Gracie was a seasoned volunteer who had previously volunteered for dozens of philanthropic endeavors in the Houston area has proved invaluable. As an experienced volunteer, she understood the best way to structure her own nonprofit and was very familiar with the demands of managing a volunteer organization.
Nonetheless, the road to success hasn't been without its challenges. Managing an organization with twenty-five employees (and counting) has been a self-described stretch for Gracie, who in her former careers as a model, architect, and journalist had always purposefully avoided being a manager. But as the director of an evolving organization, Gracie realized that if she wanted RFS to be more than just a "flash in the pan," she needed to learn to thrive outside her comfort zone. "It's been a real growth path for me," she notes, "learning in my mid-fifties how to manage an organization, how to create and execute a long-range plan, and how to scale our program for a national audience." As the foundation's full-time executive director, Gracie admits that she is running "full-tilt" (Gracie's husband retired nine months after she started RFS, but because she was so busy, he decided to return to work) and indicated that she thought she was about a year away from being able to cut back to a more part-time schedule. In spite of the long hours involved with running a nonprofit, Gracie has never felt more alive; she is impassioned by her mission and believes that others can experience that same wonderful sense of satisfaction from engaging in meaningful work. To learn more about Recipe for Success, visit www.recipe4success.org.
#### **Gracie's Top Three Tips for Working in the Nonprofit World**
1. **Value your business skills**. There is no shortage of people who have enthusiasm and dedication for meaningful causes, but it takes people with solid business skills to make a nonprofit successful. Broad-based business skills like accounting, HR, and marketing are always needed; administrative and office skills are also highly valued.
2. **Embrace a "roll up your sleeves" attitude**. There is a lot of fluff built into corporate. But in nonprofits, you've got to be a real renaissance person who can juggle many different tasks. "It is important to be nimble and organic in response to the market," says Gracie. "You have to have your head up at all times in order to adapt to what is going on."
3. **Don't plan an organization around the founder**. Like Terri Lloyd, Gracie also emphasizes that the organization needs to be able to thrive whether or not she is there. "That should be the goal of any organization," she says.
To learn more: Managing a nonprofit requires fund-raising, organizational, and management skills, along with an understanding of the administrative, legal, and tax side of the nonprofit world. Fortunately many colleges offer courses in nonprofit management that can help educate you on the basics for success. The Foundation Center at www.foundationcenter.org is another helpful resource. The US Small Business Administration has posted links of federal programs and services useful to nonprofits at www.sba.gov/content/nonprofit-organizations.
## CREATE PROFITS WITH A PURPOSE
Even though not everyone is cut out to work for a nonprofit, that doesn't mean you can't still find a way to give back through for-profit pursuits. Many of the people interviewed for this book have found creative ways to make a positive difference in the world through their businesses: by mentoring others, using their work to give voice to an important message, donating a portion of their profits to charity, or creating a service that makes life easier, better, or safer. Their commitment to run their businesses with a focus on making the world a better place both inspired and impressed me. I think they will do the same for you.
### **Four Socially-Minded Entrepreneurs**
**Anita Mahaffey, CEO of Cool-jams, San Diego, California**
How she makes a difference:
• Donates 20 percent of profits to charities
• Volunteers to mentor new entrepreneurs
Back when she was a high school student, Anita Mahaffey spent a year as a foreign exchange student in Turkey. At the time, it was simply a fun thing to do. But that trip ultimately played a major role in her career path, not just once but twice over the course of a thirty-year period. The first connection happened when Anita traveled back to Turkey after starting her family. While there, she visited with friends who took her on a tour of their factory, and as a result of that visit, she started a business importing bathrobes from Turkey. Anita's business ran successfully for a number of years, but as she approached her late forties, she decided to "retire" in order to spend more time with her family and volunteer activities.
During her "retirement," Anita took yet another trip back to Turkey, and once again, inspiration struck. While visiting with her former Turkish partners, she learned that they were manufacturing a new microfiber fabric that wicks moisture away from the body. As an avid hiker and runner, she was already familiar with the benefits of wearing microfiber apparel to stay warm and dry. But when Anita, who was suffering with hot flashes at that time, felt the fabric, she thought, "Why not use this to make pajamas that help keep menopausal women comfortable while they sleep?" Excited by the idea, Anita took a sample piece of the fabric home, and after bringing it to an independent laboratory that tested and confirmed the fabric's quick-drying capabilities, she was convinced that she had a winning business concept in hand.
Ever the entrepreneur, Anita decided to abandon retirement and reenter the business world. She launched Cool-jams (www.cool-jams.com) as an online store in 2008, and, despite a challenging economy, the business took off and has been profitable ever since. The site now sells bedding products and pajamas for a growing customer base of travelers, nursing mothers, and people suffering from night sweats caused by chemotherapy, obesity, menopause, and other medical issues. As the business grows, she is actively investigating ways to expand her distribution to other retail outlets.
One of the things Anita, now age fifty-three, appreciates most about her business is that it allows her to share her success with others less fortunate. Each year she donates 20 percent of the company's profits to charities focused on women and families. In just three years' time, the company has donated nearly $35,000 to charities. Anita hopes there will be many more donations in the years to come. "When we make money, we are able to give more," said Anita. "It is a win-win for everyone." In addition to donating a percentage of her business profits, Anita volunteers her time mentoring other entrepreneurs and sharing her business expertise. It is an activity that she undertakes with equal parts joy, gratitude, and obligation. "I think it is important to use our gifts to give something back," says Anita. "For me, I am good at starting businesses, so that is how I can make a contribution. I can give with my time, my products, and my profits. It makes me really happy to be able to do that."
**Dewey Crepeau, J.D., director of A Gift of Hope Adoption Agency, Columbia, Missouri**
How he makes a difference:
• Unites children in need with parents who want children
• Donates his expertise to nonprofit adoption organizations
As a young lawyer starting out in private practice in Columbia, Missouri, Dewey Crepeau worked on a variety of legal issues. Most of his caseload revolved around criminal and civil matters, but every once in a while he was given responsibility for managing an adoption case. Out of all his assignments, Dewey enjoyed the adoptions most. However, as much as he loved those types of cases, he couldn't afford to work on them full-time; he had a family to support and couldn't restrict his practice to just adoptions.
But after his children grew up and his daughter earned a master's degree in social work, Dewey finally got the chance he had been waiting for. In a case of "like father, like daughter," his daughter decided that she wanted to go to work for an adoption agency. At the time, she was unable to find work with an agency in St. Louis, but in her efforts to find a job, she connected with a woman from California, Tina Tyra, who was involved in adoption counseling on the West Coast. As luck would have it, Tina was interested in the possibility of establishing an adoption agency in the Midwest. The two of them started talking, and it wasn't long before they turned to Dewey for advice about opening an agency. Dewey was finally at a point in his own career when he was ready to focus on adoption cases. After many conversations (and lots of paperwork), the three of them teamed up to establish A Gift of Hope Adoptions agency in 2005.
Dewey now earns his living as the executive director of the agency while also maintaining a small private practice on the side. His daughter works as the director of placement services (primarily working from home while caring for three small children), and Tina, who still lives in California, functions as their West Coast adoption and communication consultant. Dewey, now age fifty-seven, is delighted that after all these years he is able to apply his professional expertise to an arena that means so much to him. (And as an added bonus, he also gets to spend more time with his daughter.) Although he could earn more doing other types of work, he knows that his legal expertise makes a very real difference to both the children and the parents involved in the adoptions, and no matter how many cases he handles, he never tires of the joy he feels each time after helping to place a child in need with a loving family.
**Lisa Dudley, singer and performer, Troy, New York**
How she makes a difference:
• Promotes inspiration, hope, and healing through her music
• Performs benefit concerts for veterans
Lisa Dudley was "born singing." Growing up, she sang at Girl Scout events, in the choir, and at church. She planned to major in music in college—a plan that was derailed after she transferred schools, got married, and started working, first as a secretary and later as a home mortgage loan officer. Even though music took a back seat to earning a living, she still always found a way to keep music in her life: singing, writing songs, and performing whenever and wherever she could.
When her father fell ill and needed surgery, she sang to him in the recovery room, moving the attending nurses to tears. "That was when it really hit me that my singing affects people in very profound ways," says Lisa. She traveled to Nashville, where she recorded her unique blend of country, gospel, and folk songs. Lisa's music is about hope: hope for war veterans struggling with their injuries, hope for patients recovering from illness, and hope for older women coming to terms with their changing bodies and circumstances. Lisa says her goal is to use her music to help move people from darkness into a place of joy.
Over the years, Lisa divorced, moved to upstate New York, and remarried. Now, at age fifty, she is finally able to focus more of her energies on building her music career. She sells her CDs at her performances and online through CDBaby.com. Lisa is also promoting her scores for use in television and movies, and she trusts that, with time, she will be able to earn a full-time income from her music. She is performing more frequently and has donated the proceeds from some of her concerts to organizations that work with veterans' groups. She is also hoping to find a major Latin artist to record the Spanish version of her song _I Believe in America_ , a project that has been encouraged by her Latino friends who want to have an inspirational patriotic song recorded in their native tongue.
**Susan Nisinzweig, founder,EytanArt.com, Riverside, Connecticut**
How she makes a difference:
• Anti-bullying advocate
• Donates a percentage of profits to charities
Susan Nisinzweig's oldest son, Eytan, is a twenty-five year-old man with autism. Although he has limited social skills, Eytan is a gifted artist who draws with a simple and captivating style that reflects a childlike wonder of the world. For many years, Susan, a social worker by training, thought about doing something special with Eytan's art, but her good intentions never translated into action—that is, until one day when she began to consider the possibility of pairing Eytan's drawings with inspirational sayings. She began to wonder whether she could have phrases that celebrate our differences, encourage civility, and promote respect for others printed on products like T-shirts and posters, and the more she thought about this idea, the more excited she became.
Looking back on that moment, Susan knew she had found her mission. "The thrill, or shiver was unmistakable, and the ideas were so powerful that this time they didn't disappear down the drain of the shower," said Susan. "I knew that this was one of those ideas that I had to make a reality. I knew that this one really mattered and was what I was meant to do." With focus, drive, and determination, the pieces of the entrepreneurial puzzle quickly began to fall into place. Although Susan had no prior experience with the retail clothing business, she researched the worlds of shirt manufacturing, online sales, and internet marketing. Talking to anyone who would listen, and adjusting plans as she learned, Susan quickly found a printer to produce the shirts, built a website, and launched her business selling EytanArt's products online, at craft fairs, and at fund-raising events.
The reaction to Eytan's work has been overwhelmingly positive, and orders have come in from around the globe. In addition to championing a message that celebrates differences, Susan delights in using her business as a vehicle to support meaningful causes and organizations. To date, sales of Eytan's work have already helped to provide over twelve thousand nutritious meals to malnourished children overseas, and his artwork has been displayed by organizations that support research for autism. Looking toward the future, Susan, age fifty-four, jokes that she has so many ideas for growing the business and spreading Eytan's messages of inclusion and acceptance that she expects to work well into her eighties in order to make them all a reality!
### Three Additional Insights from Socially Minded Entrepreneurs
1. "Don't be so in love with your original idea that you fail to see what else is out there. If you keep banging your head against the wall, you need to go in a different direction. The people that are successful are the ones that are willing to tweak things as they go along." —Anita Mahaffey
2. "When I've had success in something, it's normally something I really didn't slave away for and get; it's like the right moment came. I often think of the Shakespeare quote, 'There is a tide in the affairs of men.' You can do all the background work, but if the timing isn't right, none of it will come to fruition. Don't try to force it. Wait and let it all come together." —Dewey Crepeau, J.D.
3. "Starting something new in my fifties was a little scary and intimidating because I knew I'd have to use a lot of the new technology and I didn't know much about any of it. I had never created a website, didn't even know what a blog was, or what a tweet looked like, or how to use Facebook. But I was highly motivated by sharing Eytan's art and by the messages about respecting differences, so I concluded that I had to follow my intuition and trust that I would learn what I needed to learn." —Susan Nisinzweig
## WORK FOR A BUSINESS WITH A CONSCIENCE
Finally, this last idea is for those of you who want to continue working within your industry, but in a more socially conscious manner. Idealist.org, an outstanding site for people interested in socially responsible careers, suggests that job seekers can enter into a business career with social impact through three different paths:
1. You can find a position focused on corporate responsibility and sustainability within a for-profit entity.
2. You can secure employment with a socially responsible company that values the triple-bottom-line approach (people, planet, and profits) as a core value in their business.
3. You can focus on opportunities within an industry sector that is focused on social responsibility goals.
For example, if you used to work for an oil company, you might want to now work for a company focused on renewable energy; if you used to work in commercial banking, you might want to shift into microfinance. Figuring out just the right way to leverage these strategies within your industry will take a bit of research. Here are three suggestions to help you make the shift:
1. Take a look at the socially responsible–oriented courses that are now being offered to professionals in your industry. You may be surprised to discover that the range of options has changed considerably since you were a student. Check with your industry association (industry journals and magazines often have articles about emerging trends) to learn about new certifications and classes that will help you gain the needed credentials to specialize in a more socially responsible niche.
2. Several of this country's leading universities—including Harvard, Duke, Stanford, and Dartmouth—have developed innovative programs in social entrepreneurship, sustainability, and microfinance. Reading about their programs will educate you about the range of ways you might be able to use your skills to make a difference in the for-profit arena.
3. Community colleges and trade schools are offering an increasing number of certificate and credentialing programs that have a socially conscious focus. For example, many design schools are now offering classes in green design and community colleges are training people in the skills needed to address climate change, environmental stewardship, and the green workforce.
Here are some additional resources to help you find information and listings about socially responsible jobs:
• **Justmeans (www.justmeans.com)**. This site is an excellent source of information about sustainability and social enterprise.
• **Ethical Performance (www.ethicalperformance.com)**. This website focuses on corporate social responsibility and socially responsible investment.
• **Green America (www.greenbusinessnetwork.org)**. This site has information about thousands of companies that are committed to working in a more environmentally responsible way.
**THREE FINAL THOUGHTS ON MAKING A LIVING WHILE MAKING A DIFFERENCE**
1. **Don't believe the myths about working for nonprofits**. Blanket statements like "You won't earn any money" or "Nonprofits are frustrating places to work" are simply unfounded. Organizations are as diverse as the people who run them. Do your homework, find a good fit, and actively tune out the doubters.
2. **Money matters**. Nonprofits look for people with a wide variety of skills. But if you are adept at fund-raising, development, or writing grants, you are going to be a particularly attractive candidate in the nonprofit world. People who can bring funds into organizations are always in demand.
3. **Commit to action**. Whether you choose to work for a nonprofit, act as a socially conscious entrepreneur, or focus on a more socially responsible way to work in your industry, remember that the paths to doing good works are limitless, but the time to act is not. As we conclude this chapter, it's helpful to reflect on these words from the late great Arthur Ashe: "From what we get, we can make a living; what we give, however, can make a life."
# CHAPTER SEVEN
# **Get Paid to Travel**
Okay, I'll admit that I saved the most fun category of second-act careers for last. And, I suspect that more than one of you skipped over the preceding chapters so you could read this one first! Indeed, the prospect of getting paid to travel is enticing, especially when you're at a point in life that you already plan to do a lot of travel, regardless of the costs involved. Although the idea of being compensated for travel may sound like a fantasy, the reality is that it _can_ happen, but the amount you get paid will depend on a number of variables. In some cases, you will be paid a fee for your services; in other situations, you'll receive "in-kind" compensation (free lodging, meals, and so on) that will offset the costs associated with your travels.
Please keep your expectations in check and know that none of the options in this chapter are going to earn you a fortune. But they might significantly enrich your world by enabling you to travel more frequently, visit places you otherwise could not afford, and enjoy one-of-a-kind immersion travel experiences—all without having to dip into your savings account. If that strikes you as a priceless combination, I think you'll find this chapter an especially appealing read.
## TOUR DIRECTOR
How would you like to get paid for leading tours in beautiful places? Tour directors are hired by tour companies to lead groups of people on multiday excursions throughout the world. It is not only a fun job, but it is also a job that appears to have strong growth potential; more than eighty million Americans travel on group tours annually, and as the baby boomers enter their retirement years, those numbers are likely to increase significantly. As a tour director, you'll be responsible for keeping your charges entertained, engaged, and on schedule while you lead the group from place to place. In some parts of the world, tour directors must be professionally certified, licensed, or both before being allowed to work, but certification is generally not required in the States. The following interview will help you learn about this intriguing career.
**INTERVIEW WITH THE TOUR DIRECTOR EXPERT**
**"It's a vocation, not a vacation. But it's the best job in the world as far as I am concerned."**
—FRANK M. SLATER, CEO and owner of International Guide Academy
**What types of characteristics are important for success as a tour director?**
F.S: This job is for a people person: someone who is outgoing and energetic and enjoys educating others. Hopefully you are the type of person who never tires of travel; you'll be as awed by the Grand Canyon the tenth time you see it as you were the first.
**Is this job a good fit for people over fifty?**
F.S: No question! This is a profession that is "age insensitive." It may be one of the few jobs where age is an advantage—people tend to like having a more "mature" person leading the groups, especially when the group consists of people who are seniors themselves.
**How much are tour directors paid?**
F.S: As a tour director, you can expect to earn an average of about $3,000 in wages, tips, and commissions over the course of a ten-day assignment. In addition, all your travel costs will be covered; you'll get to enjoy the same hotels, dining experiences, and outings as your group. That means if you go on a trip valued at $8,000, and you get paid $3,000 in wages, your total compensation will be roughly equal to $11,000—not bad for ten days worth of work!
**What are the some of the challenges of being a tour director?**
F.S: It can be tiring. You need to be comfortable with the idea of being away from home for weeks at a time. As the person in charge, you have to be ready to respond calmly when things don't go according to plan. The unexpected happens: people get sick, planes get delayed, hotels lose reservations, and buses break down. Most of the time trips run smoothly, but it helps if you're the type of person who doesn't get flustered easily.
**Can spouses travel along?**
F.S: Yes, most of the time. Some companies will allow your spouse to travel along for free (a rarity), but even if they need to pay for their trip, their room will be free because you will be sharing accommodations.
**Can people do this on a part-time basis?**
F.S: Most people work part-time. You can work as much or as little as you want, within reason. Of course, if you only make yourself available for a few weeks a year, you won't be as in demand as someone who works six months out of the year. But if you only want to run tours during leaf-season in New England (or some other seasonal event), it is possible to work that way.
**What trends do you see that might impact this opportunity?**
F.S: Women-only tours, ecotourism, and adventure tours are some of the fastest-growing niches in the tour industry.
For more information, consult these resources:
• The International Guide Academy (www.bepaidtotravel.com)
• International Tour Management Institute (www.itmitourtraining.com)
• Local colleges, for tour guide training programs
## TOUR GUIDES
If you like the idea of leading tours but don't want to have to do the overnight trips associated with being a tour director, you might prefer to work as a local tour guide. Private tour companies, conventions, and tourist bureaus hire tour guides to lead groups on visits to national parks, historic neighborhoods, famous sites, and scenic places. Like tour directors, tour guides can work part-time or year-round, although most guides work on a part-time basis. As a tour guide, you can earn an average of $20 to $50 per hour (bilingual guides can command up to $75 per hour).
The variety of tours being offered is growing all the time. These days you can find food tours, ghost tours, tours that cater to grandparents, and tours unique to a specific locale, such as A Slice of Brooklyn Pizza Tours in Brooklyn, New York, or the Savannah Historic Homes Walk offered in Savannah, Georgia. If you live in a major city or tourist area, you may be able to create a specialty tour of your own that you market through hotels, convention services, and other tourist attractions. Tour guides are generally trained on the job, but many people obtain additional training through certificate programs offered by tourism schools and community colleges. Although it is not always necessary to be certified, you can earn a Certified Tour Professional (CTP) certification through the National Tour Association (NTA) (www.ntaonline.com).
To learn more:
• International Guide Academy (www.bepaidtotravel.com)
• International Tour Management Institute (www.itmitourtraining.com)
• Food Tour Pros, for guidance in creating a food tour or culinary tour in your city (www.foodtourpros.com)
Associations can also be a good source of information about training, jobs, and employers. Here is a sampling of tour guide associations located in different cities:
• Chicago: www.tourguidesofchicago.com
• Dallas/Fort Worth: www.dfwtourguides.com
• New Orleans: www.nolatourguides.org
• New York: www.ganyc.org
• San Diego: sdtourguides.com
## START AN IMPORT-EXPORT BUSINESS
When I travel, I love nothing more than to spend time meandering in and out of the local shops, browsing street vendors and neighborhood markets in search of unique and unusual native products. But until I did research for this book, I never realized that I could use that shopping as a way to generate a positive cash flow.
As it turns out, there is good money to be earned from importing high-demand products like artisanal foods, furniture, and unique crafts. According to the US Small Business Administration, you can command margins of up to 700 percent for certain items. Of course, before you get involved with any type of importing activity, you should research US trade barriers and local in-country laws to be sure that you can legally export your goods out of the country and into the United States. There are safety, quality, and environmental controls that may also impact your importing activities, and you may need a license or permit before importing certain goods.
To help you learn more about this career option, I turned to Alison Talbert of Wilmington, North Carolina, who found a second-act career as an importer and recently developed both an online training program and a "group buying trip" for people interested in learning how to make a business out of importing goods from Ecuador.
### Getting Paid to Shop
_"If you have a passion for travel and love beautiful things, this is a wonderful business."_
—Alison Talbert, founder of Income from Ecuador (www.incomefromecuador.com)
Several years ago Alison Talbert, a former travel agent turned stay-at-home mom, was itching to go back to work. But with two teens still living at home, she didn't want to return to work on a full-time basis. After considering a variety of options, Alison learned about a course for people interested in importing goods from Ecuador. Intrigued by the idea of a flexible job that would allow her to travel (and after consulting a map to learn where Ecuador was located!), Alison took off for a learning trip to Ecuador. As part of her training program, she had the opportunity to travel the countryside and meet with local artisans. She fell in love with the people and products of Ecuador; by the time she headed home, she had filled two suitcases with crafts, and her head was buzzing with business ideas.
Since that first visit, Alison, now age forty-five, has been back to Ecuador dozens of times. On each trip she buys new items—buttery leather bags, finely woven shawls, and one-of-a-kind jewelry pieces—that she sells to her growing list of clients back home. Over the years, she has developed a good understanding of what her clients look for, and she advises her vendors on the best ways to customize their products to maximize the sales of their goods. In addition to buying handicrafts, she now also imports roses and other flowers that she is able to sell at extremely competitive prices. Alison has plans to open an online retail store and is working with her vendors to prepare them to handle the additional orders.
What started as a fun way to make some extra money has slowly evolved into a more serious home-based business enterprise. But no matter how busy she gets, Alison continues to have a wonderful time shopping, exploring, and discovering new treasures to import. She is living her dream life and teaching others how to do the same. "I love to see when the lightbulb goes on and people realize that this is a real opportunity, not some pie-in-the-sky thing," says Allison. Perhaps most important, she feels great about helping her vendors in Ecuador prosper. Knowing that her business helps them to earn a good living and provide a better life for their families is immensely rewarding. "The people are so lovely and sweet," says Alison. "Every time I place an order, it helps them. And, for me, that's the best part of the business."
#### **Alison's Top Three Tips for the Import Business**
1. **There are many ways to sell your goods**. You can sell at home parties, crafts fairs, boutiques, and festivals. You could also sell the items online, either through your own website or by listing your goods with an online marketplace like Etsy.com or eBay.com.
2. **Consult high-end travel magazines**. _International Living_ (www.internationalliving-magazine.com), for example, offers helpful information and articles about retirement living and business opportunities in different countries.
3. **Consider taking a course about importing goods from the country where you intend to operate**. To find an appropriate course, talk to people for recommendations, Google "export training course," and check the advertisements listed in travel magazines.
To learn more, consult the SBA website at www.sba.gov/content/importing-goods for links to a number of helpful resources.
## INNSITTERS
If you've ever dreamed about running your own bed and breakfast, but you don't want to be tied down to the business 24-7, you may be excited to learn about a career as an innsitter. As the name implies, innsitters work on a temporary basis, filling in for short periods of time while the inn's owners are away from the property. While on the job, you'll be the person in charge, with responsibility for ensuring the safety, comfort, and enjoyment of the guests. (You will typically spend at least a day with the innkeeper to learn the routine and procedures before the owner leaves the premises.) You'll cook omelets, schmooze with the guests, serve wine and cheese, and otherwise be the "hostess with the mostest." But once your assignment is completed, you are free to leave—and then you can return to your nice quiet home.
People who stay at inns expect to enjoy top-notch, personal service and attention to detail, so you need to be willing to work hard, be cheerful, and go the extra mile for your guests. For the right personality, it's a nice way to indulge your innkeeper fantasies, earn some extra income, and enjoy the chance to travel to different locales, without having to commit to the innkeeper's life full time. And if you think you might want to buy an inn at some point, working as an innsitter is a smart way to put that to the test and learn the business before investing in an inn of your own.
To learn more: There are numerous training courses and associations that can help you educate yourself about this career option. Here are three to get you started:
• Interim Innkeepers Network (www.interiminnkeepers.net)
• Inn Caring (training classes and seminars) (www.inncaring.com)
• Professional Association of Innkeepers International (www.innkeeping.org)
## PROPERTY CARETAKING
Do you remember that television show _Lifestyles of the Rich and Famous_ , hosted by Robin Leach and featuring the opulent homes of celebrities, stars, and moguls? I spent hours watching the parade of mansions and thinking that it would be very cool to live in one of those houses, at least for a few days. As it turns out, there might just be a way to finally make my "champagne wishes and caviar dreams" come true—should I ever care to pursue work as a temporary caretaker.
Who hires caretakers? Owners of private homes, resorts, boats, and villas all hire caretakers to watch over their properties and homes in their absence; the bigger and more expensive the property, the more likely it is that a caretaker will be needed. As a caretaker, your job duties and compensation will vary considerably from situation to situation. Sometimes all that is needed is for someone to stay on the premises so that the house appears occupied. In other cases, you'll be asked to work quite hard; you could help run a farm, oversee a small resort, or be in charge of maintenance.
You will almost always be provided free lodging in exchange for your caretaking services. In addition, you might be compensated in the form of meals, a salary, and even access to the family's swimming pool, tennis courts, cars, and other amenities. In general, caretaking jobs that involve more extensive responsibilities are compensated more generously than "stay and sleep" situations. You will probably have ample free time while you are "in residence," so this can be a fabulous arrangement if you're looking to live rent-free in a beautiful location, while you spend time pursuing other interests like writing, painting, or developing your own internet-based business.
To learn more about caretaking opportunities, consult the Caretaking Gazette (www.caretaker.org), a website and newsletter that lists caretaking jobs worldwide. Trusted Housesitters is another good resource at www.trustedhousesitters.com.
## VOLUNTEER VACATIONS
How would you like the chance to blend travel with the opportunity to make the world a better place? If that sounds like a worthy goal, you may want to consider signing up for a volunteer vacation. As you may suspect from the use of the word "volunteer," it is unusual to actually be _paid_ to take a volunteer vacation. In fact, in the majority of cases, you will incur some costs to pay for these trips. Nonetheless, volunteer vacations provide a meaningful and unique way to indulge your love of travel, at a fraction of the cost of a more conventional vacation. If you plan on doing a lot of travel in retirement, this is a wonderful way to do it for pennies on the dollar. (You may be able to further defray the costs of your travel if your church, synagogue, or local volunteer organization is willing to sponsor your efforts as part of their charitable outreach initiatives). And there are some exceptions to the "no-pay" rule—in some cases you will be paid a small stipend for your volunteer services. Paid or not, these trips can truly be a once-in-a-lifetime experience that will enrich your life and nourish your soul in a way that few other trips ever will. To help you learn more about this option, I interviewed Sheryl Kane, an expert on immersion travel, who recently wrote two books on this topic.
**ADVICE FROM THE VOLUNTEER VACATION EXPERT**
**"Stipends and internships are no longer just for the young."**
—SHERYL KAYNE, author
When Sheryl Kayne thought about writing a book about volunteer vacations, she was surprised to discover that all the available books on the subject focused on international volunteer opportunities. Sheryl knew that there were hundreds of volunteer opportunities in the United States, so she decided to write two books, _Immersion Travel USA_ (Countryman Press, 2008) and _Volunteer_ _Vacations across America_ (Chicago Review Press, 2009) that highlight those domestic opportunities. The best way to appreciate the full range of options is to read her books, but for now, here is a small sampling of possibilities:
• **Casting for Recovery (castingforrecovery.org)**. This nonprofit provides fly-fishing retreats for women who have or have had breast cancer. They look for volunteers with fly-fishing experience, psychotherapists with experience leading group sessions, and people willing to act as retreat leaders and helpers. The program is free for volunteers, but you will need to pay the costs of your transportation to and from the retreat locations.
• **Jackson Hole Film Festival (jacksonholefilminstitute.org)**. If you have a passion for both the arts and nature, consider spending a week in beautiful Jackson Hole, Wyoming, working at a film festival that advances the art of independent films. Although you'll have to pay for your own transportation and housing, if you volunteer for over twelve hours, you'll get a free five-day cinema pass, free food, and an insider's peek into this exciting event.
• **Wolf Rescue, Wild Spirit Wolf Sanctuary (www.wildspiritwolfsanctuary.org)**. The wolf sanctuary rescues abused and abandoned wolves and provides educational services on this subject for the public. You must commit to work for at least two months or longer; in exchange, you'll be given housing, a food allotment, and (when funding allows) a small stipend.
• **Lighthouse keeper**. How would you like to live in a lighthouse rent-free? You can—in exchange for providing services such as facilitating tours and assisting park rangers. To find out more, check The Lighthouse News at www.lighthouse-news.com for news reports and job openings at lighthouses.
• **National Park Service (NPS) (www.nps.gov)**. Over one hundred thousand people volunteer at our national parks each year, and some of those volunteers get to live in the parks for free. For example, the artist-in-residence program provides an opportunity for visual artists, sculptors, performers, writers, composers, and other artists to live and work in the parks. Sheryl applied for the program as a writer and received free housing, a free pass to the Everglades National Park, and the opportunity to have plenty of time to devote to her writing.
**Sheryl's Top Three Tips for Volunteer Vacationers**
1. **Check references**. Ask for the opinions and suggestions of people who have previously gone on a volunteer vacation. You'll want to ensure that the living and working conditions are as good as promised.
2. **Look into tax breaks**. Many volunteer vacations qualify in part or wholly as a tax-deductible expense. (Be sure to check with the program staff and your tax adviser.)
3. **Just do it!** Volunteer vacations can be one of the least expensive but most meaningful vacation experiences of your life. You will return home a very different person from the one who left.
To learn more about domestic volunteer vacations, consult Sheryl's books or her site at www.immersiontraveler.com. For information about international volunteer vacations, try these resources:
• Globe Aware, a nonprofit that develops short-term volunteer programs in international environments (www.globeaware.org).
• Global Volunteers, an organization that hosts short- and long-term volunteer trips (www.globalvolunteers.org).
• Worldwide Opportunities on Organic Farms offers a list of different places where you can work on organic farms (www.wwoof.org).
## JOBS IN COOL PLACES
As I hope you realize by now, there are all sorts of interesting ways to combine work and travel. Before concluding this chapter, here are three more ideas to ponder:
1. **The National Parks**. Our parks can't depend only on volunteers to run efficiently—they employ thousands of paid workers each summer as well. The range of jobs at the parks covers gift shop sales, administrative posts, and jobs as oral interpreters. There are ample opportunities for people with all sorts of skills and talents interested in temporary and seasonal positions. For example, Glacier National Park has a fleet of historic red buses that are driven by seasonally hired drivers who give oral histories of the park to visiting tourists. If you prefer sea to land, look into getting hired for a summer season as a boat captain by the Glacier Park Boat Company (www.glacierparkboats.com). To learn more about jobs in our parks, consult the park's official website at www.nps.gov.
2. **Cruise ships**. Cruise ships hire people to help feed, entertain, educate, and take care of their guests. Whether you want to work in the gift shop, bake in the kitchen, or sing in the theaters, there are opportunities to get paid to work at sea. Although the pay is generally a bit less than what you will be paid on land for the same work, your room and board will be covered. People who are "experts" can sometimes earn free cruises in exchange for giving lectures or teaching classes on the ship.
To learn more, go to the careers page of any of the major cruise lines or consult the JobMonkeys.com page about careers on cruise ships at www.jobmonkey.com/cruise.
3. **Teaching English overseas**. Even in a weak global economy, the opportunities to teach English overseas are robust. In most instances, all you need to qualify for a teaching job is a bachelor's degree, but candidates with advanced training and either a certificate in English as a Second Language (ESL) or a master's degree in Teaching English to Speakers of Other Languages (TESOL) enjoy greater job opportunities and earnings potential. Many programs require a minimum one-year commitment from job applicants. Earnings potential can range from a small living stipend to $50,000 or more depending on your expertise and location. As an added bonus, your income may be exempt from federal and/or state taxes if you meet the qualifications for the foreign earned income exemption.
To learn more, consult the Teach English as a Foreign Language database at www.tefl.net/tefl-courses/index.htm; TransitionsAbroad.com has listings for teaching jobs as well as other listings of overseas employment (www.transitionsabroad.com).
**THREE FINAL TIPS ON GETTING PAID TO TRAVEL**
1. **Learn more**. There are many more ways to get paid to travel than I had space for in this chapter. Take the time to read some of the many great books that are available on this topic. One particularly helpful resource is _Work Your Way Around the World_ by Susan Griffiths (Crimson Publishing, 14th edition, 2009).
2. **Get creative**. It is easy to get lured into the luxury travel ideal perpetuated by the tourism industry. But with just a little bit of creativity and a willingness to forgo fancy golf courses and chocolate on your pillows (at least some of the time), you can significantly reduce your travel expenses and enjoy top travel destinations at a fraction of the cost of a conventional vacation. Living in a cabin while working in the national parks or working on an organic farm can be just as rejuvenating as relaxing in a spa at a luxury hotel.
3. **Think like a teenager**. As I write this, my daughter has just left for a semester of study abroad in Copenhagen. This isn't her first trip out of the country. At the ripe old age of twenty-one, she has already done two service trips: one helping to build a school in Costa Rica and the other working on an organic farm in Puerto Rico. Our children have grown up in a world where immersion travel and volunteer vacations are no longer an exotic option. They are using the Internet to find rewarding ways to travel and organizations willing to help fund their trips. They aren't waiting until they can afford the Ritz-Carlton, and neither should we. There is literally a world of options for adventure travel—you just have to be willing to loosen up and let go of your preconceptions of what constitutes a great travel experience.
# CHAPTER EIGHT
# Ten Reinvention Lessons Learned
Before we move on to the next part of this book, I want to take a moment to pause and consider the lessons learned from the people profiled thus far. Reflecting back on all the wonderful conversations I was privileged to have, I was impressed by how much each of them taught me about what it takes to have a successful career reinvention. Of course, in my job as a career coach, I get to see career reinvention in action all the time. But the reality is that when I coach clients, they are "works in progress," and their stories can take months and sometimes even years to unfold. Writing this book gave me a very different perspective, as I listened to dozens of success stories—from start to finish—in rapid-fire succession. There was one week in particular in which I conducted nearly twenty interviews, and although the details of each story were as unique as the personalities involved, I couldn't help but notice that I was hearing certain underlying themes repeated over and over again. Let's now take a closer look at those lessons learned:
1. **Let go to grow**. All too many of us fall into the trap of allowing society to define success for us. But knowing and claiming what you _really_ want, as opposed to what society claims you _should_ want, is a critical link to success in the reinvention process. When you're willing to let go of the glossy trappings of your career in favor of more personally significant paths, amazing transformations can and will happen. Of course, saying it and doing it are two different things, and letting go of old identities isn't easy, especially when you've spent years working hard to establish yourself in your professional life. But one of the commonalities I noticed among the people I interviewed was their willingness to trade in their old "acceptable" titles for newer "riskier" roles. Bob Alper, the rabbi turned stand-up comedian; Eve Young, the mom and volunteer turned acting extra; and Dewey Crepeau, the attorney turned adoption agency owner—all took that risk, and it paid off handsomely. I love it when Eve says of her decision to pursue acting: "I finally realized the only person stopping me, was me."
2. **Recognize that adversity can lead to opportunity**. Many of the people profiled in this book weren't necessarily looking to change their careers. But a significant number of them were forced to do so in response to the financial crisis of 2008. (I was amazed by the number of times I typed some version of the phrase "and then in 2008...") They succeeded in part because they chose to interpret the turbulence in their lives as an opportunity instead of an obstacle. Once they got over the initial shock of their new reality, they decided to view the fork in the road as a fresh start. It wasn't fun or easy, but their willingness to reframe adversity into a potential advantage allowed them to explore options that they might not have previously considered.
3. **Plan for serendipity**. I realize that is an oxymoron; you can't plan where, when, or how serendipity will happen. But as the Roman philosopher Seneca wrote, "Luck is what happens when preparation meets opportunity." The people profiled in this book seem to intuitively understand this, and they consistently act accordingly. They make it a point to speak to strangers. They ask a lot of questions. They join clubs, participate in professional groups, and get involved with their communities. When presented with an opportunity, their default response is to ask "why not?" instead of "why?" And as a result, they "get lucky." Take a page from their playbook: the next time someone extends an invitation, accept it; the next time you hesitate to try something new, gulp and go for it; and the next time you're sitting next to someone on an airplane, start a conversation and see where it leads. If you do, you might just find your new attitude will lead to a world of "lucky" career options and unexpected good fortune.
4. **Adopt an opportunity-seeker mind-set**. Never before in history have we enjoyed easier access to more information. Every day we have the opportunity to learn about thousands, even millions, of new ideas and possibilities from newspapers, television, and the Internet. You can make it a point to consciously pay attention to this information, or you can choose to ignore it. Many of the people profiled in this book found their second-act opportunities simply by keeping their "opportunity antenna" on alert and paying closer attention to what they were reading. Joanne Schumacher, the VP profiled in chapter five, discovered her flexible job one morning while browsing through an e-mail newsletter. She wasn't actively looking for a job, but she took the time to interview, and it led to a wonderful opportunity. Eve Young read an article about the Celebrant Foundation in her local newspaper, and that story resulted in her new career as a life-cycle celebrant. Beth Chapman, the senior move manager profiled in chapter three, learned about her new career though a newspaper article a friend sent her. Opportunity is everywhere. But you have to be alert enough to recognize it, take the time to consider it, and then be willing to act on it.
5. **Attitude trumps ability**. The people I interviewed for this book represent a wide range of talent, ability, and backgrounds. But there was one characteristic that they appeared to share in common: a healthy optimism and can-do spirit. It's no wonder. A positive outlook enables people to more easily try new challenges and situations, and that, in turn, leads to a higher rate of success. As hockey great Wayne Gretzky once famously said, "You miss 100 percent of the shots you don't take." Maintaining a positive outlook is not always easy (and there is no question that some people are naturally more optimistic than others), but simply being aware of your attitude, and making small adjustments when possible, is a good first step toward creating a more positive mind-set. Make it a habit to adopt behaviors that have been proven to enhance well-being: surround yourself with a strong support team, exercise on a daily basis, get out in the sunshine, develop an attitude of gratitude, and limit your daily intake of negative media. You'll be surprised at how effectively—and easily—those behavioral habits will enhance the upward trajectory of your reinvention journey.
6. **Appreciate your age as an advantage**. We are all too familiar with the problems of age—the graying hair, bulging belly, failing eyesight, and aching back. And there is no question that age discrimination is alive and well in the workplace. But if you choose your career options wisely, age doesn't have to be a negative. The second half of life should be a time to reap the benefits of the wisdom gained from your many years of learning, working, and traveling. Terri Lloyd, the cofounder of the Haggus Society, says, "I realize now that in my twenties and thirties I didn't have the maturity or the chops to succeed. If I had been successful then, I worry that I would have squandered that success." I heard that same sentiment repeated by other people in different ways. Susan Nisinzweig, founder of Eytan Art, says that she hopes to work until she is eighty so she'll have enough time to put all of her ideas into action. Other people talked about the benefits of finally being freed up from the worries associated with raising a family, paying the mortgage, and climbing the corporate ladder. Choosing to focus on the very real benefits of this life stage will enable you to explore opportunities that might have been closed off to you at a younger age.
7. **Change is a constant, so embrace it**. We live in a world where the traditional formulas for business success have been turned upside down by the unpredictable forces of an internet-based global economy. "We're throwing spaghetti against the wall to see what sticks," says business coach, author, and speaker Jane Pollak. "Boiling that water. Dropping in the pasta. Tossing it at the wall. Noticing what happens, then rinsing and repeating. This is the new normal." That unrelenting change is both scary and intimidating, particularly for boomers used to a more structured workplace. But the people I interviewed showed an unusual willingness to adapt their career plans and business models to changing circumstances. They embraced technology and learned how to leverage tools like blogs, digital downloads, and video to advance their businesses. There are no hard and fast rules in this rapidly evolving economy, but a willingness to adapt and continually learn new technologies will be critical for success in virtually every career-related endeavor.
8. **Perseverance pays off**. Success isn't the result of one isolated decision, action, or event. It is the small actions you take each day that add up to big change over the course of the years. Each step builds on the next, and true progress comes from the lessons and insights gained with every choice you make. Terri Lloyd says, "It isn't like a firecracker that goes off and suddenly you are catapulted. It is many, many small steps, lots of failures, and the accumulation of the learning along the way. All roads lead to someplace. Everything I've learned in my life has contributed to this moment." Terri is right. Don't expect overnight success. Be patient, have confidence in your abilities, and trust that with time, your smaller steps will lead to larger triumphs.
9. **Fear is inevitable, but you can overcome it**. No matter how old we get, fear plays a role in our lives. But as I once heard a therapist explain, sometimes FEAR is just an acronym for "False Evidence Appearing Real." The people profiled in this book are no different from the rest of us; they all expressed some level of fear and insecurity. What made them different is that they didn't let their fears dictate their choices. They succeeded in spite of their concerns, by building on their strengths, minimizing unnecessary risks, and keeping themselves focused on what they could control and change.
10. **Education is the single best antidote for fear**. One of the best ways to conquer fear as you transition into your second-act career is with education and training. A great example of the power of education comes from Linda Pond, a fifty-five-year-old Canadian who, with the help of her daughter, invented the FAB light (FAB stands for "Find a Beer"), a nifty little lighting gadget that sticks to the inside lid of a camping cooler (www.lindaleepond.com). Linda had no prior experience with product invention, but over time she learned—now major retailers throughout North America sell the FAB light. She self-published a book about the adventure, called _Top Secrets of a Girl Entrepreneur_ , and the publication of that book helped launch her career as a public speaker. Interestingly Linda says that until she was in her mid-forties, she often lacked confidence in her abilities. But once she recognized that the best way to deal with her insecurities was by getting training and experience, then she began to enjoy a steady stream of successes. As she gained confidence in her professional life, she became bolder in her personal life as well. She decided to try her hand at acting and landed a part in a local theater production. Then her goal became to both act and sing, and she did that too. Each success led to the next, and over time, she saw that she was far more capable then she had previously believed. The same is true for many of the people I interviewed. Their willingness to try new things and invest in lifelong learning helped them overcome obstacles and be more successful in their second-act journeys.
They did it—and you can too. And I can think of no better way to illustrate this point than with this next and final profile.
### From Cop to Comedian:
A Lesson in Arresting Fear
_"I'm getting pretty far in comedy. I have such a passion for it and I think when you have a passion, things just happen naturally."_
—Gina Scarda, stand-up comic and actress
Gina Scarda's first career didn't take place anywhere near a stage, but it certainly involved more than its fair share of human drama. Back then her stage was the streets of New York, and her costars were pimps, murderers, and little old ladies in need of assistance. You see, Gina earned her living not as a performer but as a policewoman with the famed New York City Police Department. She began her career patrolling the streets of Coney Island and says she loved every minute of it. Whether she was doing quality-of-life sweeps ("you know, things like prostitution, underage drinking sweeps, anything that affects the quality of life in the neighborhood") or just talking with the people on the streets, life as a cop was a surprisingly fun fit. "Probably the best time in my life was when I started as a young cop," says Gina. "I had such a great time."
At age forty-six, after twenty years of service on the force, Gina retired with a full pension and benefits, right around the same time that her daughter, who had been active in theater in high school, was heading off to college. Gina hoped that her daughter would continue to pursue theatre in college ("I mean, what parent actually wants that for her daughter?" jokes Gina). But like most kids, her daughter had other plans, and she ultimately decided to focus on the sciences instead. Gina was disappointed by her daughter's decision, but when she made her sentiments known, her daughter responded by saying, "Mom, if you are so disappointed, why don't _you_ go and become an actress yourself?"
Gina readily admits that she didn't even know that she harbored a passion for acting until her daughter pointed it out. But her daughter's challenge gave Gina just the nudge she needed to acknowledge both her hidden passion—and her hidden fears. Looking back on that conversation, Gina laughs as she acknowledges the irony in the situation. "You would think I would be braver. After all, I was a cop! But I guess the fear of failure kept me from doing it. Rejection is a horrible thing." After recognizing the fear, Gina decided the best way to conquer her nerves would be to get some training. She enrolled in a comedy class, and from the minute she walked on the stage, she felt like she was at home. A few months after taking her first class, she entered a contest for Long Island's Funniest Comedian and, much to her surprise, won the top prize. "That really helped boost my confidence," she says.
With her newfound self-assurance, Gina began to audition at openmic nights at New York comedy clubs, a process that allowed her to try out new material and create a routine. Then one day "out of the blue," she received a phone call from a woman who had seen Gina's comedy video posted on the Internet. The woman explained that she thought Gina would be a good fit for a comedy group called The Italian Chicks, and she asked her to send a headshot and bio for review. Gina was flattered, but instead of jumping on the opportunity, she did nothing. "I didn't have either an updated resume or a headshot, so I kind of ignored it," she says. "I guess it was the fear again."
Three months later the same woman called her back, and this time Gina decided to give it a try. "I guess she was desperate," recalls Gina with a chuckle. "I freaked out a little, but I went and did it, and the minute I met the other girls in the act, I knew it was going to work. We connected immediately." The group started out doing dinner theatre pieces for fifty people and quickly built a following. They now travel all over the country and perform in front of audiences of five hundred people or more. At the same time that Gina works on her comedy, she continues to pursue more serious acting opportunities. In addition to working as an acting extra, she has done some small student films and commercial work. The week we spoke, she had just received her Screen Actors Guild (SAG) card, an accomplishment that she admitted brought tears to her eyes ("I must be menopausal," she jokes).
Gina is amazed at the great luck she has enjoyed since she "retired." She is quick to credit her husband for supporting and encouraging her along the way. And even though her children are still a bit mortified by her act (her seventeen-year-old son refuses to come to her shows), she knows they have been inspired by both her success and her willingness to conquer her fears. "It's been such a great influence on my children to have them see me going after my dreams," says Gina. "For the longest time, I felt guilty about doing something for myself. But they love it. It shows them that they can do anything. I want them to know they can have dreams too."
#### **Gina's Top Three Tips for Aspiring Comics and Actors**
1. **Be willing to take on small jobs**. Gina says that her experiences working as an extra on movie and television sets have provided invaluable networking opportunities that she knows will lead to better opportunities over time.
2. **Don't assume you need to live in New York to pursue acting**. You don't need to be in New York or Los Angeles to do this type of work (although it helps). There are acting jobs in many other cities. For people in the New York tri-state area, Gina recommends NYCastings.com.
3. **Take baby steps toward success**. Start with a class to see whether you like performing in front of an audience. If you can't get up in front of a small class and perform, then this isn't for you. Build up your audiences slowly. You start with six people, which turns into fifty people, which turns into an audience of hundreds. Bit by bit, you'll grow more comfortable and confident.
#
Are you feeling energized, excited, and hopeful about the possibilities for your second-act career? I certainly hope so! After all, as you discovered from reading the stories in part one, it's not just a second act; it's a second chance! But as enticing as that sounds, I suspect that right about now many of you are also feeling a bit uncertain about your own next steps. _How do I get started? What should I be focused on? What are my best options?_ This section of the book will help you answer those questions, and others, as you build the road map for your own second act.
As we go along, you'll discover that planning for your semi-retirement career is a somewhat different process from your previous career transitions. When you think back to the last time you planned your career (junior year in college?), it's likely that your decisions were based more on practical concerns, like paying the rent and putting food on the table, than on your personal hopes and dreams. But now it is time to switch things up. Instead of allowing your career to dominate your life, it's time for your life to take center stage. This is a welcome opportunity to make time for travel, to learn a new language or work for a meaningful cause; the freedom to explore new interests, take calculated risks, and stretch beyond your comfort zone; and a chance to live a more balanced life, with time for exercising, reading, playing golf, or visits with the grandchildren.
In this section, I am going to walk you through a five-step process designed to help you gain clarity about the type of life—and the type of work—that you want to pursue during your semi-retirement. As you work through the steps, you'll be answering a variety of questions intended to help you better understand your motivating interests, skills, and drivers. There are many methodologies for reassessing our careers: assessments, quizzes, and the like. Ultimately, however, my professional experience has taught me that there is no better way to understand yourself than good old-fashioned self-reflection. After all, _you_ are the only person who actually knows what you really want. The exercises in this section will help you gain a better understanding of what that is.
## HOW TO USE THIS SECTION
Work through the exercises at your own pace and come back and revise them as necessary. But do try to start this sooner rather than later. The speed of the reinvention process varies from person to person; some people find quick gratification, whereas others slowly build toward success. Allow enough space for the process to unfold and evolve without unneeded pressure.
I encourage you to use a separate notebook (or computer file) to record your thoughts as you work through these exercises. Whichever method you choose, please be sure to write down your answers to the questions in this section. Capturing your ideas on paper (or on your computer) is always more effective than keeping your thoughts locked up inside your head. Writing them down will also create a permanent record of your thoughts for future reference. Finally, you may also find it beneficial to discuss the results of your exercises with friends or family—sharing your thoughts with others will help to both clarify your thinking and provide needed encouragement and support along your reinvention journey.
# CHAPTER NINE
# Envision the Life You Want
When you are freed up from _having_ to work a traditional nine-to-five job, the options for how, when, and where you might _choose_ to work expand exponentially. But choosing from that world of possibilities can feel downright overwhelming. So, before figuring out the career piece of the semi-retirement puzzle, it's helpful to spend some time clarifying your lifestyle goals: How many hours do you want to work? Do you want to run your own business? What type of balance do you want to strike between work, family, community, play, and self?
This first exercise will help you to develop a vision of your ideal semi-retirement lifestyle—not the "let's take off for the Bahamas and drink rum punches all day" type of ideal, but a life you see yourself happily living day after day. You want a vision that makes you think, "This works. I can see myself doing this. It feels right." Once you've defined the type of life you want to lead, it will be far easier to focus in on the types of businesses, income streams, and jobs that will best support your lifestyle.
## EXERCISE: VISUALIZE YOUR IDEAL LIFE
**Instructions:** Close your eyes, quiet your mind, and try to picture what your day will be like when you are semi-retired. Visualize yourself as you go through the day. Make note of the details: the time you get out of bed, what you eat for breakfast, and the clothes you are wearing. Picture yourself as you go about your day and notice your surroundings. Who are you with? What types of activities are you involved in? Do you take time for lunch with a friend or indulge in a midday siesta? Are you taking classes or reading or listening to music? What do you eat for dinner? What do you talk about over dinner? How do you wrap up the day?
Open your eyes. What did you "see" during your ideal day? Think about what jumped out at you, surprised you, and impressed you. Now, while that vision is fresh in your mind, please answer the following questions:
• What activities and experiences do you want to make more time for in your life? This can include "big" items like travel or simple things like having time to make a nutritious dinner every night. Don't forget to include personal development priorities like spiritual growth, personal relationships, intellectual development, community involvement, cultural enrichment, or fitness goals.
• What type of schedule is going to work for your second act? Are you interested in seasonal employment, part-time work, work-from-home jobs, or simply having more control over your work schedule? Do you want summers off or evenings free?
• Do you want to work for someone else or be self-employed?
• What type of work setting appeals to you?
• What types of people do you want to work with or around?
• What topics, issues, or ideas do you want to incorporate into your day?
Write down a summary of your "Ideal Life Vision".
Now that your mind is focused on the type of lifestyle you want, the next exercise will help you gain additional clarity about your key motivators and drivers. In other words, what is going to make you want to jump out of bed and enjoy your work and life each day?
## EXERCISE: DISCOVER YOUR PERSONAL MOTIVATORS
As you review your ideal life vision, think about what you really value or need in your work life: What motivates you to get up in the morning? Which job duties, work missions, and environments make you love your work? There are so many things you could do, but knowing what is most important to you in this next phase of your life will make it much easier to focus in on opportunities that really feed your soul.
**Instructions:** The following are work-related needs and values. Thinking about what you want for this next stage in your life (not what you may have chosen in the past), please rank them on a continuum of one to five (one is not important, three is neutral, five is extremely important):
Achievement: Have opportunities to excel and produce significant results
1 ———— 2 ———— 3 ———— 4 ————5
Adventure: Do work that involves risk and allows for frequent new experiences
1 ———— 2 ———— 3 ———— 4 ———— 5
Aesthetics: Be involved with work that involves beautiful things and settings
1 ———— 2 ———— 3 ———— 4———— 5
Affiliation: Identify myself as an integral part of a group where I can develop close working relationships in pursuit of a common goal
1 ———— 2 ———— 3 ———— 4 ———— 5
Animals and Nature: Do work that allows me to spend time with animals and/or in nature
1 ———— 2 ———— 3 ———— 4 ———— 5
Autonomy: Work with little supervision and have control over my day-to-day activities
1 ———— 2 ———— 3 ———— 4 ———— 5
Artistic Expression: Engage in a creative and/or artistic endeavor
1 ———— 2 ———— 3 ———— 4 ———— 5
Builds on Experience: Get involved with work that builds on my professional experience and allows me to stay in my field of expertise
1 ———— 2 ———— 3 ———— 4 ———— 5
Community: Align with work that has a strong community component
1 ———— 2 ———— 3 ———— 4 ————5
Competition: Work in environments that encourage and reward competition
1 ———— 2 ———— 3 ———— 4 ————5
Cultural Diversity: Be involved in work that supports, promotes, or fosters cultural diversity and understanding
1 ———— 2 ———— 3 ———— 4 ———— 5
Ethics: Engage in work that is strongly in sync with my personal code of ethics
1 ———— 2 ———— 3 ———— 4 ———— 5
Fame: Do work that allows me to be recognized and lauded by my peers
1 ———— 2 ———— 3 ———— 4 ———— 5
Fun: Work in an environment that perpetually fosters fun, laughter, and play
1 ———— 2 ———— 3 ———— 4 ———— 5
Give Back: Be involved in work that easily allows me to give back to society
1 ———— 2 ———— 3 ———— 4 ———— 5
Influence: Be in a position of authority that allows me to affect how people think
1 ———— 2 ———— 3 ———— 4 ———— 5
Leadership: Do work that allows me to function as a leader of others
1 ———— 2 ———— 3 ———— 4 ———— 5
Mentorship: Be in a position that allows me to teach, coach, and inspire others
1 ———— 2 ———— 3 ———— 4 ———— 5
Nurturing Others: Participate in work that rewards me for nurturing others
1 ———— 2 ———— 3 ———— 4 ———— 5
Organization and Order: Do work that values order, systems, and planning
1 ———— 2 ———— 3 ———— 4 ———— 5
Power: Operate from a position of authority and have control over key decisions
1 ———— 2 ———— 3 ———— 4 ———— 5
Prestige: Work in a field that is considered very prestigious by society
1 ———— 2 ———— 3 ———— 4 ———— 5
Profit: Be responsible for impacting the bottom line
1 ———— 2 ———— 3 ———— 4 ———— 5
Public Exposure: Work in a field that allows me to frequently interact with the public
1 ———— 2 ———— 3 ———— 4 ———— 5
Stability: Work in a field that is considered stable and relatively "secure"
1 ———— 2 ———— 3 ———— 4 ——— 5
Travel: Do work that incorporates my love of travel
1 ———— 2 ———— 3 ———— 4 ———— 5
**Instructions:** Looking over your answers, what are the most important work-related motivators to look for in your second act? Write down your top ten motivators.
**THREE MORE WAYS TO VISUALIZE YOUR FUTURE**
Visualization is a powerful and transformative tool for people looking to reinvent their careers. Expressing your career and lifestyle goals through pictures, as opposed to articulating them in words, can be a useful way to unlock vital clues and patterns that you may have been struggling to express using words alone. Here are three ways to use the power of images in your life to help supplement the exercises in this section:
1. **Keep a clippings file**. Do you sometimes clip articles and photos from magazines for a "dream" file of beautiful homes or vacation ideas? Do the same for your career. Collect pictures and articles that speak to you and capture your imagination. Don't be judgmental about what you choose to keep—with time you'll discover interesting commonalities and patterns among the items you have saved.
2. **Meditate**. Set aside some quiet time to meditate on the types of activities and work environment that would make you happy. Notice the images that come to mind. Do you prefer to be in a fast-paced office or a quiet one? Urban or rural settings? Are you happier being with lots of people or working in solitude? Look for patterns and themes in your mental images.
3. **Build a vision board**. A vision board is a collection of visual images (photos, memorabilia, pictures torn from magazines) displayed on a bulletin board or poster as a graphic representation of your dreams and ambitions. Once you've completed the board, display it in a prominent place as a visual reminder of your ambitions and career goals. If you're comfortable with technology, try using Pinterest.com, an online site where you can "pin" images from the Web to create virtual vision boards.
## EXERCISE: WHAT _DON'T_ YOU WANT?
One of the joys of planning a semi-retirement career is that you are finally at a point where you no longer have to do those things you really hate doing. Knowing what you want to avoid in your next career is as valuable as knowing what you want to include. Although every job or business is going to have some percentage of tasks that you are not happy about doing, the key is to focus on opportunities that minimize those negatives as much as possible.
**Instructions:** I'd like you to think about what you don't want to have to do anymore. Don't ever want to work a night shift again? Write it down. Tired of the stresses of running your own business? Make a note of that. Not interested in doing any more business travel? Okay then, put that down too. Make a thorough list of your pet peeves and then write down your top three.
## EXERCISE: FINANCIAL VISION
This book is not intended to be a financial guide. That said, there are financial issues that must be taken into account when deciding on your vision for your semi-retirement, even if income is not a primary concern. At a minimum, you should have clear answers to the following questions:
• How much money do you need to earn?
• How much do you want to earn?
• Do you need to purchase health insurance?
• How much are you willing to invest in education and training?
• How much are you willing to invest in a new business?
If you are unsure about the answers to these questions, please take the time to think about them and, if appropriate, discuss them with your spouse or partner before you get much farther into the planning process. You don't want to get into a situation where you spend a lot of time investigating an idea, only to later discover that you can't afford to go down that path because of your financial restrictions.
**Instructions:** Write down your answers to the financial questions just listed.
**An important note of caution:** If you collect Social Security payments before you reach your normal retirement age (NRA) as defined by the Social Security Administration, your benefits may be reduced as a result of income you generate in your second-act career. This restriction ends once you reach your NRA. This calculation is a moving target, so please be sure to check with the Social Security Administration at www.socialsecurity.gov for the most up-to-date information regarding this provision.
**THREE TIPS FROM THE FINANCIAL EXPERT**
**"A lot of the stress and panic I see comes from people not knowing the numbers. You'll feel better once you know where you're at."**
—GALIA GICHON, founder of Down to Earth Finance
(www.downtoearthfinance.com)
The more financial flexibility you have, the greater your ability to do what you want during your semi-retirement. Here are three suggestions from an independent personal financial expert on smart ways to maximize your income during this phase of life:
1. **Renovate your semi-retirement budget to reflect your current lifestyle**. Do you still need that million-dollar life insurance policy? Is it time to stop paying your children's cell phone bills? Is the super-jumbo pack of toilet paper at Costco really still a smart purchase? You might still be spending like you've got a family to support when you could easily cut some of those expenses out of your budget.
2. **Hold off on claiming Social Security benefits as long as possible**. You can currently start claiming Social Security benefits as early as age sixty-two or as late as age seventy, but within that range, the longer you delay, the larger your monthly payments will be (you can file even later than age seventy, but your benefit amount won't be any larger). Use the online calculators provided by the Social Security Administration at www.ssa.gov/oact/anypia/index.html to run the numbers and figure out the best time to start your payments.
3. **Leverage online tools and apps to better manage your finances**. T. Rowe Price has an excellent retirement income calculator that can help you figure out what you need to live on in retirement. Galia also recommends Expenditure (www.expenditureapp.com) and MoneyBook (www.moneybookapp.com) as useful apps for setting budgets and tracking and managing your finances.
### A Note about Health Insurance
What are your options for health insurance coverage if you are not yet eligible for Medicare and you will not receive health insurance retirement benefits from your employer? The answer to that question will depend on the outcome of the healthcare reform debate (with the specifics of the 2010 Affordable Care Act in flux at the time of this writing). Understanding that, here are several alternatives to consider:
• If you are covered by an employer plan, in most cases you will be eligible for COBRA, which means you can opt to continue on your employer plan for up to eighteen months (or thirty-six months for extenuating circumstances) after you terminate employment (you are responsible for paying the full premium cost, which comes as a shock to most former employees, so it's worth investigating the likely cost in advance). If you took an early retirement package, you might be able to purchase medical insurance from your employer's plan until you are eligible for Medicare.
• If your spouse or partner is still employed, you may be able to obtain benefits by enrolling in his or her plan.
• You can find more affordable group rates offered through organizations like the Freelancers Union (www.freelancersunion.org), National Association for the Self-Employed (www.nase.org), college alumni groups, and professional associations.
• If you create a small business that has a minimum of two employees, you are eligible to apply for a small business group health insurance plan. These types of plans are especially attractive if you have a preexisting condition; some states require insurance companies to offer coverage to small groups regardless of whether any person has a preexisting condition.
To more fully research your options, consult a private insurance broker or visit the website of eHealthInsurance.com.
## EXERCISE: LOCATION, LOCATION, LOCATION
Where you choose to live impacts your career options. If relocation is something you are considering—whether for personal, lifestyle, or financial reasons—don't forget to factor in your second-act career as part of the equation when deciding where to live. When you relocate, it can open up access to career options that you might not have previously considered, particularly if you are able to free up capital from your home that can be applied toward your career transition.
Different towns and cities are known as "hotbeds" for different types of industries. For example:
• Beer is all the rage in Asheville, North Carolina, where they have over ten local breweries; even the bakeries and ice cream parlors carry beer-flavored products.
• Nashville, Tennessee, is well known as a home to country music, but it is also home to over 250 healthcare-related companies.
• Albany, New York, is now a popular location for the growing field of nanotechnology.
There are big benefits to setting up your career or business in the right spot. Living in an area that is filled with your peers will make it easier to find work, gain easy access to resources, and/or get a new business off the ground (beer tasting workshops, anyone?). College towns, in particular, can provide a very enriching environment for semi-retirement. They offer a compelling mix of culture, state-of-the art medical and research facilities, and easy access to reduced-rate college courses and lectures.
Relocating to a different country is also an option to consider. Countries like Costa Rica—with its high quality of life, affordable healthcare, and low housing costs—are very attractive to retirees. On a recent trip to Costa Rica, I met a woman who used to work as an attorney in the States. She opened a small café in a mountain village, where she enjoys baking and socializing with customers. To supplement her income, she works remotely several days a month on legal assignments for a firm back in the States. When the tourist season is slow, she enjoys traveling to other countries and visits with her family back home.
Even if you have no desire to relocate, be sure to take the time to appreciate the career inspiration that is right outside your door: a town that has cheap farmland might be a great spot to start an organic mushroom farm, a community with a large number of young children might be perfect for a children's birthday party service, and a town with a high percentage of seniors could be a great place to open a home healthcare agency. Once you look at your hometown as a potential career asset instead of just a place to live, your world of possibilities will expand in interesting ways.
**Instructions:** Jot down your thoughts about where you plan to live during semi-retirement.
For more information about relocation options, you may find these websites valuable:
• CNN/Money, AARP, Kiplinger's, Forbes, HufffingtonPost.com, _US News & World Report_, and _CBS MoneyWatch_ all publish different variations of the Best Places to Retire, Best Places to Live, and Best Places to Work lists. Go to their main website to find their most recent information.
• Topretirements.com is another site with helpful information on this topic.
## MY LIFESTYLE VISION SUMMARY
In Journalism 101, college students are instructed to use the Five Ws (when, what, where, why, and who) when researching and writing their stories. Using that same formula, I'd like you to summarize the key factors you have identified as your main lifestyle goals. You can then refer back to this summary when evaluating career ideas for lifestyle fit.
**Instructions:** Using the exercises in this section, answer these questions.
WHEN do you want to work (hours, schedule, and so on)?
WHAT types of activities do you want to include/exclude in your career/life mix?
WHERE do you want to conduct your work activities (office setting, at home, on the road, in a small town, and so on)?
WHY do you want to keep working (motivators)?
WHO do you want to work with? Who do you want to make more time for in your professional and personal life?
# CHAPTER TEN
# Look to the Past for Clues to Your Future
Now that you have a better idea of the type of life you'd like to create during your semi-retirement, we are going to shift our focus to the career piece of the reinvention puzzle. As you reflect on and analyze your past accomplishments and experiences, you'll start to see very clear patterns emerge about what you love, what you do best, and what you find most meaningful in your life and work. Those unique patterns hold important clues to what you'll be happiest doing in the future. And once you know who you are and what is most important to you, it will be so much easier to connect with income ideas that are truly a good fit.
I know some of you may be tempted to skip this section of the book. But if you have any doubts about what you want to do next, please take the time to do the exercises in this chapter. You'll feel more at peace with your career-related decisions, if you know that you've given this process the time and attention it deserves. And you know what else? You're going to discover that this type of reflection is actually a lot of fun—you'll find yourself thinking about people, accomplishments, and events that you haven't thought about in years. It will allow you to make decisions based on a lifetime of data, as opposed to decisions that are in reaction to your most recent life experiences (for example, "I hated my last boss, so I never want to work for an employer again").
Of course, remembering forty-plus years of personal history at our age can be a bit of a challenge. I don't know about you, but I have enough trouble remembering where I put my keys, let alone what I used to like in fourth grade. So before beginning this process, I think you'll find it invaluable to take a bit of time to dust off the mental cobwebs and get the memory pipeline flowing. Here are some things you can do to help the process along:
• **Sit down with your old photo albums, family movies, scrapbooks, and yearbooks**. As you look at them, think about what they say about your past: Were you shy or the life of the party? Do you tend to be serious or silly? Who did you like to spend time with? What types of activities filled your days?
• **Clean out your closets and garage**. It's amazing how much stuff you'll find hidden away: crafts projects, sports equipment, and boxes filled with old trophies. As you go through these items, think about how your passions, hobbies, and dreams are manifested in these physical mementos.
• **Review your checkbook register and other financial documents**. What are you spending your money on? Music? Gardening? Trips? Fancy food? What we say is important doesn't always match up with how we spend our money; analyzing your spending patterns can give you important insights into your real priorities.
• **Inventory your media**. Review your collection of books, magazines, and frequented websites. Think about your television and movie viewing habits. What does your choice of media reveal about your interests?
• **Look through your personal files**. Review old resumes, performance evaluations, and other paperwork associated with your work and volunteer life. What do those files tell you about your accomplishments, interests, passions, skills, and talents?
• **Walk around your house and property**. Is your house filled with plants? Do you have a lot of artwork from different cultures? Are there collections of family photos on display? Do you have piles of sports equipment, books, or videos waiting to be enjoyed? Make note of what the items in your house say about you, your aesthetic sensibilities, and your personal priorities.
Finally, pick up the phone and call your siblings, parents, old friends, and former schoolmates to talk about your childhood and other relevant personal history. Their recollections can help fill in the blanks about your formative years.
**PLAN WITH THE END IN MIND**
How would you like to write your own obituary? Although this may strike you as a morbid (and premature) suggestion, it is an exercise I frequently ask my clients to do, and the results can be profound. By forcing yourself to concentrate on the big picture, you'll gain clarity about what really matters in your life and in your work. Here are some questions to ponder as you write:
• What are some professional and personal goals you have left to achieve?
• What would you do if you knew you could not fail?
• Which personality traits, quirks, and values would you like to be remembered for?
• What would you like people to say when you're gone about your contribution to your family, your community, and the greater world?
Remember, you don't need to share this obituary with anyone. Use it as a way to gain clarity about what you would like to do and achieve in the years ahead.
## EXERCISE: ORGANIZE YOUR LIFE STORY WORKSHEETS
Once you've got those memories flowing, the next step in this process is to capture and organize all of that data on paper. Please segment the information into four distinct time periods as outlined:
### **LIFE STORY WORKSHEET #1:
CHILDHOOD**
It may strike you as odd to think about your childhood years when you are at or near retirement age. Trust me on this one. I can't tell you the number of times I've worked with clients who have all sorts of impressive professional accomplishments, but they end up reinventing their careers around a long-lost childhood passion. When we are children, we are free to do what we want without worry: we dance, make daisy chains, battle imaginary dragons, sing to our heart's content, and dream about becoming firemen and ballerinas. Sadly, all too often, in our efforts to be responsible adults, we lose touch with what we really love to do most, and our natural gifts and talents get crushed under the weight of all the "shoulds" and "musts" of our adult lives. Now is the time to get reacquainted with your inner child and reconnect with those long-forgotten dreams and talents. Please think about the following questions:
• What were your favorite activities and subjects during grade school?
• How did you like to spend your free time?
• What were your favorite books, movies, or television shows?
• Who were your favorite adults?
• What did you fantasize about becoming when you grew up? What did others think (or say) you would be as an adult?
**Instructions:** Write down your key recollections of your childhood. It is not necessary to answer every one of these questions. Instead, use them as a starting point to inspire your writing about what you were like as a child, the types of activities you most enjoyed, and your favorite recollections of your preschool and grade school years.
### **LIFE STORY WORKSHEET #2:
HIGH SCHOOL AND COLLEGE**
Our school years were a period of exploration, growth, and change—and also a time of conflict and anxiety as we struggled to define our place in the world. This is the life stage when most of us began to get a clearer sense of our interests, talents, and skills, both in the classroom and through our extracurricular activities. Please consider the following:
• What were your favorite subjects in high school?
• Did you have any teachers who played an influential role in your life?
• What subject(s) did you choose to focus on in college? Why?
• What were your grades like? Did you receive any special academic honors?
• Which extracurricular activities did you enjoy most?
• What profession did your friends and teachers think you'd pursue as an adult?
• How did you spend your spare time?
• Did you have any meaningful internships or part-time jobs?
• What was your social life like?
• What did you enjoy most about high school and/or college?
**Instructions:** write down your recollections of your high school and college experiences. Once again, it is not necessary to answer all of the above questions individually. Use them as a prompt to inspire your writing about your most meaningful achievements, favorite things, challenges, and aspirations during your teen years.
### LIFE STORY WORKSHEET #3:
THE PROFESSIONAL YEARS
Now it is time to capture information about your working life. Even if you intend to do something very different from your old (or current) line of work, it is still important to spend time thinking about your past jobs in order to identify your motivating strengths and skills. It may be helpful to take notes for each of your jobs and list the tasks, projects, and responsibilities you handled. As tempting as it is to list only your most recent or most impressive work experiences, I urge you to include details about meaningful summer or part-time jobs, as those experiences often reveal interests and talents that may not be reflected in your more "serious" jobs. Sometimes the most insignificant work experiences turn out to be the ones we enjoyed the most.
• What were your favorite jobs?
• What were your least favorite jobs?
• Which business-related skills did you most enjoy using (for example, networking, public speaking, research)? Be sure to include all of your favorite skills, not just those that were part of your official job responsibilities.
• What were your favorite work-related accomplishments?
• What kind of work environment brings out the best in you?
• Who do you want to work with? This is a big one! When I ask clients to describe the jobs they enjoyed most, do you know what they always talk about? People. The people they worked with, the people they worked for, and the people who were their clients, vendors, and colleagues. When they enjoyed the people, they loved the job; when they really didn't like the people, they inevitably disliked the job. Knowing who you most enjoy working with can help you focus in on careers that attract like-minded thinkers. Do you prefer being around women or men, children or the elderly, a homogenous group or a culturally diverse crowd, intellectuals or blue-collar types, creative or analytical personalities?
• What kinds of work-related problems and challenges do you like to solve?
**Instructions:** Write down your reflections, observations, and realizations about your work-related experiences, skills, and accomplishments. Be sure to make notes about the types of people, industries, work environments, and work tasks that are your "best fit."
### LIFE STORY WORKSHEET #4:
PERSONAL LIFE
How you chose to spend your personal time away from work—the books you read, the friends you choose, your hobbies and travel plans—can provide illuminating insights into your strongest interests, talents, and passions.
• How do you like to spend your free time on the weekends?
• What topic(s) do you most like to talk about with your friends?
• Which subjects do you like to read about in magazines or books (for example, decorating, biking, travel, parenting, health)?
• What do you regard as your family's greatest achievement?
• Which volunteer jobs do (or did) you find most fulfilling? Why?
• Have you attended any workshops, training sessions, or continuing-education programs that you found particularly interesting?
• As a result of life experience (for example, traveling, renovating a home, cooking gourmet meals), you may have developed new interests and skills. Are there any that you consider especially meaningful or interesting?
• People gain skills and knowledge as a result of personal struggles and challenges. Note any skills or areas of expertise that you've acquired as a result of facing adversity (for example, weight loss, dealing with a learning disability).
• What role(s) do you play in your personal or family life (for example, mother hen or researcher or family events organizer or negotiator)?
**Instructions:** Describe your achievements, your favorite ways to spend your free time, and your greatest strengths as a friend, volunteer, and family member.
# CHAPTER ELEVEN
# Ask, Analyze, and Assess
Once you've had a chance to record your thoughts and feel satisfied with your responses, it is time to focus on the analysis phase of this process. Normally this is the point in most career books when you are asked to complete a series of in-depth exercises to help identify your motivating skills, accomplishments, interests, and values. Those exercises are invaluable; they work, and if you have any doubts about what you want to do or what you are good at, you should absolutely do these exercises when given the opportunity.
But we're going to take a slightly different approach here, for two reasons: First, there are already a number of excellent books and websites that cover the assessment process in far greater detail than I have space for here (more on this in just a bit). Second, I suspect that most of you already have a good sense of who you are. After all, you're no longer an eighteen-year-old kid just starting out. You've had years of experiences, accomplishments, and opportunities to discover what you love, what you do well, and what you find meaningful. My guess is that you've already had a few "aha!" moments while gathering the information for your life story worksheets. So instead of trying to persuade you to complete yet another series of exercises (which, odds are, many readers will skip), I am asking that you simply commit to answer ten key questions; then you can decide whether you need to do additional work on your own. Fair enough?
One more thing before we dig in. I want to talk for just a moment about the word "passion." I know that right about now some of you are feeling really worried that you may never find your passion. I understand. PASSION is one heck of a big word. When I hear it, I think of romance novels starring the beautiful young heroine who falls hopelessly in love with her handsome prince. Passion implies an all-consuming, "I can't sleep or think about anything else," combustive energy.
And therein lies the problem.
The word "passion" is so strong and powerful that it sets up an incredibly intimidating standard by which to evaluate your options. You might really like something. Or find it interesting. But, because you aren't totally infatuated, you dismiss it as not being good enough to work with—and over time that search for your one true passion becomes an exercise in futility.
Well, I've got news for you. Most of us aren't born with one clear passion. Sure, there are people like Michael Jordan who are blessed from birth with a clear passion for one specific career. But the majority of us mere mortals have a diverse range of interests and talents that we develop a passion for over time. I am passionate about my husband and my children, but I didn't know I would be the first day that I met them. Truth be told, I remember feeling incredibly guilty that I didn't fall in love with my first child the moment I saw her. I thought she was cute and all, but even after finally getting to hold her after nine long months, I was perfectly happy to hand her back to the nurse so I could get some sleep after a long labor. It was only over time that I fell hopelessly in love.
So if you've been feeling like you are destined for failure with this process because you can't find your one true passion, relax. Forget about passion. Focus on interests and causes you find compelling. Concentrate on the things you do really well. Think about what makes you smile. Reflect on the types of jobs you'd be proud to do and the people you would love to work with. Good enough can turn into great, intriguing can turn into enchanting, and possibilities can, and will, become passions over time. Finding your path in life is a journey. Don't let the quest for the "one and only" mythical passion derail you before you even get started.
## EXERCISE: TEN KEY QUESTIONS FOR YOUR SECOND ACT
These ten questions will help give you clarity about what you like to do, what you do well, and what you find meaningful. Please refer back to your life story worksheets for help in answering these questions:
1. **Do you want to continue to do work related to your "old" profession or industry?**
Before you answer this, let me remind you that, all things being equal, it is always easiest to do something related to what you did before (and it is the typically the best way to maximize your income). That said, I suspect that many of you would love nothing more than to shed your old career and pivot 180 degrees to a new direction. But before you make that decision final, I urge you to consider whether there isn't some piece or part of what you did before that might be worth saving.
I leaned this lesson the hard way. After having my first child, I left my corporate human resources career to pursue a more family-friendly way to work. At the time, I fantasized about all sorts of new possibilities; one day I wanted to be a nutritionist, and the next I wanted to be in fashion. Finally, after months of patient listening, my husband grew tired of my "brainstorm of the day" and said, "Honey, I'll support whatever decision you make. But why don't you focus on something at least remotely connected to human resources? It's what you know, it's the field where you have a degree, and it is where you've invested your energy for over a decade. Isn't there _something_ you can do that will build on that?"
I wasn't happy to hear that, but as much as I hated to admit it, my husband was on to something. He wasn't saying I should stay in corporate or work in human resources. He was simply suggesting that, in light of my obvious lack of a clear direction, I should consider alternatives that were in some way, shape, or form remotely connected to my professional background and education. So, recognizing that I might have been a bit hasty in my desire to start anew, I decided to figure out which pieces of my past I wanted to carry forward into my next act. And with just a little bit of analysis, it became clear that indeed there _were_ parts of my career that I found quite rewarding: I enjoyed talking about jobs, I liked helping people figure out their career paths, and I was good at coaching and encouraging people. And even though the career-coaching piece had been only a small part of my former responsibilities, I learned that with additional training I could transform that part of my experience into a work-from-home business.
At the time, it was an eye-opening revelation. But now, having spent over fifteen years working with clients on their own midlife transitions, I am quite convinced that career reinvention does not have to equate to a total "do-over." There are always pieces of your previous work experience, no matter how small or seemingly insignificant, worth using as the foundational pieces of your second act.
So now let me ask you this question again, but in a slightly different way:
1. **Do you want to continue to do work related to your "old" profession or industry? And which pieces of your past work would you like to take with you into your next act?**
When you answer this question, think in terms of your favorite work-related skills—for example, "I was great at leading meetings," or "I loved putting together budgets," or "Everyone came to me for help with technical issues." Also think about the special projects that you enjoyed, like organizing the company picnic, as well as the little things that made you happy at work, such as the opportunity to work around really smart people. Now list ten things about your past jobs (skills, projects, industry expertise, and so on) that you might consider incorporating into your next act.
2. **What opportunities, problems, or gaps in the market do you see?**
Within every profession there are opportunities to create needed products, tools, and services. In your industry, you may have noticed a need for a recruiting service, a job board, an association, or a new training program. You may belong to a volunteer group that needs help with writing grants or fund-raising. Or perhaps you live in a community that has a big need for a senior daycare service. What needs have you noticed? Write down at least one suggestion for a needed product or service in each of your "worlds":
Professional life: ______________
Personal/self-improvement: ____________
Friends and family: ______________
Local community: ___________
Global community: ___________
3. **What are your strengths?**
This question conjures up a lot of angst for many people, but this is no time for modesty. Here are some questions to get your thoughts flowing:
• What is something that you find easy to do that others find difficult?
• What are you a natural at?
• What are your special gifts or talents?
• What can't you stop yourself from doing?
• What advice or help do people ask you for?
• What type of compliments do you receive? (For example, "You are so funny," or "You should be a model," or "Why don't you have a business selling your cakes?" or "Have you ever thought of doing voiceovers?" or "You are an amazing mom.")
List your ten greatest strengths.
4. **What types of problems do you like to solve?**
At the end of the day, almost all businesses and careers revolve around solving problems or making things better. Think about the types of problems that interest you. Do you enjoy dealing with management challenges, piecing together puzzles, designing gardens, or helping people plan parties? Write down the types of problems that intrigue you in both your professional and personal lives.
5. **What are your weaknesses?**
We all have our weaknesses and it's important to acknowledge them in order to avoid problematic situations. But rather than thinking of a weakness as something you don't do well, I recommend you think of a weakness the way Marcus Buckingham describes it in his book _Find Your Strongest Life_ (Thomas Nelson, 2009) as an activity that "makes you feel weak." In other words, if it bores you, frustrates you, or saps your energy, it is a weakness. Keeping that description in mind, list your weaknesses.
6. **What do you dream about doing?**
Now is the time to act on your dreams. After all, if you don't do it now, when will you? Think about the types of jobs or business ideas that you've always thought would be fun to do. Whose job would you love to have? When you look back on your career, or what you chose for your major in college, do you have buyer's remorse? If so, what would you have done differently with the benefit of hindsight? Look for the commonalities among those situations and make note of your observations.
7. **What makes you happy?**
When you're not happy, not much else matters. Think back to the times in your life when you felt most energized, creative, joyful, or "in the zone." What were you doing? Who were you with? Where were you? Think also about the little things that brighten your world, like spending time with friends, finding a great bargain, planting a vegetable garden, mastering a new song on the guitar, or planning a surprise party. List up to twenty activities that nurture your soul, make you smile, and enhance your well-being.
8. **What do you want to spend your days talking about?**
I know this sounds basic, but sometimes there is brilliance hidden in simplicity. Do you want to talk about human potential or shoe colors? Are you more intrigued by the wildlife of Africa or the differences between sea salt and kosher salt? Make notes about the subjects, topics, and interests that you find most interesting, compelling, or meaningful.
9. **What political, global, community, or spiritual issues would you like to be involved with?**
We all have causes that we care about, and your second act can be a wonderful time to finally do something connected to your favorite causes. That said, please don't feel obligated to fill this in if nothing comes to mind.
10. **Do you have any "easy" opportunities waiting for you?**
Sometimes we are surprisingly blind when it comes to spotting easy opportunities. A friend might be thrilled to have you join their business, your old company could be delighted to welcome you back as a consultant, or your church youth might need a group leader and you would be the perfect person. What is the "low-hanging fruit" that could, and should, be plucked from your opportunity tree?
Finally, record any additional thoughts about your career reinvention that are important to note:
Congratulations, you made it! I hope that these questions have really started you thinking and helped you to gain more clarity about your gifts, skills, and interests. But please don't be concerned if you are still are unclear about the specific jobs or careers that are your best fit. These questions are not meant to give you definitive answers about what you should do next, at least not at this point. They are intended to give you a better sense of who you are—so that when you begin to explore your options, you'll know a good fit when you see it.
If you're still feeling a bit confused as to what it is you want to do, rest assured that there are many fine career resources available to help you explore further. The easiest way to continue your exploration is by reading a few of the many wonderful books devoted to career assessment. There are hundreds of books to choose from, but here are three of my personal favorites, all of which are considered classics in their genre:
• _What Color Is Your Parachute?_ by Richard Bolles (Ten Speed Press, updated yearly). If the last time you read this book was when you were in college, you are in for a pleasant surprise. _Parachute_ has been revamped and updated for forty years running and is the gold standard for career changers of all ages from teens to seniors.
• _Do What You Are_ by Paul D. Tieger and Barbara Barron-Tieger (Little, Brown and Company, fourth revised edition, 2007). This book helps you determine your personality type (based on the Myers-Briggs Type Indicator) and then shows you the best occupations for your type.
• _Wishcraft_ by Barbara Sher with Annie Gottleib (Ballantine Books, second edition, 2003). Even though it's been a while since this book was last updated, Sher's exercises and advice are timeless. Many people describe this book as life-changing, and I agree.
Some of you may also find it beneficial to invest in working with a career professional. You can find a qualified career coach by asking for recommendations from friends or by checking the directory of the Career Thought Leaders Consortium at www.careerthoughtleaders.com. A number of universities now offer coaching services to their alumni, and you can enroll in career development workshops offered by many community colleges and continuing education programs as well. The North Carolina Center for Creative Leadership (ncccr.unca.edu/paths-creative-retirement) offers a three-day Paths to Creative Retirement seminar several times a year on the campus of the University of North Carolina at Asheville.
Knowing what you love to do, do well, and find meaningful is critical to crafting a fulfilling second-act career. But it is not enough to focus only on what is important to you. After all, if there is no ready market for your services or products, then it will be impossible to turn your passions into profits. That is why the next step in this process is to explore ways to match your skills, talents, and motivators with real-world opportunities. Chapter twelve will teach you how to do just that.
# CHAPTER TWELVE
# Research the World of Possibilities
For those of you who are concerned that "doing research" sounds like an unwelcome school project, let me assure you that this is an exciting, interesting, and thought-provoking experience. Learning about new career options is going to make you feel like a kid in a career candy store: "I had no idea I could earn income doing that!" "Who knew there was a training program for that type of business?" "I can't believe I never considered this option before!" Take the time to browse, brainstorm, and savor those "aha!" moments. Even if you think you already have a pretty good idea of what you want to do next, I urge you to spend at least a little time poking around the resources included in this section. Many of you chose your careers when you were only twenty years old, and although you may have tweaked and adjusted that initial plan as your career progressed, it's probably been a long time since you've had a reason to do any serious career exploration. If you're going to make the effort to start something new, don't you owe it to yourself to familiarize yourself with the full range of possibilities?
As you learned by reading the first part of this book, the world of work has changed dramatically since we all started our careers (back in the prehistoric twentieth century). People are now earning income in ways that we never could have even imagined just a few short years ago: selling on the Internet, self-publishing books on demand, and teaching webinars online. Jobs we aspired to when we were younger have become obsolete, and new careers—like virtual assistants, app designers, social media consultants, and bloggers—have filled the void.
How do you learn about these new paths? By paying attention—reading, watching informational videos, and making it a point to be an "active learner." By engaging with people—talking, asking questions, and doing a lot of listening. By "doing"—taking classes, interning, volunteering, and traveling. Each action you take becomes its own mini-research project, and over time you'll find yourself becoming an expert about a whole new world of exciting career options.
So if you're ready to do some exploring, here are sixteen different ideas that will help you as you continue this process on your own going forward.
## HELPFUL TOOLS, STRATEGIES, AND RESOURCES
1. **Consult your colleagues**. Here is an obvious but sometimes overlooked career research strategy: If you want to do something connected to your former profession, but you're trying to figure out how to do it on a more flexible basis, there is no better way to get ideas than to talk with your industry colleagues. They know you, and they know the industry. And assuming the two of you are close in age, they may be actively thinking about the very same issues themselves. This is a case where two heads are indeed better than one; together you can brainstorm ideas, discuss training programs, and investigate ways to create multiple income streams around needed products or services.
2. **Explore industry associations**. Industry associations are a fabulous resource for learning more about career options within any industry (and believe me when I say there is an association for virtually every type of career and business that you can imagine). You can benefit from their offerings in a number of different ways:
• **Visit their websites**. This is the fastest way to get familiar with the association's products, services, members, and training programs. To locate your industry association, consult the _Gale Encyclopedia of Associations_ (you can find the book in the reference section of your library), or simply do a Google search using the appropriate keywords, such as "personal fitness association."
• **Read your industry trade journal or newsletter**. Larger industries produce trade journals and magazines; smaller ones tend to have newsletters, many of which are accessible online. In either format, these publications can be an excellent source of ideas and inspiration.
• **Get involved**. National associations and trade groups have local chapters that host networking and educational meetings. Attending a meeting is a smart way to meet people and learn about career-related opportunities. Volunteering to help the group in a leadership capacity is also a great way to make important connections, form partnerships, and raise your profile among your peers.
• **Attend their annual conference**. Conferences are a terrific place to hear industry leaders speak, make new friends, and learn about new vendors, products, and services for people in your profession. Several of the people I interviewed for this book said that conferences played an important role in their business success, and they found them to be well worth the price of admission. If you can't afford to fly to a conference, consider attending a one-day workshop in your local area or take advantage of online webinars instead.
• **Explore their training programs and options for certifications**. Trade and association groups sponsor a wide range of educational and certification opportunities, many of which are exclusive to their membership.
3. **Consult the college catalogs (even if you don't plan to go back to school)**. Hands down, one of my favorite ways to research career options is to read through the programs and classes offered by colleges and universities. I discovered the value of "catalog surfing" when going through my own career reinvention many years ago. At the time, I was working in corporate human resources and was desperate to figure out a way to transition into a more lifestyle-friendly career; I really wanted to get out of a corporate environment, but I didn't know what else to do. So I went to the library to research advanced degree programs for people with a background in psychology, sat down with the _Peterson's Guide to the Colleges_ , and, purely by chance, stumbled upon a master's degree program in career development. After reading the description of the courses, I was convinced that their program was a perfect fit with my background and interests. Many of my clients have experienced the same "luck" by scrolling through college catalogs and websites to uncover exciting variations of careers that they didn't even know existed.
Even if you don't plan on going back to school, it's worthwhile to check the school catalogs and continuing education offerings, just to see what courses are being offered. Their catalogs can provide you with ideas about emerging fields and "hot" careers, as well as information about certificate programs and certification options. Two of my favorite resources for researching educational programs are _US News & World Report_ (www.usnews.com) and Peterson's Guides (www.petersons.com). When you look for college programs, be sure to also check with community colleges and continuing education programs, which typically have classes that are great for people who want to start their own businesses. For example, my local continuing education program offers classes that include How to Make Money as a Photographer, How to Earn Money as a Voiceover Professional, and How to Become an Event Planner.
4. **Check out the "career idea" books**. There are hundreds, if not thousands, of books that can help you research a great new career. Some of the books, such as this one, provide mini-snapshots of a variety of careers; other titles feature detailed step-by-step advice on a specific career or business idea, such as how to earn an income online, how to make money selling gourmet products, or how to flourish as a consultant. In addition to locating these books at brick-and-mortar bookstores or on online sites, many industry association websites have online bookstores that sell industry-specific books and other informational products.
5. **Look at the US Department of Labor sites**. It may surprise you to learn that our federal government funds much of the career data that is produced in this country, but they do, and their sites are excellent. I consider them the equivalent of the _Encyclopedia Britannica_ of the careers world: chock full of more information than one person could possibly digest, and a tremendous resource when you need to explore career possibilities. Here are four of their most helpful websites:
• **America's CareerInfoNet (www.acinet.org)**. On this mega-site you can research wages and employment trends, occupational requirements, and state-by-state labor market conditions and take advantage of the most extensive career resource library online.
• **My Skills, My Future (www.myskillsmyfuture.org)**. This site asks you to input your old job title; it then responds with suggestions of jobs that match your background and skills. It is a very helpful tool for generating ideas that you might not have previously considered.
• **O*NET Resource Center (www.onetcenter.org)**. The O*NET program is the nation's primary source of occupational information, with a robust database of hundreds of occupations. This resource is so extensive that they have now created the O*NET Academy (www.onetacademy.org), a site that teaches how to maximize your use of O*NET's capabilities and resources (and of course, all the training is provided free of charge).
• **The Occupational Outlook Handbook (OOH) (www.bls.gov/ooh)**. The OOH, updated every two years by the Bureau of Labor Statistics, provides detailed information about hundreds of careers. As the name implies, this is a great resource to help you both learn about different professions and decide which industries should have strong growth potential in the future. It is one of my all-time favorite resources.
6. **Visit career portal sites**. In addition to the sites sponsored by the government, there are numerous private and university sites that offer a helpful overview of careers. Here are three worth mentioning:
• **MyPlan.com (www.myplan.com)**. This site features comprehensive information about over nine hundred careers. You can read career profiles, watch videos about five hundred different careers and industries, and learn about the types of people who typically go into each career. Although this site is geared toward college students, it is still worth a visit, no matter your age.
• **The Riley Guide (www.rileyguide.com)**. The Riley Guide was one of the first major career research sites on the Web, and it remains a favorite among career professionals. Don't be put off by its low-tech appearance; what it lacks in glitz, it makes up for in quality, scope, and content.
• **eHow (www.ehow.com/careers)**. This site has short videos about how to get started in a number of careers and entrepreneurial ventures. Their current roster of offerings includes How to Earn Passive Income Writing, What to Put into a Modeling Portfolio, and How to Become a Stockbroker.
7. **Leverage the social media sites**. All three of the big players in the social media sphere—Twitter, LinkedIn, and Facebook—are helpful tools for people looking to research business and career ideas. Learning how to use all the many features of these sites takes some focus, but I think you'll find it to be a worthwhile investment of your time. Here are five easy ways to engage social media as part of your career research endeavors:
• **Post a question on Facebook, tweet a question on Twitter, or submit a question to your LinkedIn network**. Keep your request for information short, simple, and specific. For example, "I am exploring career opportunities as a food writer. Looking for recommendations of good training programs." You never know who might be able to provide you with a helpful tip or suggestion.
• **Follow groups on Facebook**. There are thousands of niche industry groups on Facebook that you can follow. Identify a few that might be beneficial and connect with them to automatically receive their news feeds and updates.
• **Follow industry "gurus" on Twitter**. Every industry has its star performers, and these days many of those people are sharing their thoughts on Twitter. Sign up for a Twitter account at Twitter.com (don't worry, you don't need to tweet in order to maintain your account) and then find interesting people to follow by using search directories like Twellow.com ("the Twitter Yellow Pages") or WeFollow.com.
• **Join an industry-related group on LinkedIn**. Go to the "Groups" tab and search to find groups that you would like to join. Some groups have restricted membership, but most are open to all interested parties. Once you're a member of a group, sign up to receive automated updates so you'll be kept informed about relevant events, training programs, and news on a regular basis. Participate in the group discussions—it's a great way to meet people and build relationships in your new field of interest.
• **Search for jobs on LinkedIn or Twitter**. Even if you are not actively seeking a job, reviewing the job postings on LinkedIn or Twitter can provide you with helpful information about the variety of jobs available in your field of interest.
8. **Learn from the job listings**. One of the simplest ways to research careers is to scan the job boards (even if you are not actively looking for a job); you'll learn about the skills, educational requirements, salary ranges, and opportunities for lots of different careers. There are thousands of job boards on the Internet where you could do research; here are five of the best:
• **Job board aggregators**. There are now several sites that pull millions of job listings from other job boards and post them in one central location. Sites like Indeed.com, SimplyHired.com, and Guru.com (for freelancers) are great first stops for anyone doing career research via the job boards.
• **Industry niche sites**. Once you have focused on an industry, it can be helpful to look through the job listings on industry-specific boards like Mediabistro.com (media industry) or Idealist.org (nonprofits). To find a job board in your industry, do a Google search using appropriate keywords or consult Job-hunt.org or Rileyguide.com.
• **Associations**. Almost all associations now host some sort of job board or careers page on their websites.
• **Company sites**. Companies, universities, and nonprofits almost always list job openings on their websites.
• **Craigslist.org**. Entrepreneurs and small businesses love to list their job openings and contract work opportunities on Craigslist.org. It is the go-to site for locating unique entrepreneurial job and freelance opportunities.
9. **ExploreAlltop.com**. If you're one of those people who enjoys browsing the mega-magazine displays at airports, then you're going to love Alltop, which bills itself as the online "magazine rack" of the Web. Alltop.com helps you quickly locate the highest-quality information on hundreds of interesting and diverse topics ranging from business to cheese to sports. They compile the latest stories and headlines from their hand-picked list of blogs and websites, and because they feature only stories from trusted sources, their results are free of the junk you normally need to sift through on other search engines.
10. **VisitYouTube.com**. YouTube is the go-to destination for informational videos about thousands of careers and entrepreneurial options. It's easy, it's free, and all you need to do is go to the site (or find the videos on Google.com) and input the relevant search words (for example, "Green Careers" or "Executive Coaching Business" or "How to Become a Makeup Artist"); with any luck, your search will return at least a few relevant videos. Of course, you'll need to be careful to look for videos from credible sources, because anyone can post a video on YouTube.com.
11. **Read business magazines and newspapers**. Although most people read business magazines and newspapers to get financial information and business news, these can also be a good source of inspiration, resources, and ideas for career changers. The _Wall Street Journal, Fortune, Fast Company, US News & World Report, Kiplinger's, AARP_, and _Money_ , along with their related websites, all feature stories about hot careers, great business ideas, and profiles of successful entrepreneurs.
12. **Browse through popular and niche magazines**. Most of us read magazines for fun and diversion, but they can also be a surprisingly helpful source of ideas about new career paths and business opportunities. Here are some tips for maximizing the use of magazines in your career research:
• **Learn about trends**. Magazines like _Inc_. and _Entrepreneur_ routinely print articles about small business trends. Every year _Entrepreneur_ publishes their predictions for the hottest business trends likely to emerge in the coming year, along with suggestions on how to capitalize on those trends.
• **Read niche publications**. Did you ever notice how many magazines are targeted to specific hobbies and niche interests? There are magazines for pet lovers, chocolate fanatics, golfers, parents, crafters, and wine enthusiasts (just to name a few). Those magazines focus their coverage on the people, businesses, and products associated with those niches—highly specific information that can be difficult to find elsewhere.
• **Get inspired by profiles**. Many magazines have columns showcasing inspirational stories about entrepreneurs, career changers, and business leaders. Reading their stories will help you discover innovative ways to turn your passions into profits.
• **Pay attention to advertisements**. The advertisements in niche magazines feature information about industry-specific training programs, franchises, and business opportunities that might be a good match for your needs. The advertisements are also a good way to learn about clever niche-related products, gizmos, and inventions that might inspire your thinking and help you innovate new product offerings of your own.
13. **Throw an idea party**. I first learned of "idea parties" from career counselor and best-selling author Barbara Sher in her book _Live the Life You Love_ (Dell, 1996). Sher defines an idea party as "a potluck dinner where you invite people into your home for the express purpose of sitting down with a plate of good food and brainstorming on your particular problem." It's a fun evening of camaraderie and conversation that can lead to a new direction for your career.
This idea makes perfect sense. After all, you turn to your friends if you need help choosing a paint color or finding the best hip surgeon, so why not enlist their aid with your career reinvention? They can help you brainstorm ideas, find resources, and think about options that you might never consider on your own. Before you send out the invitations, it is important to do your own preliminary research and personal assessment. After all, you can't expect your friends to solve your "What should I be when I grow up?" dilemma for you; that is up to you. But the idea party can help generate specific ideas, resources, and strategies that will move you closer to your goals. Here are some tips on how to create a successful idea party:
• **The purpose of an idea party is to generate ideas through an open brainstorming session**. You'll want to invite people who are good outside-the-box thinkers, supportive personalities, and creative thinkers; leave the "Debbie Downers" home. And feel free to ask friends to invite someone you don't know. The input of people outside your normal circle of influence could prove to be extremely enlightening.
• **Make it easy for your friends to help you by asking for specific information and resources**. The more specific you are, the greater the likelihood that your friends will be able to respond in concrete and meaningful ways.
• **Serve good food and drink**. It will make your guests feel appreciated.
• **Remember to send each of your guests a thank-you note**. This may seem like an unnecessary formality, but it will be very much appreciated.
Finally, don't forget to pay it forward. Let your friends know that you'll be there for them when they need your help and assistance down the road.
14. **Get inspired by second-act career stories**. Reading and hearing motivational stories is, well, inspiring. There are a number of excellent sites on the Web that have motivational stories about people over forty reinventing their careers. In no particular order, here are some that you may find quite useful:
• **AARP (www.aarp.org/work/working-after-retirement)**. AARP has built a robust work and retirement section on their website, complete with recommendations of work-from-home and part-time employment ideas. AARP's "Your Life Calling" with Jane Pauley is an award-winning TV series on the NBC _TODAY_ show highlighting people age fifty-plus who are reinventing themselves in new and different ways. You can visit www.aarp.org/your_life_calling/ for more information on the TV series or, for a full archive of stories, <http://www.aarp.org/personal-growth/transitions/ylc_index>.
• **Next Avenue (www.nextavenue.org)**. The Public Broadcasting Service (PBS) launched this site in May 2012 to help "grownups keep growing"; it features numerous articles and profiles focused on work and purpose.
• **Huff/Post50 (www.huffingtonpost.com/50)**. All of the content on this Huffington Post site is geared for the baby boomer generation and includes many posts related to career and reinvention topics.
• **Encore.org (www.encore.org)**. Encore.org is for people interested in encore careers—jobs that combine personal meaning, income, and social impact. Their site is an excellent resource for people who want to create their second acts in the nonprofit world.
• **More.com (www.more.com)**. The website for _More_ magazine has many stories about career reinvention for women over forty. Although the magazine is intended for women, the stories are equally useful for men.
• **TED (Technology, Entertainment, Design) (www.ted.com)**. If you're not already familiar with TED, you should check out their TED Talk videos that feature over one thousand of the world's most inspirational speakers on a wide range of topics. They are both educational and awe inspiring. This site is one of my personal favorites.
15. **Gaze into the crystal ball**. The world of work is changing rapidly. What is hot today may be obsolete tomorrow. Take the time to learn about emerging trends and predictions for the future. That futuristic orientation will serve you well and will inspire you to think more broadly about potential business ideas and career possibilities. Here are some sites to help do just that:
• **World Future Society (www.wfs.org)**. The World Future Society is an organization dedicated to exploring the future. Their magazine, _The Futurist_ , is sold on newsstands, and their website is a great resource about future trends and predictions.
• **Faith Popcorn (www.faithpopcorn.com)**. Faith Popcorn is a renowned futurist and founder and CEO of the marketing consulting firm, BrainReserve. Most of the information on her site is geared toward corporate clients, but if you look carefully, you'll find several free reports summarizing her key trends and predictions.
• **Springwise.com (www.springwise.com)**. Springwise.com's tag line is "Your essential fix of entrepreneurial ideas." Their site features promising business venture ideas and concepts—a fantastic resource for entrepreneurs looking for the "next big thing."
• **Trendwatching.com (www.trendwatching.com)**. Trendwatching.com reports on emerging consumer trends, insights, and innovations. You can sign up for their free monthly trend reports.
• **Trend Hunter (www.trendhunter.com)**. This is the site for people interested in trends in fashion, pop culture, art and design, social media and technology. As of this writing, this site was averaging over thirty-five million views a month—now that is one trendy site!
• **Mashable (mashable.com)**. Although not technically a trend site, Mashable is the largest independent online news site dedicated to covering digital culture, social media, and technology—an outstanding resource for all things tech.
16. **Conduct informational interviews**. There is a limit to what you can learn about prospective careers from just reading and research. At some point, you'll need to turn off the computer, close the books, and start talking with people who are doing what you'd like to do. Speaking with other people is the single most effective way to learn about new career options, and conducting informational interviews will help you get a real-life perspective of what it's like to work in a specific job or business, before you invest time or money transitioning into a new career.
Some people are reluctant to ask for informational interviews, fearing that they might appear foolish (especially if the person they are contacting is much younger) or that their request will be viewed as an imposition. That is understandable, but the reality is that most people will be flattered by your request and will want to help—most people love to talk about themselves! You can ease into this process by first contacting your inner circle of friends, neighbors, and relatives, and then expanding your outreach to their extended network of contacts. Here are some sample questions to ask during your informational interview:
• What do you enjoy most about your job?
• What are the most frustrating aspects of your job?
• What are the most important characteristics for success in this career?
• What training should I pursue to make myself more marketable in this field?
• Which professional associations would you recommend I join?
• What are the challenges, trends, and opportunities in this profession?
• Are there good options for freelance or consulting work within this industry?
• Which magazines, journals, or websites do you recommend?
• Are there opportunities for flexible work arrangements?
• Is there someone else you recommend I speak to?
• May I use your name in making the introduction?
Of course, you should always follow up your meetings with a thank-you note (these days e-mail notes are sufficient, but a handwritten note is still a lovely surprise). And do be sure to circle back with your contacts and let them know about your progress as your plans evolve.
# CHAPTER THIRTEEN
# Try It Out!
After you've identified some intriguing career or home-based business options, and have gathered useful data about each choice, the next step is to assess those options for "fit" by trying them out. Evaluating each option against your unique package of skills, interests, experience, and values will help you answer the question, "Is this a good fit?" Here are some key questions to ask as you weigh your choices:
• Does this career or business take advantage of my experience and background?
• Is this a good match for my motivating skills, interests, and values?
• Is this a good fit with my lifestyle and salary objectives?
• What additional training, certification, or licensing do I need to get started in this field? Are there schools around me that offer the training I need? If not, are there online options for education? Am I willing to invest in this additional education? Are there industry or entrepreneurial associations I should join to help build my skills and contacts in this field?
• Do I have the time, money, and energy to prepare myself for success in this job? If not, are there alternative careers in this industry that might be a more suitable fit?
Lots of potential career or home-based business ideas will sound exciting when you read about them, but you won't really know whether they are a good choice until you've had a chance to actually test them out. Fortunately there are several low-risk ways to do that:
**Volunteer**. Volunteering is a win-win for all involved; the organization benefits from your efforts, and you gain experience that you can leverage as part of your career reinvention. To maximize the benefits, be strategic about where and how you choose to volunteer. For example, if you're thinking about transitioning into healthcare, you should try to find opportunities to volunteer in a healthcare setting that is focused on your specific field of interest; if you're considering a pet-related business, you can volunteer at a vet's office or animal shelter.
**Pursue a part-time or freelance job**. Sometimes it makes sense to take on a small part-time job as a way to learn about a new industry. For example, if you're interested in selling your prized brownies online, but you have no real experience in the food industry, you might want to work for a local bakery to get a taste of life in the baking world. Or if you're thinking of getting a certificate in health coaching, you might want to get a part-time job as a meeting leader with Weight Watchers to determine whether you like working in that industry. Although working in a lower-level job may require a bit of an ego adjustment, you will enjoy them more if you think of them as an apprenticeship and research opportunity.
**Intern**. There once was a time when only college students took advantage of internships. But in today's competitive global market, people of all ages have discovered the value of internships as a way to evaluate and build new career paths. To learn more about how to locate an internship in your field of interest, consult Internship.com or the Guide to Internships on About.com at <http://internships.about.com>.
**Indulge in a vocation vacation**. How would you like a chance to work alongside a winemaker in Napa, a director on Broadway, or an alpaca rancher in Oregon? VocationVacations is a service that offers you the chance to test-drive your target career while being mentored by a professional in that field. To learn more, be sure to check out their site at www.vocationvacations.com.
**Take a class**. Taking a class, even if it is just a short workshop or seminar, will provide you with an opportunity to evaluate your interest in potential career and business options, learn new skills, and meet new people who can stimulate your thinking about your future career plans. Adult education is a big business these days, and there are more opportunities than ever to indulge in lifelong learning. As you may have gathered while reading part one of this book, there is a training program for every business imaginable, from dog walking to jewelry making (heck, I even came across a training program for hot dog vendors!). That said, you'd be wise to exercise caution if you plan to invest in a certificate program, boot camp, or "university" run by an independent entrepreneur. The quality and legitimacy of those programs vary considerably, so ask lots of questions, do your homework, and always check around before investing your hard-earned dollars.
Of course, enrolling to study with an established school or college is generally a safer bet. There are an increasing number of online programs being offered by, or in conjunction with, leading colleges and universities, and some of these programs are specifically targeting the second-act market. One example is Empowered.com, an online educator that offers certificate programs in "hot" fields such as patient advocacy, college counseling, and financial planning. Their courses are taught by the faculty of UCLA's extension program using iPad technology (all students who enroll in their year-long certificate programs receive an iPad), and students are also provided access to extensive career guidance services to help them as they plan for their next acts.
Here are several more reasons why now might be the prime time for you to return to school:
• **Tuition waivers**. More than half of accredited degree-granting educational institutions offer tuition waivers or discounts for older adults. Many colleges allow people age sixty or older to audit classes (meaning you can attend lectures without the homework and exams). Although you won't be eligible for college credit, you will enjoy the same learning opportunity as your twenty-something classmates.
• **Low-cost community colleges**. Community colleges provide a very affordable way to continue your education, and they offer valuable certification and trade-specific vocational training options. Some community colleges also participate in the Plus 50 Initiative, a national program that helps community colleges create or expand "ageless learning" programs and life transition counseling services for people over fifty. To find a participating community college near you, consult www.aacc.nche.edu/pages/ccfinder.aspx.
• **Classes for people over fifty**. A growing number of colleges are offering continuing education classes geared specifically for older adults. Worth a special mention is the network of Osher Lifelong Learning Institutes, located at approximately 120 colleges and universities throughout the United States, including schools like Duke, Johns Hopkins, and Vanderbilt. Osher provides a robust calendar of adult learning opportunities with the emphasis on learning for the joy of learning—without the burden of homework and exams. Fees vary considerably by location, but they tend to be very affordable, especially when compared to traditional college classes.
• **Residential campus learning communities**. A growing number of colleges, including Dartmouth College and the University of Florida at Gainesville, have retirement communities that are located on or near the campus. Residents of these communities are often allowed to attend classes for free (and may be entitled to other benefits, like tickets to college sporting events).
• **Opportunities to learn while traveling**. Road Scholar (formerly known as Elderhostel) is a nonprofit organization offering a wide variety of experiential and adventure learning opportunities. Road Scholar (www.roadscholar.org) works in partnership with nonprofit educational institutions, such as museums and universities, to provide high-quality, college-level educational programs and classes.
# Conclusion: Some Final Tips on Creating Your Second-Act Career
As we come to the end of this journey, I want to leave you with some thoughts on how to get the most out of this reinvention process as you move forward on your own. In some ways, creating a new career works a bit like planting a garden: you ready the soil, plant the seeds, water regularly, wait patiently, and over time new growth emerges from the ground up. The same is true when people reinvent their careers: it takes a bit of work to get things rolling, but if you invest the time to create fertile growing conditions, then you get to enjoy a bountiful harvest. So before concluding, here are some tips on the best ways to ensure optimal growing conditions for your second act:
• **Budget for success**. Career transitions take time, so plan your finances accordingly. Most experts advise that you set aside at least eighteen months of living expenses to tide you over as you go through the process of planning, training for, and implementing a new career plan. As early as you can, start paying down outstanding debts, downsize your lifestyle if necessary, and plan to take advantage of any employer tuition reimbursement plans and training programs before leaving your job.
• **Set a reinvention research and development "R &D" budget**. Put aside some funds to invest in your personal R&D activities. It doesn't need to be much, but knowing that you have earmarked funds for your personal development will make it more likely that you'll take advantage of learning opportunities as they surface. That money can then be used—guilt free—for classes, retreats, books, and other training that could significantly accelerate the speed of your progress.
• **Keep a reinvention journal**. Writing things down will help you capture your thoughts and remember important facts. It will also help create clarity during a sometimes confusing transition; it is remarkable how much easier it is to analyze issues when you write them down instead of simply trying to think them through.
• **Schedule your reinvention projects on a calendar**. Scheduling these activities on your calendar will make your commitment real. I ask my clients (most of whom fall into the overworked and overwhelmed category) to use this time-management technique, and the ones who put it into practice, love it. It gives them a structure, workable boundaries, and improved productivity.
• **Buddy up for success**. This process is so much more enjoyable—and effective—when you share it with others. Ideally your spouse or life partner will act as your most enthusiastic ally and cheerleader. But if not, buddy up with a trusted friend or group of people who are actively in the process of building their second-act careers. Remember, a great support system turns possibilities into probabilities—and dreams into reality.
• **Expect resistance**. Change is uncomfortable; human beings are hardwired to resist venturing into the unknown. Know that there will be times when you will be stuck at a crossroads or frustrated by indecision. And it's not just _you_ who may be feeling fear. Family and friends may be scared by the changes as well ("You want to do _what_?"), and they may not always be as supportive or encouraging as you'd wish. Be patient, stay calm, keep communicating, and give everyone time to adjust.
• **Don't force it**. Sometimes taking a break will speed up your progress more than trying to force your way to an answer. I periodically remind my husband of this when he works on the _New York Times_ crossword puzzle. He always starts the puzzle with great enthusiasm, but as the clues become more challenging and his progress slows, he grows more frustrated. Ironically when he does force himself to take a break, when he returns to the puzzle he is able to finish it with relative ease. Walking away from the puzzle gives him a chance to relax, refresh, and look at the clues with fresh eyes. Crafting a new career is a bit like solving a crossword puzzle. Sometimes your breakthrough moments will happen when you least expect them, so be willing to step away and take a break in order to gain some needed perspective.
• **Reinvention is going to take the time it takes, so start early!** I have yet to see a career reinvention unfold exactly according to schedule. It's a process that can take months, or even years, to fully evolve, and no matter how well you plan, there will be unexpected twists and turns. You'll get excited about an idea, begin to research options, and discover that you need to take a few classes before you can begin to move forward with your plans. Or you'll come down with the flu. Or the doctor says you may soon be needing a knee replacement. Or—well, you get the idea. Bottom line is that you should expect the unexpected, so the sooner you begin the reinvention process, the better off you'll be.
The path to a second-act career is rarely a straight line; it is a meandering journey, on which you are propelled by patience, determination, and a willingness to adapt as circumstances change. It is characterized by failure, doubt, and false starts, but it is also graced by generosity, moments of clarity, and serendipity. Career reinvention is not one seamless transition, but a series of smaller actions that link together to create lasting change. You'll have a conversation—that leads to an introduction to a new person—who leads you to a fun part-time job; or you'll read a book—that gets you excited about taking a course—that leads to learning a new skill—that enables you to start a new business.
You never know where or when or how reinvention magic will happen. But it will. So relax, and remember to have fun as you go on your way. And as you proceed, keep in mind this thought from Gracie Cavnar, the founder of Recipe for Success, who says, "I know it sounds trite, and people have been saying it for decades, but find your bliss. Something you love so much that you can't wait when you wake in the morning to get started. Now is the time to do that. Life is what is happening while you are waiting for it."
What are you waiting for? Now is your time. The curtain is going up, and your second act is about to begin. Godspeed, and enjoy the journey.
# Resources
Websites change constantly, so if you don't find a resource under the suggested URL, do a keyword search to find similar resources. Also, please be sure to sign up for my newsletter at MyLifestyleCareer.com to receive automatic updates about additional great resources for creating a lifestyle-friendly career.
## Advice for People Wanting to Work Without a 9-to-5 Job
I turn to this list of experts and authors whenever I am looking for new ideas, insights, and resources about flexible work. They represent a wide range of ages, values, and sensibilities (some of which might not match your own), but putting value and age differences aside, I think you'll learn a lot from their blogs, books, classes, and other informational offerings.
• Barbara Winter (www.joyfullyjobless.com)
• Chris Guillebeau (www.chrisguillebeau.com)
• Dan Miller (www.48days.com)
• Jonathan Fields (www.jonathanfields.com)
• Jonathan Mead (www.paidtoexist.com)
• Kerry Hannon (www.kerryhannon.com)
• Michael Hyatt (www.michaelhyatt.com)
• Natalie Sisson (www.suitcaseentrepreneur.com)
• Pamela Slim (http://www.escapefromcubiclenation.com)
• Scott Dinsmore (www.liveyourlegend.net)
• Sean Ogle (www.seanogle.com)
• Valerie Young (www.changingcourse.com)
## **Online Career Tests**
While I am not a big fan of online career tests in general, as I think many are designed to deliver quick answers as opposed to truly useful insights, they can be helpful if you use them in conjunction with other tools. Here are some you might find useful:
• Myers Briggs Type Indicator (MBTI) (www.myersbriggs.org)
• Strong Life Test (www.stronglifetest.com)
• Career Key (www.careerkey.org/asp/your_personality/take_test.html)
• Questionnaire Center of the Positive Psychology program at the University of Pennsylvania (www.authentichappiness.sas.upenn.edu/questionnaires.aspx). Although these are not technically career tests, they will help you gain insight into your strengths, motivators, and happiness drivers.
## **Entrepreneurial Resources**
• BizStarters (www.bizstarters.com). Advice for entrepreneurs over fifty.
• _Entrepreneur_ magazine (www.entrepreneur.com).
• FabJob Guides (www.fabjob.com). Step-by-step guides to starting your own business.
• Freelancers Academy (www.freelancersacademy.com). Site for both new and experienced freelancers.
• Open Forum (www.openforum.com). A wealth of resources for small business owners.
• PivotPlanet (www.pivotplanet.com). One-on-one video or voice sessions with expert advisors working in hundreds of different fields (a fee applies).
• Rise to the Top (www.risetothetop.com). Video interviews with entrepreneurs.
• Small Business Administration (www.sba.gov). Government-sponsored site brimming with information and resources for entrepreneurs.
• SmartBrief on Entrepreneurs (www.smartbrief.com). Free e-mail newsletter.
• Spark and Hustle (www.sparkandhustle.com). Regional conferences for female entrepreneurs.
## **Job Search Sites Specifically for People 50+**
• BoomerJobs (www.boomerjobs.com)
• RetirementJobs (www.retirementjobs.com)
• Seniors4Hire (www.seniors4hire.org)
• Workforce50 (www.workforce50.com)
• Work Reimagined (www.workreimagined.aarp.org/#about)
# About the Author
Nancy Collamer, MS, is a career coach, author, and speaker who is an expert at helping people create lifestyle-friendly careers. In private practice since 1996, Nancy gained national prominence as the Career Transitions columnist for Oxygen Media and as the founder of the popular websites MyLifestyleCareer.com and Jobsandmoms.com. She holds a MS in career development from the College of New Rochelle and a BA in psychology from the University of North Carolina at Chapel Hill.
Her advice has been featured in numerous media outlets, including _NBC Nightly News;_ the _New York Times; CNN;_ the _Wall Street Journal; Redbook; Ladies' Home Journal; More; O, The Oprah Magazine;_ and _Fortune_. She has written columns about lifestyle-friendly careers for a number of major websites, including AARP.org, MariaShriver.com, NextAvenue.org, and Job-Hunt.org. Nancy enjoys sharing her expertise with live audiences, both large and small, and has spoken at venues ranging from Harvard Business School to the California Governor and First Lady's Conference on Women.
When not at work, Nancy loves spending time at her home in Old Greenwich, Connecticut, with her husband, Joel, their two daughters, Danielle and Juliana, and her one-eyed cat, Annabelle. She is a rabid UNC Tar Heel basketball fan and a proud card-carrying member of AARP.
**To Contact Nancy**
I really want to hear your success stories and your own "lessons learned", so please don't be a stranger! There are several ways to connect with me:
**VisitMyLifestyleCareer.com:** You'll find lots of information, profiles, and resources to help you as you craft your semi-retirement career. Be sure to sign up for my updates on the site.
Connect on Twitter @NancyCollamer
Follow me on Facebook at www.facebook.com/mylifestylecareer
**Speaking engagements:** I adore speaking to audiences, both large and small, about semi-retirement careers, and I always enjoy the opportunity to share inspirational stories, actionable strategies, and little-known resources. Most of all, I love making those lightbulb moments happen! To inquire about booking a speaking engagement, e-mail me at njcollamer@gmail.com.
**Consulting/coaching:** If you're interested in hiring me as a coach who can help jump-start your semi-retirement plans, I'd love to hear from you. Best way to reach me is by e-mail at njcollamer@gmail.com.
# More Career Guidance from TEN SPEED PRESS
**What Color Is Your Parachute?**
**Guide to Job-Hunting Online**
**6TH EDITION**
by Mark Emery Bolles and Richard Nelson Bolles
$12.99 paperback (Canada: $14.99)
ISBN: 978-1-60774-033-9
eBook ISBN: 978-1-60774-042-1
**The New Job Security**
**The 5 Best Strategies for Taking Control of Your Career**
**REVISED**
by Pam Lassiter
$14.99 paperback (Canada: $16.99)
ISBN: 978-1-58008-377-5
eBook ISBN: 978-1-58008-673-8
**The 2-Hour Job Search**
**Using Technology to Get the Right Job Faster**
by Steve Dalton
$12.99 paperback (Canada: $14.99)
ISBN: 978-1-60774-170-1
eBook ISBN: 978-1-60774-171-8
**Strategies for Successful Career Change**
**Finding Your Very Best Next Work Life**
by Martha E. Mangelsdorf
$16.99 paperback (Canada: $21.99)
ISBN 978-1-58008-824-4
eBook ISBN: 978-0-307-76854-4
Available from Ten Speed Press wherever books are sold.
**www.tenspeed.com**
| {
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Dino Jr. Terminal 5 show – one of Lou Barlow's 'Best Moments'
By BrooklynVegan Staff January 2, 2013 9:31 AM
Lou Barlow @ Terminal 5 (more by Gretchen Robinette)
Like Dave Hill, Gretchen Robinette and many of us, The Dinosaur Jr. 'you're living all over me' 25 year celebration show at Terminal 5 was a major highlight of 2012 for Dinosaur Jr.'s own Lou Barlow. He told Pitchfork:
people kept saying 'can you believe it's been 25 years since that record was released??' yes, yes i can.. easily.. so much happened since the release of that record..many bands, more band mates, lotsa fights, lotsa love..children! babies were born in the interim, human children ..so , i -can- believe it ..what REALLY surprised me was Frank Black singing one of the new dinosaur jr tunes ( 'almost there' (? , it really is impossible to figure out the names of J's songs) – the one i like to call the 'birkenstock tune' ) AND dinosaur jr playing a pixies song ('tame') with francis on vocals.. yea.. that part blew me away.. after years of fighting it i am ready to be a pixies fan, i will resist no longer.. he's got a serious set of lungs and learned our song like a proper musician.. much respect.. that ridiculous anniversary show was the #2 highlight of my year..or maybe it was number #1 ..i can't really rate events like this , once my mind is blown it's all equal, if you know what i mean..
More pictures and a recap of that show HERE. Lou's full list of three 'Best Moments' of 2012, below….
when i wasn't busy tugging at the loose threads of the fabric of my life, these musical events made me stop for a second and say ' wow, i never thought -that- would happen!' or ' yea, i like that!'
#1 dinosaur jr + sebadoh at that portland festival that has an sxsw kind of name nwxnw? pdxnw? wxpdxnw? .. yes, dinosaur jr and sebadoh shared a stage.. i.e. sebadoh opened for dinosaur jr.. this is significant, to me, because i am in both bands..significant because i was fairly certain it would never be -allowed- to happen..why? because it's too much -me- in an evening , that's why.. because people might forget that J Mascis is the Reason…. that didn't happen, of course.. sebadoh did a rushed set after not playing together for a couple of months, to a smattering of applause, then Dinosaur Jr came on and CRUSHED everyone..the end… i got really drunk afterwards in earnest celebration and puked for the first time in a long while.. anyway, thank you to whomever paid the ungodly sum it took to make the show happen ( i've been lobbying for a show like this for 7 years to no avail ) .. i forget who now but they also set up a storefront to promote the show that included memorabilia from both bands and played dinosaur jr and sebadoh tunes one after another for days..surreal in the utmost.. oh yea..it was Red Bull , they set it up.. bless them and their bizarre and addictive beverage..
#2 dinosaur jr 'you're living all over me' 25 year celebration show , NYC december.. people kept saying 'can you believe it's been 25 years since that record was released??' yes, yes i can.. easily.. so much happened since the release of that record..many bands, more band mates, lotsa fights, lotsa love..children! babies were born in the interim, human children ..so , i -can- believe it ..what REALLY surprised me was Frank Black singing one of the new dinosaur jr tunes ( 'almost there' (? , it really is impossible to figure out the names of J's songs) – the one i like to call the 'birkenstock tune' ) AND dinosaur jr playing a pixies song ('tame') with francis on vocals.. yea.. that part blew me away.. after years of fighting it i am ready to be a pixies fan, i will resist no longer.. he's got a serious set of lungs and learned our song like a proper musician.. much respect.. that ridiculous anniversary show was the #2 highlight of my year..or maybe it was number #1 ..i can't really rate events like this , once my mind is blown it's all equal, if you know what i mean..
#3 a festival in Champaign Illinois that featured almost every newish band i wanted to see, one after the other.. Willis Earl Beal , Unknown Mortal Orchestra, Lower Dens .. Grizzly Bear .. Willis was as odd as i could have expected, UMO was as fucked up and soulful as i could have desired and Lower Dens were.. sublime.. sounding nothing like Sublime , of course but, y'know..spare and beautiful..i love how younger kids these days sound like the older guys from my day.. the late 70's early 80's new wave/post-punkers from new york that wore big framed glasses and captured my teenage imagination.. i also saw Cloud Nothings that day which was interesting because they sounded like all the bands sebadoh played with in the mid-90's -combined- .. in conclusion , a great festival i can't remember the name of …another musical highlight..
Filed Under: Best of 2012 | Dinosaur Jr. | Frank Black | Lou Barlow | Pixies | Terminal 5 Category: Music News | {
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{"url":"https:\/\/proofwiki.org\/wiki\/Best_Rational_Approximations_to_Root_2_generate_Pythagorean_Triples","text":"# Best Rational Approximations to Root 2 generate Pythagorean Triples\n\n## Theorem\n\n$\\left\\langle{S}\\right\\rangle := \\dfrac 1 1, \\dfrac 3 2, \\dfrac 7 5, \\dfrac {17} {12}, \\dfrac {41} {29}, \\dfrac {99} {70}, \\dfrac {239} {169}, \\dfrac {577} {408}, \\ldots$\n\nEvery other term of $\\left\\langle{S}\\right\\rangle$ can be expressed as:\n\n$\\dfrac {2 a + 1} b$\n\nsuch that:\n\n$a^2 + \\left({a + 1}\\right)^2 = b^2$\n$b$ is odd.\n\n## Proof\n\nThe numerators of the terms of $\\left\\langle{S}\\right\\rangle$ are all odd.\nFor all $n$, the parity of the denominator of term $S_n$ is the same as the parity of $n$.\n\nThus it follows that every other term of $\\left\\langle{S}\\right\\rangle$ has a numerator and a denominator which are both odd.","date":"2018-02-17 21:38:25","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\": 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\": 0.9582878351211548, \"perplexity\": 232.11807927533195}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-09\/segments\/1518891807825.38\/warc\/CC-MAIN-20180217204928-20180217224928-00481.warc.gz\"}"} | null | null |
Prev Seasons Greetings to all our Readers21 December 2018NextMini robots plan to fix underground pipes04 January 2019
A joint venture between Morgan Sindall and VolkerFitzpatrick has secured the London Overground rail extension from Barking to the planned 10,000 homes Riverside scheme.
The planned new station at Barking Riverside
Transport for London negotiated the deal with the joint venture for a price of £196m, including a new Barking Riverside station.
Balfour Beatty was the other contender left in the race after Carillion's collapse last year.
The joint venture contractors will construct the 4.5 km extension of the Gospel Oak to Barking line.
Works include the modification of the existing railway lines from Barking station over a stretch of 3km with a new 1.5km railway viaduct extension from Renwick Road overbridge to the new terminus station.
This will involve constructing an embankment ramp up to the new concrete viaduct supporting a 2-track railway extension into the heart of the new residential development at Barking Riverside.
The extension is fully funded, with £172m of the overall cost of the scheme being met by the developers, Barking Riverside Limited.
Works to prepare the site have already taken place, including the demolition of several redundant Network Rail buildings and a disused ramp where the new viaduct will land.
The deal paves the way now for main works to start in May. | {
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Парк Партизанської слави — назва об'єктів природно-заповідного фонду України
Парк Партизанської слави — парк-пам'ятка садово-паркового мистецтва загальнодержавного значення в Заріччі Надвірнянського району Івано-Франківської області
Парк Партизанської слави — регіональний ландшафтний парк у Дарницькому районі Києва
Див. також
Парк Слави
Парк Вічної Слави (Київ)
Парки
Багатозначні терміни: урбаноніми | {
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\section{Introduction}
Hidden Markov models (HMMs) are flexible probabilistic models for sequential data which assume the observations to depend on an underlying latent state process.
Emerging from the field of speech recognition \citep{rab89}, they find applications in various areas, such as medicine \citep{lan13}, psychology \citep{vis02}, finance \citep{ngu18}, and ecology \citep{beu20}, where they are used for classification tasks, forecasting, or general inference on the data-generating process; for an overview of the various HMM applications, see, for example, \citet{zuc16}. In an HMM's basic model formulation, the underlying state sequence is assumed to be a finite-state first-order Markov chain. This assumption is mathematically and computationally very convenient and allows for an efficient likelihood evaluation and inference \citep{zuc16}. However, it also implicitly restricts the state dwell time, that is the number of consecutive time points spent in a given state, to follow a geometric distribution. Thus, the modal dwell time is fixed at one and the dwell time's distributional shape, with a strictly monotonically decreasing probability function, is completely predefined \citep{lan11}. This might be appropriate for some applications, but inappropriate or too restrictive for others. Examples for the latter include the modelling of daily share returns \citep{bul06}, the analysis of rainfall event data \citep{san01}, and speech unit modelling \citep{gue90}.
Hidden semi-Markov models (HSMMs) overcome this limitation by assuming the underlying state sequence to be a semi-Markov chain, thereby allowing for arbitrary dwell-time distributions defined on the natural numbers. First introduced in the field of speech recognition \citep{fer80}, the additional flexibility makes HSMMs attractive for various areas of application; an overview is provided by \citet{yu10}. However, in order to formulate an HSMM and apply it to data, again some class of dwell-time distributions must be chosen. This raises a new problem: How to select distributions which adequately describe the unobserved states' dwell times? The usual choice is a family of standard discrete parametric distributions, such as the (shifted) Poisson or negative binomial \citep{bul06,eco14,van15}. In that case, the geometric dwell-time distribution implied by conventional HMMs is replaced by another parametric distribution, which again corresponds to a restrictive assumption on the distribution's shape, and hence on the way the state process evolves over time.
An alternative approach which avoids restrictions on the distribution's shape is the use of discrete non-parametric distributions, that is, for each dwell time and state, an individual dwell-time probability is estimated (see, for example, \citealp{san01, gue03}). Such procedures usually require finite dwell-time domains with fixed maximum dwell times for each state \citep{bul10}. This is not necessarily restrictive if the domain is chosen large enough to capture the main dwell-time support, however, a large domain implies a large number of parameters to be estimated. Thus, usually, a large number of observations is needed to fit the model \citep{bul10}. More importantly, there is a high risk to obtain wiggly dwell-time distributions with implausible gaps and spikes. Consequently, the estimation could suffer from both overfitting and numerical instability due to probabilities estimated close to zero.
We aim to overcome these problems by proposing a penalised maximum likelihood (PML) approach that allows for the exploration of the underlying state dynamics in a data-driven way while providing flexible yet smooth estimates. Our method is built on dwell-time distributions with an unstructured (i.e.\ `non-parametric') start and a geometric tail \citep{san01, lan11} to avoid the use of finite dwell-time domains. The introduced penalty term then penalises higher-order differences between adjacent dwell-time probabilities of the unstructured start. This leads to smoothed probability functions and thereby helps to avoid overfitting. Using a state expansion trick, the considered HSMM can exactly be represented by an HMM, thereby opening the way for an efficient likelihood evaluation and numerical (penalised) maximum likelihood estimation \citep{lan11}.
The remaining paper is structured as follows: In Section \ref{Sec2}, we discuss the HSMM model formulation and introduce our PML approach. Section \ref{Sec3} illustrates the feasibility and potential usefulness of the method with a real data case study using movement data from a muskox tracked in northeast Greenland. We conclude with a discussion in Section \ref{Sec4}.
\section{Methodology}\label{Sec2}
\subsection{Hidden semi-Markov models}\label{Sec2.1}
An HSMM is a doubly stochastic process comprising a latent $N$-state semi-Markov chain $\{S_{t}\}_{t=1}^{T}$ and an observed state-dependent process $\{Y_{t}\}_{t=1}^{T}$. Its basic dependence structure is illustrated in Figure \ref{fig:HSMM}. The model assumes that at each time point, the observation $Y_{t}$ is generated by one out of $N$ \textit{state-dependent distributions} $f(y_{t}|S_{t}=i)=f_{i}(y_{t})$, $i=1,\ldots,N$, as selected by the current state. Thus, given the current state $S_t=s_t$, $Y_{t}$ is assumed to be conditionally independent of past observations and states. Note that here, $f$ is used either to denote a probability mass function, if $Y_{t}$ is discrete, or a density function, if $Y_{t}$ is continuous-valued. For multivariate time series, $\mathbf{Y}_{t}=(Y_{1,t},\ldots,Y_{p,t})$, another simplifying assumption is often made, that is, given the current state $S_{t}=s_{t}$, the observations are contemporaneously conditionally independent of each other: $f(\mathbf{y}_t|S_{t}=s_{t})=\prod_{k=1}^{p} f(y_{k,t}|S_{t}=s_{t})$. This allows to choose suitable classes of univariate distributions for the different variables observed. Alternatively, multivariate state-dependent distributions can be used.
The underlying semi-Markov chain $\{S_{t}\}_{t=1}^{T}$ is described by two components: (i) Whenever the chain enters a new state $i$ at some time point $t$, a draw from the corresponding \textit{state dwell-time distribution} $d_{i}$ determines the number of consecutive time points the chain spends in that state. It is defined by its probability mass function (PMF)
$$
d_{i}(r)=\Pr(S_{t+r} \neq i, S_{t+r-1}=i,\ldots,S_{t}=i|S_{t}=i,S_{t-1} \neq i),
$$
with $r\in \mathbb{N}$ denoting the duration; (ii) The state switching is described by an \textit{embedded Markov chain} with \textit{conditional transition probabilities} $\omega_{ij}=\Pr(S_{t}=j|S_{t-1}=i, S_{t} \neq i)$, summarised in the $N \times N$ conditional transition probability matrix $\boldsymbol{\Omega}$ with $\omega_{ii}=0$. The \textit{initial distribution} describes the state probabilities at $t=1$, $\bm{\delta}=(\Pr(S_{1}=1),\ldots,\Pr(S_{1}=N))$.
In case that all state dwell times are geometrically distributed, the HSMM reduces to the special case of an HMM and the underlying state-sequence $\{S_{t}\}_{t=1}^{T}$ becomes a first-order Markov chain. The state-switching is then characterised by the $N \times N$ \textit{transition probability matrix} (TPM) $\boldsymbol{\Gamma}=(\gamma_{ij})$ with $\gamma_{ij}=\Pr(S_{t}=j|S_{t-1}=i)$ denoting the \textit{transition probabilities}. This automatically implies the geometric dwell-time distribution with $d_{i}(r)=(1-\gamma_{ii})\gamma_{ii}^{r-1}$ for each state $i=1,\ldots,N$.
The parameter vector $\bm{\theta}$ characterising an $N$-state HSMM contains the parameters defining the dwell-time distributions $d_i(r)$ and the state-dependent distributions $f_{i}(y_{t})$, for $i=1,\ldots,N$, the conditional transition probabilities $\omega_{ij}$, for $i,j=1,\ldots,N$, $i\neq j$, and the initial probabilities $\delta_i$, $i=1,\ldots,N$. Thus, for parameter estimation, it is necessary to choose classes of parametric or non-parametric state-dependent and state dwell-time distributions. Although not trivial, the former can usually be chosen and evaluated directly based on an inspection of the observations at hand. For instance, for daily share return data, normal or t-distributions are common options \citep{bul06, oel20}, and for movement data, gamma or Weibull distributions are often suitable to model the observed step lengths \citep{lan12}. The state dwell times, however, are usually unobserved, which makes the choice of appropriate distributions difficult. As a way to solve this problem, in the subsequent section, we propose a penalised maximum likelihood approach which avoids strong assumptions about the distributions' shape.
\begin{center}
\begin{figure}[!t]
\centering
\begin{tikzpicture}[node distance = 1.5cm]
\tikzset{state/.style = {circle, draw, minimum size = 55pt, scale = 0.725}}
\node [state] (1) at (0,0) {$S_{t-1}=j$};
\node [state] (2) at (2,0) {$S_{t}=i$};
\node [state] (3) at (4,0) {$S_{t+1}=i$};
\node [] (4) at (6,0) {$\ldots$};
\node [state] (5) at (8,0) {$S_{t+r-1}=i$};
\node [state] (6) at (10,0) {$S_{t+r}=j$};
\node [state] (7) at (0,2) {$Y_{t-1}$};
\node [state] (8) at (2,2) {$Y_{t}$};
\node [state] (9) at (4,2) {$Y_{t+1}$};
\node [state] (11) at (8,2) {$Y_{t+r-1}$};
\node [state] (12) at (10,2) {$Y_{t+r}$};
\draw[->, line width=0.3pt, black] (1) to (2);
\draw[->, line width=0.3pt,black] (2) to (3);
\draw[->, line width=0.3pt,black] (3) to (4);
\draw[->, line width=0.3pt,black] (4) to (5);
\draw[->, line width=0.3pt,black] (5) to (6);
\draw[->, line width=0.3pt,black] (1) to (7);
\draw[->, line width=0.3pt,black] (2) to (8);
\draw[->, line width=0.3pt,black] (3) to (9);
\draw[->, line width=0.3pt,black] (5) to (11);
\draw[->, line width=0.3pt,black] (6) to (12);
\draw[decoration={brace,mirror,raise=0.5cm,amplitude=1em},decorate,thick] (2,-0.6) to (8,-0.6);
\node[] (13) at (5,-2) {\footnotesize{dwell time $r$ drawn from $d_i$}};
\draw [->] (1) to [out=-60,in=-120] (2);
\node[] (15) at (1,-1.2) {\footnotesize{$\omega_{ji}$}};
\draw [->] (5) to [out=-60,in=-120] (6);
\node[] (16) at (9,-1.2) {\footnotesize{$\omega_{ij}$}};
\end{tikzpicture}
\caption{Dependence structure of an HSMM. Whenever the semi-Markov chain enters a new state $i$ at time $t$, the dwell time $r$, i.e.\ the time spent in that state, is drawn from the corresponding dwell-time distribution $d_i(r)$. Consequently, a state switch must occur at time $t+r$ and state $j$ is entered with the conditional probability $\omega_{ij}$. Each observation $Y_t$ depends on the corresponding state $S_t$ and is generated by the associated state-dependent distribution $f_{S_{t}}(y_t)$.}
\label{fig:HSMM}
\end{figure}
\end{center}
\subsection{Flexible estimation of the state dwell-time distributions}\label{Sec2.2}
\subsubsection{Flexible dwell-time distributions and HMM representation}\label{Sec2.2.1}
Similar to \citet{san01} and \citet{lan11}, we consider dwell-time distributions with an unstructured start and a geometric tail. That is, for each state $i=1,\ldots, N$ and dwell times $r \in \{1,2,\ldots,R_{i}\}$, we assign a parameter $\pi_{i,r}$ to each individual dwell-time probability $d_{i}(r)$, where $R_i$ denotes the upper boundary for the unstructured start. A geometric tail accounts for dwell-times $r>R_{i}$:
$$d_{i}(r)=\begin{cases}
\pi_{i,r} & \text{if } 0<r\leq R_{i}; \\
\pi_{i,R_{i}}\left(\ \cfrac{1-\sum_{r=1}^{R_{i}} \pi_{i,r}}{1-\sum_{r=1}^{R_{i}-1} \pi_{i,r}} \right)^{r-R_{i}} & \text{if }r>R_{i},
\end{cases}
$$
with $0 < \pi_{i,r} < 1$ and $\sum_{r=1}^{R_{i}} \pi_{i,r} < 1$. This allows for a flexible and data-driven shape on the support $\{1,\ldots,R_i\}$ while avoiding a restriction for the dwell-time domain. Usually, only small ranges are considered for the unstructured start (for instance, $R_i=1$ in \citealp{san01}; $R_i \in \{1,2,3\}$ in \citealp{lan11}); for our purposes, however, the upper boundary $R_{i}$ should be chosen large enough to capture the main dwell-time support. This can be explored by initially using large values for $R_{i}$, which can subsequently be replaced by suitable smaller values.
Using a state-space expansion and a suitable block structure in the resulting enlarged TPM, an HSMM with such dwell-time distributions can \textit{exactly} be represented as an HMM \citep{lan11,zuc16}. This opens up the way for the efficient standard HMM machinery for parameter estimation and further inference. In the HMM representation, each HSMM state $i$ is represented by a set of $R_{i}$ sub-states forming a so-called state aggregate $I_i=\{\tilde{i}_{1},\ldots, \tilde{i}_{R_{i}}\}$, which leads to a state space of dimension $\tilde{N}=\sum_{i=1}^{N} R_{i}$. We denote the corresponding HMM Markov chain by $\{\tilde{S_t}\}_{t=1}^{T}$. Each HMM sub-state belonging to the state aggregate $I_i$ is associated with the same state-dependent distribution $f_i(y_t)$ and the corresponding transition probabilities are structured and parameterised such that they exactly mirror the HSMM dwell-time distribution $d_i(r)$. For instance, except for the last sub-state $\tilde{i}_{R_{i}}$ which is associated with the geometric tail, no self-transitions are allowed and the state aggregate can only be traversed through in the indexed order, starting with $\tilde{i}_{1}$. This structure is illustrated in Figure \ref{fig:transition_graph} for a 2-state HSMM. For the HMM transition probabilities within the state aggregates, this implies: $\gamma_{\tilde{i}_{r},\tilde{i}_{r}}=\Pr( \tilde{S}_{t}=\tilde{i}_{r}|\tilde{S}_{t}=\tilde{i}_{r})=0$ and $\gamma_{\tilde{i}_{r},\tilde{i}_{l}}=\Pr(\tilde{S}_{t}=\tilde{i}_{l}|\tilde{S}_{t}=\tilde{i}_{r})=0$ for $r=1,\ldots,R_{i}-1$ and $l \neq r+1$. Furthermore, $\gamma_{\tilde{i}_{R_i},\tilde{i}_{r}}=\Pr( \tilde{S}_{t}=\tilde{i}_{r}|\tilde{S}_{t}=\tilde{i}_{R_i})=0$ for $r \neq R_i$. Thus, most of the transition probabilities are fixed to zero. Further details about the HMM representation are provided in the appendix.
\begin{center}
\begin{figure}[!t]
\centering
\begin{tikzpicture}[node distance = 1.5cm]
\tikzset{state/.style = {circle, draw, minimum size = 55pt, scale = 0.725},every loop/.style={}}
\node [state] (1) at (-0.55,0) {$\tilde{i}_1$};
\node [state] (2) at (1.5,0) {$\tilde{i}_2$};
\node [] (3) at (3,0) {$\ldots$};
\node [state] (4) at (4.5,0) {$\tilde{i}_{R_{i}}$};
\node [state] (5) at (1.5,2) {$\tilde{j}_{1}$};
\node [] (6) at (3,2) {$\ldots$};
\node [state] (7) at (4.5,2) {$\tilde{j}_{R_{j}}$};
\draw[->, line width=0.3pt, black] (1) to (2);
\draw[->, line width=0.3pt,black] (2) to (3);
\draw[->, line width=0.3pt,black] (3) to (4);
\draw[->, line width=0.3pt,black] (1) to (5);
\draw[->, line width=0.3pt,black] (2) to (5);
\draw[->, line width=0.3pt,black] (4) to (5);
\draw[->, line width=0.3pt,black] (5) to (6);
\draw[->, line width=0.3pt,black] (6) to (7);
\path (4) edge [loop right,<-,line width=0.3pt,black] (4);
\draw [->] (5) to [out=180,in=90] (1);
\path (7) edge [loop right,<-,line width=0.3pt,black] (7);
\draw [->] (7) to [out=120,in=120] (1);
\end{tikzpicture}
\caption{Example transition graph illustrating the structure of the HMM-representation for a 2-state HSMM. The actual HSMM states are represented by the state aggregates $I_{i}=\{\tilde{i}_{1}, \ldots, \tilde{i}_{R_{i}}\}$ and $I_{j}=\{\tilde{j}_{1},\ldots,\tilde{j}_{R_{j}}\}$, respectively.}
\label{fig:transition_graph}
\end{figure}
\end{center}
\subsubsection{Penalised maximum likelihood estimation}\label{Sec2.2.2}
For parameter estimation, we use the HMM representation described above (Section \ref{Sec2.2.1}) and focus on numerical maximisation of the (penalised) log-likelihood. Alternatively, maximum likelihood estimation can be carried out using expectation-maximisation (EM) algorithms specifically tailored for HSMM applications (for example, \citealp{san01,gue03,yu03}). However, they usually assume that a new state is entered at the beginning of the observation period ($t=0$). Besides being unrealistic in some cases, this also impedes stationarity \citep{lan11}. For Bayesian HSMM parameter estimation, see, for example, \citet{eco14}.
Using its HMM representation, the likelihood of the HSMM can efficiently be evaluated using the so-called forward algorithm (see, for example, \citealp{zuc16}). It exploits the fact that the likelihood of an HMM can be written as a matrix product,
$$\mathcal{L}(\boldsymbol{\theta}|y_1,\ldots,y_T)=\bm{\delta}\bm{\Gamma}\mathbf{P}(y_{1})\bm{\Gamma}\mathbf{P}(y_{2})\ldots \bm{\Gamma}\mathbf{P}(y_{T})\bm{1}^\top,$$
where $\bm{\delta}$ is the $\Tilde{N}$-dimensional initial distribution, $\bm{\Gamma}$ is the corresponding $\Tilde{N} \times \Tilde{N}$ TPM (see the appendix for further details on its structure), $\bm{1}$ is an $\Tilde{N}$-dimensional row-vector of ones, and $\mathbf{P}(y_t)$ is an $\tilde{N} \times \tilde{N}$ diagonal matrix containing the state-dependent densities evaluated at $y_t$,
$$\mathbf{P}(y_t)=\text{diag} \bigl(\underbrace{f_{1}(y_{t}),\ldots,f_{1}(y_{t})}_{R_{1} \text{ times}},\ldots,\underbrace{f_{N}(y_{t}),\ldots,f_{N}(y_{t})}_{R_{N} \text{ times}}\bigr).$$
The forward algorithm corresponds to a recursive calculation of the likelihood with computational costs of order $\mathcal{O}(\Tilde{N}^2T)$, which renders numerical maximisation practically feasible. We denote the corresponding log-likelihood by $\ell(\boldsymbol{\theta}|y_1,\ldots,y_T)=\log(\mathcal{L}(\boldsymbol{\theta}|y_1,\ldots,y_T))$.
To avoid overfitting with respect to the dwell-time PMFs, we enforce smoothness by adding a penalty term for the $m$-th order differences of adjacent state dwell-time probabilities. Thus, for parameter estimation, we maximise the resulting penalised log-likelihood,
$$\hat{\boldsymbol{\theta}} = \underset{\boldsymbol{\theta}}{\text{argmax}} \; \ell(\boldsymbol{\theta}|y_1,\ldots,y_T)-\sum_{i=1}^{N} \lambda_{i} \sum_{r=m+1}^{R_{i}} (\Delta^m \pi_{i,r})^{2},$$
where $\Delta^m \pi_{i,r}$ denotes the $m$-th order difference, $\Delta \pi_{i,r}=\pi_{i,r}-\pi_{i,r-1}$ and $\Delta^{m}=\Delta^{m-1} (\Delta \pi_{i,r})$. There are three types of tuning parameters which influence the estimation. First, the smoothing parameter vector $\bm{\lambda}=(\lambda_{1},\ldots,\lambda_N)$ controls the balance between goodness-of-fit and smoothness of the dwell-time PMFs $d_{i}(r)$. For $\bm{\lambda}=\bm{0}$, the penalty term completely disappears from the equation and the estimation reduces to a simple maximum likelihood estimation. Since in general, the different states' dwell-time distributions require different degrees of smoothing, the smoothing parameters are chosen for each state individually, i.e.\ $\lambda_i \neq \lambda_j$ for $i \neq j$ is possible. A common way to select the smoothing parameters is via cross validation (see \citealp{lan15, ada19}). Second, the difference order $m$ influences the shape of $d_{i}(r)$, especially when $\lambda_{i}$ becomes large. For instance, for $m=1$ and $\lambda_{i} \rightarrow \infty$, $d_i(r)$ approaches a uniform distribution, while for $m=2$ and $\lambda_{i} \rightarrow \infty$, $d_i(r)$ approaches a distribution with a linearly decreasing PMF. Higher-order differences can result in more flexible distributional shapes. We recommend a pragmatic choice of $m$ based on the data at hand, the results arising from an initial unpenalised estimation and a close inspection of the goodness of fit. Similar to \citet{ada19}, we made the experience that $m \ge 3$ provides a reasonable choice in many applications. Third, the upper boundary $R_{i}$ determines the range for which $d_{i}(r)$ is explored. If chosen too small, the estimation might miss important patterns of the dwell-time distribution. If chosen very large, numerical instabilities might arise (especially for small $\lambda_{i}$), the required memory increases and the computational costs become demanding. A simple and pragmatic approach to find suitable boundary values for the unstructured start is to carry out an initial estimation with large values for $R_{i}$, $i=1,\ldots,N$, and no penalisation, i.e.\ $\bm{\lambda}=\bm{0}$. This provides first insights about the core dwell-time support which can then be used to adjust $R_i$ accordingly.
\section{Case study: Investigating dwell times in muskox movements}\label{Sec3}
\label{Sec3}
We illustrate our PML approach using real GPS-based muskox (\textit{Ovibos moschatus}) movement data. For HMMs, movement ecology is an important area of application with the states usually being interpreted as proxies for the animals' unobserved behavioural modes driving the observed movement patters \citep{mcc20}. Similarly, HSMMs with parametric (e.g.\ shifted Poisson and negative binomial) dwell-time distributions have successfully been applied in this context \citep{lan12,lan14,van15}. For muskox movements in northeast Greenland, \citet{beu20} found that a 3-state HMM adequately describes the main behavioural states `resting', `foraging', and `relocating'. They applied the model to step length (metre) and turning angle (radian) based on hourly GPS locations. While \citet{beu20} account for temporal variation in the transition probabilities using environmental covariates, here, we focus on the direct estimation of the state dwell-time distribution. As ruminants, muskoxen need to forage and rest on a regular basis. Thus, the explicit estimation of the states' dwell-time distributions could provide new insights into the animals' behavioural patterns, in particular into the durations of foraging and resting bouts.
For simplicity, we consider the movement track from a single muskox during the winter season 2013/14 with length $T=6825$ (including $6769$ registered GPS locations and $56$ missing locations), a subset of the data used by \citet{beu20}.
\begin{figure}[h!t]
\centering
\includegraphics[width=0.8\textwidth]{track14_1314_zoom_x.pdf}
\caption{Recorded muskox movement track based on hourly GPS locations.}
\label{fig:track}
\end{figure}
The movement track is displayed in Figure \ref{fig:track}. Assuming contemporaneous conditional independence, we consider a 3-state HMM and 3-state PML-based HSMMs, hereafter denoted as PML-HSMMs, with state-dependent gamma distributions for step length and von Mises distributions for turning angle. This is in line with the analysis of \citet{beu20}. To account for the zero step length observations included in the data, we consider additional parameters corresponding to point masses on zero. The tuning parameters $R_{i}$ within the PML-HSMM are selected based on a preliminary unpenalised estimation ($\bm{\lambda}=\bm{0}$) using $30$ freely estimated dwell-time probabilities for each state, respectively (i.e.\ $R_1=R_2=R_3=R=30$). The resulting PMFs are displayed in Figure S1 in the Supplementary Material, indicating that dwell times $r \le 10$ capture most of the probability mass for all three states ($98.24 \%$, $98.74 \%$, and $94.73 \%$ for state 1, 2, and 3, respectively). This is also biologically reasonable as the muskox is generally expected to switch its behavioural modes during the day. Thus, for our analysis, we use an unstructured start of length $R=10$ for all states. To ensure enough flexibility for the dwell-time distributions, we penalise the $4$-th order differences ($m=4$). However, in the Supplementary Material, we provide results arising from $m \in \{1,2,3\}$ using $R=10$, and $R \in \{5,20\}$ using $m=4$, to provide information about the sensitivity of these choices. All models were fitted in \texttt{R} \citep{rco20} using the numerical optimisation procedure \texttt{nlm}. To speed up estimation, the forward algorithm was implemented in \texttt{C++}.
To demonstrate the effect of the penalisation, we first present results from simplified PML-HSMMs with $\lambda_{1}=\lambda_{2}=\lambda_{3}=\lambda$ and $\lambda \in \{0,10^1,10^2,10^5\}$. Figure \ref{fig:sdd} shows the estimated state-dependent gamma distributions (for step length) and von Mises distributions (for turning angle) resulting from the fitted 3-state HMM and PML-HSMMs, respectively. The state-specific patterns are very similar across the models and comparable to the results of \citet{beu20}. Thus, the states can reasonably be interpreted as corresponding roughly to resting (state 1), foraging (state 2), and relocating (state 3), respectively.
\begin{figure}[!t]
\centering
\includegraphics[width=0.95\textwidth]{sdds_step_diff4.pdf}
\vspace{-3em}
\includegraphics[width=0.95\textwidth]{sdds_angle_diff4.pdf}
\caption{Estimated state-dependent gamma distributions for step length and von Mises distributions for turning angles, resulting from the 3-state models considered. The left panels show the results of the HMM. The right panel shows the results of all PML-HSMMs for which the distributions resulting from different choices of $\lambda$ are plotted on top of each other. It is, however, difficult to see any differences between the results of the different PML-HSMMs, because the corresponding estimates are very similar to each other. All distributions are weighted by the stationary distribution and the background shows the corresponding histograms of the observed variables.}
\label{fig:sdd}
\end{figure}
The dwell-time distributions, however, are very different across the fitted models, as displayed in Figure \ref{fig:dwell_time_sl}. Regardless of the choice of $\lambda$, the estimated PML-HSMM dwell-time distributions differ substantially from geometric distributions, especially for state 2 and 3 where the modal dwell time is clearly greater than one. This suggests that a basic HMM would not correctly represent the dynamics in the state process. The necessity of penalisation becomes clear for example in view of $\hat{d}_3(r)$, the dwell-time distribution estimated for state 3: when increasing $\lambda$, the distribution becomes smoother, and in particular the gaps in the PMF, as obtained when not penalising ($\lambda=0$; top right panel in Figure \ref{fig:dwell_time_sl}), are filled due to the enforced smoothness. With a strong penalisation using $\lambda=10^5$, even the second mode in $\hat{d}_3(r)$ diminishes (bottom right panel), which otherwise appears when using the smaller smoothing parameter values. Note that especially for large values of $\lambda$, the shape of the smoothed PMFs depends on the choice of the difference order $m$. This is illustrated in the Supplementary Material where Figures S2--S4 display the dwell-time distributions resulting from $m=1,2,3$, respectively. While for $\lambda=10^1$ and $\lambda=10^2$, the results are comparable across the choice of $m$, for $\lambda=10^5$, the estimated dwell-time distributions greatly differ. For instance, the PMFs approach uniform distributions on $r \le 10$ when penalising the first-order differences ($m=1$, Figure S2) and linearly decreasing distributions using the second-order differences ($m=2$, Figure S3). Based on the biological context and the results from $\lambda=0$, both do not seem to be appropriate in this case study. We expect this to be the case for most applications.
\begin{figure}[!t]
\centering
\includegraphics[width=\textwidth]{d_i_diff4_HMM.pdf}
\caption{Estimated dwell-time distributions of the 3-state HMM and 3-state PML-HSMMs using different smoothing parameter values $\lambda$.}
\label{fig:dwell_time_sl}
\end{figure}
To find an appropriate model for the muskox movement data, we carried out a two-step model selection procedure: (i) To select an appropriate vector $\bm{\lambda}=(\lambda_{1},\lambda_{2},\lambda_{3})$ for the PML-HSMM, we used a $10$-fold cross validation based on the neighbourhood algorithm proposed by \citet{lan15} with scores being the averaged log-likelihood across the validation samples. With the focus being on the dwell-time distributions, we used a blockwise partitioning of the data and considered a $3$-dimensional grid of powers of tens, i.e.\ $\{10^0,10^1,10^2,\ldots\}^3$. This resulted in the selection of $\bm{\lambda}=(10^5,10^4,10^2)$. (ii) The HMM, HSMM with negative binomial distribution, and PML-HSMM with $\bm{\lambda}=\bm{0}$ form a set of natural candidate models for the PML-HSMM selected via cross validation. We used AIC to select among these candidate models, where for the PML-HSMM, we approximated the effective degrees of freedom using the trace of the empirical Fisher matrix of the unpenalised model ($\bm{\lambda}=\bm{0}$) multiplied by the Fisher matrix of the penalised model with $\bm{\lambda}=(10^5,10^4,10^2)$ (following the approach of \citealp{gra92}; see also \citealp{lan18}).
For estimation, the 3-state HSMM with negative binomial distribution was approximated by an HMM as proposed by \citet{lan11} with state aggregates of dimension $30$ per HSMM state. The resulting AIC values are displayed in Table \ref{tab:AIC}. The PML-HSMM is clearly preferred over both the HMM and the negative binomial HSMM. According to the AIC, the best model among the candidate models is the PML-HSMM with $\bm{\lambda}=(10^5,10^4,10^2)$.
The corresponding dwell-time distributions are displayed in Figure \ref{fig:dwell_time_cv}. The results suggest that the tracked muskox tends to forage and travel for several hours before switching to a different state, with modal values being $r=4$ and $r=3$, respectively. However, $\hat{d}_3(r)$ seems to be almost bimodal, indicating that there might be different types of travelling periods, i.e.\ long and short travelling phases. This distributional shape would not have been captured by standard parametric HSMMs. The modal dwell time for state 1 (resting) is $r=1$, but with a rather slow decay compared to the geometric distribution. Thus, the resting periods tend to be slightly shorter than the foraging and relocation periods and tend to last only a few hours. A pseudo-residual analysis is provided in Section 2 of the Supplementary Material, indicating a good model fit for the selected PML-HSMM.
\begin{table}[t!]
\centering
\begin{tabular}{l|cccc}
\toprule
model & no.\ par.\ / df & $\ell$ & AIC & $\Delta$ AIC \\\midrule
HMM & 21 & -44964.04 & 89970.07 & 231.31 \\
nbHSMM & 24 & -44897.09 & 89842.18 & 103.41 \\
PML-HSMM$_{(0,0,0)}$ & 48 & -44823.71 & 89743.43 & 4.66\\
PML-HSMM$_{(10^5,10^4,10^2)}$ & 32.70 & -44835.96 & \textbf{89737.32} & 0\\
\bottomrule
\end{tabular}
\caption{Number of parameters/effective degrees of freedom, log-likelihood values, AIC values and $\Delta$ AIC for the 3-state models considered.}
\label{tab:AIC}
\end{table}
\begin{figure}[t!]
\centering
\includegraphics[width=\textwidth]{d_i_selected_diff4.pdf}
\caption{Estimated dwell-time distributions of the 3-state PML-HSMM selected by cross validation with smoothing parameter vector $\bm{\lambda}=(10^5,10^4,10^2)$.}
\label{fig:dwell_time_cv}
\end{figure}
\section{Discussion and conclusions}\label{Sec4}
As the state process is unobserved, it is often unclear how to select a model that appropriately reflects the underlying state dynamics. We introduced a penalised estimation approach which combines PMFs with an unstructured start and higher-order difference penalties to derive flexible yet smooth estimates for the states' dwell-time distributions. While HSMMs with standard parametric distributions are in general more parsimonious than PML-HSMMs, they are restricted in their distributional shapes and therefore might fail in capturing the underling dwell-time patterns. For instance, consider the negative binomial distribution shifted by one, which comprises the geometric distribution as a special case (with shape parameter equal to one). Thus, to some extent, negative binomial HSMMs actually allow for different shapes, can identify states for which geometric dwell-time distributions suffice \citep{gue05} and can be tested against the nested HMMs \citep{bul06}. However, they are not able to identify more complex patterns like bimodal dwell-time distributions. Avoiding strong distributional assumptions, our penalised estimation approach can be used as an exploratory tool to investigate the unknown shapes of the states' dwell-time distributions. The method can either serve for direct modelling purposes, or as a basis for subsequent modelling choices, for example, in order to decide whether an HMM would be appropriate for the data at hand, or what distributional assumption may be adequate within a conventional HSMM (in the spirit of \citealp{san01}). Thereby, it could also indicate if different states require different families of parametric distributions.
Due to the HMM representation, inference is straightforward and can completely rely on well-known HMM techniques \citep{lan11}. This is in line with \citet{joh05} who, based on a comparison of different algorithms and HSMM-like model formulation, argues that the use of standard models with special state topologies is practically more reasonable than the use of more complex and expensive algorithms. The HMM representation makes it fairly easy to change the distributional assumption in the state-dependent process and to adapt the model to the application at hand. Only when the number of states or the number of sub-states in the state aggregates becomes large, the likelihood evaluation might suffer from the use of large matrices and the memory required. An alternative approach would be the implementation of an EM algorithm with a roughness penalty term which is shortly discussed by \citet{gue03} for HSMMs with non-parametric dwell-time distributions.
The PML-HSMM approach allows for a straightforward incorporation of covariates into the state-dependent process \citep{lan11}. However, as for HSMMs in general, it is conceptually unclear how to integrate covariates into the state process of the model. Especially in movement ecology, the interest often lies in the influence of environmental variables on the animal's movement behaviours (for example, \citealp{vbe19,beu20,pho20}). Within HMMs, the transition probabilities and covariates can be linked via (multinomial) logit link functions \citep{zuc16}. Thus, depending on the covariate values, the transition probabilities change over time. This also affects the probability to remain in the current state and consequently, the implicit states' dwell-time distributions. While in principle, the conditional transition probabilities of an HSMM can be linked to covariates in the same way, this would not directly affect the dwell-time distributions of the model as within an HSMM, the dwell-time distributions are modelled separately from the conditional transition probabilities. Alternatively, the HSMM parameters defining the dwell-time distributions could be linked to covariates. But as the time at which the state process enters a new state is unknown, it is unclear on which covariate observations the dwell-time parameters should depend on. Therefore, if the interest of the analysis lies on the influence of time-varying covariates on the state process, HMMs provide a more convenient framework. However, in cases where covariates are not assumed to influence the state process, or where no covariates are available, the proposed PML-HSMM approach can provide new insights into the states' dwell-time distributions and the underlying latent state dynamics. For univariate time series and common state-dependent distributions, the PML-HSMM approach is implemented in the \texttt{R} package \texttt{PHSMM} \citep{poh21} on CRAN.
\section*{Acknowledgements}
The authors are very grateful to Roland Langrock for inspiring and valuable discussions and helpful advice that considerably improved the paper. They also thank Niels Martin Schmidt for providing the muskox tracking data.
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\section{Additional PML-HSMM results for the muskox case study}
\subsection{Main dwell-time support}
In this section, we provide supplementary results for the muskox movement data discussed in Section 3 in the main manuscript. Figure \ref{fig:d_i_l0} displays the estimated 3-state PML-HSMM dwell-time distributions using $\lambda_{1}=\lambda_{2}=\lambda_{3}=\lambda=0$ and $R_{1}=R_{2}=R_{3}=R=30$. It indicates that the core dwell-time support for the muskox movement data is $\{1,\ldots,10\}$. For $r > 10$, most dwell-time probabilities are estimated very close to zero. This result is the basis for setting $R=10$ for the subsequent analysis.
\vspace{5em}
\begin{figure}[h]
\centering
\includegraphics[width=\textwidth]{d_i_HSMM_l0.pdf}
\caption{Estimated dwell-time distributions of the 3-state PLM-HSMM with $\lambda=0$ and an unstructured start of length $R=30$ for each state.}
\label{fig:d_i_l0}
\end{figure}
\newpage
\subsection{Influence of the difference order}
To illustrate the influence of the choice of the difference order $m$ on the resulting dwell-time distributions, for $\lambda \in \{10^1,10^2,10^5\}$ and $R=10$, we additionally fitted 3-state PML-HSMMs with $m=1,2,3$ to the muskox movement data. The resulting probability mass functions (PMFs) are displayed in Figures \ref{fig:d_i_df1}, \ref{fig:d_i_df2}, and \ref{fig:d_i_df3}, respectively. For $\lambda=10^1$ and $\lambda=10^2$, the fitted dwell-time distributions only differ slightly across the choice of $m$. However, using a strong difference penalisation, i.e.\ $\lambda=10^5$, the difference order $m$ clearly affects the shape of the estimated distributions: For $m=1$, the PMFs approach uniform distributions on $r \le 10$ (with a geometric tail for $r >10$; Figure \ref{fig:d_i_df1}, bottom panel), for $m=2$, a linearly decreasing distribution is approached (with a geometric tail for $r >10$; Figure \ref{fig:d_i_df2}, bottom panel). When penalising third-order differences ($m=3$), the estimated PML-HSMM is able to capture more complex patters. For instance, the estimated distributions $\hat{d}_1(r)$ and $\hat{d}_2(r)$ differ in their shapes (Figure \ref{fig:d_i_df3}, bottom panel).
\vspace{5em}
\begin{figure}[hb]
\centering
\includegraphics[width=\textwidth]{d_i_HSMM_diff1.pdf}
\caption{Estimated dwell-time distributions of the 3-state PLM-HSMMs with penalisation of first-order differences ($m=1$) and an unstructured start of length $R=10$ for each state.}
\label{fig:d_i_df1}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{d_i_HSMM_diff2.pdf}
\caption{Estimated dwell-time distributions of the 3-state PLM-HSMMs with penalisation of second-order differences ($m=2$) and an unstructured start of length $R=10$ for each state.}
\label{fig:d_i_df2}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{d_i_HSMM_diff3.pdf}
\caption{Estimated dwell-time distributions of the 3-state PLM-HSMMs with penalisation of third-order differences ($m=3$) and an unstructured start of length $R=10$ for each state.}
\label{fig:d_i_df3}
\end{figure}
\clearpage
\subsection{Length of the unstructured start}
To illustrate the influence of the length of the unstructured start, for $\lambda \in \{10^1,10^2,10^5\}$ and $m=4$, we further estimated 3-state PML-HSMMs using $R=5$ and $R=20$, respectively. The resulting PMFs are displayed in Figures \ref{fig:d_i_5df4} and \ref{fig:d_i_20df4}. With $R=5$, the penalisation has hardly any effect on the estimation. This can partly be explained by the fact that the unpenalised estimation ($\lambda=0$; Figure \ref{fig:d_i_5df4}, top panels) already results in smooth PMFs and the geometric tails carry a considerable share of the probability masses, namely $19.33\%$, $26.46\%$, and $30.50\%$ in state 1, 2, and 3, respectively. Furthermore, for only $R=5$ freely estimated probabilities, the difference order $m=4$ is chosen too large.
The PMFs resulting from $R=20$ are comparable to the ones arising from setting $R=10$ (Figure 5 in the main manuscript). Hence, the choice of $R=10$ seems suitable for the muskox case study, as it captures the main patterns, is more parsimonious than $R=20$ and computationally less expensive.
\vspace{5em}
\begin{figure}[hb]
\centering
\includegraphics[width=\textwidth]{d_i_HSMM5_diff4.pdf}
\caption{Estimated dwell-time distributions of the 3-state PLM-HSMMs with penalisation of fourth-order differences ($m=4$) and an unstructured start of length $R=5$ for each state.}
\label{fig:d_i_5df4}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{d_i_HSMM20_diff4.pdf}
\caption{Estimated dwell-time distributions of the 3-state PLM-HSMMs with penalisation of fourth-order differences ($m=4$) and an unstructured start of length $R=20$ for each state.}
\label{fig:d_i_20df4}
\end{figure}
\clearpage
\section{Step length pseudo-residuals for the selected PML-HSMM}
For model checking, we consider ordinary pseudo-residuals as described in \citet{zuc16}. We focus on the pseudo-residuals for the step length observations, as due to their cyclic nature, a residual analysis for turning angles is less amenable. A good model fit is indicated by standard normally distributed pseudo-residuals. Figure \ref{fig:pr} displays the histogram, qq-plot, autocorrelation function, and a time series sequence of the ordinary pseudo-residuals corresponding to the 3-state PML-HSMM with $\lambda=(10^{5},10^{4},10^{2})$ as selected via cross-validation (see main manuscript, Section 3). Overall, the model provides a reasonable fit to the data.
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{pseudo_res.pdf}
\caption{Ordinary step lengths pseudo-residuals of the PLM-HSMM with $\lambda=(10^{5},10^{4},10^{2})$ which was selected for the muskox movement data. The top left panel shows the histogram of the pseudo-residuals overlaid with the standard normal density function. The upper right panel displays the qq-plot comparing the quantiles of the empirical pseudo-residual distribution and the standard normal distribution. On the bottom, the left panel shows the empirical autocorrelation function and the right panel a sequence of the calculated ordinary pseudo residuals.}
\label{fig:pr}
\end{figure}
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| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,286 |
[By Agnes Conway]
A. C.
The day, being a Friday, was a holiday from the dig.
Dr Canaan began his work on local place names, which he is deriving from the local Bedouins, especially the Bdûl, and took one with him to the Deir. He also began a collection of local flora to get the local names.
Dr Nielsen and A.E.C. went up the Wady Turkamaniya to a hill at Idhra' al Hisha which commands a superb view of the whole city area of Petra and the great mountain circle. The circle at the top of the hill is outlined with enormous stones and was thought by them to be the northern fort of Petra (First discovery of Megalithic circle). They visited the Turkamaniya Tomb and the sanctuary visited yesterday, which turns out to be Dalman's Ma'aisera Sanctuary No 4. They compared Dalman's plan on the spot, and considered some of it a romance.
Mr Horsfield and A.E.C. went in the afternoon over part of the same ground and decided to dig out the 2 sarcophagi in the vault of the Turkamaniya tomb. Mr Horsfield noticed 2 stone coffins at the bottom of the Turkamaniya Wady, opposite the Tomb, under 10 ft of deposit, which may be very early and unrifled. (Xtian)
The stone circle at the top of the hill, unhewn and very small for a fort, he thought might turn out to be the enclosure wall of a very early sanctuary, as a worn away rock inside might conceivably be an early alter and is on the most dominating site in Petra. A.E.C. decided to take telephoto plates of the views in every direction to make a panorama of the Petra basin. They walked down to the Wady Mataba where a wall of large stones built on no foundations canalized the Wady – they followed up lengths of wall as far as the Nymphaeum, all of which represent important problems as the fortification of Petra.
Dr Nielsen continued his work on the Sanctuaries on El Habis.
Reference: Conway, A. 1929 (transcribed by A. Thornton). Petra Exploration Fund Diary. "Business Papers to be Kept", Horsfield Collection Box 8, UCL Institute of Archaeology, 29 March: 14-15.
[By George Horsfield and probably Agnes Conway]
G. H.
Thirty men arrived to work – took on 25 and started to dig again and some progress was made. The pottery is more perfect, but the ordinary Graeco Roman type-lamps and various small pots, finer fragments of red pottery and 2 pieces of glass. Picked up various fragments of thin red painted pottery, a base and part of a rim – all on the surface and in different parts of the S. side of the site.
Examined the graves found in Wadi Turkomaniya [sic] and made notes in last part of the morning – doubtful as to their antiquity. In afternoon spent some time on dig – it was uninteresting. The top of the Scarp has appeared on the left hand side – so that now the rock surface is appearing across the whole width of the cut. Pottery is scarce.
Examined the Nabataean wall from El Habis as far as the dig, and noted it all. There is a grave yard at the El Habis end which contains graves on the surface of the same type as those in the Turkamaniya Wadi – presumably Christian – many are orientated E & W.
Money is running short – more is to be obtained – the problem is how? Mahmud is doubtful about riding in, as it takes a long time and an equally long time to return. Took on a scullion (Ali) and seems to have satisfied the cook's wants for the moment. He has quarrelled with the Circassians and removed to the kitchen to sleep. We now have 3 Arabs as servants, Deifullah the night watchman and general go-between – Huaymil, wood and water fetcher and the scullion. We seem more settled down, but I am constantly worried by idiotic domestic details which require settling, but it is often difficult to make the necessary politic decision, so that the matter is arranged and no one is disgruntled.
Dr. Canaan continued his long walks, picking up place-names, and found two High Places on Al Qantara. Dr. Nielsen went to El Ma'aisera No III sanctuary and was greatly impressed.
A.E.C. visited the circle on the mount with the American party, who thought the masonry either very early or Byzantine, and probably the former. After leaving Colonel Armstrong at Sextus Florentinus, she explored the N.W. wall beyond, finding Dalman's Sanctuaries under el Hubta, which seemed to her to belong to a Hadrianic suburb. She climbed the S. peak of El Habis in the afternoon to see Dolman's [sic] Sanctuary I, which seemed to bear no signs of cult but was inexplicable. (Certainly a quarry).
Reference: Horsfield, G. [and probably Conway, A] 1929 (transcribed by A. Thornton). Petra Exploration Fund Diary. "Business Papers to be Kept", Horsfield Collection Box 8, UCL Institute of Archaeology, 31 March: 17-18.
[by George Horsfield and possibly Agnes Conway)
G.H. Worked on 3rd level and finished clearing of second.
From this came three fragments of figurines etc., camel's head and horse's body with trappings and the upper part of a female figure. Cleared up the washing water supply in the morning and finished clearing of high place, el Habis, and cleaned out the tomb chamber on lower level – found nothing. The whole area has been quarried at the high place and part of the basin fronting "altar" cut away.
The proper name of rubbish heap "el Aziz" is "katoote" meaning "that which slides down" from "Kalta" to slide.
Some of the other things bought at Amman arrived. Examined the West side of El Habis for fortifications.
A.E.C. took notes of the caves and foundations of the buildings, some of them built with large unhewn stones, leading up to the Megalithic circle from the South, on the chance that they may prove to be in some way connected. She finished planning the rock inside the circle. Explored the caves and houses at the opening of the Siyagh on the N side, finding that to be a house area with remains of good plaster work and stucco and two pieces of worked white limestone. One of the houses seems to be built in three stories; but the red sandstone has lost its surface to such an extent that it is no good studying houses in that area.
Reference: Horsfield, G. [and Conway, A.] 1929 (transcribed by A. Thornton). Petra Exploration Fund Diary. "Business Papers to be Kept", Horsfield Collection Box 8, UCL Institute of Archaeology, 4 April: 22-23.
[By George Horsfield and probably Agnes Conway)
G. H.
Excavated Miss Conway's stone circle to the N. Ali in charge.
Dig went on. The stratifications are clearly defined; plenty of house rubbish, mixed with bones, but hardly any pottery – such as is coming out much coarser; mostly cooking pots but occasional pieces of finer sorts. The wall on W side is now showing its foundations, which are only just below the surface and consist of a mass of loose material, carelessly thrown in, seemingly in mud, though the earth in the interstices shows an appearance of lime and poor stuff. The wall I have not dated; it could be Byzantine – but the pottery overlying it is all of the 2nd century – so it must be earlier.
A.E.C. spent the morning with the diggers in her stone circle. At one point on the outside it was dug down to bed rock, 2 ½ metres below the top of the stones. Nothing was found in the earth except charcoal. The ground in front of the central red stone was dug down to the rock and had nothing at all in it, showing that the earth had been filled in to level it when the circle was first built. The gaps in the circle were filled up with underground stones, but the E. end ran in to a black rock, beyond the end of which there was a 6 metre gap. This entrance is in the right place to suit a flight of steps in the sandstone, found by Dr Nielsen – to the S.W. of the circle. She completed the plan in the afternoon, putting in the black and white rocks, which are evidently part of the sanctuary. All agree that this an early sanctuary, probably the earliest building yet found in Petra, and presumably Edomite.
Reference: Horsfield, G. [and probably Conway, A.] 1929 (transcribed by A. Thornton). Petra Exploration Fund Diary. "Business Papers to be Kept", Horsfield Collection Box 8, UCL Institute of Archaeology, 6 April: 25-26.
[By George Horsfield and possibly Agnes Conway]
G. H.
Dug at B. v C. to east of Ez Zantour. The pottery similar to that from a 1st cent [? In pencil] at lower level. This part of the city must have been abandoned at this period. And lies S. of Dalman's Byzantine wall.
Spent the morning with Miss C. in El Farasa E. and El Farasa W. exploring tombs.
Dug out three tombs that Miss C discovered in Farasa W., moved much filth from two niches – tombs unexcavated – the other had been excavated but yielded nothing but mutton bones and sheep manure. In Farasa W. saw other niches high up in right hand tombs which may contain something – all accessible ones have been visited by local Arabs.
Saw interesting cistern found by Mahmud on top of Garden Tomb with a vaulted chamber beyond. Hall of fluted columns visited; corrected plan and made notes in Weygand. The horizontal slit on front looks as though it were intended to spring vault from. Saw new type of Tomb; a low chamber with small square door high up in the wall; one on other side of Wady, - half of which has been cut away – exposing section. Have discovered meaning of the horizontal slits in walls – they are to spring arches from; then the interval is covered with slabs to form roof.
At dig in the afternoon – worked quite well – Ali and Arif at one each; spent rest of afternoon in finding N Wall – in which I was successful – but it is very different to Dalman. Cook complains of being roasted – must put shelter over kitchen. A.E.C. went to the Edomite High Place in afternoon and took 3 panorama photographs with the ½ plate camera.
Reference: Horsfield, G. [and possibly Conway, A.] 1929 (transcribed by A. Thornton). Petra Exploration Fund Diary. "Business Papers to be Kept", Horsfield Collection Box 8, UCL Institute of Archaeology, 8 April: 28-30.
Went on with dig, which was showing signs of reaching undisturbed level. Cleared up all the dangerous overhanging parts. The pottery coming out is mostly fragments of cookery pots – large wine jars with inscribed handles – and some fragments of black glazed ware undecorated. (This Mr Crowfoot says is dated 300-150 BC). A small black lamp slightly oval with a small projection on one side – and poorly modelled – and a spoon-handle broken, same as another found yesterday, came out.
Took photographs of S wall and Zantour.
In early afternoon bottom was definitely reached at six metres – red crumply sandstone. Have decided to dig a long trench into the tell on S. side near the Habis – beginning Saturday, as that seems to be the most ancient and the deepest place.
Paid the men for two weeks' work; no grumbles and all passed off in an orderly manner.
George Horsfield paying workmen at Petra during excavations in the mid 1930s. Copyright UCL Institute of Archaeology.
The High Commissioner arrived and is staying with Cooks. [Austen] Harrison write to say he was unable to come and visit us.
A.E.C. spent the morning on the nearer El Ma'aisera ridge looking at Kennedy's Memorandum queries in connection with the great tomb, Fives court etc. She could find no sign of a sanctuary, but think the whole lay-out may be an elaborate example of the type of enceinte described on the Turkomanya tomb. A new type of tomb turned up, and two unfinished very early tombs, as well as more cisterns. A complete investigation of the ridge might be done and would be interesting if there is time for anything intensive. She took 5 panorama telephoto views from the Edomite circle in the afternoon glow.
Reference: Horsfield, G [and probably Conway, A] 1929 (transcribed by A. Thornton). Petra Exploration Fund Diary. "Business Papers to be Kept", Horsfield Collection Box 8, UCL Institute of Archaeology, 11 April: 31-32.
No. 2 cave continues being cleared in the inner room which has gone more rapidly. No. 3. is cleared except for the floor – a bench of stone about 80 cents. wide existed on right side apparently running the whole length. There is a channel in rear wall to fix it in. The niche at back proves to be only 45 cents deep – purpose unknown. No more pottery.
Began to dig two shaft tombs on Ma'aisera plateau – one was entered from a hole on a corner without touching shaft – Byzantine pottery fragments and nothing else so far. This No. 2. The other shaft No. 1. was filled to the brim with earth. This being cleared to 1 metre disclosed side chamber. On entering found about 10 skulls in disorder on the floor, a mass of bones – 2 pots in a corner – another near a corpse on right side and a Byzantine pot. A lot of pots came out of the shaft – including base of Rabbit Thyton with stone metal eyes – the head of a female with a hook nose – an open mouth and a crescent moon bound on her forehead. Small pots, lamps etc.
A.E.C. climbed El Biyara in the morning, passing a terrace with 3 Dushara niches (given by Dalman as a sanctuary) and then going by two great inclined planes in the rock like the entrance to El Hubta. Above these, right out in the open, is a charming country house of two rooms and a terrace, with a superb view. Steps go all the way to the top, which is a long flat plateau with remains of squared stone ruins all over it, flat with the ground. I could not date them at all. The surface pottery is Byzantine, Greco-Roman, and some very rough stuff, possibly bronze age? There are six enormous cisterns; large round openings in the ground, going down deep and with stones, in some cases squared, that have fallen in from the top. Near the Arabah side of the hill and close up against another hill for shelter, is a rounded topped cave with an early plain door; date unknown. The whole hill was evidently a fastness [sic], and commands the whole country; the views are superb. The easy route from Elji to El Barid is clearly visible and the spur from it that would lead to the Edomite High Place – the first ridge of El Ma'aisera is seen absolutely crammed with buildings, the other ridges by contrast, looking quite empty. A big quarried valley seemed to lead N out of the Siyagh; the last course of the Wady Musa, through black spiky rocks, looked magnificent.
Reference: Horsfield, G. [and possibly Conway, A.] 1929 (transcribed by A. Thornton). Petra Exploration Fund Diary. "Business Papers to be Kept", Horsfield Collection Box 8, UCL Institute of Archaeology, 23 April: 52-53.
Completed Cave No. 2. which shows only intrusive burials. The back recess is divided in two, the left being larger and slightly deeper – this had one burial, accompanied by a number of small bells which look as though they belonged to camel trappings cylindrical in shape. The shallower niche had a variety of bones including four jaw bones. One burial seemed more complete and between the knees was found a Byzantine bottle with a long neck. A shaft grave was found on right side against wall and was covered by two slabs of scaly sandstone at the upper end – the lower being open. The neck and part of the body of a large Byzantine pot was found under the slab, and the remains of bones in the sand which filled the hole completely. 70 cents down is a groove on both sides extending all the length – which indicates that it was made for more than one occupant. What is under is awaiting excavation. Tomb No. 1 (in front of Triple Dushara) was worked on and yielded more Byzantine pottery. It contains 13 skulls and a mass of bones which are all mixed up together – suggesting that these people had taken refuge in this tomb and eventually died there. The reason not apparent. The pottery is Byzantine and seems to have contained food. A bottle with long neck and handle blackened with [blank] seems an intrusion as it lay on the sand fallen down shafts. Tomb No 2 is cleared to the floor. Lamps, small bowls and some fragments of thin painted pottery turned up [original emphasis]. At the floor level are apparently 4 graves covered with stone slabs awaiting investigation.
No 3. shaft has disclosed a chamber – but is full to brim with earth work proceeding – nothing found.
Cleared five simple shafts farther to south – found nothing but a mass of stones and broken bones in one – others empty. They were of same type as those in Farasa east, with stone slabs some 60 cents. above corpse – and probably filled in with earth to top.
A.E.C. photographed in the Edomite High Place; watched the dig at tomb No 2, (1?) and found a Byzantine cistern on El Ma'aisera made out of an early tomb. She went with Dr. Nielsen in the afternoon to the Kataar el Deir and the Klausenschluct, finding Dalman's 2 sanctuaries after a great deal of trouble. These are country houses, with niches, water-basins and grottoes; once more a charming country suburb, probably Roman like the Deir. The houses are unusually small, but cut out of the best white sand stone, the dressing of which might have been done yesterday and looks like the finest plaster. On the top of the Hill E. of the road to the Deir from the Klausenschluct, is what may be the remains of a fort with a lot of built stone. Above it are 3 Greek crosses.
The Deir and Klausenschluct from the summit of El Biyara. Copyright UCL Institute of Archaeology
By George Horsfield [and possibly Agnes Conway]
Cleared out the "Tomb" House Triple Dushara and found seven graves which had been broken into but retained in part covering slabs, found bones and burnt ashes with them – but no objects or pottery. They seemed undisturbed below surface.
The "Triple Dushara Tomb" photographed in the mid-1930s. Copyright UCL Institute of Archaeology.
Cleared several shaft graves in vicinity to South – found nothing. One is SW side of Terrace 200 ms. away had mass of bones – human and animal – at the bottom one pot with rim base – of 1st century?
Tombs Nos 1, 2, 3 went on being cleared. Nothing was found in graves. No. 2 had four and was filled with kitchen debris. No. 3 is partly clear but a number of graves not known.
So far the evidence obtained gives no indication of Ma'aisera's age nor character of occupants. Triple Dushara tomb promised well but nothing but very crude burials so far found.
All the other Tombs so far examined yielded nothing. The pottery from No 1 all Byzantine?
A.E.C. spent the whole morning in grilling sun wearily taking 6 panorama photographs from the Edomite High Place. She visited the dig in the afternoon and the second ridge of El Ma'aisera, puzzling over Dalman's sanctuary No. 2, which seemed to her a water collecting place and quarry block accidentally left on the roof. But the lower story is also puzzling, as the staircase goes to the roof and gives no access to the 1st floor room with niches. The three huge white stone buildings on this dominating white terrace are unique in Petra, but so much destroyed as to be unfathomable at present. She visited the valley from the Siyagh seen from el Biyara, which proved to be merely a wady with nothing in it and very short.
Went on clearing Triple Dushara Tomb. In one case all the covering slabs were in position – the grave above these was filled nearly to ground level with lime concrete – on removing sand (slab?) – found grave full of red sand: on removing slowly and with extreme care centimetre by centimetre, found a layer of lime down centre of grave and extending to sides but not completely filling grave at this level – it was compact and smooth. Scraping thus away came on black calcined substance which was not very thick – possessed no shape, and whose depth was difficult to estimate. In it were fragments of bone – friable and dry. Scraping thus away came on more lime and eventually to sand again. At one end was a large piece of stone. This grave I have numbered No. 3.
No. 2 was of the same order, but was completely calcined without a fragment of bone. Of this a sample was obtained and put in a jar – found in another place – for future investigation. This explains the absence of remains found in other graves examined – which evidenced ("ashes") calcined remains and which at the time were not understood – in spite of the lime – which was thought to be accidental and probably rubbish thrown in. All the deep graves, five in the Triple Dushara, gave the same evidence, but only in the one case was the calcinations combustion perfect: of the two other graves – one was empty and the other had the remains of an adult and of a child side by side – divided roughly with stones. This grave was shallow and lay at right angles inside a pair of the others – that is, between two ends and the inside wall.
Now working at shafts in neighbourhood – front and sides of same tomb – finding Byzantine pottery and in one a welter of bones thrown in anyhow – some of which have a burnt appearance. This shaft leads to an interior chamber not yet cleared. Byzantine pottery was found with bones in shaft. Tomb next door Triple Dushara cleared and seemed same type, but had been disturbed – graves shallow and same type as empty one in T.D. modern coffin shape and shallow, divided by thin walls – no evidence of covering slabs.
Clearing out the Tombs above T.D. with low Assyrian facades. They are plain and square – work proceeding. No other graves have brought anything to light. There is an entire absence of pottery until Byzantine period – all of which is of a domestic character.
A.E.C. spent the morning with Dr. Neilsen photographing the tiny Roman? houses in the Klausenschluct and going to the Deir. The building that looked like a fort is much more likely to be a Byzantine dwelling. It is built of large and small stones very roughly, is high up against the cliff, on which are cut four Greek crosses, and has small windows like arrow-shoots. There are two Nestorian crosses and one Greek cross on the small two-storied house, and the whole quarter may in Byzantine times have been lived in by Christians. This is Br 460, who gives the Christian inscriptions inside and calls it a hermitage. A large cistern, seemingly Byzantine, is near the houses.
All the buildings on the Deir plateau, forming Dalman's seven sanctuaries, seem to be houses. There was not time to finish examining these. In Dalman, No. 506, the finish of the black tooling, with a black border around it, resembles the best finished Roman tomb by the bottom of the western Ma'aisera wady, and the four obelisk Tomb and the one below it.
Took five Edomite High Place ½ plate panoramas in the afternoon.
Reference: Horsfield, G. 1929. [and possibly Conway, A.] 1929 (transcribed by A. Thornton). Petra Exploration Fund Diary. "Business Papers to be Kept", Horsfield Collection Box 8, UCL Institute of Archaeology, 27 April: 56-59. | {
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GYPSY VERSES
Gypsy Verses
_By_
HELEN HAY WHITNEY
AUTHOR OF
"_Some Verses_," "_The Bed Time Book_."
NEW YORK
Duffield & Company
1907
COPYRIGHT, 1907, BY
DUFFIELD & COMPANY
_Published October, 1907_
To
_G. V. W.
because she is my friend_
CONTENTS
PAGE
ATARAH 3
AGE 4
LOVE AND DAWN 5
L'AMOUR AMBIGUEUX 6
SAPPHICS 7
SATAN, PRINCE OF DARKNESS 8
IN PRISON 9
GHOSTS 10
LILIS 11
THE OLD WOMEN 12
TO HIPPOLYTUS 13
THE GARDEN HEDGE 14
THE SLAVE WOMAN 15
SONG 16
SANS-JOY 17
OUT OF THE JUNGLE 18
IN PORT 19
SONNY BOY 21
SUNRISE 22
DEAD LADIES 24
WHEN TRISTAN SAILED 25
THE BATTLE 27
RECOMPENSE 28
THE LOTUS EATERS 29
LOST APHRODITE 30
THE FOOLS 32
THE AWAKENING 33
THE DARK WOMAN 34
SUMMER SONG 35
SERAPHIS 36
VENGEMENT 37
AUTUMN LOVE 38
THE WITCH 40
THE MAN 42
DOWN IN MALDONADO TOWN 43
THE CHOICE 45
THE BROOK 46
AT THE END OF THE WORLD 47
THE GYPSY 48
BOY O' DREAMS 49
BALLAD OF THE SLAVE 51
FOAM 53
THE SEAL 54
RELEASE 55
SIN, THE SWORD 56
FANTASTIC SPRING 57
SONG 58
CONTRAST 59
THE PRICE 60
THE KING'S DAUGHTER 61
LAIS 62
THE HERITAGE 63
THE MONK IN HIS GARDEN 64
BIANCA 65
FREE 66
BLACK AND GOLD 67
THE ANSWER 68
PEACE 69
BARNABAS 70
LOST DREAMS 71
LADY OF LIGHT 72
SONG 73
THE GYPSY BLOOD 74
AND YET 75
THRO' THE PLEACHED ALLEYS 76
_Acknowledgment is made to Messrs. Harper and Brothers, the Century
Company, and the Metropolitan Magazine for courteous permission to
reproduce certain of the verses included in this volume._
GYPSY VERSES
_Oh, you were not so idle--
You wore a sprig of green;
You wore a feather in your cap,
The reddest ever seen._
_Your face was laughing gypsy brown,
Your eyes were of the blue;
You wandered up and down the world,
For you had much to do._
_For oh, you were not idle,
Whatever men might say--
You made the colour of the year
Magnificent and gay._
ATARAH
With painted slender folded hands
She waited what might come,
Her head was tyred with jewelled bands,
Her mouth was sweet and dumb.
Her cymar was of ardassine,
Fire red from throat to hem,
Broidered with Turkis stones therein--
She gave her soul for them.
Faint cassia and love-haunted myrrh
Made perilous her hair,
And what was Sidon's woe to her
Whose face was king's despair?
Nor life nor love from those cold lips,
But ah, in what degree,
Her passionate lover leans and sips
Her death-bright poesy.
AGE
Blindness, and women wailing on white seas,
Seas where no placid sails have ever been,
Dreams like wan demons on waste marshes seen
Thro' dulling, fevered eyes. The dregs and lees
Of wine long spilt to dead divinities.
Grey, empty days when Spring is never green,
Can the heart answer what these riddles mean--
Can the life hold such hopelessness as these?
Love lying low in the long pleasant grass,
Youth with his eager face against the sun,
They may not guess the hours when these shall pass,
In what drear coin such lovely dreams are paid,
At what grim cost their flowery days are won,
When man is old and lonely and afraid.
LOVE AND DAWN
Dawn shaking long light pennons in the East--
Is love the least
And love the greatest of the morning's woes?
See how the rose
Breaks in a hundred petals down the sky.
Darkness must die,
And in the heart, where flutters sad desire,
Wakes the new fire
Silver and azure of the open day.
So, grief, away!
We will be glad with flagons, drown old pain,
And Dawn shall bring us to her own again.
L'AMOUR AMBIGUEUX
You are the dreams we do not dare to dream,
The dim florescence of a mystic rose,
In poverty or pride love comes and goes,
We do not question what the deeps may seem
Launched on the steady current of the stream.
Gaily and hardily we hear the prose;
In youth, red sun, in age the charnel snows.
Nor see the banks where subtle flowers gleam,
In green sweet beds of moly and of thyme
Wild as an errant fancy. All the while
We know you, mystic rose; we know your smile,
Your deep, still eyes, your fragrant floating hair,
The peacock purple of the gown you wear,
O lyric alchemist of rune and rhyme!
SAPPHICS
Leave the Vine, Ah Love, and the wreath of myrtle,
Leave the Song, to die, on the lips of laughter,
Come, for love is faint with the choric measure,
Weary of waiting.
Down the sky in lines of pellucid amber
Blows the hair of her whom the gods have treasured,
Fair, more fair is mine in the ring of maidens,
Mine for the taking.
SATAN, PRINCE OF DARKNESS
I sinned, but gloriously. I bore the fall
From Heaven's high places as becomes a king.
I did not shrink before the utmost sting
Of torture or of banishment. The pall
Of Dis, I cried, should be the hall
Where sad proud men of men should meet and sing
The woes of that defeat ambitions bring
Hurled from the last vain fight against the wall.
I thought I had been punished. To forego
All lovely sights, the whisper of fresh rain,
To brood forever endlessly on pain
Yet still a Prince, Ah God, I dreamed,--and then
I learned my Fate, this wandering to and fro
In Devil's work among the sons of men.
IN PRISON
Above her task the long year through
She works with steady hands,
The while her heart is tired with dreams
Which no man understands.
For long and long ago she knew
Green trees and open sky,
Before the law condemned her days
To doom until she die.
And so she dreams in mystic peace,
Indifferent to the scene,
Because her heart retains and knows
The little stain of green.
GHOSTS
The long lost lights of love I know,
They thrill from ultimate space, they blow
Like small bewildered stars, tossed high
On some unknown and passionate sky.
I know them for the loved lost lights
That made the glamour of my nights
Long, long ago, and now I fear
Their coming, and the garb they wear.
For they are very white and cold,
They are not as of old,
In trailing radiance, rose and red,
For these are ghosts, and they are dead.
LILIS
We have forgiven you because you are so fair,
Eloquent by virtue of your dark enchanting eyes,
Evil to your heart of hearts, shall we blame or care,
You are very beautiful, and love has made you wise.
With a splendid insolence you exist to sin,
Scorn us for the weaknesses that bring us to our pain.
Weak you are and false you are and never may we win,
Yet we have forgiven you, and shall forgive again.
THE OLD WOMEN
We are very, very old,
We have had our day,
So we bend above our work
While the others play.
Do they call us women, we
Gaunt and grey and grim,
Hideous and sexless things
Weak of brain and limb?
Beauty ended, love long past,
Yet, when all else flees,
We are women, for we still
Have our memories.
TO HIPPOLYTUS
It is too late to part. I dreamed a dream
That love had loosed me, that no more your name
Should vex my soul, for very pride and shame
I hid you out of mind; I said, The stream
Has grown too wide between us, it would seem
To sunder even memory. Your fame
Rang hollow on my ear, and then you came
And love laughed for the lie he would redeem.
It is too late. Love will not let me go.
The bare suns burn me, and the strong winds blow;
I take them fearlessly, for I am wise
At last; for being yours I must be brave,
Tho' you give nothing, still am I your slave,
The light within my heart your eyes, your eyes.
THE GARDEN HEDGE
I live in a beautiful garden,
All joyous with fountains and flowers;
I reck not of penance or pardon,
At ease thro' the exquisite hours.
My blossoms of lilies and <DW29>s,
Pale heliotrope, rosemary, rue,
All lull me with delicate fancies
As shy as the dawn and the dew.
But the ghost--Gods--the ghost in the gloaming,
How it lures me with whispers and cries,
How it speaks of the wind and the roaming,
Free, free, 'neath the Romany skies.
'Tis the hedge that is crimson with roses,
All wonderfully crimson and gold,
And caged in my beautiful closes
I know what it is to be old.
THE SLAVE WOMAN
Her eyes are dark with unknown deeps,
Old woes and new despair,
Her shackled spirit feels the thong
That breaks her body bare.
The savage master of her days
Who mocks her passive pain,
How should he know her scorn of him.
Indifferent to the stain?
For in her heart she sees the glow
Of sacrificial fires,
A priestess of a mystic rite
Performed on nameless pyres.
The incident of shame and toil
She takes with idle breath,
For she remembers Africa,
And what to her is death?
SONG
The sky is more blue than the eyes of a boy,
A riot of roses entangles the year;
Ah, come to me, run to me, fill me with joy,
Dear, dear, dear.
The air is a passion of perfume and song,
The little moon swings up above, look above,
I cannot wait longer, I've waited so long,
Love, love, love.
SANS-JOY
Hide your eyes, Angels, beneath your gold phylacteries,
Israfel will charm you with the magic of his song:
Yet you will not smile for him, by reason of your memories,
For Lucifer is absent, and the cry goes up, How long!
For his expiation you would give your dreams and destinies,
Paradise is clouded by the measure of your pain;
Hide your eyes, Angels, beneath your gold phylacteries,
Till the jasper gates swing wide to bring him home again.
OUT OF THE JUNGLE
Out of the jungle he came, he came,
Man of the lion's breed,
His heart was fire and his eyes were flame,
And he piped on a singing reed.
Spring was sweet and keen in his blood,
Singing, he sought his mate,
The wife for the life and time of his mood,
Formed for his needs by fate.
Over his reed he piped and sang,
His eyes were the eyes of a man,
But the jungle knew how his changes rang,
For his heart was the heart of Pan.
IN PORT
Wave buffeted and sick with storm,
The ships came reeling in,
The harbour lights were kind and warm,
And yet, so hard to win.
Like wings, the tired sails fluttered down,
While night began to fall,
Then came, sea-scarred, toward the town,
The smallest ship of all.
At last in harbour, safe and still,
No more she need be brave,
No more she'd meet the winds' rough will,
The wanton of each wave.
The harbour lights! but where the moon
Should murmur blessings bright,
Clouded instead the dread typhoon,
That thundered down the night.
What curse the luring harbour bore
Of false security;
The port held desolation more
Than boasted all the sea.
When morning came with leering lip,
What death lay on her breast,
And oh! the little weary ship
Was wrecked with all the rest.
SONNY BOY
(A bust by H. F.)
Grave as a little god, erect and wise,
He dares the years that open to his gaze.
Brave in his charming beauty, he portrays
A bright eternal youth, and in his eyes
Sweet moons that are no more. No sad surprise
Has gloomed the gay adventure of his ways,
And from the flower-lit meadow of the days
He leaps clean-hearted to life's enterprise.
SUNRISE
There was a cry from the sky,
A cry at night;
It wakened the breeze in the trees
When the moon was white;
And I, only I,
Adrift on life's terrible seas,
Read the cry aright.
Pennants of gold were unrolled,
They told of sun;
Night's pain with the dark and the rain,
Was over and done.
The travail of old
Had passed from the mother again,
And the fight was won.
There was a cry from the sky,
And my soul was torn
With a passion divine, as of wine,
From the breast of morn;
For I, only I,
Knew the cry as the signal and sign
That love was born.
DEAD LADIES
Thais and Lalage, your eyes are closed,
Phryne, Aholibah, your lips are dust.
Your tinkling feet are idle and composed,
All your gold beauty vanished into rust.
Nor Dionysian mysteries taught you this,
Since the gold serpent was your seal and sign;
Tho' deathless be the imprint of your kiss,
The lips that redden are not yours, but mine.
How you would scorn us, Lalage, the lure
Of your mad moments, us, the motley crew;
Yet shall your beauty only so endure
Imperishable, that we sing of you.
WHEN TRISTAN SAILED
When Tristan sailed from Ireland
Across the summer sea,
How young he was, how debonnaire,
How glad he was and free.
Why should he know the gales would blow,
The skies be black above,
How should he dream his port was Death,
And Doom, whose name is Love?
The Lady Iseult, sweet as prayer,
We hardly dare to pray,
Pearl-pale beneath her shadow hair,
Grows fairer day by day,
The ichor gains her spring-kissed veins,
Her skies the eyes of youth.
How should she dream the ichor Love,
Was hellebore in truth?
So Tristan sailed from Ireland
As youth must always sail;
He quaffed the cup, nor asked the wine;
He dared, nor feared to fail.
And be it poison, be it life,
Or wrecks that strew the shore,
Tristan set forth! nor ask the end,
Else youth shall sail no more.
THE BATTLE
Ah, never, never, never! for the flag
Is twined about my body, and my back
Is braced against the wall! I know the lack
Of crust and water, and a man might brag
For fighting thus, yet--how a soul may lag,
For want of just so little, when the rack
Of hopeless strife from dawn to bivouac
Finds the foe now who storms the utmost crag.
Never surrender! You who storm my heart
Till I am faint with love and hunger, all
Starved for your lips--how can I say "depart"?
And yet--drag up the sword again--and thrust!
Ah, Love, mine enemy--I will not fall
Until my honour's flag and I are dust.
RECOMPENSE
Those who ask for a star
Often receive but a stone,
Yet they asked for a star,
Does the high thought not atone?
I, who asked but a stone,
A plaything of azure or red,
May I count it for gain
That I won a star instead?
THE LOTUS EATERS
We have no rain, we have no sun,
We only watch the moments run
Like little adders thro' the leaves,
Lost ere their flitting has begun.
The cool light airs that fan our brow,
What aromatic sweets they know!
The tall tired trees that make our sky
Are lapped in spices as they bow.
The bright-eyed flowers that form our bed,
Like eager jewels, blue and red,
Seem brimmed with gay immortal life,
Yet we dream on when they are dead.
LOST APHRODITE
The gods upon the hills no more are seen,
Couched on the virginal green,
No more their cry upon the silence grieves,
The shadow of dark leaves.
The blazonry of Spring must now abate,
Without the purple state
Of Aphrodite, amorous and frail,
Cinctured with lilies pale.
She who was love and every man's desire,
Now only can inspire,
The mutual love of mortals, and alone
Like wind her plaints are blown.
About the unregarding world her hands
Yearn forth across the lands
Once passionate with her lovers, but in vain,
They will not come again!
She who was Aphrodite, tho' she gives
Love to each heart that lives,
Gives and receives not. She, of love the breath,
Doomed now with utter death.
THE FOOLS
On the wrist a paroquet,
Motley on the shoulder,
We exist for joy of life,
Never growing older.
Dancing down the lane of years,
Rosy garlands trailing,
Who would pause for time or tears,
Barren days bewailing.
Brighter burden never were
Than the smiles we scatter,
Loving deeds and laughing love,
This is our great matter.
And the wise who scorn our bells
Mate with melancholy,
We are wiser than the wise,
Holding hands with folly.
THE AWAKENING
Perhaps the world is tired of pageantries,
And all the weary women called the Hours,
Jaded with jewels, shall exchange for flowers
Their badge of pride. In violet harmonies,
With sweet blue veils of silence o'er their eyes,
They shall return to Spring's most languorous bowers;
And Light and Beauty shall come down as showers
Releasing life from all its pedantries.
Only the bloomy purple hill to see
Thro' half-closed lids, and only to be blind
With asphodils! Shall these things ever be?
Surely the time is ripe to live for this
Dawn, springing radiant from her sleep to find
A world of lovers waiting for her kiss.
THE DARK WOMAN
My dark, wild woman of the braes,
I know your heart, I know your ways,
I know the raw, sweet food you taste,
I love the colours 'round your waist.
Ribbons of green and gold you wear,
Threaded about your shadowy hair,
My colours--and your eyes are mine,
Dark as the deeps of love--and wine.
I wake with you at budding Dawn,
Leaving this life of dew-spread lawn,
To join your spirit in the wild,
Your brother, lover, or your child.
Take me upon your savage breast,
Teach me your calms and your unrest.
Take me, I know the jungle cry,
Teach me your love, or let me die.
SUMMER SONG
My heart's a yellow butterfly
That flutters down the road;
A beggar, tricksy, dancing thing
That scorns a fixed abode.
The aigrette of the thistle bloom
Becomes the swinging sign
Of merry hostelries, where I
May pause awhile and dine.
The sky is lapis lazuli
Bestrewn by clouds of pearl,--
Who would not be a butterfly
Instead of just a girl?
SERAPHIS
He tasted dragon's blood
From the dark dragon tree,
In those far islands where the mood
Is faery-like and free.
With cinnamon and nard
His strange gay clothes were sweet,
His lips were fanciful with fard,
Red flames played 'round his feet.
Sharp dancing pointed flames,
Detached as butterflies,
He called them all by secret names,
They were his ecstasies.
No love, no maiden bright
Might woo him from his swoon,
For he had tasted strange delight
In lands beyond the moon.
VENGEMENT
What was his offense to you,
You who sit thro' dreamless days,
Sifting thro' your fingers slim
Ashes in a porphyry vase?
Hatred makes your eyes grow hard,
As you conjure forth his name
From the dust that was his face,
From the heart that was his flame.
Then she, lifting heavy eyes,
Spoke: "When this man walked the world
Him I loved, he loved not me;
So his days to death I hurled.
"Dying, then, he touched my hand,
Smiled and whispered, 'I forgive';
This his vengeance on my soul,
I must hate him while I live."
AUTUMN LOVE
I
Once I could love this season of the year,
And watch the calm and delicate decline
Of Summer gladly; I could see the pine
Deep green on bluest sky, and laugh for cheer
Of very living. Yet I'd fain appear
Th' unhurried gourmet, tasting of my wine,
Lingering o'er memories of the purpled vine,
Loath for each passing moment. Ah, my dear,
Now like a careless child, I toss the hours
Over my shoulder, I forget the sun,
The dewy dawn, the white moon and the flowers.
Like a tired pilgrim with his goal in view,
Looking not right nor left, I run, I run
To that bright day of days that brings me you.
II
I feel as murderers feel, who, having slain
Their love, laugh with red hands and do not care.
I took sweet Summer by her lovely hair,
Bent her white throat, and gladly saw the stain
Crimson her green leaf-gown of hill and plain.
I would not wait for her last kiss, nor spare
One splendid flying hour, for chill and fair
Autumn, my love, comes near me thro' the rain.
Pale with mysterious wonder, her deep eyes
Are wells of wisdom; fugitive, astray
From a blue land that dreams beyond the skies.
'Tis done. I lay young Summer on her pyre,
And turning, burn thro' distance to the day
That brings me to the lips of my desire.
THE WITCH
Whence came the fire in her eyes, eyes of a beast in the jungle,
Desperate, golden and green, wild as a river in spate?
Her long lithe limbs were brown, and she took the world as a leopard,
Grave, disdainful and strong, takes of his prey without hate.
Glamourie slept in her eyes, terribly calm in the tumult,
Hidden and secret and sweet was the smile of her crimson mouth.
A marigold wound in her hair, she swayed like wind in the desert,
Burning and thrilling to thirst the hearts that dream of the South.
Whence came the fire in her eyes? I, only I, knew the secret,
The thing that hung on her breast, hid by her stormy hair,
Amber drops on a string, her talisman, witches' amber,
Golden, yellow and brown, that only a witch may wear.
THE MAN
The flame is spent, I can no more
Hold the tall candle by your door.
Too often have I watched to see
Your lagging steps come home to me.
The Tyrian traders taught me this.
They came, perfumed with ambergris,
With amethystine robes, and hair
Curled by the kisses of salt air.
They mocked me for my weary hands,
Holding your light as love demands,
They sang the lure of poppied sleep,
Their lips were warm, their eyes were deep.
The flame is spent! Your pale weak face
Must seek another resting place.
Win me, and hold me now who can!
The Tyrian trader was a man!
DOWN IN MALDONADO TOWN
There's a town called Maldonado,
That's the place where I would be;
There's a girl in Maldonado,
And she gave her heart to me.
Starved with sixty days of sailing,
How we swaggered to the shore,
Hands in pockets, eyes cocked sideways,
At the girl in every door.
Sweet they fluttered to our shoulders,
She, my girl, the fairest girl,
And I took her for a plaything,
Face of flower and heart of pearl.
Round my neck she clung and pleaded,
But I told her to be wise;
Said no sailor could be faithful,
And his love was ever lies.
Then she turned and left me silent,
Stepping weary, stepping slow;
Merry was I to have won her,
And I laughed to see her go.
Now 'tis done--I have lost her,
Seas between us thunder wide,
"Dear," I said, "I shall forget you,"
And God knows that I have lied!
Many girls have smiled upon me,
Up and down the Northern coast,
But their kisses only taunt me
With the kiss that I have lost.
Oh! You're killing me by inches,
Velvet lips and eyes of brown,
For it's love I left behind me,
Down in Maldonado town.
THE CHOICE
The long well rose above me, a slim shaft,
With wet, black walls, and high aloft the light
Round as a moon intensified my night.
I ate the air and bitterly I quaffed
The death damp; nor my pleading nor my craft
Availed to aid me in my desperate plight:
The vista of high heaven the only sight
To see, and at my woe high heaven had laughed.
Suddenly the darkness deepened, and a face
Gloomed on the opening, terrible and grim
An Afreet! In his hands he held disgrace
And direst poverty and ruinous strife.
"Choose now between," he cried, "calm Death by him
And Life empoisoned," yet I cried, "Give Life."
THE BROOK
I have a little brook in the deeps of my heart.
What does it matter if the day be chill or clear,
like a tourmaline and winged like a dart,
Voiced like a nightingale, it sings all the year.
Small bright herbs on the banks of the stream,
Moon-pale primroses, and tapestries of fern,
This is the reality and life is just a dream,
Iridescent bubble that the moon tides turn.
AT THE END OF THE WORLD
To the world's end, to the world's end,
Did I wander seeking you,
And wide was the water and dark was the fell,
With Time at my heels like a hound of hell,
And the worst still left to do.
To the world's end, to the world's end,
And the void to verify.
They told me of a tale of love supreme.
"Sometimes," I cried, "I have caught the gleam,
I shall seek it tho' I die."
At the world's end, at the world's end,
At the end of the endless mile,
Nothing to see but the silent snow--
I turned with my tears to your heart, and lo!
Love was with me all the while!
THE GYPSY
O, she was most precious, as the wind's self was fair.
What did I give her when I had her on my knee?
Red kisses for her coral lips, and a red comb for her hair.
She took my gifts, she took my heart, and fled away from me.
O, but she was fanciful, she found a savage mate,
He scorned her, he spurned her, he drove her from his door;
She cuddled in his inglenook and laughed at all his hate,
She took his curses, took his blows, and never left him more.
BOY O' DREAMS
Must I leave you in the mountains,
Boy o' dreams,
Must I leave you where the fountains
Toss the silver of their streams,
Where the trees are clothed in samite,
And the little broken moon
Is a symbol and an answer,
Like the reading of a rune?
May I take you to the city,
Boy o' dreams,
Where your heart will break with pity
At the lethargy that seems
Only half alive to living,
Only enemy to mirth,
Where the dusty facts will blind you
To the fancies of the earth?
I must take you--but I'll keep you,
Boy o' dreams,
Where no alien winds shall sweep you,
In a secret place that gleams,
With the light of your own laughter,
Yours the vessel, yours the chart,
And we'll brave the storm together.
You, the captain of my heart.
BALLAD OF THE SLAVE
The helot got him a hempen cord,
A slave of love was he,
"She made me dance to her circumstance--
In the air one dances free!"
She sits on a throne of ivory
Serene in her silver gown,
"Ah, woe," he cried, "but the world is wide,
But 'tis straight where I lie down.
"She mocked, she scorned, and she hated me,
She shall pity me not," he said;
"Too late for the nether way of hate,
I may flout her when I'm dead."
Out in the dark of the moonless sky,
The rope was round his neck,
"'Tis the torque of gold from her throat so cold,
Why should I rue or reck?"
Tighter tangled the hempen cord;
"'Tis her fingers hot with fire,
In a tempest of fear she draws me near,--
Now dying is not so dire!"
Black, more black grew the empty void,
"And I but a broken reed,
For there's only her face in this grisly place"--
But his love stood there indeed!
Close to her heart she took his head,
And she kissed him back to breath,
"You are mine by right of that line of white,
You are mine--by Life and Death!"
FOAM
I have dallied with wantons, made mad by their passionate wine,
Time, like a golden ball, I have tossed to the wastes of the air.
I have whispered with Beauty, whose song has been sister to mine,
Laughed with the long late hours who lie with the stars in their hair.
Like the spume on the crest of the wave blowing back to the sea,
Cast from the depths beneath, now to riot and dance in the light,
I have flung you the foam of my heart, to be mask unto me,
Caught to my heart again from the doom of your fugitive sight.
THE SEAL
The document of day is folded down,
Night, the great lawyer, takes the waiting sheet,
And o'er the murky shadows of the town
Sets his red seal, to make the deed complete.
RELEASE
I asked to be released, I did not know
'Twas hate, not love, that would not let me go.
Vengeance had burned your image on my mind,
I gazed and gazed until my eyes were blind.
Now--neither pride nor love has set me free,
But happy chance--in wonderful degree.
Shackled by memory, a prey to fear,
Once you were mine by the black load I bore,
But now, released, I lose you--O my Dear,
Ever, irrevocably mine no more!
SIN, THE SWORD
Sin was a terrible and ruddy sword,
My hands were only lilies, only made
To lay against his lips, and so I prayed
Another weapon. Willingly I poured
On his strong heart the gifts that could accord
With my life's fact, but Ah! the gifts were weighed
And all found wanting--and I was afraid
Of love which was so dreadfully my lord.
He showed me the magnificence, the height
To be attained for those who dare to seek,
For those who dare the wonder and delight.
I might attain--I might--but if I should!--
I was afraid, my fainting heart was weak,
And so, Love help me, I was only--good!
FANTASTIC SPRING
Wear a lure fantastical,
Farthingales of Spring,
Till the out-worn city hearts
Dance for you and sing.
Lime us with grotesque desires,
Warm with green and gold;
Apathetic we have grown,
Tired and hard and old.
Draw us gently to your truth,
Calm our hopes and fears;
Till at last the grass blades speak
To attentive ears.
SONG
We only ask for sunshine,
We did not want the rain;
But see the flowers that spring from showers
All up and down the plain.
We beg the gods for laughter,
We shrink, we dread the tears;
But grief's redress is happiness,
Alternate through the years.
CONTRAST
Steady stand the ilex trees,
All the leaves are still,
Motionless the opal haze
Drowses on the hill.
There a marble statue waits
Patient of the hours,
Ringed about with silent sun
Over dreamy flowers.
Nature mirrors perfect peace,
Round me everywhere,
Only in my heart is found
Torment and despair.
THE PRICE
We are so tired of merely being human,
Loving or loved, the sweet imperfect woman.
Masters, you know not what your lips have missed,
On the rose mouths you keep but to be kissed.
We are Astarte, we are Lilith, we
Know the blue veils which you have named the sea
Cover the eyes of Isis; that the sky
Is the white body of Neith, arched so on high.
Ours is a secret language, when we smile,
Dreams are denied at birth, all to beguile
Your earthy substance. Ah, at what fell cost
We pay you, so our heritage is lost.
THE KING'S DAUGHTER
She was the fairest of the King's fair daughters,
Gold and rubies glittered on her hands;
Her voice was the lilting of a rain of silver waters,
And her lovers were as endless as her lands.
Down thro' the birch wood with her maidens all about her,
So virginal she came with dainty tread,
At my eyes she was silent,--could a gypsy turn and flout her:
Love I looked and love I spoke, till white grew red.
Free she was as fair, she forgot her father's palace,
Left her lands to wander at my side;
She is crowned with forest leaves, with my two curved hands for chalice:
Spring and love must bring a gypsy to his bride.
LAIS
You are white as the moths of Twilight,
You are secret as mist and dew,
And your down-dropped eyes
Are eternally wise,
Strange sins have wrought their hue.
Mother of men and women,
They are ghosts, not men you have bred;
In infinite scorn
Their bodies were born
While their souls were worse than dead.
We are what your lips have made us,
Empty, and bitterly old;
Our faith has lied,
Oh, barren bride,
And the fires of the world are cold.
THE HERITAGE
How shall the present verify the past?
Like flames we strove, still onward, upward rising,
Spurning the singing continents--at last,
Wrecked on this fatal day of our devising.
Nurtured by lunar rainbows, chill and sweet,
Our fancy was a gossamer of beauty;
Now like a web it drags about our feet,
Named with the symbols drear of fact and duty.
We who were heirs to Egypt, India's child,
Suckled by Greece, and cradled by Cathay,
How tacitly we waive this breeding wild,
Deny our parents in our deeds to-day.
Let us awake--obedient to our dreams,
Let us embrace huge issues, comprehending
The scheme entire--Great Beauty's birth, which seems
The glorious urge for life, unchecked, unending.
THE MONK IN HIS GARDEN
The air is heavy with a mist of spice,
Vervain and agrimony, clove and rue,
Have I not paid, have I not paid the price?
How shall these tempters torture me anew?
I close my eyes and dream the incense drifts
Over the monstrance, and the acolyte
Swings the gold censer. Then the vision lifts:
I know the poisonous joys I have to fight.
Day with its flowers and yellow butterflies,
Holds for my heart no pain, the wind is free
That blows upon my garden from far skies,
Yet may I hold it in white chastity.
But night!--and the still air!--Ah, God above,
Have I the strength to wage thy war anew?
Blot out my senses or I die for love,--
Vervain and agrimony, clove and rue!
BIANCA
The orchard apples hung above,
Golden and red and green.
Her face beneath was ripe for love,
Cat-eyed with sparks between.
Simples she came to gather there
With hands of ivory;
Gold fillets bound her golden hair;
Her gown was cramosie.
She plucked the herbs with subtle grace,
Derisive in her deed.
Was there no Prince to read her face,
No Prince with Beauty's need?
Her hands with cassia buds were sweet:
"Come, love," her young heart cried,
The Prince with delicate swift feet,
Was even at her side!
Her tamed white leopard leaped in fear,
Love beckons love so soon.
They gathered no more simples there,
The long late afternoon.
FREE
Beyond the hill the hearth fires burn,
A hundred flags in air,
But one which tossed but yesterday
Is dead, one hearth is bare.
The wife whose fingers fed the fire
Grew weary of the play,
A lad laughed thro' the open door
And stole my dear away.
And now alone I face the road;
No hearth, no home for me.
And yet--Ah Life!--come sun, come rain,
My beggar soul is free.
BLACK AND GOLD
Round her knees her lovers yearned,
She who sat in black and gold,
What recked she who begged or burned,
Sister to the gods of old.
Darkness was her pedigree,
Light her ever living flame,
Lovers die for such as she,
Paying for her smiles with shame.
Round her head the music floats,
Black by night and gold by day;
These are Time's inchoate notes,
Calling, "Sister, come away."
Bride of eager-blooded gods,
Wife to man's primeval age,
What to her shall serve these clods
Save to irk her pilgrimage?
THE ANSWER
The themes of women! Mounting up the sky,
Beating the air with tremulous weak wings,
How shall so small a matter win so high,
The vain sweet goal of their imaginings?
Striving for Beauty, dark philosophy,
Or the obscure and purple deeps of truth,
How shall they know their one great verity,
The answer to their queries and their youth?
Simple vain themes of women! Only this
One theme may lift their wings to goals above,--
To spill their hearts out blindly in a kiss,
An infinite surrendering to love.
PEACE
Night thundered down the valley
From off the rocky steeps,
Like wind it broke the silences
That light divinely keeps.
As low dark clouds concealing
The things one dare not see,
So grimly dark and ominous
Hung low each shadowy tree.
Night, the dread terror-master,
What wordless woe he weaves!
Suddenly peace, and all the air
Is scented with green leaves.
BARNABAS
They all are dead but Barnabas; he'll wait,
With his old groping hands and haggard eyes,
Which nothing in the world can now surprise,
Till the last leaf whirls thro' the clanging gate
Of the last sunrise. Did he learn too late?
Maybe, that one may hear the moans and cries
That ring by night, and yet be calm and wise.
And teach the women how a man can hate!
I did not think a soul could live so long,
And be so little. He remembers youth
With a wry smile of disbelief; the wrong
Was this, he squeezed the fruit so dry
So long ago; and now must live, forsooth
Because a woman will not let him die.
LOST DREAMS
Coming thro' the porch of dreams
To the portal of the day,
Vacant all the ether seems
With a grief that leaves her grey.
In a threnody of sighs,
With the cloud wreaths 'round her face,
Morning veils her heavy eyes,
Weeping for her vanished grace.
Ah! in gaining lusty Dawn,
Life, and pleasant facts of light,
Why must we, the darkness gone,
Lose the dreams that haunt the night?
LADY OF LIGHT
Light of the World, what are violets but eyes of you,
Perfume, your hair blowing back on the breeze,
Ah, but the fugitive dainty surprise of you,
Pricking in green on the blossomy trees.
Give me the sun of your smile to be fire to me,
Give me the moon when the passion is gone,
Give me the light to be dream and desire to me
Down the dark alleys that lead to the dawn.
SONG
You are the dawning of dreams.
You are the end of desire.
You are the gladness and glory that seems
Dauntless, to urge and aspire.
Cradle my soul on your wings,
Cradle my head on your breast.
Teach me the ardour that conquers and sings.
Grant me your infinite rest.
THE GYPSY BLOOD
Because the lover cares for daffodils
Must we be stranger to the passion flower,
Or slight the iris, dewy from a shower?
The gypsy heather bloom upon the hill
Strikes fiercely on a gypsy heart, and thrills
New argosies of dreams to sail the hours.
No rosy perfume blown from garden bowers
May bear the subtle perfume this distills.
Must we forego the dreamy twilight stars
Because the true-love lives for morning sun?
Love dare not hold the sense behind such bars.
The moon drips scented petals on our hair,
And gypsy hearts to gypsy flowers must run
While life is everything, tho' love be fair.
AND YET
Inadequate and void, the days
Are not more tired than tears;
And yet, how long, how long the ways,
Down the bare lane of years.
The bird that flutters from the nest
Is fused of fire and spring,
And yet how soon the throbbing breast
Will lose the life to sing.
How long the lane, how soon 'tis past,
Rough road, dark sky above,
And yet, dear heart, there's home at last,
With light, and life, and love!
THRO' THE PLEACHED ALLEYS
Thro' the pleached alley in my garden of the Spring
Merry leaves tossed over me with elfish whispering.
I was not alone, alone, for Love with blowing hair
Touched my hands and touched my heart, dancing everywhere.
Darting round about my steps, as a swallow slips,
How she laughed and laughed at me, with little rosy lips,
Ghostly wise she kissed my eyes, her mouth was chill as snow,
For she had died, my Love had died, so very long ago.
End of the Project Gutenberg EBook of Gypsy Verses, by Helen Hay Whitney
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Anselm Berrigan
Photo by Michael Grimaldi.
Poet, Editor
Born 1972, Chicago, IL
The grant was spirit lifting, alleviated some job-hunt anxiety, and helped realize a few different poetry-related endeavors that had been on hold at the mostly imaginary stage of in the works. I was also able to get some writing done at various points of the year, and complete two manuscripts of poetry, one of which will be published by Wave Books in 2019... I'm especially thankful for the support of poets who work unconventionally—it's a rare gift.
- Anselm Berrigan, December 15, 2017
Anselm Berrigan is a poet working in long, serial, and stand-alone forms, shaped to make space for language to operate on as many of its known and unknown levels as possible. He is the author of eight books of poetry, two collaborative books, and several chapbooks.
Berrigan's 2017 Grants to Artists award supported the publication of Degrets (Couch Press, 2017), and the publication of poet Brendan Lorber's first full-length book, If this is paradise why are we still driving, by Berrigan's publishing collective Subpress. Berrigan's award also funded his travel to Kenya to participate in the Kistrech International Poetry Festival, hosted by Kisii University with readings across Western Kenya.
Berrigan's books of poetry include Integrity and Dramatic Life (Edge, 1999); Zero Star Hotel (Edge, 2002); Some Notes on My Programming (Edge, 2006); Free Cell (City Lights Books, 2009); a selection from an ongoing series, Notes from Irrelevance (Wave Books, 2011); Pregrets (Vagabond Press, 2014); the book-length scroll Primitive State (Edge, 2015); and Come In Alone (Wave Books, 2016), a book of poems composed out at the edge of the page. He is also co-author of two collaborative books, Skasers, with poet John Coletti (Flowers & Cream, 2012), and Loading, with visual artist Jonathan Allen (Brooklyn Arts Press, 2013).
Berrigan is the Poetry Editor for The Brooklyn Rail, an arts and culture monthly. He co-edited The Collected Poems of Ted Berrigan (U. California, 2005) and the Selected Poems of Ted Berrigan (U. California, 2011) with his mother Alice Notley and brother Edmund Berrigan. Berrigan is a member of the subpress publishing collective, and has published Selected Poems of Steve Carey (2009), Your Ancient See Through by Hoa Nguyen (2002), and Adam DeGraff's Wherewithal (2016). He also edited What Is Poetry? (Just kidding, I know you know): Interviews from the Poetry Project Newsletter 1983-2009 (Wave Books, 2017).
Berrigan was awarded a residency by the Robert Rauschenberg Foundation (2014) and a Process Space Residency by the Lower Manhattan Cultural Council (2015). He was a New York State Foundation for the Arts Fellow in Poetry (2007), and has received three grants from the Fund for Poetry. From 2003-2007 Berrigan was Artistic Director of The Poetry Project at St. Mark's Church, where he also hosted the Wednesday Night Reading Series. He is Co-Chair, Writing at the Milton Avery Graduate School of the Arts interdisciplinary M.F.A. program, and also teaches part-time at Brooklyn College.
I started writing poems when I was eighteen and broke a line instead of making a sentence. I write by hand, I work a space out for a long time then go on, it all feels like one poem that has to get exhausted to change, it changes dramatically and often. The poems should be gotten and not gotten at the same time but time keeps moving so they're all sound disappearing with words extending their surfaces and blowing holes into them. The senses at work, the dispersal of power, the binding of humor and melancholy, putting things together that don't go together, rendering tone as shape, tampering with the endless external manipulations of perception, pretending prosody and the pictures plane are siblings, stealing compositional ideas from painters, and making everything in the poem be out of equilibrium except, spontaneously, all of it, are things my work seems interested in doing these days.
Excerpt from the FCA-supported chapbook Degrets, Couch Press, 2017.
"Degrets," 2016.
"Pregrets," 2016.
"Deflategret," 2016. | {
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{"url":"http:\/\/blog.datadive.net\/interpreting-random-forests\/","text":"# Interpreting random forests\n\n## Why model interpretation?\n\nImagine a situation where a credit card company has built a fraud detection model using a random forest. The model can classify every transaction as either valid or fraudulent, based on a large number of features. What if, upon the classification of a transaction as fraudulent, the analyst wold like to know why the model made this decision, i.e. how much each feature contributed to the final outcome?\n\nOr what if a random forest model that worked as expected on an old data set, is producing unexpected results on a new data set. How would one check which features contribute most to the change in the expected behaviour.\n\n## Random forest as a black box\n\nMost literature on random forests and interpretable models would lead you to believe this is nigh impossible, since random forests are typically treated as a black box. Indeed, a forest consists of a large number of deep trees, where each tree is trained on bagged data using random selection of features, so gaining a full understanding of the decision process by examining each individual tree is infeasible. Furthermore, even if we are to examine just a single tree, it is only feasible in the case where it has a small depth and low number of features. A tree of depth 10 can already have thousands of nodes, meaning that using it as an explanatory model is almost impossible.\n\nOne way of getting an insight into a random forest is to compute feature importances, either by permuting the values of each feature one by one and checking how it changes the model performance or computing the amount of \u201cimpurity\u201d (typically variance in case of regression trees and gini coefficient or entropy in case of classification trees) each feature removes when it is used in node. Both approaches are useful, but crude and static in the sense that they give little insight in understanding individual decisions on actual data.\n\n## Turning a black box into a white box: decision paths\n\nWhen considering a decision tree, it is intuitively clear that for each decision that a tree (or a forest) makes there is a path (or paths) from the root of the tree to the leaf, consisting of a series of decisions, guarded by a particular feature, each of which contribute to the final predictions.\nA decision tree with $$M$$ leaves divides the feature space into $$M$$ regions $$R_m, 1\\leq m \\leq M$$. In the classical definition (see e.g. Elements of Statistical Learning), the prediction function of a tree is then defined as $$f(x) = \\sum\\limits_{m=1}^M c_m I(x, R_m)$$ where $$M$$ is the number of leaves in the tree(i.e. regions in the feature space), $$R_m$$ is a region in the feature space (corresponding to leaf $$m$$), $$c_m$$ is a constants corresponding to region $$m$$ and finally $$I$$ is the indicator function (returning 1 if $$x \\in R_m$$, 0 otherwise). The value of $$c_m$$ is determined in the training phase of the tree, which in case of regression trees corresponds to the mean of the response variables of samples that belong to region $$R_m$$ (or ratio(s) in case of a classification tree). The definition is concise and captures the meaning of tree: the decision function returns the value at the correct leaf of the tree. But it ignores the \u201coperational\u201d side of the decision tree, namely the path through the decision nodes and the information that is available there.\n\n## Example: Boston housing data\n\nLet\u2019s take the Boston housing price data set, which includes housing prices in suburbs of Boston together with a number of key attributes such as air quality (NOX variable below), distance from the city center (DIST) and a number of others \u2013 check the page for the full description of the dataset and the features. We\u2019ll build a regression decision tree (of depth 3 to keep things readable) to predict housing prices. As usual, the tree has conditions on each internal node and a value associated with each leaf (i.e. the value to be predicted). But additionally we\u2019ve plotted out the value at each internal node i.e. the mean of the response variables in that region.\n\nRM LSTAT NOX DIST\n3.14.50.542.6Predict\n6.516.10.122.2Predict\n7.110.50.311.8Predict\n\nYou can hover on the leaves of the tree or click \u201cpredict\u201d in the table (which includes sample values from the data set) to see the decision paths that lead to each prediction.\nWhat\u2019s novel here is that you can see the breakdown of the prediction, written down in terms of value changes along the prediction path, together with feature names that \u201ccaused\u201d every value change due to being in the guard (the numbers are approximate due to rounding).\n\nWhat this example should make apparent is that there is another, a more \u201coperational\u201d way to define the prediction, namely through the sequence of regions that correspond to each node\/decision in the tree. Since each decision is guarded by a feature, and the decision either adds or subtracts from the value given in the parent node, the prediction can be defined as the sum of the feature contributions + the \u201cbias\u201d (i.e. the mean given by the topmost region that covers the entire training set).\nWithout writing out the full derivation, the prediction function can be written down as $$f(x) = c_{full} + \\sum\\limits_{k=1}^K contrib(x, k)$$ where $$K$$ is the number of features, $$c_{full}$$ is the value at the root of the node and $$contrib(x, k)$$ is the contribution from the k-th feature in the feature vector $$x$$. This is superficially similar to linear regression ($$f(x) = a + bx$$). For linear regression the coefficients $$b$$ are fixed, with a single constant for every feature that determines the contribution. For the decision tree, the contribution of each feature is not a single predetermined value, but depends on the rest of the feature vector which determines the decision path that traverses the tree and thus the guards\/contributions that are passed along the way.\n\n## From decision trees to forest\n\nWe started the discussion with random forests, so how do we move from a decision tree to a forest? This is straightforward, since the prediction of a forest is the average of the predictions of its trees: $$F(x) = \\frac{1}{J} \\sum\\limits_{j=1}^J f_j(x)$$, where $$J$$ is the number of trees in the forest. From this, it is easy to see that for a forest, the prediction is simply the average of the bias terms plus the average contribution of each feature: $$F(x) = \\frac{1}{J}{\\sum\\limits_{j=1}^J {c_{j}}_{full}} + \\sum\\limits_{k=1}^K (\\frac{1}{J}\\sum\\limits_{j=1}^J contrib_j(x, k))$$.\n\n### Running the interpreter\n\nUpdate (Aug 12, 2015)\nRunning the interpretation algorithm with actual random forest model and data is straightforward via using the treeinterpreter (pip install treeinterpreter) library that can decompose scikit-learn\u2018s decision tree and random forest model predictions. More information and examples available in this blog post.\n\n## Summary\n\nThere is a very straightforward way to make random forest predictions more interpretable, leading to a similar level of interpretability as linear models \u2014 not in the static but dynamic sense. Every prediction can be trivially presented as a sum of feature contributions, showing how the features lead to a particular prediction. This opens up a lot of opportunities in practical machine learning and data science tasks:\n\n\u2022 Explain to an analyst why a particular prediction is made\n\u2022 Debug models when results are unexpected\n\u2022 Explain the differences of two datasets (for example, behavior before and after treatment), by comparing their average predictions and corresponding average feature contributions.\n\n## 22 comments on \u201cInterpreting random forests\u201d\n\n1. Thank you sir for such a informative description.\n\n2. How did you create the great interactive visualization figure? Would you say your techniques are scalable to a large tree?\n\n3. I created it using D3 (http:\/\/d3js.org\/), a great Javascript visualization library.\nYou can see a lot of examples of tree visualizations at https:\/\/github.com\/mbostock\/d3\/wiki\/Gallery\n\nAs for large trees, the number of nodes grows exponentially in the depth of the tree. So a tree of depth 10 can already have ~2000 nodes. A tree of this size will be very difficult for a human to read, since there is simply too much too fine grained information there. But that\u2019s where the usefulness of the described approach comes in, since it is agnostic to the size of the tree (or the number of trees in case of a forest).\n\n4. I\u2019m thinking this approach could also be adapted to gradient boosted trees, which are also (at least as I understand their implementation in SAS EM) an ensemble of a number of trees from bootstrapped samples of the data (but using all features vs. a sample of features) ? I\u2019ve also seen examples of using trees to visualize neural nets.\n\n5. Yes, it would indeed also work for gradient boosted trees in a similar way. Basically, any time the prediction is made via trees, the prediction can be broken down into a sum of feature contributions.\n\n\u2022 @Basically, any time the prediction is made via trees, the prediction can be broken down into a sum of feature contributions\n\nThe definition of feature contributions should be modified for gradient boosting. The sum of decision paths (aka. local increments) should no longer be divided with number of trees, in order to maintain \u201cprediction = bias + sum of feature contributions\u201d. Each bagged tree maps from bias (aka. base rate +stratification or grand mean) to target and the ensemble prediction is the average vote and therefore division by number of trees. Each boosted tree only maps from residual to target, and the boosted ensemble maps only once from bias to target, therefore division by 1.\n\nI appended a short proof-of-concept for computing and visualizing feature contributions for gradient boosting with R in ancillary files for this paper, http:\/\/arxiv.org\/abs\/1605.09196\n\n6. There is a typ0.\n\nline 5 up from the last sentence. \u201canlyst\u201d should be \u201canalyst\u201d.\n\n7. Thanks to this post, I understood the \u2018theorical equation\u2019 behind Random Forest running.\nDo you have a source where the equation came?\nThanks Again for everything,\n\nBobbie\n\n\u2022 Hi Ando, any luck with this? I was wondering if we could maybe make a standalone module, should it not be merged.\n\n\u2022 In current 0.17dev, my commit to keep values in all nodes was merged. Additionally, a method to get the leaf labels when predicting was added. Combining these, the interpretation can be done on the 0.17dev version. Planning to write a blog post on this in the near future.\n\n8. This is great stuff Ando. I was thinking about how to apply this to \u2018understand\u2019 a whole dataset\/model combination. You could, e.g., pick a few top features and cluster the entire population according to the feature contributions, for these features, from a RF model. On the Boston housing data, this leads to 8-10 clusters with clear descriptions like \u201cNeighborhoods that are expensive because they are right near the city center\u201d, or \u201cNeighborhoods that are expensive because the houses are huge\u201d. You could even then compare two data sets by fitting the clusters and seeing how the proportions change.\n\nThanks for the contribution \u2013 looking forward to seeing decision_paths in sklearn.\n\n9. Pingback: \u4f7f\u7528scikit-learn\u89e3\u91ca\u968f\u673a\u68ee\u6797\u7b97\u6cd5 - IT\u5927\u9053\n\n10. This is great! Do you know if this is available with the R random forest package?\n\n11. What would it be the interpretation of a negative value, for a specific variable, in a classification problem? Does it mean that higher values of this variable decrease the predicted probability? I.e. Given Predicted_prob(x) = Bias + 0.01*A \u2013 0.02*B, is it correct to assume that probability to belong to class X is inversely proportional to the value assumed by B?\n\n\u2022 Remember, all of these breakdowns are exact contribution from features per datapoint\/instance.\nSo in your example, it means that for datapoint x, B reduces the probability. It doesnt mean that B always (or on average) reduces the probability. For some other datapoint, B could be positive.\n\n12. Great post!\nQuestion though\u2026 Quoting this:\n\n\u201d For the decision tree, the contribution of each feature is not a single predetermined value, but depends on the rest of the feature vector which determines the decision path that traverses the tree and thus the guards\/contributions that are passed along the way\u201d\n\nIf in case I get the mean of the contributions of each feature for all the training data in my decision tree model, and then just use the linear regression f(x) = a + bx (where a is the mean bias and b is now the mean contributions) to do predictions for incoming data, do you think this will work?\n\n13. Hi \u2013 I would like to use the figure above in an O\u2019Reilly media article about interpretable machine learning. This article would feature treeinterpreter among many other techniques. Please let me know ASAP. Thanks!\n\n\u2022 We will link to this blog. I followed you on twitter recently. Please let me know here or there if you would like any other specific citation.","date":"2017-04-23 21:40:18","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\": 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\": 0.5246654152870178, \"perplexity\": 637.0419789791223}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-17\/segments\/1492917118831.16\/warc\/CC-MAIN-20170423031158-00289-ip-10-145-167-34.ec2.internal.warc.gz\"}"} | null | null |
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British Airways operates direct flights to Tel Aviv from London Heathrow, so you can be in the White City by the sea in less than 5 hours. There are frequent flights to Tel Aviv's Ben Gurion International Airport, which is about a 30-minute drive from the city's centre.
Tel Aviv's location on the eastern edge of the Med makes it a perfect year-round destination for anyone seeking a beach holiday with world-renowned architecture, a bewildering range of restaurants, and one of the world's top places to party. If it all gets too much (or too hot), Jerusalem is just one hour away by car.
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Flights to Tel Aviv from London Heathrow take 4 hours 50 minutes – enough time to squeeze in two feature films, or a decent rest. As Israel is just 2 hours ahead of London, there's no jet lag. English is widely spoken and understood, so don't fret about not speaking Hebrew (or Arabic, or Russian).
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British Airways flies from London Heathrow (LHR) to Tel Aviv (TLV). There are plenty of options – and cheap flights to Tel Aviv – offering passengers a choice of timings and cabins, including First, Club World, World Traveller Plus or World Traveller. You get your first taste of Israel as soon as you arrive: the recently remodelled concourse to and from passport control is made from the iconic, cream-coloured Jerusalem stone.
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Fly directly from London to Tel Aviv in less than 5 hours and visit a thriving seaside city that treasures its past and embraces the future. A World Heritage Site for its 1930s architecture, Tel Aviv is also the engine of the country's high-tech economy – Israel is widely recognized as being second only to Silicon Valley when it comes to technological innovation.
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Tel Aviv International Airport is known as Ben Gurion. It's Tel Aviv – and Israel's – only hub. Depending on traffic, downtown is some 30 minutes away; head in the other direction and you'll get to Jerusalem in about 45. The easiest way to go is by taxi. There is also a fast train, shuttle buses and car hire. Since you need to get a bus to the car hire area, you may want to consider picking up your rental in town.
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{"url":"https:\/\/teamcore.seas.harvard.edu\/publications\/price-usability-designing-operationalizable-strategies-security-games-0","text":"# The Price of Usability: Designing Operationalizable Strategies for Security Games\n\n### Citation:\n\nSara Marie Mc Carthy, Corine M. Laan, Kai Wang, Phebe Vayanos, Arunesh Sinha, and Milind Tambe. 2018. \u201cThe Price of Usability: Designing Operationalizable Strategies for Security Games .\u201d In 27th International Joint Conference on Artificial Intelligence (IJCAI).\n\n### Abstract:\n\nWe consider the problem of allocating scarce security resources among heterogeneous targets to thwart a possible attack. It is well known that deterministic solutions to this problem being highly predictable are severely suboptimal. To mitigate this predictability, the game-theoretic security game model was proposed which randomizes over pure (deterministic) strategies, causing confusion in the adversary. Unfortunately, such mixed strategies typically randomize over a large number of strategies, requiring security personnel to be familiar with numerous protocols, making them hard to operationalize. Motivated by these practical considerations, we propose an easy to use approach for computing strategies that are easy to operationalize and that bridge the gap between the static solution and the optimal mixed strategy. These strategies only randomize over an optimally chosen subset of pure strategies whose cardinality is selected by the defender, enabling them to conveniently tune the trade-off between ease of operationalization and efficiency using a single design parameter. We show that the problem of computing such operationalizable strategies is NP-hard, formulate it as a mixedinteger optimization problem, provide an algorithm for computing \u270f-optimal equilibria, and an efficient heuristic. We evaluate the performance of our approach on the problem of screening for threats at airport checkpoints and show that the Price of Usability, i.e., the loss in optimality to obtain a strategy that is easier to operationalize, is typically not high.","date":"2023-01-28 00:40:08","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\": 0.856944739818573, \"perplexity\": 2001.5925209597763}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764499468.22\/warc\/CC-MAIN-20230127231443-20230128021443-00758.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.jobilize.com\/physics-ap\/course\/25-4-total-internal-reflection-by-openstax?qcr=www.quizover.com&page=2","text":"25.4 Total internal reflection \u00a0(Page 3\/8)\n\n Page 3 \/ 8\n\nThe cladding prevents light from being transmitted between fibers in a bundle.\n\nSpecial tiny lenses that can be attached to the ends of bundles of fibers are being designed and fabricated. Light emerging from a fiber bundle can be focused and a tiny spot can be imaged. In some cases the spot can be scanned, allowing quality imaging of a region inside the body. Special minute optical filters inserted at the end of the fiber bundle have the capacity to image tens of microns below the surface without cutting the surface\u2014non-intrusive diagnostics. This is particularly useful for determining the extent of cancers in the stomach and bowel.\n\nMost telephone conversations and Internet communications are now carried by laser signals along optical fibers. Extensive optical fiber cables have been placed on the ocean floor and underground to enable optical communications. Optical fiber communication systems offer several advantages over electrical (copper) based systems, particularly for long distances. The fibers can be made so transparent that light can travel many kilometers before it becomes dim enough to require amplification\u2014much superior to copper conductors. This property of optical fibers is called low loss . Lasers emit light with characteristics that allow far more conversations in one fiber than are possible with electric signals on a single conductor. This property of optical fibers is called high bandwidth . Optical signals in one fiber do not produce undesirable effects in other adjacent fibers. This property of optical fibers is called reduced crosstalk . We shall explore the unique characteristics of laser radiation in a later chapter.\n\nCorner reflectors and diamonds\n\nA light ray that strikes an object consisting of two mutually perpendicular reflecting surfaces is reflected back exactly parallel to the direction from which it came. This is true whenever the reflecting surfaces are perpendicular, and it is independent of the angle of incidence. Such an object, shown in [link] , is called a corner reflector \u00a0 \u00a0, since the light bounces from its inside corner. Many inexpensive reflector buttons on bicycles, cars, and warning signs have corner reflectors designed to return light in the direction from which it originated. It was more expensive for astronauts to place one on the moon. Laser signals can be bounced from that corner reflector to measure the gradually increasing distance to the moon with great precision.\n\nCorner reflectors are perfectly efficient when the conditions for total internal reflection are satisfied. With common materials, it is easy to obtain a critical angle that is less than $\\text{45\u00ba}$ . One use of these perfect mirrors is in binoculars, as shown in [link] . Another use is in periscopes found in submarines.\n\nresistance of thermometer in relation to temperature\nhow\nBernard\nthat resistance is not measured yet, it may be probably in the next generation of scientists\nPaul\nIs fundamental quantities under physical quantities?\nplease I didn't not understand the concept of the physical therapy\nphysiotherapy - it's a practice of exercising for healthy living.\nPaul\nwhat chapter is this?\nAnderson\nthis is not in this book, it's from other experiences.\nPaul\nSure\nWhat is Boyce law\nhow to convert meter per second to kilometers per hour\nDivide with 3.6\nMateo\nmultiply by (km\/1000m) x (3600 s\/h) -> 3.6\n2 how heat loss is prevented in a vacuum flask\nwhat is science\nHelen\nlogical reasoning for a particular phenomenon.\nAjay\nI don't know anything about it \ud83d\ude14. I'm sorry, please forgive \ud83d\ude14\ndue to non in contact mean no conduction and no convection bec of non conducting base and walls and also their is a grape between the layer like to take the example of thermo flask\nAbdul\ndimensions v\u00b2=u\u00b2+2at\nwhat if time is not given in finding the average velocity?\nthe magnetic circuit of a certain of the flux paths in each of the long and short sides being 25cm and 20cm reprectielectrove. there is an air gap of 2mm long in one the long sides if a flux density of 0.8weber\/m is to produce in the magnet of 1500 turns..\nHow do you calculate precision\nwhat module is that?\nFillemon\nChemisty 1A?\nFillemon\nNo it has something to do with measurements bro... What we did today in class\nSacky\nTah bra honestly I didn't understand a thing in that class..when re your Tutorials?\nFillemon\nFriday bro... But the topics we did are in this app... Just try to master them quickly before the test dates... Are you done with the Maths sheet\nSacky\nI eat ass\nAnderson\nI'll work on the maths sheet tomorrow bra @Sacky Malyenge but I'll try mastering them\nFillemon\nI'll eat your mom's ass with a side of tendies\nAnderson\n@Fillemon Nanwaapo\nAnderson\nlol, hush\nEmi\nThere are very large numbers of charged particles in most objects. Why, then, don\u2019t most objects exhibit static electricity?\nBecause there's an equal number of negative and positive charges... objects are neutral in nature\nNELSON\nwhen a ball rolls on a smooth level ground,the motion of its centre is?\nwhat is electro magnetic field?\nMary\nelectromagnetic field is a special type of field been produced by electric charges..!!! like the word electro from Electricity and the word magnetic from Magnetism.. so it is more of a join field..!!!\nNELSON\nElectromagnetic field is caused by moving electric charge\nwhen a ball rolls on a smooth level ground,the motion of its centre is?\nMumeh\nwhat's the relationship btw displacement and position\ndisplacement is the change of position 8======\u270a=D \ud83d\udca6\ud83d\udca6\nAnderson\nwhat is the meaning of elasticity\nis the ability of a material to or any object to expand to a limit point\nking\nthis is about kinematics you bonk\nEmi","date":"2020-02-22 21:38:54","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 1, \"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\": 0.43056201934814453, \"perplexity\": 1435.5669042699355}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-10\/segments\/1581875145729.69\/warc\/CC-MAIN-20200222211056-20200223001056-00496.warc.gz\"}"} | null | null |
Mometasone furoate, formoterol fumarate dihydrate 100mcg/5mcg, 200mcg/5mcg; per inh; metered-dose inhaler; contains HFA.
Treatment of asthma in patients not adequately controlled on a long-term asthma control medication [eg, inhaled corticosteroid (ICS)] or whose disease warrants initiation of both an ICS and LABA.
Not for relief of acute bronchospasm.
Initially 2 inh of 100mcg/5mcg or 200mcg/5mcg twice daily (AM & PM), based on disease severity and previous asthma therapy. Max 2 inh of 200mcg/5mcg twice daily (max 800mcg/20mcg per day). Rinse mouth after use.
Primary treatment of status asthmaticus or other acute episodes of asthma requiring intensive measures.
Increased risk of asthma-related events (death, hospitalizations, intubations) with LABA monotherapy (without ICS). Do not initiate in rapidly or acutely deteriorating asthma. Not for use with other long-acting β2-agonists. Do not exceed recommended dose. Prescribe a short-acting, inhaled β2-agonist for acute symptoms; monitor for increased need. Immunosuppressed. Tuberculosis. Systemic infections. Ocular herpes simplex. If exposed to chickenpox or measles, consider immune globulin prophylaxis or antiviral treatment. Monitor for adrenal insufficiency when transferring from systemic steroids. May need supplemental systemic corticosteroids during periods of stress or severe asthma attack. May unmask previously suppressed allergic conditions. Reevaluate periodically. Monitor for hypercorticism and HPA axis suppression (if occurs, discontinue gradually), growth in children, intraocular pressure, glaucoma, or cataracts. Discontinue if paradoxical bronchospasm occurs; use alternative therapy. Cardiovascular disease (esp. coronary insufficiency, arrhythmias, hypertension). Aneurysm. Pheochromocytoma. Convulsive disorders. Thyrotoxicosis. Hyperresponsiveness to sympathomimetics. Diabetes. Ketoacidosis. Hypokalemia. Hyperglycemia. Hepatic impairment. Assess bone mineral density if risk factors exist (eg, prolonged immobilization, osteoporosis, or chronic use of drugs that can reduce bone mass [eg, anticonvulsants, oral steroids]). Labor & delivery. Pregnancy. Nursing mothers.
Corticosteroid + long-acting beta-2 agonist (LABA).
Caution with concomitant strong CYP3A4 inhibitors (eg, ketoconazole, itraconazole, ritonavir, cobicistat-containing products, atazanavir, clarithromycin, indinavir, nefazodone, nelfinavir, saquinavir, telithromycin), during or within 2 weeks of discontinuing MAOIs, tricyclic antidepressants, macrolides, or drugs known to prolong QT interval (increased cardiac effects), adrenergic agents, β-blockers (consider cardioselective), K+-depleting diuretics. Hypokalemia potentiated by xanthine derivatives. Increased risk of arrhythmias with concomitant anesthesia with halogenated hydrocarbons.
Nasopharyngitis, sinusitis, headache; oral candidiasis, hypersensitivity reactions. | {
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OVER 743 small and medium enterprises (SMEs), have undergone specially packaged capacity building, which is crucial for contracts in the oil and gas sector.
The beneficiaries were drawn from Central, Northern, Western, and Eastern regions of Uganda. In terms of individuals, a total of 1660 people were trained in sessions held in Kololo (Kampala), Mbarara, and Hoima, the epicenter of the oil and gas activities.
Dubbed the Business Incubator, the imparting of skills, is the result of a collaboration between Uganda National Oil Company Limited (UNOC) and Stanbic Bank, one of the leading financial institutions.
UNOC and the Bank early this year inked a Memorandum of Understanding (MOU) to facilitate the activities. Overall, the ongoing program is preparing SMEs for lucrative opportunities in Uganda's oil and gas sector.
Accordingly, the lessons include financial management, business planning, and analysis. Others are customer care, strategic thinking, branding, and marketing. The list also includes teamwork, leadership skills, communication, presentation skills, and preparing winning bids.
Thus far, said Stanbic Business Incubator Limited, Program Coordinator, Lyndah Kamasaka, the training has culminated in funding and access to new markets, increased jobs and revenue for some SMEs.
These, and more, will continue to be the program's focus so that beneficiaries access funding, markets and increase profitability, Kamasaka added.
Indeed, some of the above were among the benefits UNOC CEO, Ms. Proscovia Nabbanja and counterpart, Patrick Mweheire mentioned at a signing ceremony in Kampala on February 5th, 2020.
Then, the two leaders reiterated their commitment to local content and, development of SMEs. Local content refers to the participation of indigenous people and companies in provision of services and goods to the sector.
"We are pleased to be partnering with UNOC in this critical initiative that aims to facilitate the participation and development of national content in the oil and gas sector. Oil is a game-changer in many economies and the only way we can benefit as Ugandans is if we have as many local companies participating as possible," stated Mweheire.
The UNOC CEO said that the institution would offer "capabilities", which would boost the beneficiaries' potential to participate and benefit from the sector.
"Partnerships with institutions like Stanbic are instrumental in promoting national content through providing training and information on the opportunities for local businesses in the oil and gas sector," she stated.
"UNOC will provide subject matter experts to support the development of businesses on the Enterprise Development programme and also provide support to the Stanbic Business Incubator Centre's training and research activities in Enterprise Development."
In conformity with the local content, she stressed, the law ring-fenced for Ugandans provision of certain services and goods. This, thus, improves opportunities for Ugandan companies to participate in the sector. Uganda's confirmed petroleum resource, situated in the Albertine Graben, is estimated at 6.5bn barrels. Of these, 1.4-1.7bn barrels are recoverable and await the final investment (FID) decision before development and production. It is estimated that about US$16bn will be invested in the sector during this phase. The Business Incubator started in February 2018 as way of, among others, supporting SMEs boost their potential. Intent on further ensuring local content, and as key player in the oil and gas sector, in February 2020, the partnership with UNOC, started. Shortly, because of the COVID-19 challenge, the sessions have since gone online. The second intake for this year kicked off in September and will be online.
Tullow Completes $575 Million Sale Of Uganda Assets To Total
Ministry of Energy and Mineral Development
Ministry of Finance, Planning and Economic Development
Petroleum Authority of Uganda
National Environment Management Authority
Directorate of Petroleum-Uganda
© 2021 UNOC | Uganda National Oil Company Limited. All Rights Reserved. Muffin group
what is 31*21? | {
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Donald Kirkpatrick was NOT the Originator of the Four-Level Model of Learning Evaluation
Learning Industry, Learning Measurement, Myths and Worse, News and Current Affairs, People
Donald Kirkpatrick (1924-2014) was a giant in the workplace learning and development field, widely known for creating the four-level model of learning evaluation. Evidence however contradicts this creation myth and points to Raymond Katzell, a distinguished industrial-organizational psychologist, as the true originator. This, of course, does not diminish Don Kirkpatrick's contribution to framing and popularizing the four-level framework of learning evaluation.
The Four-Levels Creation Myth
The four-level model is traditionally traced back to a series of four articles Donald Kirkpatrick wrote in 1959 and 1960, each article covering one of the four levels, Reaction, Learning, Behavior, Results. These articles were published in the magazine of ASTD (then called the American Society of Training Directors). Here's a picture of the first page of the first article:
In June of 1977, ASTD (known by then as the American Society of Training and Development, now ATD, the Association for Talent Development) reissued Kirkpatrick's original four articles, combining them into one article in the Training and Development Journal. The story has always been that it was those four articles that introduced the world to the four-level model of training evaluation.
In 1994, in the first edition of his book, Evaluating Training Programs: The Four Levels, Donald Kirkpatrick wrote:
"In 1959, I wrote a series of four articles called 'Techniques for Evaluating Training Programs,' published in Training and Development, the journal of the American Society for Training and Development (ASTD). The articles described the four levels of evaluation that I had formulated. I am not sure where I got the idea for this model, but the concept originated with work on my Ph.D. dissertation at the University of Wisconsin, Madison." (p. xiii). [Will's Note: Kirkpatrick was slightly inaccurate here. At the time of his four articles, the initials ASTD stood for the American Society of Training Directors and the four articles were published in the Journal of the American Society of Training Directors. This doesn't diminish Kirkpatrick's central point: that he was the person who formulated the four levels of learning evaluation].
In 2011, in a tribute to Dr. Kirkpatrick, he is asked about how he came up with the four levels. This is what he said in that video tribute:
"[after I finished my dissertation in 1954], between 54 and 59 I did some research on behavior and results. I went into companies. I found out are you using what you learned and if so what can you show any evidence of productivity or quality or more sales or anything from it. So I did some research and then in 1959 Bob Craig, editor of the ASTD journal, called me and said, 'Don, I understand you've done some research on evaluation would you write an article?' I said, 'Bob, I'll tell you what I'll do, I'll write four articles, one on reaction, one on learning, one on behavior, and one on results.'"
In 2014, when asked to reminisce on his legacy, Dr. Kirkpatrick said this:
"When I developed the four levels in the 1950s, I had no idea that they would turn into my legacy. I simply needed a way to determine if the programs I had developed for managers and supervisors were successful in helping them perform better on the job. No models available at that time quite fit the bill, so I created something that I thought was useful, implemented it, and wrote my dissertation about it." (Quote from blog post published January 22, 2014).
As recently as this month (January 2018), on the Kirkpatrick Partners website, the following is written:
"Don was the creator of the Kirkpatrick Model, the most recognized and widely used training evaluation model in the world. The four levels were developed in the writing of his Ph.D. dissertation, Evaluating a Human Relations Training Program for Supervisors."
Despite these public pronouncements, Kirkpatrick's legendary 1959-1960 articles were not the first published evidence of a four-level evaluation approach.
Raymond Katzell's Four-Step Framework of Evaluation
In an article written by Donald Kirkpatrick in 1956, the following "steps" were laid out and were attributed to "Raymond Katzell, a well known authority in the field [of training evaluation]."
To determine how the trainees feel about the program.
To determine how much the trainees learn in the form of increased knowledge and understanding.
To measure the changes in the on-the-job behavior of the trainees.
To determine the effects of these behavioral changes on objective criteria such as production, turnover, absenteeism, and waste.
These four steps are the same as Kirkpatrick's four levels, except there are no labels.
Raymond Katzell went on to a long and distinguished career as an industrial-organizational psychologist, even winning the Society for Industrial and Organizational Performance's Distinguished Scientific Contributions award.
Raymond Katzell. Picture used by SIOP (Society for Industrial and Organizational Psychology) when they talk about The Raymond A. Katzell Media Award in I-O Psychology.
The first page of Kirkpatrick's 1956 article—written three years before his famous 1959 introduction to the four levels—is pictured below:
And here is a higher-resolution view of the quote from that front page, regarding Katzell's contribution:
So Donald Kirkpatrick mentions Katzell's four-step model in 1956, but not in 1959 when he—Kirkpatrick—introduces the four labels in his classic set of four articles.
It Appears that Kirkpatrick Never Mentions Katzell's Four Steps Again
As far I can tell, after searching for and examining many publications, Donald Kirkpatrick never mentioned Katzell's four steps after his 1956 article.
Three years after the 1956 article, Kirkpatrick did not mention Katzell's taxonomy when he wrote his four famous articles in 1959. He did mention an unrelated article where Katzell was a co-author (Merrihue & Katzell, 1955), but he did not mention Katzell's four steps.
Neither did Kirkpatrick mention Katzell in his 1994 book, Evaluating Training Programs: The Four Levels.
Nor did Kirkpatrick mention Katzell in the third edition of the book, written with Jim Kirkpatrick, his son.
Nor was Katzell mentioned in a later version of the book written by Jim and Wendy Kirkpatrick in 2016. I spoke with Jim and Wendy recently (January 2018), and they seemed as surprised as I was about the 1956 article and about Raymond Katzell.
Nor did Donald Kirkpatrick mention Katzell in any of the interviews he did to mark the many anniversaries of his original 1959-1960 articles.
To summarize, Katzell, despite coming up with the four-step taxonomy of learning evaluation, was only given credit by Kirkpatrick once, in the 1956 article, three years prior to the articles that introduced the world to the Kirkpatrick Model's four labels.
Kirkpatrick's Dissertation
Kirkpatrick did not introduce the four-levels in his 1954 dissertation. There is not even a hint at a four-level framework.
In his dissertation, Kirkpatrick cited two publications by Katzell. The first, was an article from 1948, "Testing a Training Program in Human Relations." That article studies the effect of leadership training, but makes no mention of Katzell's four steps. It does, however, hint at the value of measuring on-the-job performance, in this case the value of leadership behaviors. Katzell writes, "Ideally, a training program of this sort [a leadership training program] should be evaluated in terms of the on-the-job behavior of those with whom the trainees come in contact."
The second Katzell article cited by Kirkpatrick in his dissertation was an article entitled, "Can We Evaluate Training?" from 1952. Unfortunately, it was a mimeographed article published by the Industrial Management Institute at the University of Wisconsin, and seems to be lost to history. Even after several weeks of effort (in late 2017), the University of Wisconsin Archives could not locate the article. Interestingly, in a 1955 publication entitled, "Monthly Checklist of State Publications" a subtitle was added to Katzell's Can We Evaluate Training? The subtitle was: "A summary of a one day Conference for Training Managers" from April 23, 1952.
To be clear, Kirkpatrick did not mention the four levels in his 1954 dissertation. The four levels notion came later.
How I Learned about Katzell's Contribution
I've spent the last several years studying learning evaluation, and as part of these efforts, I decided to find Kirkpatrick's original four articles and reread them. ATD (The Association for Talent Development) in 2017 had a wonderful archive of the articles it had published over the years. As I searched for "Kirkpatrick," several other articles—besides the famous four—came up, including the 1956 article. I was absolutely freaking stunned when I read it. Donald Kirkpatrick had cited Katzell as the originator of the four level notion!!!
I immediately began searching for more information on the Kirkpatrick-Katzell connection and found that I wasn't the first person to uncover the connection. I found an article by Stephen Smith who acknowledged Kazell's contribution in 2008, also in an ASTD publication. I communicated with Smith recently (December 2017) and he had nothing but kind words to say about Donald Kirkpatrick, who he said coached him on training evaluations. Here is a graphic taken directly from Smith's 2008 article:
Smith's article was not focused on Katzell's contribution to the four levels, which is probably why it wasn't more widely cited. In 2011, Cynthia Lewis wrote a dissertation and directly compared the Katzell and Kirkpatrick formulations. She appears to have learned about Katzell's contribution from Smith's 2008 article. Lewis's (2011) comparison chart is reproduced below:
In 2004, four years before Smith wrote his article with the Katzell sidebar, ASTD republished Kirkpatrick's 1956 article—the one in which Kirkpatrick acknowledges Katzell's four steps. Here is the front page of that article:
In 2016, an academic article appeared in a book that referred to the Katzell-Kirkpatrick connection. The book is only available in French and the article appears to have had little impact in the English-speaking learning field. Whereas neither Kirkpatrick's 2004 reprint nor Smith's 2008 article offered commentary about Katzell's contribution except to acknowledge it, Bouteiller, Cossette, & Bleau (2016) were clear in stating that Katzell deserves to be known as the person who conceptualized the four levels of training evaluation, while Kirkpatrick should get credit for popularizing it. The authors also lamented that Kirkpatrick, who himself recognized Katzell as the father of the four-level model of evaluation in his 1956 article, completely ignored Katzell for the next 55 years and declared himself in all his books and on his website as the sole inventor of the model. I accessed their chapter through Google Scholar and used Google Translate to make sense of it. I also followed up with two of the authors (Bouteiller and Cossette in January 2018) to confirm I was understanding their messaging clearly.
Is There Evidence of a Transgression?
Raymond Katzell seems to be the true originator of the four-level framework of learning evaluation and yet Donald Kirkpatrick on multiple occasions claimed to be the creator of the four-level model.
Of course, we can never know the full story. Kirkpatrick and Katzell are dead. Perhaps Katzell willingly gave his work away. Perhaps Kirkpatrick asked Katzell if he could use it. Perhaps Kirkpatrick cited Katzell because he wanted to bolster the credibility of a framework he developed himself. Perhaps Kirkpatrick simply forgot Katzell's four steps when he went on to write his now-legendary 1959-1960 articles. This last explanation may seem a bit forced given that Kirkpatrick referred to the Merrihue and Katzell work in the last of his four articles—and we might expect that the name "Katzell" would trigger memories of Katzell's four steps, especially given that Katzell was cited by Kirkpatrick as a "well known authority." This forgetting hypothesis also doesn't explain why Kirkpatrick would continue to fail to acknowledge Katzell's contribution after ASTD republished Kirkpatrick's 1956 article in 2004 or after Steven Smith's 2008 article showed Katzell's four steps. Smith was well-known to Kirkpatrick and is likely to have at least mentioned his article to Kirkpatrick.
We can't know for certain what transpired, but we can analyze the possibilities. Plagiarism means that we take another person's work and claim it as our own. Plagiarism, then, has two essential features (see this article for details). First, an idea or creation is copied in some way. Second, no attribution is offered. That is, no credit is given to the originator. Kirkpatrick had clear contact with the essential features of Katzell's four-level framework. He wrote about them in 1956! This doesn't guarantee that he copied them intentionally. He could have generated the four levels subconsciously, without knowing that Katzell's ideas were influencing his thinking. Alternatively, he could have spontaneously created them without any influence from Katzell's ideas. People often generate similar ideas when the stimuli they encounter are similar. How many people claim that they invented the term, "email?" Plagiarism does not require intent, but intentional plagiarism is generally considered a higher-level transgression than sloppy scholarship.
A personal example of how easy it is to think you invented something: In the 1990's or early 2000's, I searched for just the right words to explain a concept. I wrangled on it for several weeks. Finally, I came up with the perfect wording, with just the right connotation. "Retrieval Practice." It was better than the prevailing terminology at the time—the testing effect—because people could retrieve without being tested. Eureka I thought! Brilliant I thought! It was several years later, rereading Robert Bjork's 1988 article, "Retrieval practice and the maintenance of knowledge," that I realized that my label was not original to me, and that even if I did generate it without consciously thinking of Bjork's work, that my previous contact with the term "retrieval practice" almost certainly influenced my creative construction.
The second requirement for plagiarism is that the original creator is not given credit. This is evident in the case of the four levels of learning evaluation. Donald Kirkpatrick never mentioned Katzell after 1956. He certainly never mentioned Katzell when it would have been most appropriate, for example when he first wrote about the four levels in 1959, when he first published a book on the four levels in 1994, and when he received awards for the four levels.
Finally, one comment may be telling, Kirkpatrick's statement from his 1994 book: "I am not sure where I got the idea for this model, but the concept originated with work on my Ph.D. dissertation at the University of Wisconsin, Madison." The statement seems to suggest that Kirkpatrick recognized that there was a source for the four-level model—a source that was not Kirkpatrick himself.
Here is the critical timeline:
Katzell was doing work on learning evaluation as early at 1948.
Kirkpatrick's 1954 dissertation offers no trace of a four-part learning-evaluation framework.
In 1956, the first reference to a four-part learning evaluation framework was offered by Kirkpatrick and attributed to Raymond Katzell.
In 1959, the first mention of the Kirkpatrick terminology (i.e., Reaction, Learning, Behavior, Results) was published, but Katzell was not credited.
In 1994, Kirkpatrick published his book on the four levels, saying specifically that he formulated the four levels. He did not mention Katzell's contribution.
In 2004, Kirkpatrick's 1956 article was republished, repeating Kirkpatrick's acknowledgement that Katzell invented the four-part framework of learning evaluation.
In 2008, Smith published the article where he cited Katzell's contribution.
In 2014, Kirkpatrick claimed to have developed the four levels in the 1950s.
As far as I've been able to tell—corroborated by Bouteiller, Cossette, & Bleau (2016)—Donald Kirkpatrick never mentioned Katzell's four-step formulation after 1956.
Judge Not Too Quickly
I have struggled writing this article, and have rewritten it dozens of times. I shared an earlier version with four trusted colleagues in the learning field and asked them if I was being fair. I've searched exhaustively for source documents. I reached out to key players to see if I was missing something.
It is not a trifle to curate evidence that impacts other people's reputations. It is a sacred responsibility. I as the writer have the most responsibility, but you as a reader have a responsibility too to weigh the evidence and make your own judgments.
First we should not be too quick to judge. We simply don't know why Donald Kirkpatrick never mentioned Katzell after the original 1956 article. Indeed, perhaps he did mention Katzell in his workshops and teachings. We just don't know.
Here are some distinct possibilities:
Perhaps Katzell and Kirkpatrick had an agreement that Kirkpatrick could write about the four levels. Let's remember the 1959-1960 articles were not written to boost Kirkpatrick's business interests. He didn't have any business interests at that time—he was an employee—and his writing seemed aimed specifically at helping others do better evaluation.
Perhaps Kirkpatrick, being a young man without much of résumé in 1956, had developed a four-level framework but felt he needed to cite Katzell in 1956 to add credibility to his own ideas. Perhaps later in 1959 he dropped this false attribution to give himself the credit he deserved.
Perhaps Kirkpatrick felt that citing Katzell once was enough. Where many academics and researchers see plagiarism as one of the deadly sins, others have not been acculturated into the strongest form of this ethos. Let's remember that in 1959 Kirkpatrick was not intending to create a legendary meme, he was just writing some articles. Perhaps at the time it didn't seem important to acknowledge Katzell's contribution. I don't mean to dismiss this lightly. All of us are raised to believe in fairness and giving credit where credit is due. Indeed, research suggests that even the youngest infants have a sense of fairness. Kirkpatrick earned his doctorate at a prestigious research university. He should have been aware of the ethic of attribution, but perhaps because the 1959-1960 articles seemed so insignificant at the time, it didn't seem important to site Katzell.
Perhaps Kirkpatrick intended to cite Katzell's contribution in his 1959-1960 articles but the journal editor talked him out of it or disallowed it.
Perhaps Kirkpatrick realized that Katzell's four steps were simply not resonant enough to be important. Let's admit that Kirkpatrick's framing of the four levels into the four labels was a brilliant marketing masterstroke. If Kirkpatrick believed this, he might have seen Katzell's contribution as minimal and not deserving of acknowledgement.
Perhaps Kirkpatrick completely forget Katzell's four-step taxonomy. Perhaps it didn't influence him when he created his four labels, that he didn't think of Katzell's contribution when he wrote about Katzell's article with Merrihue, that for the rest of his life he never remembered Katzell's formulation, that he never saw the 2004 reprinting of his 1956 article, that he never saw Smith's 2008 article, and that he never talked with Smith about Katzell's work even though Smith has claimed a working relationship. Admittedly, this last possibility seems unlikely.
Let us also not judge Jim and Wendy Kirkpatrick, proprietors of Kirkpatrick Partners, a global provider of learning-evaluation workshops and consulting. None of this is on them! They were genuinely surprised to hear the news when I told them. They seemed to have no idea about Katzell or his contribution. What is past is past, and Jim and Wendy bear no responsibility for the history recounted here. What they do henceforth is their responsibility. Already, since we spoke last week, they have updated their website to acknowledge Katzell's contribution!
Article Update (two days after original publication of this article): Yesterday, on the 31st of January 2018, Jim and Wendy Kirkpatrick posted a blog entry (copied here for the historic record) that admitted Katzell's contribution but ignored Donald Kirkpatrick's failure to acknowledge Katzell's contribution as the originator of the four-level concept.
What about our trade associations and their responsibilities? It seems that ASTD bears a responsibility for their actions over the years, not only as the American Society of Training Directors who published the 1959-1960 articles without insisting that Katzell be acknowledged even though they themselves had published the 1956 articles where Katzell's four-step framework was included on the first page; but also as the American Society of Training and Development who republished Kirkpatrick's 1956 article in 2004 and republished the 1959-1960 articles in 1977. Recently rebranded as ATD (Association for Talent Development), the organization should now make amends. Other trade associations should also help set the record straight by acknowledging Katzell's contribution to the four-level model of learning evaluation.
Donald Kirkpatrick's Enduring Contribution
Regardless of who invented the four-level model of evaluation, it was Donald Kirkpatrick who framed it to perfection with the four labels and popularized it, helping it spread worldwide throughout the workplace learning and performance field.
As I have communicated elsewhere, I think the four-level model has issues—that it sends messages about learning evaluation that are not helpful.
On the other hand, the four-level model has been instrumental in pushing the field toward a focus on performance improvement. This shift—away from training as our sole responsibility, toward a focus on how to improve on-the-job performance—is one of the most important paradigm shifts in the long history of workplace learning. Kirkpatrick's popularization of the four levels enabled us—indeed, it pushed us—to see the importance of focusing on work outcomes. For this, we owe Donald Kirkpatrick a debt of gratitude.
And we owe Raymond Katzell our gratitude as well. Not only did he originate the four levels, but he also put forth the idea that it was valuable to measure the impact learners have on their organizations.
What Should We Do Now?
What now is our responsibility as workplace learning professionals? What is ethical? The preponderance of the evidence points to Katzell as the originator of the four levels and Donald Kirkpatrick as the creator of the four labels (Reaction, Learning, Behavior, Results) and the person responsible for the popularization of the four levels. Kirkpatrick himself in 1956 acknowledged Katzell's contribution, so it seems appropriate that we acknowledge it too.
Should we call them Katzell's Four Levels of Evaluation? Or, the Katzell-Kirkpatrick Four Levels? I can't answer this question for you, but it seems that we should acknowledge that Katzell was the first to consider a four-part taxonomy for learning evaluation.
For me, for the foreseeable future, I will either call it the Kirkpatrick Model and then explain that Raymond Katzell was the originator of the four levels, or I'll simply call it the Kirkpatrick-Katzell Model.
Indeed, I think in fairness to both men—Kirkpatrick for the powerful framing of his four labels and his exhaustive efforts to popularize the model and Katzell for the original formulation—I recommend that we call it the Kirkpatrick-Katzell Four-Level Model of Training Evaluation. Or simply, the Kirkpatrick-Katzell Model.
Research Cited
Bjork, R. A. (1988). Retrieval practice and the maintenance of knowledge. In M. M. Gruneberg, P. E. Morris, R. N. Sykes (Eds.), Practical Aspects of Memory: Current Research and Issues, Vol. 1., Memory in Everyday Life (pp. 396-401). NY: Wiley.
Bouteiller, D., Cossette, M., & Bleau, M-P. (2016). Modèle d'évaluation de la formation de Kirkpatrick: retour sur les origins et mise en perspective. Dans M. Lauzier et D. Denis (éds.), Accroître le transfert des apprentissages: Vers de nouvelles connaissances, pratiques et expériences. Presses de l'Université du Québec, Chapitre 10, 297-339. [In English: Bouteiller, D., Cossette, M., & Bleau, M-P. (2016). Kirkpatrick training evaluation model: back to the origins and put into perspective. In M. Lauzier and D. Denis (eds.), Increasing the Transfer of Learning: Towards New Knowledge, Practices and Experiences. Presses de l'Université du Québec, Chapter 10, 297-339.]
Katzell, R. A. (1948). Testing a training program in human relations. Personnel Psychology, 1, 319-329.
Katzell, R. A. (1952). Can we evaluate training? A summary of a one day conference for training managers. A publication of the Industrial Management Institute, University of Wisconsin, April, 1952.
Kirkpatrick, D. L. (1956). How to start an objective evaluation of your training program. Journal of the American Society of Training Directors, 10, 18-22.
Kirkpatrick, D. L. (1959a). Techniques for evaluating training programs. Journal of the American Society of Training Directors, 13(11), 3-9.
Kirkpatrick, D. L. (1959b). Techniques for evaluating training programs: Part 2—Learning. Journal of the American Society of Training Directors, 13(12), 21-26.
Kirkpatrick, D. L. (1960a). Techniques for evaluating training programs: Part 3—Behavior. Journal of the American Society of Training Directors, 14(1), 13-18.
Kirkpatrick, D. L. (1960b). Techniques for evaluating training programs: Part 4—Results. Journal of the American Society of Training Directors, 14(2), 28-32.
Kirkpatrick, D. L. (1956-2004). A T+D classic: How to start an objective evaluation of your training program. T+D, 58(5), 1-3.
Lewis, C. J. (2011). A study of the impact of the workplace learning function on organizational excellence by examining the workplace learning practices of six Malcolm Baldridge Quality Award recipients. San Diego: CA. Available at http://sdsu-dspace.calstate.edu/bitstream/handle/10211.10/1424/Lewis_Cynthia.pdf.
Merrihue, W. V., & Katzell, R. A. (1955). ERI: Yardstick of employee relations. Harvard Business Review, 33, 91-99.
Salas, E., Tannenbaum, S. I., Kraiger, K., & Smith-Jentsch, K. A. (2012). The science of training and development in organizations: What matters in practice. Psychological Science in the Public Interest, 13(2), 74–101.
Smith, S. (2008). Why follow levels when you can build bridges? T+D, September 2008, 58-62.
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cover
# Copyright
Copyright © 2018 by John Eisenberg
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Basic Books
Hachette Book Group
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First Edition: October 2018
Published by Basic Books, an imprint of Perseus Books, LLC, a subsidiary of Hachette Book Group, Inc. The Basic Books name and logo is a trademark of the Hachette Book Group.
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The Library of Congress has cataloged the hardcover edition as follows:
Names: Eisenberg, John, 1956– author.
Title: The League : how five rivals created the NFL and launched a sports empire / John Eisenberg.
Description: First Edition. | New York : Basic Books, an imprint of Perseus Books, LLC, a subsidiary of Hachette Book Group, Inc., [2018] | Includes bibliographical references and index.
Identifiers: LCCN 2018012386 (print) | LCCN 2018016380 (ebook) | ISBN 9781541617377 (ebook) | ISBN 9780465048700 (hardcover)
Subjects: LCSH: National Football League—History. | Football—United States—History.
Classification: LCC GV955.5.N35 (ebook) | LCC GV955.5.N35 E58 2018 (print) |
DDC 796.332/64—dc23
LC record available at https://lccn.loc.gov/2018012386
ISBNs: 978-0-465-04870-0 (hardcover), 978-1-541-61737-7 (ebook)
E3-20180829-JV-PC
# Contents
Cover
Title Page
Copyright
Dedication
**Prologue**
PART ONE
1 **Halas: The Founder**
2 **Mara: The Promoter**
3 **Marshall: The Showman**
4 **Bell: The Profligate Son**
5 **Rooney: The Gambler**
PART TWO
6 **Almost Broke**
7 **New Ideas**
8 **Benny and the Giants**
9 **Instituting a Draft**
10 **Betting Bonanza**
11 **Move to DC**
PART THREE
12 **Brotherhood of Rivals**
13 **A Step Forward**
14 **The Greatest Rout**
15 **Same Old Pirates**
16 **Political Winds**
17 **Dog Meat**
18 **Two Wars**
19 **The Right Guy in Charge**
PART FOUR
20 **Back Across the Color Line**
21 **Scandal**
22 **Everyone Loses**
23 **The Little Black Box**
24 **All-White Redskins**
25 **Forty Million Viewers**
**Epilogue**
Acknowledgments
About the Author
Also by John Eisenberg
Praise for _The League_
Note on Sources
Bibliography
Notes
Index
_For my press box colleagues_
# PROLOGUE
WHEN THE NATIONAL FOOTBALL LEAGUE'S TEAM OWNERS met at the Victoria Hotel in midtown Manhattan on a cold Monday morning in December 1934, the media contingent covering the event consisted of a single photographer. Not one of New York's major newspapers bothered to send a reporter. And the one photographer did not stay long.
After fifteen years in business, the NFL was still languishing on the fringe of America's sports scene. Millions of sports fans around the country followed baseball, college football, horse racing, and boxing, but many did not even know a professional football league existed. A meeting of the men who ran the league could not possibly produce news that a majority of fans cared about.
A day earlier at the Polo Grounds in New York, the NFL had staged a championship game for just the second time. Before then, the league had simply recognized the team with the best win-loss record as that year's champion. But some teams played more games than others, and ties were commonplace, complicating the calculations. To end the confusion, the owners had decided to split their teams into two divisions and match up the division winners in a single game that determined the league title. They hoped the championship contest might one day become a landmark event, like baseball's World Series.
The game at the Polo Grounds, a renowned baseball venue, had mixed results. A brutal ice storm hit New York, limiting the crowd to slightly more than half of the stadium's capacity. That was disappointing. But the game itself was memorable. The visiting Chicago Bears, undefeated and heavily favored, built a lead and seemed in control until the New York Giants switched from cleats to sneakers after halftime to improve their footing on the icy field. The Giants proceeded to score four straight touchdowns and win by a wide margin.
Some of the other team owners had attended the game as a show of support, and now they were meeting to review their season, consider rule changes, and present a championship trophy to Tim Mara, who owned the Giants. The second-floor conference room quickly filled. Mara, tall and grinning, was among the early arrivals. Known in New York sports circles more as a horseracing bookmaker and boxing promoter than as a football team owner, he was accompanied by his twenty-six-year-old son, Jack, who handled the Giants' business as the team's president.
George Halas, who owned and coached the Bears, also arrived early along with his older brother. A fiercely competitive midwesterner who had played for the Bears until he was thirty-four years old, Halas was in no mood to congratulate the Giants again after praising them in his postgame interviews with reporters the day before. But his scowl gave way to a sporting smile; Tim Mara was his rival on the field but a good partner in the football business, deserving of a handshake.
Wearing a high-collared suit and round glasses, Joe Carr, the league's president since 1921, sat at a head table, ready to run the meeting. Also present were Bert Bell and Lud Wray, former University of Pennsylvania football teammates who co-owned the Philadelphia Eagles, one of the league's newest teams; George Preston Marshall, an opinionated laundry magnate who owned the Boston Redskins; and Art Rooney, a diminutive, cigar-chomping sportsman and gambler who owned the Pittsburgh Pirates. The owners of the Brooklyn Dodgers and Detroit Lions rounded out the group.
Joe Carr (with glasses) hands the 1934 championship trophy to Jack Mara, as Tim Mara smiles. George Halas stands by Carr's right shoulder. (Associated Press)
When the meeting began, the men gathered around Carr and the Maras. Carr uttered "words of congratulation" to the elder Mara and presented his son with the Ed Thorp Memorial Trophy, a silver-plated cup named for a well-known referee, rules aficionado, and equipment supplier who had died earlier that year. The lone photographer on hand, representing a wire service, snapped a photo that would run in the _New York Times_ and other newspapers around the country the next day, giving the NFL a rare moment of widespread publicity.
The photographer quickly departed after that, as the owners returned to their seats. They had much to discuss. Although their just-concluded season had produced several positives, it was not clear the NFL was headed in the right direction. Its average per-game crowd of 13,247 in 1934 set a record, but larger crowds in Chicago and New York had pulled that figure up; other than the Bears and Giants, most teams drew poorly and lost money. The pitiful Cincinnati Reds had suspended operations after scoring 10 points and allowing 243 in eight games, forcing Carr to take on a semipro squad, the St. Louis Gunners, as a late-season replacement. The Gunners then beat Rooney's Pirates in their first game, making quite a statement about the modest caliber of the league's lower echelon.
The NFL had formally organized in 1920 out of a loose coalition of semipro squads, mostly located in small and midsize towns in America's industrial belt. By 1926, twenty-two teams were competing for the league title. But most had since folded, unable to draw crowds or break even financially. Long gone were such squads as the Rock Island Independents, Pottsville Maroons, and Dayton Triangles. The Packers, in tiny Green Bay, Wisconsin, were the last surviving remnant of the NFL's industrial-town origins.
Carr had led a drive to make the league more of a big-city venture. The Frankford (Pennsylvania) Yellow Jackets had become the Philadelphia Eagles. The Portsmouth (Ohio) Spartans had become the Detroit Lions. The owners of those and the other surviving teams believed this was necessary; if pro football was ever going to compete with baseball, it needed to succeed in the nation's largest cities. But even after breaking into major markets, the NFL still had fundamental problems. With the country in an economic depression, Halas and several other owners continually borrowed money to keep their teams afloat. On the field, there was a dangerous competitive imbalance—the Bears and Giants dominated, along with the Packers, who had recently won three straight titles—and a general lack of action. In more than half of the games in 1934, the losing team had failed to score. No wonder attendance in most stadiums was so low.
As the owners began discussing possible rule changes at the Victoria Hotel, they understood they had to make their league more competitive and their sport more exciting. Marshall dominated the conversation, as he had since he joined the league in 1932. A former actor, he thought a game should be entertainment, like a Broadway production, and constantly suggested rules aimed at giving fans more to like. He had previously led the charge to make passing a much larger part of the game and had convinced his colleagues to give offenses more room to operate by moving the action away from the sidelines and into the middle of the field, with plays starting on a set of "hash marks." At this meeting, Marshall proposed eleven of the fourteen motions that were raised, many governing intricacies such as the marking-off of penalties and the placement of the ball after fumbles. In each case, the idea was to give offenses a boost.
Before Carr banged the gavel to close the meeting, the owners also voted to put Bell and Halas in charge of a finance committee and established a "waiver rule" preventing players from changing teams in the second half of the season. Historians would not recall it as a momentous session. The owners of the Packers, Gunners, and Chicago Cardinals were not even present. The new rules, although important, would not prove as transformative as Marshall's proposals in prior meetings.
But this meeting was historically noteworthy because it marked the first time Marshall, Halas, Bell, Rooney, and Tim Mara were together in the same room discussing league affairs. These five men would keep the league afloat during its difficult early decades through their innovations, resourcefulness, and resolve, laying the foundation for the NFL to emerge as a sports superpower in the 1960s.
Other important figures in the early decades of pro football included Curly Lambeau, who ran the Packers; Carr, who produced order out of disarray; and Dan Reeves, an owner who tore down racial barriers and brought the game to the West Coast when he moved the Rams to Los Angeles. But Mara, Halas, Bell, Rooney, and Marshall were the ones most responsible for keeping pro football alive. They spent years watching their teams play a brutal sport on Sundays, then argued with each other, at times bitterly, at league meetings over rules, referees, and the schedule. "They fought with each other more than today's NFL owners ever will," recalled Upton Bell, Bert's son. But they almost always put aside their hard feelings for the sake of the league, sometimes damaging their own team's prospects to achieve collective progress. "The credo of sharing became the foundation of our league," Halas said later. Indeed, it was the key to the league's survival and eventual success. Today, pro football is a multi-billion-dollar colossus, looming over all American sports, and is at times accused of prioritizing profits over all other goals. It is thus surprising, if not remarkable, that the men who made the league did not subscribe to an individualistic, capitalistic ethos.
Pro football's early history reveals another irony. Unlike today's NFL owners, these were not men of immense family wealth. Mara was an Irish cop's son who been schooled on the streets of Lower Manhattan. Rooney's dad owned a bar. Halas's parents lived modestly after emigrating from Bohemia, a territory in the Austrian Empire in what is now the Czech Republic. Marshall had to fend for himself as a young man after his father died. Bell was the only one born to the manor, but he wasted his fortune and disavowed his place in high society. "They were on their own. No one was going to save them," Upton Bell said.
Though the Victoria Hotel meeting was the first that found them all together, they were not strangers. Halas and Marshall had backed teams in a failed professional basketball league in the 1920s. Rooney, Bell, and Mara had spent many summer days and nights together in Saratoga, New York, the horseracing spa that attracted high-rolling gamblers. Rooney and Bell, in particular, were two-fisted bettors.
Halas was the only real founding father, having attended the meeting at a car dealership in Canton, Ohio, on September 17, 1920, where the American Professional Football Association—as it was originally known—was organized. Mara came along five years later, as the NFL staggered through its infancy. Marshall, Bell, and Rooney arrived in the early 1930s. They were unlikely devotees of "paid football," as it was known in its early years. Marshall's first love was the theater. Mara had never seen a football game when he started the Giants. Bell was a college football loyalist who had once sneered at the pros; his father helped found the National Collegiate Athletic Association. Rooney hesitated to disband his successful semipro team to join the NFL.
On this Monday in December 1934, no one could have envisioned the NFL's spectacular future. Sports fans across the country were not talking about the title game between the Giants and Bears the day before. They were still focused on the classic college game between Army and Navy, played a week earlier before 79,000 fans in Philadelphia—far more than Bell's Eagles had drawn _all season_ in that city. Baseball fans were debating what might happen to Babe Ruth now that the New York Yankees had parted ways with their legendary slugger, who had grown too old and round to hit as many home runs as he once did.
As the football owners met at the Victoria Hotel, baseball's owners and executives were also meeting that morning, just blocks away in New York, at the Waldorf Hotel. Their "winter convention" received far more press coverage, befitting baseball's status as America's preeminent professional sport. Most of New York's major newspapers dispatched a reporter to cover the event and, in some cases, also sent a columnist on the expectation that important news would develop.
The NFL could not begin to match baseball or college football in generating headlines or interest—a persistent frustration for the men who ran the league. By 1934, their collaborative efforts did not seem to have much impact. Much of America continued to view pro football as little more than a lark, a cousin of professional wrestling. Halas, Mara, Marshall, Bell, and Rooney were about the only ones who believed the sport had any future. Many of their friends thought they were out of their minds to continue to support it, and they wondered, at times, whether those friends might be right.
# PART ONE
#
# HALAS: THE FOUNDER
IN 1920, GEORGE HALAS WAS A FORMER FOOTBALL MAN, seemingly done with the sport. He had played in college and in the military during the Great War, but there was no major professional league to advance to; once you graduated from college, your only option was semiprofessional ball, a sandlot game. Halas had tried it, suiting up on a half-dozen Sundays for a team near his Chicago home. After his experience with that ragtag group, he had decided to give up _all_ sports, get a job, and get on with his life. He was twenty-five.
Putting to use the engineering degree he had earned from the University of Illinois, Halas now drew a salary of fifty-five dollars a week as a safety expert for the Chicago, Burlington and Quincy Railroad, testing bridges for "stresses and strains" to ensure they would not collapse. In his spare time, he courted his future wife, Wilhelmina "Min" Bushing, a pretty brunette from Pilsen, the Chicago neighborhood where he had grown up. Halas could see the outline of a contented, white-collar life coming into view. His mother was delighted that he had given up football, the roughest of the sports he enjoyed playing.
Then one morning in March 1920 he received a phone call in the bridge design department at the railroad office in downtown Chicago. A man named George Chamberlain was on the other end. The general manager of the A. E. Staley Manufacturing Company, a starch-maker in Decatur, Illinois, Chamberlain had a job in mind for Halas and was in Chicago hoping to discuss it with him in person. Could they meet that evening at the Sherman Hotel?
Hours later, Halas entered the hotel lobby and strode across the carpet with a natural athlete's loose-limbed, rolling gait. Broad through the chest and just under six feet tall, he sported tousled, dark bangs that fell at an angle across his pale forehead. He shook hands with Chamberlain, who was bald and had a Teddy Roosevelt moustache and round, steel-rimmed spectacles. "I found Mr. Chamberlain to be a very determined man, about fifty, well-muscled; he had played football and baseball in his younger days," Halas wrote. Both men were engineers. They hit it off.
Chamberlain got down to business. His boss, Eugene Staley, believed sports could boost employee morale and help sell Staley products. Three years earlier, Staley had started a company baseball team coached by a former major league pitcher, Joe "Ironman" McGinnity. It competed in an industrial league against other major company teams through the Midwest, including the Samson Tractors of Janesville, Wisconsin; the Indian Refining Company Havolines of Lawrenceville, Illinois; and the Republic Trucks of Alma, Michigan. The Staley team drew crowds and newspaper coverage, and now Staley wanted to start a football team.
Chamberlain asked whether Halas was interested in coaching the football team, as well as playing for it. Halas quickly said yes. Although he was challenged by his railroad job, he remained an athlete at heart. He had played football, baseball, and basketball in both high school and college, showing enough potential on the diamond to briefly make the majors as an outfielder for the Yankees. For as long as he could recall, he had always had a new season to prepare for, more games to anticipate. But the Yankees had found a better right fielder, someone named Babe Ruth, and Halas had reached a dead end in football. He missed having games to look forward to. Staley's offer could provide a new outlet for his competitive energies.
There was no doubt Halas was qualified to coach a team. He had been mentored by two of the greats during his career. At Illinois, he played football for one of the sport's shrewdest coaches, Robert Zuppke. While with the Yankees, he played for thoughtful, pipe-smoking Miller Huggins, destined to manage the team to three World Series wins. Halas already had begun transitioning into coaching, having helped run a team of former college stars at the Great Lakes Naval Training Base, near Chicago, during the Great War.
Halas asked Chamberlain several questions. Could he recruit players? Yes, Chamberlain said, he could offer prospects full-time work at Staley as well as the chance to play football. The response excited Halas. Several of his Great Lakes teammates had been All-Americans; he could field a powerful team. His next question: Could the team practice two hours a day? It sounded like more than any team needed, but Chamberlain assented, telling Halas, "You're the expert." Finally, Halas asked whether those long practices could occur on company time. Sure, Chamberlain said.
The salary offer was modest, around what the railroad paid him, but it was not about money for Halas. He would get to coach and play for the company football team, play on the baseball team, and maybe start a basketball team. His calendar would positively overflow with sports and games. Meanwhile, he would learn to make starch, continuing to put his engineering and chemical training to use. Within a week, he quit the railroad, took the job with Staley, and moved 170 miles to Decatur, no longer a former football man. His mother was disappointed. Halas was thrilled.
BARBARA HALAS WAS JUST SHY OF THIRTY-ONE YEARS OLD WHEN she gave birth for the eighth time on February 2, 1895, in Chicago, delivering a boy given the name George Stanley Halas. Barbara had been a child herself, no more than five, when she arrived in the United States from Bohemia, a territory in the Austrian empire, later to become part of the Czech Republic. Little is known about her journey or early life in Chicago, but we do know she married a man named Frank Halas and soon started a family.
Frank had also come from Bohemia as a youth. Weary of the domineering rule of the Hapsburgs and frustrated after a failed revolt, Bohemians immigrated to America in waves in the 1860s. They "were tired of constant wars that were sapping the best blood of their nation, wasting their fields, and fastening still more grievous tax burdens upon shoulders that were already crushed," journalist Josefa Humpal Zeman wrote. Lured by stories of religious freedom and available land and jobs, so many Bohemians settled just south of downtown Chicago that they called their neighborhood Pilsen, after the city many had inhabited in the old country. Chicago's Pilsen had Czech newspapers, Czech churches, and Czech businesses. You could walk its streets without hearing a word of English.
Like the Germans, English, and Irish immigrants arriving in America around the same time, the Bohemians fled difficult circumstances at home only to encounter more hardship in America. Their Chicago neighborhood was crowded and chaotic, rampant with disease. But there was hope, as among the immigrants were some of Bohemia's most talented, literate, and ambitious citizens. "One would find men of education and high social standing engaged in street-sweeping, cigar-making, and other humble occupations," Zeman wrote. Frank Halas, intelligent and resourceful, started out as a reporter at a Czech newspaper, but he had an eye for fashion and soon found more profitable work as a tailor. Working with Barbara, who cut the buttonholes, he built a successful business preparing men's suits for large clothiers.
The couple built a three-story house, lived on the first floor, and rented the other two, thankful to be raising their family in America. Of the eight children they produced, only four, including George, survived childhood. But, despite their loss, Frank and Barbara retained a positive outlook, demanding that George and his siblings speak English rather than the Czech they heard on the street. It was necessary, the parents said, if they wanted to make something of themselves in America.
Frank's business grew so large that he built a workshop behind the house. But then he suffered a stroke, forcing drastic changes. He sold the business, leased the workshop and apartment building, and built another structure nearby—a three-story brick residence with apartments above a ground-level grocery, which Barbara ran. The Halas family lived on the second floor. They were far from wealthy, but between what the grocery and apartment rentals brought in, there was enough. Years later, one of Halas's players, Mike Ditka, would scoff that he "threw nickels around like manhole covers." But, rather than take offense, Halas agreed, saying he was proud that he had learned a dollar's worth as a boy.
Halas's two brothers and sister called him "Kid." In a household that was loving but strict, they were all expected to dress neatly, excel in school, and worship at St. Vitus, a Roman Catholic church. Frank and Barbara emphasized education as the path to success, and George took note, building a strong academic record. But sports were his passion. As a youngster, he played street softball and cheered for the Chicago Cubs. At Crane Tech High School, he played baseball and lightweight football and ran track.
As was true for millions of other young Americans raised by immigrant parents in these years, sports were an integral part of Halas's assimilation into the country's cultural mainstream. At the ballpark, he was not viewed by others as a young man of Czech parentage, from a neighborhood where little English was spoken; he was just a Cubs fan, his passion shared with people of a variety of ethnicities and religions, who spoke many languages. Alike in their support of the home team, they became friends, or at least compatriots, rather than strangers.
Frank Halas died "quite suddenly," as Halas would later write, on Christmas Eve in 1910. Halas was fifteen. His mother, determined to see her children go to college, sold the building where they lived, closed the grocery, and opened a tavern. After his high school graduation, George worked for Western Electric for a year, mostly because he needed to add weight to play college sports. Once he was at the University of Illinois, he tried out for the football team but absorbed fearsome hits in scrimmages, suffering a broken jaw and a broken leg. He fared better in baseball, cracking the varsity lineup as a sophomore outfielder hitting .300 and making plays behind his brother Walter, a star pitcher.
But Zuppke, the Illini football coach, admired Halas. The young man played such combative defense for Illinois's basketball team that the coach had to pull him off the floor at times to keep fights from breaking out. Believing that intensity could help the football team, Zuppke kept giving Halas chances. Finally healthy as a junior in 1917, Halas returned kickoffs and punts. At the team banquet after that season, Zuppke gave a speech that resonated with him. "Just when I teach you fellows how to play football, you graduate and I lose you," Zuppke said. Those words, Halas later recalled, "would govern the rest of my life."
But he did not know that yet. It was the winter of 1917–1918, and, with the country at war in Europe, Halas volunteered for the navy and asked to be sent to sea on a submarine chaser—a small vessel designed to destroy German subs. Instead, the navy put him in the sports program at Great Lakes. Though disappointed, Halas threw himself into his duties, playing on the base's basketball and baseball teams, which took on college teams and squads from other military institutions to boost morale.
In the fall of 1918, Great Lakes fielded a magnificent football team. The quarterback, Paddy Driscoll, had been an All-American at Northwestern. The center, Charlie Bachman, had been an All-American at Notre Dame. The coach oversaw the base's officer training school, leaving him little time for football, so Halas, Driscoll, and Bachman ran practices.
Great Lakes went unbeaten and received a bid to play in the Tournament of Roses football game, soon to become known as the Rose Bowl, in Pasadena, California, on January 1, 1919. They faced another military team, the Mare Island Marines, before a packed house of 27,000 fans. On his finest day as an athlete, Halas scored a touchdown on a pass from Driscoll and returned an interception 77 yards, setting up another touchdown. Great Lakes won, and Halas earned the game's Most Valuable Player award.
After that game, Halas told his mother he was through with football and would stick to the relative safety of baseball. His military service ended, and the Yankees, who had seen him play in college, invited him to their spring training camp in Florida in 1919. Miller Huggins liked that he was a switch hitter who could cover ground in the outfield. Halas made the club, but once the season began, he managed just two hits in twenty-two at bats, his inexperience plainly evident as he flailed at major league curveballs. A hip injury set him back, and the Yankees finally dispatched him to a minor league team in St. Paul, Minnesota, for seasoning. When the season ended, he went home to Chicago and took the railroad job.
But he could not stay away from sports, especially football, which resonated with him on a fundamental level. Having been denied the chance to fight in a real war, he relished football's militaristic nature. What was the sport, with its scripted "plays," if not an approximation of two military units clashing on a battlefield? The rugged altercations between linemen certainly resembled hand-to-hand combat.
Although he had told his mother he was through with the sport, he longed to continue playing. "I ached for the excitement of a good game, for the competition, for the challenges to the muscles, for the thrill of victory," he later wrote. When he heard from a doctor who ran a semipro team in nearby Hammond, Indiana, he jumped at the chance to join. The pay was one hundred dollars a game. The team played other semipro squads such as the Canton (Ohio) Bulldogs, led by Jim Thorpe, the nation's most famous athlete, a broad-shouldered Native American who had won the decathlon at the Olympics in 1912. Playing for the Hammond team meant fitting weeknight practices and weekend games into his busy schedule, but it was worth the trouble. Halas was back alongside Paddy Driscoll. The pay was good. The team won all six games it played in 1919, including two against Canton.
"The season deepened my love for football," Halas wrote, "but I assumed my future rested with the railroad. Now and then, I would look at some of the other engineers doing the same thing day after day for thirty years. The prospect did not excite me as on cold winter days I rode the streetcar to and from the CB&Q offices. My real love was football." It was near the end of that cold winter that his office phone rang and Staley's offer beckoned.
IN HIS FIRST MONTHS AT STALEY'S SPRAWLING PLANT IN DECATUR, Halas played shortstop for the company baseball team and worked as a scale-house clerk. As summer waned, he began building his football team with a recruiting trip through the Midwest, finding plenty of takers for his unusual offer of a full-time job and the chance to play football. "I assured the men they would get paid at the end of the season for their football, depending on the size of the gate, and also told them they'd get paid weekly wages for the various duties at the plant. They all seemed to like the prospect of stability in a corporate setup," Halas would recall.
His talent haul included former All-Americans from Wisconsin, Nebraska, Illinois, and Notre Dame. Unfortunately, Paddy Driscoll had already signed with the Racine Cardinals, a Chicago semipro team that played near the city's Racine Street (some historians would later erroneously assume it played in Racine, Wisconsin). Staley had actually fielded a football team the year before, but it was a modest squad quarterbacked by Charlie Dressen, who would later play major league baseball and manage the Washington Senators. With Halas in charge, the team was far more organized, skilled, and purposeful. He handed out cloth-bound playbooks, tested players on their assignments, and schooled them in dark football arts such as how to get away with kicking and gouging opponents at the bottom of a pile.
Most American sports fans considered football a spirited amateur endeavor, a character-building exercise for high school and college boys. Played with few rules, and with some participants bare headed, it had been popular since the 1870s. "I believe in rough games and in rough, manly sports," President Theodore Roosevelt exclaimed around the turn of the century. After a spate of on-field deaths from violent collisions in the early 1900s, Roosevelt threatened to abolish the sport with an executive order unless college administrators instituted rules that made it safer. He wanted football to continue to be played, viewing it as an ideal training ground for soldiers.
Once players stopped dying on the field, college football developed a fanatical following almost rivaling that of professional baseball, a sport so preeminent that fans and sportswriters had called it the "national pastime" since the 1850s. By 1920, many college teams were playing in new, football-specific stadiums, before screeching crowds, on Saturday afternoons.
A postcollege version of the sport sprouted in the 1890s but was never nearly as popular. The first prominent teams represented athletic clubs such as the Chicago Athletic Association, Pittsburgh Athletic Club, and Latrobe (Pennsylvania) YMCA, amateur organizations that fielded teams in multiple sports. They sought to lure former college stars with under-the-table payments until they grew tired of the contrivance and simply began paying players, horrifying purists who believed that violated football's amateur essence. That version of the game, thus, did not develop a following.
Companies and independent sports entrepreneurs in the East and Midwest also began fielding football teams in the early 1900s. But unlike college football, which organized into conferences operating under a governing umbrella, the "paid" sport was a free-for-all. Players jumped from team to team during seasons in search of better pay. Active college players suited up under assumed names to make extra money, not that much was available. Teams passed a hat through the stands at games to bring in funds, hoping for a few coins and bills the players could divide up. Most games drew few fans.
Halas believed his Staley team deserved better. But when he wrote to other teams about scheduling games in the fall of 1920, he received "indifferent and vague" replies. He decided on another course. A league of semipro teams in Western Pennsylvania had become fairly popular, and several other circuits also had gained traction. Halas sent a letter to Ralph Hay, manager of the Canton Bulldogs, suggesting they start a league.
It turned out Hay, owner of an automobile dealership, had already broached the idea at a meeting with the owners of the Massilon (Ohio) Tigers and teams in Akron, Cleveland, and Dayton. They had another meeting scheduled at Hay's dealership on September 17. That day, Halas took a train to Canton with Morgan O'Brien, another Staley engineer who was helping him run the team. En route, Halas and O'Brien talked about the advantages of belonging to a league—principally, that it would give shape to their season and offer them a title to play for, meaning each game was important.
That evening, Halas and representatives from eleven other teams met in Hay's showroom, located on the first floor of the three-story Odd Fellows Building on Cleveland Avenue. "Chairs were few," Halas recalled, so the men stood around gleaming Hupmobile and Jordan cars while they drank beer, which Hay provided, and discussed football. "I sat on a runningboard," Halas recalled. The local paper covered the meeting and listed Halas as representing the Staley Athletic Club. He had many ideas and spoke frequently. The league needed rules, referees, a scheduling protocol, and a president, he told the others. Chris O'Brien, a painting contractor from Chicago, also was present; he operated the Racine Cardinals. Andrew "Doc" Young, a physician and athletic trainer, ran the team Halas had played for, the Hammond (Indiana) Pros. During the two-hour meeting, the men formed what they called the American Professional Football Association, agreeing to put up one hundred dollars each to solidify their commitment. They elected Thorpe as their commissioner even though he had no background in management, on the assumption that his selection would bring attention to their new endeavor.
The Staleys played their first game in Decatur on October 3, 1920, a sunny Sunday afternoon. Nearly two thousand fans sat in wooden bleachers and cheered as they trounced the Moline Tractors, 20–0, with Edward "Dutch" Sternaman, Halas's former teammate at Illinois, scoring three touchdowns. A week later, they routed the Kewanee Walworths, 25–7, as Halas, an end, and ten of his teammates played every snap, never leaving the field. The Staleys soon played six straight road games, mostly against outmatched squads such as the Rockford Athletic Club and Champaign Legion. Twice, they traveled to Rock Island, Illinois, to play the Independents, coming away with a victory and a tie.
The typical game was little more than a brawl loosely governed by rules poached directly from college football. Passing was legal, but the ball was fat, almost round, making it difficult to throw. That discouraged offenses and limited scoring, as did the rules. A clipping penalty set a team back 25 yards. When a pass fell incomplete in the end zone, the team lost possession. Moving the ball downfield was such a challenge that teams routinely punted on second or third down, hoping the round ball would roll farther if the opponent did not have a deep back waiting to field it. Playing for field position was a popular strategy as teams simply sat back and waited for their opponent to make a mistake. Though safer now, the sport was still rugged and bloody. Halas suffered a sprained ankle and a fractured cheekbone during the 1920 season. The Staleys' center, George Trafton, was a square-jawed roughneck described by a teammate as "the meanest, toughest player alive." Trafton injured so many opponents during one game at Rock Island that vengeful fans chased him to the team bus after the final whistle.
In late November and early December, the Staleys played three games in a row in Chicago. They defeated the Tigers, 6–0, on Thanksgiving, then lost three days later to the Racine Cardinals. It was the Staleys' only defeat in 1920. A week later, they won a rematch with the Cardinals, 10–0. As winter enveloped the Midwest, the Staleys and Akron Pros had the league's best records. The Pros had eight wins, two ties, and no defeats, and had allowed only one touchdown all season. The Staleys had ten wins, one defeat, and a tie. It was common for teams to arrange to play with little advance notice, as the league had no scheduling protocols, and Halas arranged for the Staleys to play Akron at Cubs Park in Chicago, later known as Wrigley Field, on December 12.
Halas wanted to win so badly that he signed Paddy Driscoll, his friend, to a one-game contract, even though Driscoll had played and coached all season for the Cardinals. Halas had helped write the league rule that forbade players from jumping from team to team during the season, but he reasoned this was a fair move because the Cardinals' season was over. There was no attempt to hide Driscoll's presence. He was listed with the Staleys on the lineups printed in the _Chicago Tribune_ and other papers on the morning of the game.
Twelve thousand fans paid fifty cents apiece for tickets and shivered through the contest as a cold rain fell. The Pros' best player, Fritz Pollard, a speedy halfback, was one of two African American players in the league, along with Robert "Rube" Marshall, an end for Rock Island. A Chicago native, Pollard had studied chemistry at Brown University, where, as the school's first black football player, he helped his team earn an invitation to the Rose Bowl. Opposing defenses had struggled to contain him all season, but the Staleys kept Pollard bottled up on the muddy field. The game devolved into little more than a scrum of colliding bodies, with most plays consisting of runners simply plunging into the line. Nineteen of the twenty-two starters contested every snap; Halas's squad, like most, consisted of only a few players more than the eleven-man minimum. Neither team had scored when the referee blew his whistle to end the game.
Newspaper coverage of the contest, what little there was, did not note the presence of a black player. It was potentially significant; major league baseball maintained a strict color line, permitting no blacks on its teams. But pro football was so obscure that its racial practices went unnoted. A trickle of black players would continue to suit up in the 1920s and early 1930s, until the owners abruptly adopted baseball's restrictive, racist approach. An end from Rutgers, Paul Robeson, played for Akron in 1921, switched to another team in 1922, then quit pro football, destined to become famous as an actor and activist. Most of his admirers had no idea he had ever played football.
Before the 1920 season, the APFA's owners had agreed that they would vote to select a champion rather than have the title decided on the field or by record. After the scoreless tie between the Staleys and Pros in Decatur, Akron, and Buffalo's team, the All-Americans, all claimed they deserved the title. The vote to determine a champion was scheduled for the next league meeting at the Portage Hotel in Akron on April 30, 1921.
Halas would later write that the 1920 season "confirmed my belief that professional football had a great future." But he was disappointed by the quality of many teams and the league's general mismanagement. Pro football was a pale imitation of college football's sold-out stadiums, traditional rivalries, and energetic newspaper coverage. Halas skipped the Akron meeting in April 1921, sending O'Brien in his stead. In Akron, some teams dropped out of the league, others applied to join, and most owners claimed they were losing money. They agreed they needed to organize more effectively and establish a realistic business model. Thorpe obviously had to go. He was a terrific player but had no idea how to run a league. Joe Carr, manager of the Columbus (Ohio) Panhandlers, was elected president to replace Thorpe. The Panhandlers had struggled in 1920, but they had been around for more than a decade, almost entirely because of Carr's deft management. Carr had also run a baseball minor league and now wrote a sports column for the _Ohio State Journal,_ a newspaper in Columbus. He had covered the World Series and championship boxing matches. The other owners believed he could bring order, and true know-how, to their nascent enterprise.
It was an astute decision: Carr would serve as the league's president and de facto commissioner for almost two decades. Few men would do more to ensure its eventual success. "There were a lot of pioneers, but Joe Carr was the one who kept it going," said Dan Rooney, owner of the Pittsburgh Steelers, years later. "He had a passion for it and did the right things. He knew you had to have uniforms, a rulebook, a head of officials. He worked to get the right people and the right places in the league. He doesn't get the credit but I see him as similar to Pete Rozelle and other commissioners who came later. Carr really knew what he was doing."
Minutes after Carr was elected president, Halas's surrogate, O'Brien, was elected vice president. It was a testament to the respect the other owners had for Halas and the Decatur squad. But the vote to determine the 1920 league champion went against Decatur. It was an Ohio-based league. The owners were meeting in Akron. They voted for the Pros over the Staleys because Akron had finished the season with no losses and three ties, while Decatur had one loss and two ties. According to a biographer, Halas "seethed about that 'lost title' for the rest of his life."
JOE CARR BEGAN TO RUN THE LEAGUE FROM HIS DESK AT THE _Ohio State Journal._ Within months, he had drafted a constitution and set up bylaws, which the other owners approved before the 1921 season. Carr wanted to stop teams from using disguised college players, a piece of chicanery in which many indulged. Carr also wanted to take a harder position against players jumping from team to team during the season, which caused a great deal of confusion and undermined the notion that each city, in fact, fielded its own team.
When the APFA kicked off its second season that fall, it had seventeen teams, including a new one in Green Bay, Wisconsin, a tiny shipping and meatpacking outpost on the Fox River. Halas anticipated another winning season for the Staleys. He had taken another recruiting trip and signed a fresh haul of talent that included Chic Harley, an All-American back from Ohio State. Harley's brother, Bill, had stepped in as a negotiator and asked for a cut of the Staleys' profits in exchange for the opportunity to sign Chic and two other players. Halas had agreed to the arrangement.
Shortly before the season began, Eugene Staley called Halas in and delivered a shock: he could not afford to keep funding the football team. It had cost him $16,000 in salaries and expenses in 1920—more than $200,000 in twenty-first-century dollars—and, in a town as small as Decatur, he could not possibly sell enough tickets to offset those expenditures. The team needed to play in a larger city where it could lure more fans, Staley explained.
Feeling remorseful about having convinced Halas to switch careers and move to Decatur only to cancel the enterprise after one year, Staley offered a deal. He would pay Halas $5,000 to establish the team in Chicago as an independent, for-profit concern. All Staley asked in return was that Halas continue to use the Staley name for the upcoming season, thus advertising his starch in the big city. After the season, Staley would no longer back the team, and Halas could become the owner.
Halas accepted Staley's offer. He was excited by the prospect of running a team in his hometown. Although Chicago already had the Racine Cardinals, Halas was confident he could win enough games and draw enough fans to get by. He quickly struck another deal, this one with Bill Veeck, the president of baseball's Cubs, to play his home games at Cubs Park. Veeck only asked for 15 percent of the gate and concession sales, terms Halas found eminently fair.
Halas chose orange and blue for the team's uniform colors, copying those of his alma mater, the University of Illinois. To house his players, he rented rooms at the Blackwood Apartment Hotel, near the ballpark. He also decided to take on a partner, expecting that he would need financial help once Staley's payments ceased after the season. Paddy Driscoll was his first choice, but Driscoll was under contract to the Cardinals. Dutch Sternaman, Halas's former college teammate, became his partner in the pro football business.
The Chicago Staleys played their first game at Cubs Park on October 16, 1921. They rallied to beat the Jeffersons of Rochester, New York, 16–13, which delighted Halas, who played the entire game on the edges of the offensive and defensive lines, giving and taking shoves and punches. He loved to play, but he was more excited that the game had attracted almost 8,000 fans, more than quadrupling the attendance for the team's opener in Decatur the year before.
George Halas, the player. (Associated Press)
The Staleys registered six wins and a tie before losing to the Buffalo All-Americans on Thanksgiving. Halas arranged a rematch for early December, billing the game as a "championship" that would determine the league's top team. The All-Americans were without several key players, who had been suspended by the league when Carr discovered they were also playing for a nonleague team in Philadelphia, another practice he was determined to stop. The All-Americans also stopped off in Akron and played the _day before_ they took on the Staleys, leaving them worn out for the game in Chicago.
Not surprisingly, the Staleys defeated Buffalo. It appeared they had earned the title. Halas, though, scheduled another home game, against the Canton Bulldogs, hoping to draw a crowd and generate more revenue. The extra game stirred confusion among the league's owners. What if Canton won, dealing the Staleys their second defeat of the season? Would Buffalo then deserve the title because it only had one defeat? Carr issued a ruling, declaring the league season over, the window for scheduling games closed. The outcome of this extra game between the Staleys and Bulldogs would have no bearing on the championship. In fact, Carr said, he believed it was already decided that the Staleys would be awarded the title at an upcoming league meeting, which surprised and delighted Halas.
The Staleys defeated Canton, encouraging Halas to schedule yet _another_ game, against the Racine Cardinals, shortly before Christmas. In frigid conditions, fewer than 3,000 fans watched Chicago's teams slip around on a frozen field in a scoreless tie. But the Staleys had already concluded their league season with nine wins, one defeat, and one tie, which, for the first time, and not the last, made Halas a pro football champion.
NOW THAT HE WAS HOME, HALAS BOUGHT AN ENGAGEMENT ring and proposed to Min. They were married on February 18, 1922. Within three years, they had a son, George Jr., and a daughter, Virginia. There was no doubt the growing family's future would have been more secure if Halas had kept his railroad job. The success of the APFA was hardly ensured. It was under constant attack from some of college football's most prominent and respected advocates.
In a widely lauded speech in New York in January 1922, Fielding Yost, head coach at the University of Michigan, said that paying men to play football "robs the great American game of many of its greatest character-building qualities. The ideals of generous service, loyalty, sacrifice, and whole-hearted devotion to a cause are all taken away. The game is robbed of the exhilarating inspiration of achievement merely for achievement's sake." Most fans agreed, it seemed, taking a dim view of the pro game mostly because money was involved. In a _Chicago Tribune_ "man on the street" question-and-answer column printed in the fall of 1922, five fans were asked whether they preferred college or pro football. None liked the pro game. "College athletes have something to fight for, but in the pro game they're just fighting for money," one fan told the paper.
In truth, college football was not so clean; the desire to win had so overtaken some chancellors and deans around the country that recruiting scandals and academic improprieties had become commonplace. Nonetheless, the college game remained a hallowed, puritanical endeavor in the public's eyes. By comparison, pro football seemed a tawdry imitation. Late in the 1921 season, the Green Bay Packers, coached by Curly Lambeau, a former Notre Dame player, were caught using three current Notre Dame stars in a game against the Staleys. Halas turned them in, and, though the APFA responded by kicking Lambeau and his squad out of the league after the season, the incident made the league look second rate.
Amos Alonzo Stagg, the University of Chicago's head coach, was so disturbed by the professional game that he advocated taking away the varsity letters of college players who eventually turned pro, an idea the Big Ten briefly adopted. On November 1, 1923, Stagg pleaded with "all friends of the game" to help eliminate the scourge of paid football, which, he said, was ruining the high school and college games by tempting athletes with money. "Under the guise of fair play but countenancing rank dishonesty in playing men under assumed names, scores of professional teams have sprung up within the last two or three years, most of them on a salary basis of some kind," Stagg said. "Football, when played with the amateur spirit, possesses more elements for the development of character and manhood than any sport I know. To patronize Sunday football games is to cooperate with forces which are destructive of the finest elements of interscholastic and intercollegiate football."
With the sport's powers and many fans lined up against him, Halas was cautious in his public comments. "Professional football will never replace college football and we won't want it to," he said. But he pressed ahead with his notion that pro football could survive and eventually succeed. Although he would always claim he had merely broken even in his first season in Chicago, court records would soon indicate he sold enough tickets to turn a $21,600 profit. That alone offered him sufficient encouragement to keep going.
At his suggestion, the APFA changed its name at an owners' meeting in Cleveland on June 24, 1922. "I lacked enthusiasm for our name," Halas wrote, because the word "association" connoted minor-league status in baseball. He suggested the National Football League, explaining that baseball's National League was that sport's most established, respected circuit. The other owners approved unanimously.
He also changed his team's name to the Bears. He was a Cubs fan, and his team played in the Cubs' ballpark. "Football players are bigger than baseball players, so if baseball players are cubs, then certainly football players must be bears!" he would write. Before he could proceed, however, Halas first had to gain official possession of his franchise. Staley had registered the rights with the league, so Halas applied for a transfer, seemingly a simple transaction. But Bill Harley, who had negotiated a minor ownership stake in exchange for his brother's services, also applied for the franchise. The other owners deliberated for hours before voting on who owned the Bears. Halas won, 8–2. (Harley took the league to court over the matter, and, though he lost, the case forced Halas to open his books.)
In the fall of 1922, Halas introduced his Bears to a big city rollicking through the early years of America's Roaring Twenties. With a population of 3 million, Chicago was filled with speakeasies and jazz clubs, big dreams and new ideas. Its newspapers fought to print the most outlandish tales about mobsters and murder. Its skyscrapers rose so high you had to squint to see the top floors. That summer, two women sauntered onto a beach wearing one-piece bathing suits that bared their legs, a shocking impropriety that led to their arrests.
College football riveted the city's sports fans in the fall. On October 28, 1921, a packed house of 31,000 fans watched the University of Chicago host Princeton in a matchup of top-ranked teams, as millions listened to a nationwide radio broadcast of the game, college football's first. While the University of Illinois varsity trudged through a losing season in 1922, the team's fans exchanged exciting accounts of a dashing back running wild on the school's freshman team. His name was Harold "Red" Grange.
Amid the energy and spirit of innovation prevailing in Chicago, Halas was optimistic about his team's prospects. Sports fans around the country were agape at the exploits of baseball's Babe Ruth, boxers Jack Dempsey and Gene Tunney, and tennis star Bill Tilden. Soon, Grange would join their ranks as a headline-making sensation. Was there any reason pro football and the Chicago Bears could not attain a similar level of renown?
But Halas's optimism was sorely tested. Aside from coaching his team and playing for it, he wrote press releases, courted sports editors, and traveled around the city selling pro football, but the Bears received little coverage and cultivated few fans. If 8,000 attended a game, that was a good day. Many games drew far fewer. Although Halas had turned a profit in 1921, his expenses mounted, and he continually borrowed money from a football-loving bank officer to keep the Bears afloat over the next few years. In the summer and early fall months, before his ticket revenue started rolling in, he needed help paying his bills. "In truth," Halas would write, "the Bears lived hand-to-mouth."
#
# MARA: THE PROMOTER
IN 1900, IN THE THICKLY POPULATED LOWER EAST SIDE OF Manhattan, a young man named Timothy James Mara began to carve out a life. He was thirteen years old, tall and pale and husky, a cop's son living with his parents and an older brother in a neighborhood dominated by Irish expatriates. Mara attended public schools and worked a newspaper route that took him straight up Broadway from Wanamaker's to Union Square, through crowds of newly arrived Chinese, European, and Jewish immigrants.
Although the city was full of young men with similar backstories, Mara would never be lost in a crowd. Outgoing and irrepressible, he had a glib tongue, quick mind, and wry smile that seldom faded as he worked the city's nooks and crannies. Decades later, his grandson, John Mara, said, "He was one of those people who filled up a room." That was true even as he delivered papers as a youth. His route took him into bookmaking parlors and Tammany Hall political meetings, where he met the wealthy, famous, and connected. He did not cower from them, awestruck. He thrust out his hand and introduced himself.
As with young George Halas in Chicago, sports helped Tim shed stereotypes as a son of immigrants; he became part of America's cultural mainstream through horse racing, one of the country's popular diversions at the time. While on his newspaper route, he met and befriended legal bookmakers who operated out of hotel rooms and storefronts, taking bets on races. Mara noticed they seemed to "live best and work the least," he later said. The bookies liked him, and several hired him to "run" bets. While delivering papers in the morning, he took his customers' wagers and passed the money on to the bookies. That evening, he distributed any winnings. The job required him to be organized, sharp, and, above all, honest. Some customers tipped him when they won or gave him a nickel for every bet he toted.
When Mara was fifteen, in 1902, his father died suddenly, and he quit school, which seldom interested him, anyway. He ushered at the Ziegfeld Theater, sold peanuts and programs at Madison Square Garden, and worked at a lawbook bindery. But he craved action and soon was booking bets himself. He already knew the fundamentals of the trade. He studied the horses, set odds, paid off the winners, and pocketed the rest. His clientele swelled. "He didn't have a lot of education but he had street smarts," his grandson said. "His father dying young impacted him greatly. He was forced to grow up, and he met a lot of Damon Runyon-like characters and developed certain instincts that served him well for his whole life."
In 1910, when anti-gambling legislation shut down New York horse racing for four years, Mara, operating out of a hotel suite, took bets on races in other states. In 1921, he set up a stand in the betting enclosure at Belmont Park—a hall where bettors shopped among a row of bookies for favorable odds in the frantic minutes before a race, then bet directly with the bookie they selected. Mara sat on a high stool with a fistful of bills in one hand, an odds board in the other, and a noisy jumble of bettors around him, winking at customers, making jokes and change as he constantly recalculated odds. The work introduced him to the glittering world of wealthy racing families such as the Vanderbilts, Astors, and Whitneys. They befriended Mara and invited him to their parties, quite a leap for an Irish kid from Lower Manhattan. In the summers, he followed them upstate to the races at Saratoga, where he opened another betting stand.
If horse racing was his favorite sport, boxing was his second favorite. He rooted for Gene Tunney, the champion heavyweight and light heavyweight who, like Mara, had Irish roots and had made a name in New York. Mara longed to get into the fight game. One of his best customers at the racetrack was a wealthy building contractor who had been a childhood friend of Al Smith, the governor of New York. That connection Mara helped obtain licenses to stage Tunney's fights and several others at Madison Square Garden and the Polo Grounds. While promoting fights, Mara became friendly with Tunney's manager, Billy Gibson, a prominent figure in New York boxing. Gibson had previously managed a lightweight champion and other successful fighters, and had provided some of the financial backing for a pro football franchise that flopped in New York in the early 1920s.
The football team was known as Brickley's Giants. Charlie Brickley, a former Harvard star, now in his early thirties, was the head coach, co-owner, and only well-known player on the roster. College fans recalled him as a drop-kick specialist who had once booted five field goals through the uprights as Harvard defeated Yale, 15–5. After graduating, Brickley coached at Johns Hopkins, Boston College, and Fordham while occasionally playing semipro ball. Optimistic about the future of "paid" football, he organized the Giants and joined the APFA in 1921. Unfortunately, New York's first pro football team was badly outmanned. Brickley's Giants played only two official league games, losing both by a combined score of 72–0. "Little can be said for the brand of football displayed," the _New York Times_ reported. The only interesting moment was a drop-kicking contest between Brickley and Jim Thorpe, now with the Cleveland Indians, at halftime of one of the games. The Giants dropped out of the APFA and played a few exhibitions before folding in 1923.
In the summer of 1925, Joe Carr, president of the enterprise now known as the National Football League, came to New York to convince Gibson to invest in pro football again. The NFL was flailing. The league's roster of teams, located mostly in midwestern and eastern factory towns, changed significantly every year. After watching so many clubs struggle and fail in his three years as the league's president, Carr believed the whole enterprise would collapse if it could do no better than the Duluth Kelleys and Kenosha Maroons and failed to develop fans in metropolitan areas.
When Carr traveled to New York, the start of the 1925 season was two months away. On a summer afternoon hot enough to make the men grateful for ceiling fans, Carr sat down in Gibson's office, having brought along Dr. Harry A. "Doc" March to help twist Gibson's arm. A pipe-smoking, white-haired physician, originally from Canton, Ohio, March was a man of many interests. He ran a musical troupe, March's Musical Merry Makers, which toured the East and Midwest. He had been the team physician for the Canton Bulldogs in Jim Thorpe's day. Football was his true passion—not playing it but running a team. He now lived in New York and wanted a role if the NFL put another team there. But he did not have money to buy the franchise. "Doc March was looking for an angel," Mara said later, "and I was it."
When the meeting began, only Gibson, Carr, and March were in the room. It is not known whether Mara showed up coincidentally or had been invited by Gibson; he may have come to ask for a piece of Tunney, his favorite fighter. Regardless, he knocked on the door and joined the meeting, unaware of how much the next hour would shape the rest of his life.
DESPITE THE HEAT, MARA WAS FORMALLY DRESSED DOWN TO his derby hat, and he was more wealthy and prominent than he ever could have imagined when he was delivering newspapers on Broadway at the turn of the century. He was thirty-eight years old and devoutly Catholic, with a wife, Lizette, and two sons, Jack and Wellington, ages sixteen and nine. His bookmaking business was booming. He also owned a coal company, Mara Fuel, and a lawbook bindery, the latter serving primarily to facilitate racing bets from lawyers and judges. He promoted boxing matches and would soon also try his hand at stock trading and selling scotch. "I never passed up the chance to promote anything. Not just for the profit, but for the challenge," he would say later. Decades later, Mara's grandson shook his head and smiled at the thought of his grandfather's multifaceted business world. "I'm not sure you can still live the kind of life he did, get involved in so many things, take so many chances. I'm not sure that works today," John Mara said.
In a bookie's vernacular, Tim Mara was the longest of shots to join a pro football league. He did not follow college football and barely knew the sport was played professionally. "He knew about boxing and horse racing, but nothing about football, that's for sure," John Mara said. When he sat down with Carr, Gibson, and March, Gibson had just rejected the idea of funding a new NFL team in New York. Gibson had lost money on Brickley's Giants and was not about to place another bet on such a risky proposition.
"Say, maybe you'd be interested in this, Tim. These men here have something you may want to buy," Gibson said.
"What is it?" Mara asked.
"A professional football franchise in New York," Gibson said.
"How much does it cost?" Mara asked.
No one knows who replied, though it was probably Carr, and the answer was either $500 or $2,500, depending on which version of the story one believes. "I was told it was $500, but it doesn't matter," John Mara said.
Mara initially balked. What did he know about football? The other men tried to persuade him, with Gibson offering to become a minority investor. Carr admitted Mara "might lose money at first" but eventually would turn a significant profit because "the future of pro football is tremendous." Carr's honesty and optimism were persuasive. Mara soon came around.
"I'll take it," he said, reportedly adding, "Any franchise in New York ought to be worth $500." Then he paused and said, "Now what do I do?"
Doc March jumped in. "Just leave that to me," he said.
Thus were born the New York Giants, owned by a man who barely knew football's basic rules. "He just thought, 'I'm a promoter... in New York... this is sports... it can work,'" Mara's grandson explained later. Mara himself would eventually laugh about the team's unusual origins. "The Giants were born out of a combination of brute strength and ignorance," he said. "The players supplied the brute strength and I supplied the ignorance."
But though he knew nothing about football, he did know how to run a business. Before leaving Gibson's office, he made Gibson the team president and March the secretary, responsible for building the squad. Mara was responsible for writing checks, and he wrote many in the coming weeks, quickly discovering this was not a small investment. The team needed uniforms and equipment, not to mention players and coaches. Seeing that he was spending more than he wanted, Mara asked friends to join him in the venture. Most turned him down and suggested he had lost his mind. A few said yes. Even with help, though, most of the cost still fell to Mara.
Meanwhile, March began to construct the team. He started by hiring a coach, Bob Folwell, a former wrestler whose penchant for foul language had cost him several college coaching jobs. March then signed "name" players such as Century Milstead, a tackle from Yale, and Henry "Hinky" Haines, a Penn State running back.
Mara, the innate promoter, believed the roster needed more exciting players for the Giants to compete, both on the field and for the attention of fans. It was a thrilling time for sports in New York City. Babe Ruth was bashing home runs. Tunney fought regularly at Madison Square Garden, Yankee Stadium, and the Polo Grounds, and Jack Dempsey, the world heavyweight champion, also fought in the city. The Army-Navy college football rivalry drew sellout crowds, as did games featuring Notre Dame. Fordham and New York University fielded popular football squads. Desperate to get the Giants noticed, Mara struck a deal with Jim Thorpe, hoping his presence on the team would generate newspaper coverage. But March doubted that Thorpe, now thirty-eight, could still play, given his sore knees and fondness for alcohol, so while his teammates would be paid either by the game or for the season, Thorpe would earn $250 per half, in case he tired and had to sit on the bench after halftime.
The Giants debuted on Sunday, October 11, 1925, taking on the Providence Steam Roller in Rhode Island. The setting underscored pro football's hardscrabble status. The Steam Roller's home field was the Cycledrome, a 10,000-seat oval stadium built for bicycle racing. The field was surrounded by a banked track that cut 5 yards off the corners of one end zone. There was only one cramped locker room and no public-address system. An announcer walked the sideline shouting the score, substitutions, and down-and-distance details through a megaphone. Some 8,000 fans attended the game and sat in temporary bleachers on the banked track, close to the action. Players frequently tumbled into the crowd, eliciting cheers. The Steam Roller, another new team, whipped the Giants, 14–0, eliciting more cheers. Thorpe had a few decent runs, but the Giants never came close to scoring. Mara, traveling with the team, was disappointed.
The next day, the _New York Times_ published a five-page sports section dominated by extensive coverage of the fourth game of the World Series between the Washington Senators and Pittsburgh Pirates. There was also a lengthy roundup of the college football weekend and articles about horse racing and soccer. The Giants' game received no coverage.
To drum up interest for the team's first home game on October 18 against the Frankford Yellow Jackets at the Polo Grounds, Mara hired a publicist, bought newspaper ads, courted sportswriters, and paid for sound trucks to drive around the city blaring details about the game. He walked around with packs of tickets in his pockets but gave most away, unable to sell them. It was a humbling experience. He was accustomed to his ventures enjoying immediate success.
A day before the game, the Giants and Yellow Jackets played at Frankford's tiny home field near Philadelphia. The Giants lost, 5–3, with the decisive points coming on a safety when the Yellow Jackets blocked a New York punt through the back of the end zone in the second quarter. Yet again, the game received no coverage in the _New York Times,_ which devoted its eight-page sports section the next day almost entirely to college football results. Army had defeated Notre Dame, 27–0, before 80,000 fans at Yankee Stadium.
The Giants took a Saturday evening train back to New York after their game. The next day, Mara and his wife and sons attended morning mass at Our Lady of Esperanza Church on 156th Street, then stood outside the church for a few minutes before heading to the game. "Well, I'm going to see if I can put pro football over in New York," Mara told a friend before leaving. The game attracted 27,000 fans. Although less than half had paid for their tickets and the crowd was meager compared to the big college game the day before, Mara was encouraged. This was more interest than he had expected. He hoped the Giants would put on a show. Early in the first quarter, Thorpe took a handoff and stumbled a few yards downfield. Mara, sitting on the bench, turned to his publicist and exclaimed, "Isn't that the greatest run you've ever seen?" A football expert he was not.
Mara's teenage son, Jack, was on the field with him, working a sideline yard marker. Mara's wife and younger son, nine-year-old Wellington, were seated in the stands behind New York's bench. Their side was in the shade, and Wellington came home with a cold, prompting Lizette to suggest moving the Giants' bench to the other side of the field, where the sun shone. "He made that switch and we've been on that side ever since," John Mara said.
In the end, the game was a disappointment. The Giants lost, 14–0, and the Thorpe experiment came to an inglorious conclusion. After losing a fumble in the second quarter, the once-great star limped to the sidelines and pitched forward onto a tarpaulin, either exhausted or drunk, possibly both. He would not earn $250 for playing in the second half. Mara and March had seen enough; the Giants were through with Thorpe.
The good news for Mara was the _New York Times_ finally paid attention to his team, sending a sportswriter, Alison Danzig, to cover the game. "Pro Elevens Clash Before 27,000 Here," read the headline in the next day's paper. Danzig was reasonably impressed, it seemed, writing that the game was "a far cry" from the lamentable pro contests staged by Brickley's Giants a few years earlier. Given the size of the crowd, Danzig wrote, "New York evidently is ready to support a professional league team."
Tim Mara had never seen a pro football game when he started the Giants. (Associated Press)
The game was the first of nine in a row at home for the Giants; they would spend all fall at the Polo Grounds, trying to develop a following. They delivered a victory in their next game, surprisingly routing the Cleveland Bulldogs, the defending league champions, 19–0. But without Thorpe, the game drew fewer than 10,000 paying customers. However, the victory marked the start of an encouraging turnaround on the field. The Giants' defense stiffened, and Folwell's single-wing offense flourished, with Hinky Haines breaking so many runs from his halfback slot that Mara built an advertising campaign around him: "Come See Hinky Haines and His New York Giants!" The Giants proceeded to win seven games in a row.
Their prospects were less bright off the field. Their uniforms were stolen out of their locker room before one game (seized and returned an hour before kickoff), and March and the quarterback were arrested after another game when a minister convinced a policeman that it was illegal to play football on the Sabbath. (It was indeed illegal in Pennsylvania, but not in New York, and a judge quickly dismissed the charges.) Most discouragingly, New Yorkers showed little interest even though the team continued to win. One game drew just 1,200 paying customers. Mara's financial losses piled up. He was paying $4,000 a week in expenses and at least $2,500 a week in gate guarantees to his opponents. By late in the season, he had lost $40,000, a large sum for anyone, including him.
He lamented the situation one day to Governor Smith. "Pro football will never amount to anything; why don't you give it up?" Smith responded. Mara replied that his sons enjoyed the Giants and would "run me right out of the house" if he folded the team. But Mara's patience had a limit and he was nearing it. If he could not figure out how to stop hemorrhaging money, he would have to shut the team down.
THOUGH STILL NO FOOTBALL EXPERT, MARA FOLLOWED THE college game now, recognizing that any responsible pro owner should be able to identify the sport's best young players. In the fall of 1925, Red Grange, the halfback who had exhibited such promise on Illinois's freshman team in 1922, was easily the sport's most dazzling player. Now a senior, Grange delivered so many electrifying performances for the Illini that he made the cover of _Time_ magazine, an honor usually reserved for world newsmakers. Fans across America were desperate to see Grange. Wherever he played, the stadium was full, and the crowd stood and shrieked when he took a handoff, shed tacklers, and broke into the clear, heading for the end zone. That sounded good to Mara. Why not try to lure him to New York? With Grange on the team, the Giants probably would sell enough tickets to wipe out the debt they had rolled up.
To that point, college players never contemplated turning pro until they graduated. But Grange, in a shocking development, had signed a personal management contract with an ambitious theater owner, C. C. Pyle. Informally known as "Cash and Carry," Pyle had convinced Grange to quit school and turn pro as soon as he played his last college game. College coaches such as Stagg and Yost were horrified, as were fans loyal to the college game.
Undaunted, Mara booked a stateroom on a train to Chicago and told March he planned to return with Grange. But he was too late. Pyle had already struck a deal with George Halas: Grange would play for the Chicago Bears for the rest of the 1925 season. Like Mara, Halas was in debt and had been struggling to attract fans to his games. He envisioned Grange as a savior, recognizing that signing him would come at a personal cost. Sure enough, his college coach, Robert Zuppke, a close friend, was furious with him for tempting Grange. Halas hated that, but he was desperate to survive, so desperate he agreed to give Grange almost half of the Bears' gate proceeds—an arrangement so lucrative for the player it would have wiped out most NFL teams.
But there also was good news for Mara. Halas and Pyle were planning a cross-country tour for the Bears, expecting to sell tens of thousands of tickets and rake in a fortune. More than anything, they wanted to play in New York. Mara left Chicago with a date for a game at the Polo Grounds. The Bears and Giants would play on Sunday, December 6. Mara sent a telegram to March:
Partially successful STOP
Returning on train tomorrow STOP
Will explain STOP
Tim Mara
March had no idea what that meant. Mara elaborated when he arrived. "Grange will play in the Giants-Bears game," he said, "but he will play for the Bears." It was shame Grange had signed elsewhere, Mara said, but hopefully New York fans would still pay to see him.
After the game was publicly announced, "there was almost a riot" among fans clamoring for tickets at Mara's office at the Knickerbocker Building, where the Giants were headquartered. They sold 15,000 tickets on the first day and another 25,000 in the next two days. Mara bought newspaper ads, rented sound trucks, and kept the story in the papers, building momentum in the days before the game. Babe Ruth had bought tickets, Mara announced. Gene Tunney would speak to the Giants in the locker room before the game, he said. Soon, all the Polo Grounds' 3,482 box seats were gone, and one hundred sportswriters had wired for credentials.
Meanwhile, Grange and the Bears were playing their way toward New York. Their barnstorming tour began with a pair of games at Cubs Park in Chicago. The Bears and Cardinals played a scoreless tie before a capacity crowd of 36,000 on Thanksgiving. Three days later, Grange threw a touchdown pass in a win over the Columbus Tigers that drew 28,000. The Bears then went on the road. An exhibition in St. Louis drew 8,000 fans in a blizzard. A league game against the Yellow Jackets at Shibe Park in Philadelphia drew 36,000, a capacity crowd, and Grange scored two touchdowns in Chicago's 14–7 win. For the first time, pro football was making front-page news. New York was the next stop.
After a week of rain, the skies cleared on game day. Hours before kickoff, fans began to gather on the streets around the Polo Grounds. Scalpers sold tickets for three and four times face value. Squadrons of extra police assigned to the event were overwhelmed. The crowd swelled close to 70,000, well over the stadium's capacity. Fans stood in stairwells and on landings, straining to see the field. As the teams warmed up, a marching band played, and several thousand fans wandered the field, having been assigned temporary end-zone seats. Shortly before the opening kickoff, Mara had to clear the field so the game could begin.
The fans roared as Grange led the Bears onto the field, his red hair glinting in the sun. The Giants had not lost in several months, but the Bears brought them back to reality, taking a 12–0 lead. Grange gave a solid all-around performance; by the end of the day, he would rush for 53 yards on eleven carries, catch one pass for 23 yards, and complete two of three pass attempts. The crowd went wild when he touched the ball, but quieted after he was kicked in the arm late in the first half, resulting in an injury that would linger for weeks. Grange spent the third quarter on the bench with a jacket over his shoulders, his day seemingly over.
When the Giants scored a touchdown to make the score 12–7, Grange threw off his jacket, returned to the field, and provided the magical moment the fans had come to see. When a pass by the Giants' quarterback sailed over a receiver's head, Grange grabbed the ball out of the air and raced to the end zone for a touchdown that clinched a victory for Chicago. The final score was 19–7.
Counting the gate receipts after the game, Mara was stunned when they added up to $143,000. Even after Grange, Halas, and Pyle received their sizable cuts, Mara had made enough to erase his debt and even put the Giants in the black for the season. "I was about ready to toss in my hand until Grange turned pro," Mara said later. "He proved that pro football didn't have to be a losing proposition. That more than anything else kept me in pro football."
HALAS AND PYLE HAD ARRANGED A BRUTAL SCHEDULE FOR Grange and the Bears. Two days after playing in New York, they took on a sandlot all-star team at Griffith Stadium in Washington, DC. Only 5,000 fans attended. Grange was limited by his arm injury. The promoter lost money. The very next day, the Bears were in Boston, playing the Providence Steam Roller before 18,000 fans. Grange left the game in the third quarter because his arm was sore. The day after that, the Bears lost badly in Pittsburgh to a local all-star team, with Grange unable to perform after the first quarter. He was booed as he walked to the locker room, where it was determined his injury was a broken wrist. Two days later, he did not suit up in Detroit, the Bears absorbed a 21–0 defeat, and the promoter refunded the proceeds from 9,000 of the 15,000 tickets he had sold.
But after taking a break, Halas and Pyle resumed the barnstorming tour in late December with three games in Florida, one in New Orleans, and five on the West Coast. Grange's injury had healed. He raced 70 yards for a touchdown in Tampa, tossed a scoring pass in Jacksonville. A crowd of 75,000 watched the Bears defeat a club team in Los Angeles. By the time the tour concluded in late January with a victory over an outmatched local all-star team in Seattle, the Bears had played seventeen games before slightly fewer than 300,000 spectators since leaving Chicago in early December. Although the show flopped at some stops, it had attracted the interest of famous syndicated sportswriters such as Grantland Rice, Damon Runyon, Westbrook Pegler, and Ford Frick, whose columns on Grange, although not always positive, introduced the idea of "paid football" to millions of readers. For the first time, pro football was treated as more than just a sandlot game.
The publicity came at a good time for the NFL. While the press followed Grange, several embarrassing incidents revealed the league's status as a precarious, small-time endeavor. The Milwaukee Badgers were caught using high school players in a game. The Pottsville (Pennsylvania) Maroons were suspended and stripped of the league title for defying a rule against playing an exhibition game in another team's home territory. (The game was in Philadelphia, home of the Frankford Yellow Jackets, against a team that included the members of the famed "Four Horsemen" backfield, who had led Notre Dame to a national championship.) But these incidents received little newspaper coverage because of Grange's dominance.
While partnering with Halas on the tour, C. C. Pyle had recognized that the NFL was not a sturdy institution; many of its franchises were barely surviving. But Pyle had just become the first person to make real money on pro football. He and Grange netted some $250,000 apiece on the Bears' tour, while Halas made $100,000. Now Pyle wanted to make more. At an NFL owners' meeting on February 6, 1926, shortly after the end of the tour, he announced that he and Grange had secured a five-year lease on Yankee Stadium covering every Sunday and holiday date from October 15 to December 31. He was starting his own team in New York with Grange as the star.
"I have the biggest star in football and I have the lease on the biggest stadium in the country and I am coming into your league whether you like it or not," Pyle declared. Several owners practically shouted with joy. They envisioned Grange coming to their cities, selling tickets, and stirring excitement. A sense of euphoria spread through the room. But Tim Mara sat silent, stewing. He had started the Giants with the understanding that New York was his territory. Living in Grange's shadow was not his plan. And although his own interests dominated his thoughts, he also had the league's interests in mind. Should a player and his "representative" be able tell the owners how to run their business? Would the owners also allow the next great player to just invade another team's turf?
Mara stood and stated his case. Joe Carr, who was running the meeting, recognized Mara was correct and professed his support. But the president also arranged for Pyle and Mara to meet, hoping they could agree on a deal that satisfied both. Could the new team play in Brooklyn, perhaps? Carr hoped so; he naturally saw the benefit of having Grange in the NFL.
The meeting was bound to fail. Mara had found Pyle obnoxious from the day they met. When Carr brought them together in Detroit, Mara made it clear he loathed the idea of Pyle operating a team anywhere in New York. Pyle had a shrewd, innovative cast of mind, but he had met his match. Mara reportedly almost took a swing at Pyle, who stalked out of the meeting even more determined to proceed. "No blasted Irishman is going to keep me out of New York!" Pyle supposedly told Grange.
At Carr's urging, the other owners supported Mara, leaving Pyle outside of the NFL. Pyle quickly pivoted, devising a plan to start a new league with a Grange-led New York franchise as its flagship. The team would be called the Yankees, Pyle said, and New York's fans surely would flock to see Grange. He suggested the new team would run Mara and the Giants out of town.
In the coming years, several upstart pro football leagues would form and challenge the NFL, seeking to take over, or at least share, the nascent sport. Each time, as with this first challenge from Pyle, the NFL's defense of its turf began with Mara and the Giants. The upstart leagues all put teams in New York, recognizing the necessity of success in America's largest market. The new teams challenged Mara at times when the Giants were not consistently profitable, testing Mara's patience, fortitude, business agility, and, very likely, his cash reserves. If Mara had ever tired of it all and ceded New York to a newcomer, the NFL might have been eclipsed.
But he did not. When he heard about Pyle's new league, Mara dug in for a fight, fearing that the likeliest outcome was both teams would struggle. There just was not enough interest in pro football to support two New York teams, Mara believed. "I didn't make enough money last year to stuff a hat brim," he told a reporter. "If Grange carries out his threat to put a team in New York and conflicts with our Sunday dates, neither one of us will make a nickel."
By the fall, Pyle had organized a ten-team venture known formally as the American Football League and informally as the "Grange League." It featured one former NFL squad, the Rock Island Independents, and new teams such as the Boston Bulldogs and Los Angeles Wildcats. It kicked off with high hopes and an optimistic motto: "Football for all and all for football." Carr, in an interview with Don Maxwell, sports editor of the _Chicago Tribune,_ said he welcomed the challenge of a rival league and warned Pyle about thinking it was a get-rich venture. "Oh, it's a great game, this pro football. But it's never been a great money-making game," Carr said. "Take that old team we called the Columbus Panhandles. I organized that bunch 20 years and more ago. We made some money, but I didn't get rich. No one has in this pro grid game, and a lot of us have gone broke thinking we would."
The AFL's season began encouragingly, with the Yankees drawing 22,000 fans to games in Cleveland and Philadelphia, the latter more than double what an NFL game at the same stadium drew a week later. But fans quickly lost interest. Grange, playing on an injured knee, could not replicate the dazzling runs that had made him famous. Crowds for most games shrank to a few thousand fans. Several AFL franchises folded in October, more in November. Only four were operating by the end of the season.
The NFL was also struggling badly. Its product simply was not exciting. Of 116 official league contests in 1926, almost three-fourths ended with one team having failed to score. Almost 10 percent of the games ended scoreless. There were twenty-one teams vying for the league title, but many drew meager crowds. Mara was among those experiencing problems. His usual arsenal of marketing tricks failed to lure fans to the Polo Grounds. A succession of rainy Sundays did not help. Just 5,000 fans attended one game. The return of Jim Thorpe, back with the Canton Bulldogs, drew 35,000, but most of the crowd came for a high school game that preceded the pro game, and Thorpe never left the bench.
Trying to attract attention before a mid-November game against a team from Los Angeles, Mara and the Giants resorted to a stunt. One of their players carried a football to the top of the twenty-three-story American Radiator Building on West Fortieth Street. Hinky Haines was stationed on the sidewalk below, by the building's entrance. The idea was to complete "the longest forward pass on record," according to the _New York Times._ On the first attempt, the ball hurtled downward, hit the sidewalk, and exploded. A third attempt knocked Haines over. He finally made the catch on the fifth try, and onlookers applauded, but that Sunday's game drew another small crowd.
Obsessed with the Yankees, Mara ascended to the top of the Polo Grounds one Sunday when both teams had games and trained binoculars on nearby Yankee Stadium. "There's no one over there, either!" he exclaimed. His fears had been realized. Pyle and the Yankees lost $100,000 during the season, after which the AFL folded. Mara lost $40,000 and was also tempted to give up. He again had doubts about pro football's future. How could he not? But he still believed it was possible the sport could become a winner, and, more importantly, his sons, Jack and Wellington, loved that he owned the Giants. "It was a challenge just to stay afloat. I think he was tempted many times to get out. He had a hand in many businesses, and this one was not profitable," his grandson, John Mara, said. "He enjoyed going to the games and being a part of it, but his sons were the ones who developed a passion for it. He would have sold the team and gotten out if they hadn't been so excited. I'm sure of it."
WHEN PYLE APOLOGIZED TO MARA AFTER THE DISASTROUS 1926 season, the NFL's owners relented and permitted him to bring his Yankees, with Grange, into their league. But, at Mara's insistence, the deal with Pyle put severe limits on the Yankees, who were permitted to play just a few games per season at Yankee Stadium, never conflicting with a Giants game at the Polo Grounds. In essence, Mara controlled when Pyle's team played. It was a terrible deal for Pyle, whose fate was further sealed when Grange suffered a serious knee injury early in the 1927 season and was unable to play. The football Yankees would fold before the decade ended. The Giants, meanwhile, won the NFL championship in 1927, as if to reward Mara for having triumphed in pro football's first war. It would not be the last.
#
# MARSHALL: THE SHOWMAN
EVEN AFTER GRANGE'S TOUR IN 1925 AND EARLY 1926, most American sports fans viewed pro football as a dubious enterprise, believing it lacked tradition, class, and consistent quality—the elements that had helped make college football so popular. But pro football had company at the bottom of the nation's sports ladder. Pro basketball, also in its infancy, was even more obscure.
Unlike football, basketball still was not popular on college campuses. The pro game consisted of a scattershot collection of club teams located in the East and Midwest. Some had formed leagues such as the Central Basketball League, Eastern League, and Interstate Basket Ball League, but these tenuous coalitions never lasted long. Players jumped from team to team, sometimes from one night to the next, in search of better pay. Owners ran up debts. Meager crowds were the norm.
As with pro football, though, the sport featured zealous team owners who believed it would eventually attract a larger following. Max Rosenblum, a department store magnate in Cleveland, owned a team, as did George Preston Marshall, the operator of a chain of laundries in Washington, DC. In 1925, they and several other owners convinced Joe Carr to help them put together a "major" league. The American Basketball League tipped off in the fall.
Carr talked Halas into starting a team in Chicago. Halas had played basketball at Illinois, so he understood the game. He hoped the team would provide revenue in the winter and early spring, when the Bears were not playing. Carr, becoming a close friend, was optimistic about basketball's future. Halas called his team the Bruins, continuing with his Cubs/Bears theme.
Of the basketball league's other owners, Marshall most impressed Halas. Tall and ruddy faced, with slick-backed hair and blazing blue eyes, Marshall had taken a small laundry business and built a chain with several dozen locations. Palace Laundry and Dry Cleaning was ubiquitous in the nation's capital and had made Marshall a wealthy man. He ate at expensive restaurants, drank at stylish clubs, and lived out of hotel suites. A driver chauffeured him around Washington in a limousine. He had just turned thirty. Halas had never met anyone like him.
A former actor, Marshall promoted his laundries with a theatrical flair. The presentation was just as important as the product, he believed. His stores were always freshly painted blue and gold, with bright flower arrangements in the front windows. His employees wore crisp linen uniforms, also blue and gold. His delivery trucks—painted blue and gold—were everywhere. And Marshall had a knack for devising effective sales campaigns. Once, he took out a full-page newspaper ad that was entirely blank except for a disclaimer at the bottom: "This page cleaned by Palace Laundry and Dry Cleaning Company." Thinking a basketball team could help promote his business, Marshall bought a Washington-area semipro team known as the Yankees in 1923. Marshall renamed them the Palace Five. Some fans called them the Laundrymen. Their best player, George "Horse" Haggerty, was a hulking interior player best known as the first man able to palm a basketball.
When the Palace Five joined the ABL in 1925, Marshall moved their home games to the Arcade, a 4,000-seat arena in the city's northwest quadrant. Game nights became spectacles. There was a preliminary competition, usually a matchup of local high school basketball squads, followed by a game between the Palace Five and a league rival. The evening culminated with a dance on the court, with the Meyer Davis Palace Five Orchestra providing music.
Like Tim Mara, Marshall knew how to draw a crowd. The Palace Five developed a following. After several winning seasons, though, the team lost eight straight games at the start of the 1927 campaign. With his crowds dwindling, Marshall gave up, selling the franchise to a Brooklyn club in another league. Pro basketball had become "a big business requiring more of my personal attention than I can give it without neglecting my laundry interests," he told the _Washington Post._ In truth, it remained a failing sport.
Halas was disappointed about Marshall's departure from the league. Halas had brought his Bruins to Washington and thoroughly enjoyed Marshall's lively game-night show. Games in other cities seemed drab by comparison. Halas's own home games at the Illinois National Guard Armory, on Chicago's North Side, were hardly spectacles. Instead of following Marshall's lead and giving up, though, Halas doubled down on his investment, moving the Bruins' home games to the larger Chicago Stadium. "I went to a few games. I remember the coach's wife became good friends with my mother. But there was never much attendance," Halas's daughter, Virginia McCaskey, recalled.
When the ABL suspended operations in 1931, Halas finally disbanded the team. Pro basketball would not gain traction with the public until the late 1940s. But the ABL, nevertheless, had quite an impact on American sports. It was where Carr, Halas, and Marshall first worked together, a partnership that eventually produced a sporting success story unimaginable at the time.
IF THE STORIES MARSHALL LIKED TO TELL ABOUT HIMSELF can be believed, he began honing his flair for showmanship as an eleven-year-old in Grafton, West Virginia, a railroad and coal mining town where he was born in 1896. He had a business selling rabbits, using the proceeds to buy marbles and minor league baseball tickets. Unable to sell a common momma rabbit, he took out a newspaper ad offering a "fine Jacksonville hare" for sale. That was inaccurate, but the ad attracted customers, and Marshall sold the rabbit for three times the normal price. "I've been guilty of promotional ideas and being a showman ever since I can remember," he later wrote.
Grafton, a town of 5,200, was almost entirely white and had a distinctly southern sensibility. Marshall, the only child of the local newspaper publisher, was descended from Confederate officers. His segregated upbringing nurtured views on race that he would carry into adulthood.
Though not an outstanding athlete, Marshall enjoyed sports. In the summer, he was the batboy for the local minor league team. In the fall, he organized his friends into a sandlot football squad that competed against boys from other towns. Marshall did not play, but he sold tickets to the games, making as much as twenty-five dollars per contest. Already, he was interested in the business of sports.
When he was a teenager, his father took possession of a laundry store in Washington, DC, as payment on a debt. The family moved from Grafton to the nation's capital. Marshall attended Central High, a segregated public school, and the private Friends Select School. He also attended Randolph-Macon Academy in Front Royal, Virginia. But schoolwork bored him. Tall, slender, and darkly handsome, he dreamed of becoming an actor and joined a troupe at Poli's Theater in Washington. Falling in love with the lights, music, and applause, he quit school to pursue an acting career. He liked to call himself the Magnificent Marshall; he would never be known for modesty. Initially, he enjoyed relative success, cast in roles both in New York and with a touring company. "I persisted in the conviction that I was a budding Barrymore," he would write, but, in the end, "a number of producers differed" with his assessment, and he had to admit he "was not much of an actor."
From early 1917 until late in 1918, he served in the army during the Great War, mostly in a machine-gun company at Camp Meade in Maryland. He never left the United States and returned to a changed family dynamic. His father had died during the war, and now Marshall had a $5,000 life insurance payout, a mother to support, and a laundry business to run. "My playing days were over," he explained. It was time to make money, ideally lots of it. The Magnificent Marshall did not intend to live quietly.
He dabbled in the theater business, investing in Broadway shows and producing performances at segregated venues in Washington and Baltimore. One of his favorite plays was _Getting Gertie's Garter,_ a bawdy sexual farce set in a hayloft. But he soon gave up the theater business, finding his father's modest laundry operation more profitable. In Washington, a growing city with a transient population of federal government employees, there was a need for laundry services. Marshall beat out his competitors with catchy slogans and relentless promotion, which included the blue and gold uniforms of his basketball team, with "Palace Laundry" emblazoned across the chest. His laundry chain expanded from two stores to two dozen and kept growing. "Showmanship provided the answer," he wrote.
Besides promoting his business, Marshall shamelessly promoted himself, making himself the center of attention on Washington's social circuit with his good looks, loud voice, and opinions on all subjects, many reflecting his conservative politics. Every night became a performance. Marshall could be found at Duke Zeibert's, the popular bar and eatery, or the Shoreham Hotel, where beautiful people gathered on the terrace to talk politics. Even in a city of large egos, Marshall stood out. Whatever situation he was in, he "considered it a lost opportunity were he not the center of attention," a _Washington Post_ sportswriter would write. Another journalist would say that Marshall "is not always offensive but he is never merely inoffensive. He dominates any group of people he finds himself in. He does not hold conferences, he holds court."
Marshall married a Ziegfeld Follies showgirl, but his incessant carousing doomed their union. He made no secret of his true goal. Raised in Appalachia, he sent out Christmas cards featuring himself with a laundry sack over his shoulder as he climbed a ladder marked "society." He realized his grandiose ambitions, becoming a staple of newspaper society columns in both Washington and New York, where he kept a suite at the St. Regis Hotel and was often seen attending Broadway openings and staying out late at fashionable nightspots such as the Stork Club.
George Preston Marshall. (Associated Press)
Nothing derailed him. When his nocturnal lifestyle ended his first marriage, he began dating starlets and actresses, including Louise Brooks, the former silent-movie star who glamorized the bobbed haircut. She playfully called Marshall "the West Wash King." When the stock market crashed in 1929, plunging millions into economic hardship, Marshall again stood out, this time by surviving in style.
His continued business success afforded him "more time for baseball, football, and basketball games," as he later put it, and he still corresponded with Joe Carr, his friend from the basketball league. Now Carr wanted him to buy into the NFL; running the football league was still Carr's primary job. Marshall was skeptical. Even by 1929, almost a decade after George Halas had founded the Chicago Bears and helped bring pro football into existence, the NFL was not an impressive venture. Twelve franchises had disbanded in the past four years. Four new ones had joined the league, all destined to fail. Carr wanted Marshall to back a team in Boston, where a previous franchise had lasted just one season. Putting another team in Boston did not sound like a good idea, Marshall thought.
But Carr was persistent, and Halas, another friend from the basketball league, also kept prodding Marshall to try the NFL. Finally, Marshall agreed to take the prospect seriously. On November 15, 1931, he and several friends were among a crowd of 20,000 at a game between the New York Giants and Halas's Chicago Bears at the Polo Grounds. The Bears won, 12–6. After what he called the "thrilling" contest, Marshall and company gathered for drinks. The others were Jay O'Brien, a New York investment banker; Vincent Bendix, a midwesterner who had made a fortune manufacturing starters and brakes for automobiles; Larry Doyle, a New York stockbroker; and John "Jack" Hearst, the son of newspaper publisher William Randolph Hearst. They met at Hearst's apartment in Manhattan.
According to Marshall's version of the evening's events, O'Brien asked, "Why can't we have a football team, the best in the country?" Marshall explained that it cost at least $25,000 to get a team going and operate it for a season, and "we probably don't want to shoot that sum on an enthusiasm." But the others, except for Hearst, were interested. Even when Marshall said the league wanted them to run a team in Boston, they wanted to invest. In fact, one said he knew the owner of baseball's Boston Braves and could arrange a cheap lease deal for the team at Braves Field. By the end of the night, everyone had agreed to invest $7,500 to get the project started. "My worst nature got the best of me," Marshall would later say. He called Carr with the news. The NFL president was delighted. Marshall's Boston team would kick off in 1932.
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# BELL: THE PROFLIGATE SON
AS THE TWENTIETH CENTURY BEGAN IN THE UNITED States, the richest 10 percent of the population amounted to a royal class. They owned 75 percent of the country's assets. They paid no income tax. They lived in ornate mansions on Fifth Avenue in New York; along the seaside boulevards of Newport, Rhode Island; and in other bastions of power and prestige such as Philadelphia's Rittenhouse Square, "home to more millionaires per square foot than any other American neighborhood except New York's Fifth Avenue," according to one account. This was Bert Bell's world as a boy.
Rittenhouse Square itself was a public park designed by William Penn, the English entrepreneur who founded Pennsylvania in 1681. Beginning in the 1850s, wealthy families seeking refuge from immigrants and increasing commercial development had surrounded the park with brownstone and marble mansions designed by leading architects. By 1900, the area's residents included John Wanamaker, founder of the famous department store; Alexander Cassatt, president of the Pennsylvania Railroad; and William Weightman, a chemical manufacturer who became Philadelphia's leading real estate owner.
John Cromwell Bell and his wife, the former Fleurette de Benneville Myers, fit right in. Bell was a well-known corporate attorney with a future in politics. Fleurette's relatives had wielded influence in Philadelphia since the colonial era. They were the quintessential young power couple. Indeed, we know far more about Bert Bell's family history than we do about Halas's, Mara's, or Marshall's because his family had been prominent for centuries before his birth.
Born in 1862 in central Pennsylvania, John Bell had moved to Philadelphia when he was fourteen. A strong student, he ended up at the University of Pennsylvania, where he studied law and earned a prize for his thesis. He also played varsity football at a time when many of the sport's fundamental rules, such as the scoring worth of a touchdown, were still being debated and frequently revised.
In 1884, Bell's final season, Penn defeated Harvard for the first time. Though he put away his uniform sweater after that, he would continue in the sport for years as a chairman of Penn's football committee and one of the sport's foremost rules experts. In the 1890s, he was second in command to Yale's Walter Camp on the rules committee of the Intercollegiate Athletic Association, the forerunner of the National Collegiate Athletic Association. When the NCAA was formed in the early 1900s out of Theodore Roosevelt's determination to make football safer, Bell was among the organizers.
After college, he rose quickly through Philadelphia's lawyerly ranks and attained prominence. The city's Republican elite eyed him as a potential district attorney candidate, but he turned them down; between his football obligations and his corporate clients, his days were full.
In 1890, at age twenty-eight, he married Fleurette at her family's mansion in northwest Philadelphia. Fleurette's father, Leonard Myers, was a lawyer and Civil War veteran who had been a Republican congressman and close confidant of two presidents, Abraham Lincoln and James Garfield. But it was Fleurette's maternal ancestry that provided her social bona fides; her great-great-grandfather, George de Benneville, was born in London in 1703 to aristocratic French Huguenot parents and raised in the royal court of Queen Anne.
De Benneville eventually renounced the privileged life of an aristocrat after a spiritual awakening and came to America in 1741. Settling in Pennsylvania's Oley Valley, north of Philadelphia, he married Esther Bertolet, the daughter of another influential settler. They had seven children and built a homestead that included a school, church, and medical practice. Trained as a doctor, de Benneville treated and tutored Native Americans as well as local citizens while becoming the first person in the colonies to preach a Universalist faith of salvation for all souls. After his wealthy father-in-law died in 1758, de Benneville moved to Bristol Township, near Philadelphia, where he built an estate and continued to treat patients and preach. Siding firmly with the rebels in the Revolutionary War, he ministered to soldiers but also offered his family's burial yard as a final resting place for a British general who died in combat. Two of his sons became doctors, and a daughter married into the wealthy Keim family of Reading, Pennsylvania. A bountiful family tree sprouted. By the time John Bell and Fleurette de Benneville Myers married in 1890, some 150 descendants of George de Benneville were buried in the family cemetery adjacent to the mansion where the ceremony took place.
The Bell nuptials were labeled "one of the interesting weddings of the week" by the _Times of Philadelphia,_ though it was "a quiet affair, owing to a recent death in the bride's family." (Fleurette's mother had died the year before.) Bell was described as "the well-known lawyer and member of the university football team." Fleurette wore a "gray traveling suit," and "immediately after the brief reception, the newly-wedded couple left on a wedding tour." They settled into a "handsome" three-story home at 334 South Twenty-Fourth Street, a half mile from Rittenhouse Square and across the street from another park, Fitler Square. The Bells employed servants to keep house and a cook to prepare their meals. Their first child, John Cromwell Bell Jr., was born on October 24, 1892, and another son, De Benneville Bell, was born on February 25, 1895.
Philadelphia's Republican leaders continually sought to lure Bell into politics, but he turned down a judgeship and a job in the district attorney's office. Finally, when the district attorney job itself opened up in 1902, Bell "yielded to the persistent demand of the people" and accepted the position "after receiving a petition signed by fifteen hundred members of the bar and many leading citizens of Philadelphia." As district attorney, Bell secured the second-ever first-degree murder conviction of a woman in Philadelphia, and, in a "brilliant" performance, won a verdict in a complex case in which "the leading chemists of the world were pitted against the district attorney's contention that the use of sodium sulfide as a food preservative was deleterious." Upon completing his term, he ran for reelection and won "by a very nattering majority, receiving the support of many opposed to him politically."
In 1907, Bell declined to run for another term and returned to private practice. At a testimonial dinner, the chief justice of Pennsylvania's supreme court said Bell had "followed faithfully the traditions of the office and has given them additional luster." But Bell was enticed back into politics when Pennsylvania's governor appointed him the state's attorney general in 1911. In a history of Philadelphia published the next year, it was written that Bell's "position is evident to all who know aught of the history of the Philadelphia bar and the work of the courts during the last quarter of a century. Throughout his entire professional career he has united the intensely practical with high ideality. Words, looks and actions are the alphabet by which we spell character, and in the life of John Cromwell Bell these have had no uncertain sound."
BELL AND HIS WIFE LIVED "AMID SUCH TURN OF THE CENTURY wealth and prominence that it took John O'Hara more than a dozen books to describe it," the sports journalist Phil Musick once wrote, referencing the Pennsylvania-born novelist who depicted those times. Although 1900 signaled the end of America's Gilded Age in some ways, the Bells enjoyed the trappings of their great fortune well into the twentieth century.
In the early 1900s they hired architect Horace Trumbauer to design a home for them. Trumbauer did not work on a small scale; his previous work included a 110-room mansion for industrialist Peter Widener. Trumbauer would later design the main library at Harvard. For the Bells, he created a commanding three-story brick residence at 229 South Twenty-Second Street, just west of Rittenhouse Square. With a marble staircase and marble archway framing its front door, the home featured three floors of high-ceilinged rooms that looked onto Twenty-Second Street. The staff lived on the fourth floor. It was a home befitting American royalty, destined for the National Register of Historic Places. In 1906 the Bells moved in, when their sons were fourteen and eleven. Like many in their circle, they continued to split time between their city residence and a summer estate, in their case an eleven-acre retreat in Radnor, on the Main Line. According to the Social Register of 1900, the home was known as Blithewold.
The Bells indulged their two sons. De Benneville "had a nanny when he was 2, a pony when he was 6, a tux when he was 12 and a Marmon roadster when he was 17." One of his friends, Lou Little, destined to become a college football coach, later told sportswriter W. C. Heinz, "For a fellow like me, that beautiful city home with the servants and everything was like walking into a hotel. And that summer home was like walking into a country club."
John Bell's sons grew up hearing about the law, politics, and football, their father's passions, and it was assumed they would take a similar path, utilizing the advantages their parents' success and lineage afforded them. John Jr., the dutiful and obliging eldest son, known as Jack, "wanted to follow in his father's footsteps," according to the Pennsylvania Historical and Museum Commission, and he mimicked those steps almost exactly. After his graduation from Philadelphia's Episcopal Academy in 1910, Jack attended his father's alma mater, the University of Pennsylvania. Although he did not play football, he excelled at soccer and tennis while earning a liberal arts degree. Then it was on to Penn's law school, a lucrative private practice, and political appointments that included stints as Philadelphia's assistant city solicitor and assistant district attorney—all before he turned thirty-three. A conservative Republican, Jack Bell was destined for the highest levels of state government.
Though raised in the same circumstances, young de Benneville was different from his older brother. Whenever his nannies lost track of him, they knew they could find him playing football in the park across the street. As a youth, he rejected his fanciful first name, considering it snobbish. He wanted to be called Bert. When friends teased him for it, he slugged them. "If you don't think I had to fight many times to get people to call me Bert, then I must have dreamed of all those schoolyard battles," he said later. At the Haverford School, a prestigious private academy, he was an indifferent student but was described in his senior yearbook as a "hero of countless football, basketball, and baseball battles," and "one of the best athletes in the history of the school." Though he would make his name in football, he also batted .510 as a senior baseball captain. He was a jock and something of a class clown. His classmates voted him "most sarcastic" and "best kidder."
Decades later, Bert's son, Upton, said of him, "Although he came from a proper conservative Republican family, Bert walked with a swagger as a kid and found a way to talk out of the side of his mouth. He didn't want to talk like all of those proper, jut-jawed society people. He decided that everything he was going to do was going to do was in some ways different from the way they acted."
His determination to be different did not include his college choice. That was not negotiable. "He'll go to Penn or he'll go to hell!" his father roared near the end of his high school years. But, unlike his father and brother, Bert meandered through his classes at Penn, uninterested in academic excellence or becoming a lawyer. He "never came to class if the weather was bad outside," according to some football teammates. He would eventually leave Penn without earning a degree.
But, as in high school, he attained prominence in college as an athlete, now as a quarterback for his father's beloved Quakers. Though just five feet eight and 155 pounds, Bell was a "peppery little guy," according to one sportswriter, and "a great field general who is never bluffed and never at a loss for what to do," according to another. His coach praised him as "brainy" after he started in his first varsity game in 1915. He would start at quarterback for the Quakers for most of his time on campus.
While at a preseason training camp outside Philadelphia in 1916, he received word that his mother was gravely ill. Fleurette had suffered a stroke and undergone surgery. Bell set out for home, but his mother died before he reached her bedside. Six days later, he started at quarterback for the Quakers in their season opener and tossed a long pass that set up the only points in a win over West Virginia.
The 1916 season would be the high point of his college career. Bell was briefly benched after an early-season loss to Swarthmore in which he completed just two of twenty passes, but he quickly regained his starting job and "piloted the team in masterful fashion" during an upset win at Michigan. Five thousand fans greeted the team upon its return to Philadelphia. Bell then gave a "faultless" performance in a rout of archrival Cornell. With a record of seven wins, two losses, and a tie, the Quakers were invited to take on Oregon in the Tournament of Roses football game in Pasadena, California.
Played on January 1, 1917, before 27,000 fans, the game was easily the most significant in Penn football history to that point. Outweighed by fifteen pounds per man on average, the Quakers competed well as decided underdogs, generating thirteen first downs to Oregon's eight. But Oregon's Webfoots prevailed, 14–0, scoring both of their touchdowns in the second half. Bell endured such a beating from his rugged opponents that a substitute took his place in the fourth quarter.
Like many teams across the country, Penn's 1917 varsity was impacted by America's expanding involvement in the Great War. Most upperclassmen went into the armed forces, leaving freshmen to man key positions. The Quakers still won nine of eleven games with Bell leading the way. In a decisive victory over a Michigan squad thought to be stronger, he "used such a varied selection of plays that at times he had the Michigan defense bewildered," according to the _Philadelphia Bulletin._
Bert Bell, quarterback of the Penn Quakers. (Penn Athletics Archives)
At the team's end-of-season banquet, Bell was selected as a captain for the 1918 season. But, in another act that belied his rarified social background, he volunteered for military duty with an army mobile hospital unit based out of Philadelphia. Several teammates also volunteered, as did Jack Kelly, a noted oarsman who would later win three Olympic gold medals and gain renown as a developer and the father of actress Grace Kelly. Deployed to France in the spring of 1918, Bell and his friends served at Châtel-Guyon, a health resort that had been converted into a hospital for wounded American and French soldiers as well as German prisoners. It was not a cushy assignment. Germans shelled the hospital, killing several of Bell's comrades. The unit received commendations for helping move patients to safety during the shelling.
Bell "almost never talked about his war experience," his son, Upton, would recall. But he did share lighthearted stories about cavorting through the French countryside in his off-duty hours with Jack Kelly, who became a lifelong friend. They dreamed up a bait-and-switch that worked to good effect. Bell, the big talker, would pick a fight with a tough guy in a bar, but, rather than throw a punch, he offered to bet that his friend, Jack, could whip the tough guy. Frenchmen invariably accepted the challenge, and Kelly, a muscular former bricklayer, invariably won the fight. Many nights ended with Bell and Kelly hurriedly skipping town with their pockets full and grins on their faces.
The armistice brought Bell home, and, in the autumn of 1919, he resumed his life as a big man on Penn's West Philadelphia campus, serving as the football captain and starting quarterback. His return sent expectations for the Quakers' season soaring. Bell is a "brilliant player" and "Penn seems destined to take the leading position in the intercollegiate football world in the East this fall," one columnist wrote. The Quakers overwhelmed their first five opponents by a 237–7 margin, delighting local fans. Penn added 5,000 seats at Franklin Field to meet an increased demand for tickets. But the team's initial success did not last. Bell shanked three punts, missed a field goal, and tossed a crucial interception in a stunning home loss to underdog Penn State. The Quakers then suffered a disappointing loss to Dartmouth at the Polo Grounds in New York when Bell missed a key field goal and failed to bring down two runners on their way to the end zone—a performance lambasted by the _New York Times,_ which pinned the blame for the 20–19 defeat "squarely" on Bell.
He realized he no longer needed football. He was twenty-four, a man among boys in the huddle. He had been to war and back, and now he wanted to enjoy the peace that followed. Although he still enjoyed playing football, he was ready to don a raccoon coat and take part in the Philadelphia high life, with his father paying the bills. "My father and mother gave me everything I ever asked for, and I was a pretty good asker," Bell told W. C. Heinz later.
Three days after the loss to Dartmouth, the _Philadelphia Inquirer_ reported that Bell had lost more than just the game. It turned out he had wagered his Marmon roadster. Bell confirmed the story years later, explaining that his father had just given him the thousand-dollar car, which he added to his stake after he had bet "all the money I had and could borrow" that the Quakers would defeat Dartmouth. Bell's father was surely not pleased to learn the car now belonged to a Dartmouth football fan. John C. Bell Sr., by this point one of Philadelphia's wealthiest citizens, knew his older son, Jack, would never embarrass the family in such a way. Jack was out of law school, married, and working as an assistant city solicitor. But the elder Bell continued to tolerate his rakish younger son's shenanigans. Bert was the one who had played college football, his father's favorite sport, and the one who had volunteered for frontline military service. "Despite their philosophical differences, Bert was my grandfather's favorite child," Upton Bell said. "Jack was the prized one, but my grandfather absolutely loved Bert because Bert was all the things he wasn't. Bert was a gambler, a chance-taker."
Months after playing in his final college game (the Quakers tied Pitt, 3–3, to end their ballyhooed 1919 season with a 6-2-1 record), Bell withdrew from Penn without a degree despite having been on campus since 1914. There was no chance that he would follow his father and brother into the law. Football was what he knew best. He took a job as an assistant coach at—where else?—Penn, which in 1920 hired a new head coach, John Heisman, a Penn grad and former Quaker player who had become a renowned coach at Auburn, Clemson, and Georgia Tech. New York's Downtown Athletic Club would later put Heisman's name on its prestigious award honoring the nation's top college football player.
In 1920, Heisman put Bell in charge of the backfield. Bell's close friend and former Penn teammate, Lud Wray, coached the line. They would hold those jobs for almost a decade as Penn fielded winning teams and drew big crowds. Heisman left after three seasons, but his replacement, Lou Young, kept Bell and Wray and led the Quakers to a 9-1-1 season in 1924. That success prompted speculation that Bell and Wray might soon become head coaches elsewhere, but they stayed at Penn.
When not coaching, Bell was one of Philadelphia's most prominent playboys. A staple of the high-society party scene, he stayed out late, chased girls, drank, and gambled on everything from cards to horse racing to boxing matches and football games. He spent several weeks of every summer with other scions of wealthy families at the horse races in Saratoga, New York. While betting on races during the day and staying out at supper clubs until dawn, Bell met Tim Mara, then known primarily as a bookie from New York, and became friendly with Mara's son, Jack. He also spent time with George Preston Marshall, still a laundry chain owner from Washington, and Art Rooney, a shrewd sportsman from Pittsburgh.
Bell's meager salary as an assistant football coach did not begin to fund his escapades, which included sizable gambling losses, but Bell's father always provided whatever was needed to settle his scores. The elder Bell made only one request of his younger son: that the two eat breakfast together every morning, with Bert wearing a coat and tie, regardless of how much money Bert had lost the previous day or how late he stayed out.
The family never revealed an official tally of Bert's losses, but he squandered so much money that his father eventually demanded that he work off some of the debt. The elder Bell had ventured into real estate and now owned two of Philadelphia's landmark Center City hotels. By 1928 Bert was managing the Ritz-Carlton while continuing to coach at Penn, and he later managed the St. James. But he continued to lose money. Picking the wrong time to try the stock market, he suffered losses at a brokerage house located in the Ritz-Carlton, then reportedly dropped $50,000 in the 1929 crash. His father finally ran out of patience and lashed out angrily at his son during breakfast one day. "Dammit, you're thirty-something and still drinking and gambling and running around. I'm tired of bailing you out! It's time you settled down," he exclaimed. John Bell suggested his son marry the debutante daughter of a friend. When Bert resisted, his father offered to pay him $100,000. Bert "reluctantly" agreed and the engagement was set. But, when he received a chunk of the money, Bert drove straight to Saratoga and lost it at the betting window. He returned to Philadelphia and confessed to his father that he had blown the wedding gift.
"And I ain't marrying that broad!" he exclaimed.
His father responded, "Well, Bert. If that's the way you want it, no more money. You can go run my hotels and do your coaching, or do whatever you want, but that's the last penny you're ever going to get from me. You're not going to see another red cent." Bert Bell had always relied on the safety net his family's wealth provided, but, after testing its limits for years, he could count on it no longer.
PHILADELPHIA WAS A COLLEGE FOOTBALL HOTBED IN THE 1920S and early 1930s, when Penn was a national power. Temple and Villanova opened new stadiums, aspiring to greater prominence. By 1932 the city had hosted more than a dozen Army-Navy games.
There also was pro football in Philadelphia. The Frankford Yellow Jackets, named for the small northeast Philadelphia neighborhood where they played, joined the NFL in 1924 and became consistent winners. C. C. Pyle's infamous American Football League, built around Red Grange, included a Philadelphia team called the Quakers. As elsewhere, the pros lived in the shadows of the college teams. The Quakers won the AFL title in 1926 but folded with the rest of the league. The Yellow Jackets fashioned a 55-22-8 record in their first five NFL seasons and won the league title in 1926, but many of their home games at tiny Frankford Stadium drew no more than 5,000 fans. Pro football was an afterthought in the city.
Though steeped in the college game from a young age—his father had literally helped write the rulebook—Bert Bell did not entirely ignore the pros. In 1926 he served as an informal coaching advisor for the Quakers, whose roster featured several of his former Penn teammates, including Lud Wray. Bell even suited up for one AFL game, against Jim Thorpe and the Canton Bulldogs. But he remained a loyal college football man and continued to coach Penn's backfield through the 1928 season, when he resigned over a difference of opinion with Wray and the head coach about the need for practice scrimmages. (They wanted more; Bell feared they wore the players out.) Without a coaching job in 1929, he still spent his Saturdays at college games, studying tactics. Then, in 1930, he became the backfield coach at Temple, a job he would keep for three years.
Throughout these years, Bell paid little attention to the Frankford Yellow Jackets, who began to struggle after the stock market crash. Unable to sign quality players, they lost eight straight games at one point and finished the 1930 season with a 4-13-1 record. Their attendance plummeted, and not only because the team was bad; many fans simply could no longer afford tickets. When a fire destroyed their stadium before the 1931 season, the Yellow Jackets began splitting their home games between the Baker Bowl, home of baseball's Phillies, and Municipal Stadium, the giant facility that was packed for Army-Navy games. But few of their supporters came to watch them. The press began calling them the Philadelphia Yellow Jackets in hopes of improving attendance, but they were shut out in seven of eight games, further quelling interest. Finally, the owners suspended operations in early November, leaving Philadelphia without a pro team.
As much as we know about Bert Bell's lineage, we know curiously little about how he eventually got involved with the NFL. He had met Tim Mara and Jack Mara at Saratoga. He also knew George Preston Marshall and Art Rooney, who were not in the league yet but, like Bell, would soon gain admittance. The league began looking for new ownership in Philadelphia after the Yellow Jackets collapsed, not wanting to abandon the market. Bell probably seemed like an ideal candidate with his football background and enough family wealth to withstand a downturn in interest, attendance, and revenue. Few people knew his father had cut him off. One way or another, Bell became interested in owning a pro team. It would not cost a lot—the fee for a franchise was $2,500, less than he blew at the horse races on some days—and it surely sounded more interesting to him than running a hotel.
In 1932, when Marshall joined the NFL with a franchise in Boston, he wanted to hire Lou Little as his coach. Little and Bell had been childhood friends and teammates at Penn, and Little was now a winning head coach at Columbia. He turned Marshall down after consulting with Bell but recommended Wray, who took the job.
That fall, Bell patched up his differences with Wray that had led to his departure from Penn's staff several years earlier. While following his friend's team in Boston, he and Wray discussed the fact that their hometown was without a team. They could easily step in, they agreed. For someone in Bell's position, there was little downside. One can imagine John C. Bell Sr.'s reaction to the news that his son was considering buying into pro football. Now seventy and near the end of his life, he had always looked down his nose at the pro game, practically sneered at it. He could not imagine anyone wanting to watch football played by adults. The college game was popular, he believed, because it helped shaped the character of young men.
Bert Bell was undeterred. In one of his final rebellious acts, he disavowed his father's opinion, rounded up several minority investors, and bought the dormant Frankford franchise. The group paid a $2,500 guarantee to the NFL and assumed $11,000 in debts the Yellow Jackets owed the Bears, Giants, and Packers. On the day the purchase was finalized in 1933, Bell was walking in Center City Philadelphia. At the corner of Broad and Chestnut, two major streets, he glanced up and saw a billboard promoting President Franklin Roosevelt's National Recovery Act, emblazoned with its symbol, a bald eagle. Bell had an idea. He would call his new team the Philadelphia Eagles. When John C. Bell died two years later, he went to his grave believing Bert had once again done something foolish.
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# ROONEY: THE GAMBLER
HE IS RECALLED IN THE FAMILY AS THE "FIRST ART Rooney," distinguishing him from his grandson with the same name who became famous as the Pittsburgh Steelers' cigar-loving owner. The first Art was a red-bearded ironworker who wandered the globe in search of steady work in the 1800s. His Irish parents fled the potato famine for Montreal, where Art was born and lived until he was twenty-one. When Canada's economy collapsed, he relocated to Wales, married an Irish girl, and started a family, then moved back to Canada. Eventually, he crossed the border into the United States—on foot and without a passport, according to family legend—and found work in Youngstown, Ohio, before continuing east. By 1890, he was nearly forty and living with his wife and six children in Pittsburgh, at the time a "clanging, smoke-belching metropolis" in the heart of America's industrial belt.
In a city full of immigrant laborers, the Rooneys were better off than most. Art's father had taught him how to "puddle" molten iron, that is, to stir it to maintain a certain temperature and consistency. The skill allowed him to ascend the ranks from laborer to crew chief, tripling his paycheck. Art owned a home near the giant American Iron Works mill, across the Monongahela River from downtown, and he also owned another property where he took in boarders. But in the early 1890s steel plants began taking over, and Art's union went on strike. Briefly reduced to working menial jobs, he eventually bought a boarding house with a ground-floor saloon that catered to the mill population—a wise investment, Art thought, because men drank even in tough times, when they could not afford it. Saloons became the family business. Art's oldest son, Daniel, opened one in Coulterville, a small coal town northeast of Pittsburgh, where he fell in love with Margaret Murray, a petite Irish redhead. They married and soon had a son, Arthur Joseph Rooney, born on January 27, 1901, in a room over the Coulterville saloon.
The first Art Rooney died in his early fifties in 1903, before his grandson of the same name knew him. But the first Art greatly influenced the life of the second. The first Art brought the Rooneys to Pittsburgh after years of wandering; the second Art would call Pittsburgh home for his entire life. The first Art took up the saloon business; the second Art grew up on top of one.
Daniel and Margaret Rooney moved back to Pittsburgh and bought a building in the Ward, a neighborhood on the city's north side. Located at the corner of Robinson and Corry Streets, adjacent to Exposition Park, home of the Pirates, Pittsburgh's National League baseball club, the building housed Dan Rooney's Café and Bar on the ground floor. Daniel and his family lived upstairs, while below them ballplayers, bookies, union leaders, gamblers, and ironworkers congregated, with no women allowed.
Broad shouldered and muscular, Daniel was deemed one of the toughest guys in the Ward. On Saturday nights, he broke up fights in his saloon, trudged upstairs to his wife and children, wiped off the blood, put on a clean shirt, and went back downstairs to tend bar until it was time to break up another fight. His oldest sons, Art and Dan, shared a tiny room. On some winter mornings, they awoke to find snow on their blankets that had blown through cracks in the walls. But they did not complain. They thought they lived at the center of the universe. In their father's saloon they met ballplayers and ward bosses, giving them an early introduction to their city's social and political life. By age thirteen, Art was paid to "run errands," which meant participating in political shenanigans. Years later, he told an interviewer he had no idea he was breaking the law by voting more than once in an election.
His mother attended mass every day and raised him and his siblings in the Roman Catholic faith. Once, when Art was fifteen and she was ill, he spent an entire day at church praying for her. He would become a daily communicant himself as an adult. His mother also made sure he tended to his schoolwork, but Art was more interested in sports than anything else. Unlike his grandfather or father, who worked from a young age to help support their families, Art had the freedom of leisure time, a relatively new concept among working-class families in America. Art and Dan, eventually the eldest of nine children, spent their days at the neighborhood park, dreaming of becoming baseball players like the ones they watched at Exposition Park and met in their father's saloon. They also played football, boxed, and brawled. Their father bought them boxing gloves and a punching bag for Christmas one year. "Boy, could they punch, and boy, could they fight," a family friend recalled.
Dan topped out at nearly six feet tall and inherited his father's broad shoulders; tangling with him was usually a mistake. Art would later joke that his menacing younger brother amassed more knockouts than Jack Dempsey. Art stopped growing at five feet eight but was naturally athletic and just as tough minded as Dan, especially in a boxing ring. A successful amateur fighter, he was runner-up twice in the American Athletic Union's national tournament and won an international competition in Canada. Although he never boxed in the Olympics, he defeated a lightweight who later won the gold medal at the 1920 games.
He was also a standout on the gridiron. At the University School, a prep academy, he played halfback and led the team with what the school newspaper described as "wiggling, squirming, and serpentine runs," standing "head and shoulders above his companions." Though small, he was talented enough to attract the attention of college coaches. Notre Dame's then-unknown coach, Knute Rockne, sent him a recruiting letter. Penn State offered him a cut of the proceeds from game-day program sales; the NCAA, barely a decade old, was not yet a strict, rules-obsessed overseer. Art turned down Rockne and Penn State. In an arrangement unimaginable today, he played simultaneously for Indiana Normal (now Indiana University of Pennsylvania) and Duquesne. It was an era when many schools played fast and loose with rosters and eligibility rules, and "tramp" players abounded. Art actually did not try hard to fool anyone. He played under his real name for both teams, whose games were covered by the same newspapers in Western Pennsylvania. If anyone noticed that he was playing for two schools, no one said anything.
In 1921 he left Pennsylvania to play baseball, his true love among sports, at Georgetown University in Washington, DC. He had played for semipro teams since he was fifteen and still hoped to reach the major leagues. A speedy outfielder, he hit for a high average with a left-handed swing and stole a lot of bases. To his great disappointment, though, Georgetown's coach barely allowed him on the field. A scout for the Boston Red Sox still saw enough potential to offer him a contract, but Art turned it down, reasoning that he could earn more money playing for semipro teams around Pittsburgh. That fall, he was back on the football field, playing for just one school now, Duquesne.
When his college football days ended in the early 1920s, he faced a common predicament. He wanted to keep playing, but how and where? The NFL was not an attractive option; it was lurching forward, with franchises coming and going. Pro football's potential in Pittsburgh was limited by state ordinances, known as blue laws, prohibiting commercial activity on Sundays to avoid conflicting with church services. Sundays were when NFL teams played, so as not to compete with college games on Saturdays. Instead of supporting an NFL team, Pittsburgh boasted a league of semipro squads. Art started his own team, calling it the Hope-Harveys. Hope was the name of the Ward firehouse where the players changed and showered after games. Harvey was the name of the team doctor who never charged Art for his services. The team played at Exposition Park, which the Pirates had abandoned for the newly built Forbes Field.
The Hope-Harveys were a Rooney family affair. Art was the owner, coach, and halfback. Dan was the quarterback. Two of their younger brothers, Jim and John, also played on the team. The _Pittsburgh Press_ called Art "the Red Grange of the independents," and Dan was also a formidable player, with his notable size and speed. Their games were deemed important enough to merit newspaper coverage. On November 28, 1924, the _Pittsburgh Daily Post_ reported that Art returned an interception 60 yards for a touchdown in a victory over the Boston Bulldogs. On December 13, 1925, the same paper commented that "Art Rooney, little Northside lad, had a great campaign." The Hope-Harveys were among Western Pennsylvania's best sandlot teams.
Art and Dan continued to play semipro baseball for a succession of teams, including the Pittsburgh Collegians, and in 1925, they suited up for the Wheeling (West Virginia) Stingers of the Mid-Atlantic League, a fully professional circuit. Art led the league in runs, hits, and steals, and almost won the batting title. Dan, for his part, batted an impressive .369. They loved the minor-league life, the bus rides, late nights, and camaraderie with teammates. One night in Frostburg, Maryland, anti-Catholic taunts from the opposing dugout resulted in a brawl that halted the game and then eventually resumed later, at a restaurant. Frostburg's city council sent a letter to the Wheeling team's owners, informing them that Art and Dan were banned from the city.
The Rooney boys were sportsmen for all seasons, and, eventually, they wore down. Dan entered the priesthood and went to China as a missionary. Art continued to run the Hope-Harveys, who became known as the Majestic Radios after an electronics store became a sponsor, and then Art changed the name again, to the J. P. Rooneys, to promote his brother Jim's successful run for a seat in the Pennsylvania General Assembly. By this point, Art was thirty and had given up his uniforms for a coat and tie.
FOR AS LONG AS HE LIVED, ART RELISHED TELLING THE STORY OF the one day he actually worked for a living. It came in the summer of 1918, after his senior year in high school. His mother had ideas about what he should do next. Rather than attend college, she thought he should get started in the iron mills, where so many men she knew worked, including Art's uncle, Mike Concannon, who was a foreman at a blast furnace. The family pulled a few strings, and Art reported for duty at the mill. The job was tough, sweaty, and dull. Art quickly realized he did not like it. After working all morning, he sat with Uncle Mike at lunch. "How much money do you make?" Art asked.
Mike told him and explained that Art, too, could make that much as a foreman after fifteen years. Art was not impressed. He packed up his lunch and went home without even bothering to collect his wages for a half-day's work. He had bigger ideas about how to provide for himself. He had a quick mind, a facility with numbers, and a knack for spotting opportunities—qualities that helped him make money at, of all places, the racetrack.
When Art was a boy, his father had introduced him to horse racing and gambling on an outing to a track in Cleveland. His father liked to bet, and Art loved everything about the scene: the roar of the crowd, the speed of the horses, the money on the line. Racing was illegal in Pennsylvania, but bookmakers could always be found at Dan Rooney's Bar and Café. Soon enough, Art was carrying wagers to horse parlors for some of his father's saloon customers. When he started making his own bets, he shocked his elders with his instincts and aptitude. He was "born to play the horses," his son would write, and "quickly surpassed in expertise his teachers, the touts and bookies and racing-form readers who recognized his precociousness and took him under their wings." Long before he stopped playing sports in the 1920s, Art came home from racetracks with more than enough money to live on. When a baseball team in the Southern League, a reputable minor-league circuit, offered him a contract, he turned it down and told the manager, "I can make more money at the racetrack."
Art Rooney. (Pittsburgh Steelers)
He had grown up around hustlers, quick-witted men who always seemed to have an idea and an angle, and he became one himself. Instead of getting in the boxing ring, he promoted fight cards. Instead of playing football, he ran a team. In the late 1920s he became co-owner of the Showboat, a floating casino-nightclub on the Allegheny River. Drinking and gambling were illegal, but Art knew the right cops. His co-owner was a notorious card shark, and, according to his biographers, his acquaintances also included bootleggers and ward heelers. Art "was no angel," those biographers concluded, but other than "uncorroborated hearsay," there is "scant evidence indicating that he was more than peripherally engaged" in any illicit schemes.
Whenever he really needed money, he just went to the track. Art's winnings funded a unique honeymoon with his bride, the former Kathleen McNulty, in 1931. Kathleen, known to all as Kass, was six years younger and also from the Ward, where her father made pickle barrels. Art had paid her little attention until adulthood, when he saw her for what she was: a willowy, witty brunette. Her father was lukewarm about her taking up with a gambler and sportsman with dubious friends, but she defied him, and they eloped in a civil ceremony in New York, where they had traveled to watch the Belmont Stakes.
Art made $10,000 on the race, and, flush with cash, the couple headed across the country, traveling on trains, at times with a small entourage, visiting "every racetrack from here to Tijuana," Kass recalled. They stopped in San Diego, holed up in an elegant hotel, and crossed the border for the races at Tijuana's historic Agua Caliente racetrack. America was in the throes of the Great Depression, but life was grand and exciting for Art and Kass. They eventually came home, and, when they did, it was to families still upset they had eloped, so they were married again, this time at St. Peter's Church.
The couple settled into a Northside apartment. Every morning Art rose, kissed Kass goodbye, and commuted to his office at the Fort Pitt Hotel, a downtown landmark, where the phone rang constantly as he oversaw his interests and holdings, including the Showboat, the football team, local politics, and his racetrack wagers. He knew everyone and everything, it seemed. Years later, when one of his grandchildren visited and was asked to describe what granddad did for a living, the grandchild replied, "He answers the phone."
AT FIRST, ART WAS LUKEWARM ON THE IDEA OF BUYING INTO the National Football League. His sandlot team played in a creditable league—no less creditable than the NFL, as he saw it. But after the birth of his first child, a son, in 1932, he thought he needed a more dependable way to support his family besides playing the horses. His sandlot football league was never going to bring in a great deal of revenue. The NFL was hardly prospering, but its teams played in major cities, offering more potential for growth. He knew Tim Mara, Jack Mara, and George Preston Marshall from the racing world. They told him Joe Carr wanted a team in football-mad Western Pennsylvania, and Art's political friends pointed out that there was growing support for an easing of the blue laws, a fundamental obstacle to an NFL franchise in the state.
With Carr's encouragement, Art put together a group of minority investors and presented himself to the NFL owners when they came to Pittsburgh for a meeting in late February 1933—a clear signal Pittsburgh was on their radar. The meeting was held at the Fort Pitt Hotel, where Art kept his office. At another league meeting five months later in Chicago, his franchise application was accepted along with bids from Bert Bell in Philadelphia and a Cincinnati group fronted by a local coroner.
Art was taking a gamble. A referendum on the repeal of blue laws would not take place until November, and if the vote went the wrong way, his team could not play on Sundays and would have trouble remaining in the league. But he never minded a bet, and certainly was an expert on reading odds. He liked his chances.
# **PART TWO**
#
# ALMOST BROKE
GEORGE HALAS DID NOT JUST POCKET THE WINDFALL HE received from the Bears' barnstorming tour with Red Grange in 1925 and early 1926. He was thirty, with a wife and two children to support—three children, really, the third being the Bears. Unlike many later NFL owners, as well as most of the founding fathers, Halas neither came from money nor earned a lot, forcing him to continually scrounge for cash to keep his team afloat. The Grange money enabled him to start business ventures that, he hoped, would make things easier. He opened a real estate company, invested in the stock market, and put more into his pro basketball franchise. The 1929 stock market crash curtailed his plans. Halas, along with millions of other Americans, was almost ruined by the subsequent economic depression. His broker sold his stocks for relative pennies. His real estate company folded, as did his basketball team. His Grange money was gone.
The Bears were already struggling. They slipped from nine wins in 1927 to seven in 1928 to just four in 1929. In the latter season, they lost to the Packers and Giants by a combined 67–0 score, and the crosstown Cardinals obliterated them, 40–6. Their attendance slipped with their performance. Their final home game in 1929 drew just 2,123 fans. "We couldn't pay our guarantee to the visitors from Frankford," Halas wrote.
In addition to coaching the team, Halas still suited up and played. Dutch Sternaman, his ownership partner, helped him coach, an arrangement that had become problematic. Halas favored a more wide-open offensive style, while Sternaman wanted to keep things simple. "The split hurt the team," according to Halas. "I would tell the team to do this and Sternaman would tell them to do that."
On many Sunday evenings, Halas brought Joe Carr back to his apartment for a postgame dinner with his family. Halas's daughter would recall that it was typical for the men to remain at the table long after the plates had been cleared. They had much to discuss—league affairs, refereeing controversies, team issues. Everyone in the league understood that Halas could influence Carr. "I think Pete Rozelle was the first commissioner he didn't control," Halas's grandson, George McCaskey, said decades later, referencing the NFL commissioner hired in 1960. But, in 1929, their Sunday night conversations almost surely centered on Halas's efforts to keep the Bears from folding. When the season ended, Halas studied his financial ledgers and was stunned to see that his modest proceeds from program sales were all that had kept the team in the black. Carr, too, was alarmed. The NFL could live without the Duluth Eskimos, Dayton Triangles, and most of the other teams that had already failed, but if the Bears went under, they might take the whole league down with them.
Halas continued to look for ways to generate money to pay his bills and keep the Bears in business. "He would try anything, whatever came along, just to keep things going," his daughter, Virginia McCaskey, said. "His timing on going into real estate was very bad. He tried being a car salesman, but the only car he sold was to himself. The basketball team was another one of those things."
In the end, he had no choice but to ask for help. His mother loaned him money, as did his mother-in-law, another widow, "who never let him forget it," his daughter said. He received help from one of his best friends, Charles Bidwill, a corporate attorney and sportsman who avidly supported the Bears. A brother-in-law provided a loan, too, and finally, in what surely was a low point for him, Halas asked his children for permission to "borrow" from their college savings accounts. "I was probably ten or eleven," Virginia McCaskey recalled. "All the birthday and Christmas checks my grandmother had sent me were in an account. He sat Mugs and me down in our living room and explained that he needed the money but was just borrowing it. He kept saying, 'I'll pay you back, I'll pay you back.' I didn't mind. He could have had anything I had. I was just happy he could use it."
It was clear after the 1929 season that Halas needed to stop putting on a uniform on Sundays. It was also clear the Bears needed new leadership. "The time had come for Dutch and me to stop coaching, or more accurately, mis-coaching," Halas wrote. His choice for a new coach was a surprise: Ralph Jones, the athletic director at the Lake Forest Academy, a private high school north of Chicago. The public was "astonished" by the hire, Halas wrote, but he had played for Jones on the freshman football team and varsity basketball at Illinois and liked his cerebral approach. Jones promised Halas that the Bears would win a championship in three years "and I believed him," as Halas later put it.
An original thinker, Jones was not a devotee of the run-oriented "single wing," the most popular offensive alignment at the time. It called for the center to snap the ball to a tailback lined up 5 yards deep, with a wingback and quarterback positioned nearby, on the same side. Halas employed the single wing at times with the Bears, but he preferred the T formation, in which the quarterback lined up directly behind the center, with two backs behind him. Upon taking over the Bears, Jones, with permission from Halas, tweaked the T. He had the blockers line up farther apart to create more room for ball carriers. He moved a split end wide of the blockers as a designated pass receiver. He put a halfback in motion, running parallel to the line of scrimmage, before the ball was snapped. These new ideas were intended to confuse defenders and bolster the Bears' passing game.
Jones and Halas also overhauled the team's roster. Halas had already brought back Grange; though no longer a dazzling, game-changing player after a serious knee injury, he still had a knack for finding running room while toting the ball and was a savvy defender. He was, Jones thought, perfect for the split end role in the modified T. And to keep defenses from focusing on Grange, Halas signed Bronko Nagurski, a 240-pound fullback from the University of Minnesota who often flattened defenders when he plowed into them.
After failing to score in three of their first four games in 1930 as they adjusted to Jones's new T, the Bears jelled on an October afternoon; with Grange running outside and catching passes, and Nagurski running inside, they ran over the Cardinals, 32–6. They ended the season with five straight wins and an overall record of nine wins and four losses.
But although the news on the field was better, the Bears' financial situation remained discouraging. As the Depression wore on, fans could not afford tickets and banks could not offer loans. "We had a drawer full of bills and we were overdrawn at the bank, and no change was in sight," Halas recalled. For the second straight year, he was unable to pay the Frankford Yellow Jackets their guaranteed percentage of the gate when they played in Chicago. By the end of the 1930 season, Halas owed more than $10,000.
NO ONE AT THE TIME WOULD HAVE SUGGESTED PRO FOOTBALL was a thriving concern. Twenty-two teams had competed for the NFL title in 1926, but by 1931 only ten were still in business. When the Providence Steam Roller, Cleveland Indians, and Frankford Yellow Jackets folded after that season, the number of franchises that had failed since the league's inception in 1920 rose to thirty-five. With the addition of George Preston Marshall's Boston franchise in 1932, the league consisted of just eight teams, most of them concentrated in the country's two largest cities. The Giants, Brooklyn Dodgers, and Staten Island Stapletons played in and around New York City, while the Bears and Cardinals played in Chicago. Beyond the nation's first and second cities, pro football barely existed. There was a team in Portsmouth, Ohio, one in Green Bay, Wisconsin, and another in Boston. That was it.
The NFL's fortunes did not resemble an arc pointed ever higher on a graph, continuously climbing; rather, its fortunes rose and dipped unpredictably, often changing from year to year, producing a permanent state of unease among those in charge. Halas and Tim Mara had seen enough go right to continue believing in the sport's potential, and though Marshall, Bert Bell, and Art Rooney were newcomers, they also saw the possibilities. But there was inherent risk in being a pro football man, especially during the Great Depression.
Interest in _other_ sports remained high across America, despite the economic collapse. Fans could escape their troubles for a few hours at an event or over the radio. When a horse named Twenty Grand won the Kentucky Derby on May 16, 1931, "a colorful crowd of nearly 60,000 spectators offered roaring acclaim," the Associated Press reported, while millions listened to a national radio broadcast. Later that year, baseball's St. Louis Cardinals and Philadelphia Athletics so mesmerized the country with a seven-game World Series that thousands of fans gathered in the streets just to listen to the broadcasts together. College football still generated crowds and headlines. Traditional powers such as Michigan, Pitt, Notre Dame, and Southern Cal played in packed stadiums. On November 26, 1932, Notre Dame trounced Army before 78,000 fans at Yankee Stadium. Two weeks later, Notre Dame lost to Southern Cal, with a crowd of 93,000 watching at the Los Angeles Coliseum, a magnificent edifice that had just hosted the Olympics.
Pro football did not compete for the attention of America's sports public. Even more than a decade in, the NFL was widely dismissed as something of a carnival act, played largely by men who took part only because they had nothing better to do. The league's best team, the Green Bay Packers, played in a tiny, horseshoe-shaped wooden structure located behind a high school. That encapsulated pro football in its early years.
Granted, their stadium situation notwithstanding, the Packers were a success story. A decade earlier, the NFL had kicked them out of the league after Halas caught them using college players in a game against the Bears. They were allowed to return but were on the verge of collapse a year later. Local leaders devised a unique plan to sell stock in the team to the public for five dollars per share. Hundreds of fans invested, turning the team into a community-owned, nonprofit enterprise. That put the Packers on relatively sound footing, and they started to win. The team's coach, Curly Lambeau, was a handsome and intensely competitive tailback who had briefly played at Notre Dame. He energetically recruited new talent and put his squads through long practices. The Packers went 43-20-8 between 1923 and 1928 and leapt to the top of the league after Lambeau signed Clarke Hinkle, a powerful fullback and linebacker; Mike Michalske, a rugged guard; and Johnny "Blood" McNally, an elusive back. All three would become Pro Football Hall of Fame inductees along with Lambeau.
The team prospered partly because it was community owned, which helped attendance, and partly because the publisher of the local newspaper, the _Green Bay Press-Gazette,_ was a major supporter, guaranteeing consistent coverage. Mostly, though, the Packers prospered because they won. Early in the 1931 season, which would end with them securing their third straight NFL title, they defeated the Bears, Giants, and Cardinals on successive Sundays in Green Bay. Sportswriters delighted in recounting little Green Bay's victories, casting the Wisconsin team as David and the big-city clubs as Goliaths.
Notre Dame's Knute Rockne had died in a plane crash earlier that year, prompting some columnists to suggest Lambeau was America's next great football coach. The men of the NFL were pleased to see one of their own recognized—it seldom happened—although Halas grumbled about it. The relationship between Halas and Lambeau was distantly civil at best, Halas having been the one to turn Lambeau in for using college players. Their teams and fans had since forged an intense rivalry. Whenever the Packers played in Chicago, 2,000 Green Bay fans traveled with the team to Cubs Park. But, despite the Packers' success, their home stadium held just 10,000 fans. (Fire marshals reluctantly let in another 3,000 when the Bears came to town.) There was no visiting locker room, so the Packers' opponents dressed for the game in their hotel rooms in downtown Green Bay, gathered in the hotel lobby, and shared a bus to the stadium. There also were no rest rooms, so when nature called, fans simply relieved themselves under the stands.
IN THE SUMMER OF 1931, DUTCH STERNAMAN APPROACHED Halas with a proposition. He had invested in an apartment building and a gas station rather than the stock market, so he was doing better than most. But, facing steep mortgage payments, he wanted to unload his 50 percent share of the Bears and offered it to Halas for $38,000. Halas accepted without hesitating even though he did not have the money; he wanted control of the team. He arranged to pay Sternaman in three installments over three years, then set out to find $25,000 for an initial payment. Miraculously, Charles Bidwill "raised $5,000 from a bank that was already closed," Halas wrote. The mother of George Trafton, who had played for the Bears for more than a decade, loaned Halas the bulk of the initial payment.
After making a second payment following the 1931 season, in which the Bears won eight of thirteen games, Halas needed to make a final payment of $7,000 on August 1, 1932, to gain sole control of the Bears. But he only had $2,000 as the date approached, and no bank would loan him the rest. A clause in the deal stipulated that all stock in the team, including Halas's, would revert to Sternaman if Halas missed a payment. The deadline passed. On August 3, Halas received a letter from Sternaman's lawyer stating that the Bears would be put up for sale on August 9. Halas was desperate. "I called everyone I knew. No one would help me," he later wrote. Finally, on the morning of the scheduled sale, he received a call from a banker willing to loan him the balance of the payment. Halas raced to the bank, got a check, raced to Sternaman's lawyer's office, and handed it over. Somehow, at the nadir of the Great Depression, he finally had sole ownership of the Bears.
EVEN THOUGH HE HAD BEEN REDUCED TO BORROWING FROM HIS children to pay his debts, Halas continued to look for new business opportunities. One presented itself in 1932 when William Hauk, a laundry owner who advertised in the Bears' game program, told Halas of a competing laundry service that was on the verge of going out of business and could be bought cheaply. Halas did not have the money and knew he could not keep asking friends and family members for loans. He turned to Jim McMillen, a former offensive lineman for the Bears. Like Halas, McMillen had played at Illinois and earned an engineering degree. As a senior in 1923, he helped open holes for Grange, then a sophomore sensation. After graduating, McMillen played for the Bears through 1929, but his small football salary paled next to what he earned during the offseason as a professional wrestler.
A careful investor, McMillen had plenty of money, enough to sail through the depression. He also had great respect for Halas, and he helped his former coach buy the failing laundry. Halas renamed it White Bear Laundry and hired William Hauk to run it. McMillen provided the necessary operating capital with a loan, which Halas repaid over the next decade. White Bear was a commercial laundry, serving restaurants and hotels, and Hauk was a savvy partner. Unlike his forays into real estate and basketball, Halas's laundry investment survived the Depression and became solidly profitable.
"He had a good partner. They had big White Bear Laundry trucks roaring all around Chicago," Virginia McCaskey said. "I remember going to see the business. It was fascinating to me. There was the machinery with large mangles for sheets and tablecloths. You would feed a sheet into one end and it would go through the rollers. There were women on one end to feed the material properly. The women on the other end were the folders.... It was understood that my father was all football during the season, but in the offseason, he went to the laundry offices in the morning before he went to the Bears offices, and then he stopped at the laundry on the way home."
BY 1932, CHARLES BIDWILL WAS MORE THAN JUST A LOYAL FAN of the Bears. He helped Halas run the team in the role of vice president. They were good friends with similar biographies. Both were Chicago natives, born in 1895. Bidwill was never the athlete Halas was, but he shared Halas's zeal for sports. A natty dresser with a chatty personality, Bidwill had served in the Great War, earned a law degree from Loyola University, and worked as a corporate counsel in the 1920s, making good money in the process. That enabled him to buy a printing company, develop a winning thoroughbred racing stable, and manage Hawthorne Race Course. He also ran the Chicago Stadium Operating Company, which promoted events at the vast indoor venue. Inevitably for someone so well connected in Chicago, his associates included questionable characters, including a lawyer with ties to Al Capone. But that did not tarnish the respect Bidwill earned as an energetic, self-made success.
One evening in the summer of 1932, Bidwill hosted Halas and Min on an evening dinner cruise aboard his yacht. The other guests included Arch Ward, sports editor of the _Chicago Tribune,_ and David Jones, the physician who owned Chicago's other pro football team, the Cardinals. Although their teams competed during the season, Halas and Jones were friendly. Four years earlier, Halas had arranged for Jones to buy the Cardinals for $25,000 from Chris O'Brien, the painting contractor who had started the Cardinals as a sandlot organization in the late 1800s. But Jones was already weary of competing with Halas for the favor of Chicago's sports fans. As Bidwill's elegant yacht cruised around Lake Michigan that evening, Jones expressed a willingness to sell the Cardinals.
"If I get my price," Jones said.
"What is that price?" Bidwill asked.
"Fifty thousand dollars," Jones said.
Several nights later, Bidwill called Jones and said he would buy the Cardinals. Halas was excited to bring Bidwill into the NFL's inner ranks. With his wealth and social network, he was just the kind of owner the NFL needed. Bidwill was so fond of Halas that he kept his Bears season tickets and even remained the team's vice president for a year after he bought the Cardinals. In fact, at Halas's request, Bidwill also bought a minority stake in another franchise, the Portsmouth Spartans, who would soon move to Detroit and start anew as the Lions. After that transaction, Bidwill owned one team and a piece of two others. It was a blatant conflict of interest—one the NFL never would allow decades later—but in the 1930s, the owners of the league's other teams had no problem with it.
WHEN THE 1932 SEASON BEGAN, THERE WAS MOUNTING PRESSURE on Ralph Jones. The Bears' coach had promised Halas a championship within three years. This was his third year. The Bears started slowly; their first three games were scoreless ties. Then they lost to Green Bay by the pitiful score of 2–0, with the only points coming on a blocked punt that produced a safety when the ball rolled out of the back of the end zone. The _Chicago Tribune_ 's Wilfrid Smith described the game, played before 17,500 fans, as "one of the old-fashioned brawls for which the Bears and Packers are famous." Smith certainly had an up-close view: he worked the game as a member of the officiating crew, the head linesman, before writing his game story in the press box. It was another blatant conflict unimaginable today, but sportswriters in the 1930s routinely doubled as NFL officials—in hindsight, one of the most obvious signs that the league lacked professionalism.
The conflict seemingly impacted Smith, who kindly did not point out in his game story that the Bears had now played 240 minutes of football that season without scoring a point. Halas surely approved of the omission. But the Bears' fans had not lost faith. More than 27,000 attended a home game against Staten Island on October 23 and watched Grange and Nagurski run wild in a 27–7 victory. Two weeks later, the Bears easily defeated the Giants, 28–8, inaugurating a winning streak. By the end of the season, the Bears had a 6-1-6 record, while Green Bay was 10-3-1 and Portsmouth was 6-1-4. The owners had decreed that the league title would go to the team with the best winning percentage, with ties excluded from the calculation. The NFL would not begin to include ties in the math, counted as "half victories," until 1972. As a result, Chicago and Portsmouth had higher winning percentages than Green Bay, even though the Packers boasted quite a few more wins. It was not the fairest approach.
Halas and Portsmouth's owner arranged for their teams to play at Wrigley Field, formerly known as Cubs Park, on December 18. The winner would lay claim to the title, and, oddly, the loser would finish third, behind Green Bay. When heavy snow and bitter cold battered Chicago in the days before the game, Joe Carr decided to move it to the Chicago Stadium, an indoor venue. What is surely the most unusual game in NFL history ensued. A circus had just left town, leaving a six-inch bed of tanbark on the floor. Though an advantageous cushion for the players, "the elephants had been there, and most of all, what I remember about the game is the odor," said Virginia McCaskey, who attended the game with her mother. A capacity crowd of 11,198 filled the arena as snow continued to fall outside, but the fans struggled to follow the action because of a unique set of ground rules. The field was 80 yards long, including the end zones, and 8.5 yards narrower than usual. When a team crossed midfield, it was immediately moved back 20 yards. There was a goal post at one end only. Field goals were prohibited. "It was all a bit puzzling at times," Virginia McCaskey said. "Whenever I had a question, I would ask my mother and she would know the answer."
The Spartans were playing without their biggest star, Dutch Clark, a halfback destined for the Hall of Fame. Although he enjoyed being on the team and wanted to see the Spartans win, he had more important matters to consider, namely, making enough money to live on. He had taken a job as the head basketball coach at Colorado College, and when his team's season opener conflicted with the hastily arranged extra game, Clark elected to coach basketball rather than play football. The NFL's championship was still not a prized commodity.
The indoor championship game at the Chicago Stadium, December 18, 1932. (Pro Football Hall of Fame via AP)
Neither the Bears nor the Clark-less Spartans had scored when the fourth quarter began. But a Bears halfback intercepted a pass and returned it to the Portsmouth 7 yard line. After three runs up the middle, the Bears were at the one. On fourth down, Nagurski faked a plunge into the middle of the line, stepped back, and lobbed a pass to Grange, who was open in the end zone. When Grange made the catch, an official raised his arms, signaling a touchdown. The Spartans erupted. According to NFL rules, which the league simply copied from the college game, a forward pass had to originate from at least five yards behind the line of scrimmage. Nagurski had been within five yards of the line when he threw the ball, the Spartans argued. The officials did not change the call. The touchdown stood. The Bears wound up winning, 9–0, earning their first NFL title since 1921.
But Halas did not have time to revel in the victory, as he lacked the funds to pay the salaries he had promised his players and coach for the season. Instead of asking the banks and his friends and relatives for more loans, he tried another strategy, offering IOUs. According to Halas, Jones took one IOU for $1,000 and another for $500. Grange took one for $1,000. Nagurski took one for $500. "Some of the greatest players in history, and he's giving them promissory notes? They could have told him to take a flying leap, but they stayed with him," said Halas's grandson, George McCaskey. "I can only speculate, but at some level, it had to be the result of relationships that were more than typical coach-player or typical employee-employer. They had to have some measure of faith in his vision for the sport's future. They also had to respect his sheer doggedness, the fact that he simply would not give up."
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# NEW IDEAS
WHEN THE NFL EXPANDED TO BOSTON AT AN OWNERS' meeting in Atlantic City, New Jersey, on July 9, 1932, the national sports media could not be bothered to notice. The next day's _New York Times_ included an eight-page sports section with articles about major league baseball, horse racing, polo, tennis, sailing, minor league baseball, and the Olympics. There was no mention at all of the NFL. A day later, _Times_ sportswriters covered golf, rowing, shooting, more baseball, more horse racing, but still no pro football.
The Associated Press eventually reported the news, as did Boston's newspapers. But Boston's sportswriters were indifferent. The NFL had already tried their city once, with a team called the Bulldogs, formerly the Pottsville Maroons, in 1929. The Bulldogs folded after one miserable season, and there was no reason to believe another pro football venture would end differently. Boston was a busy sports town, with fans supporting two major league baseball clubs, the Red Sox and Braves, as well as teams from Harvard and Boston College in various sports. Local sportswriters believed there was no future for pro football, which had flopped not only in Boston but almost everywhere else, too.
Yet the city's general enthusiasm for sports was the reason Joe Carr wanted a team there. George Preston Marshall, leader of the group that owned the new team, had preferred to put his team in Washington, where he lived. But the nation's capital was not yet the sprawling metropolis it would become within several decades. Buffalo, Milwaukee, Pittsburgh, St. Louis, San Francisco, and Baltimore all were larger, as was Boston.
Washington's cause also was not helped by the fact that it was south of the Mason-Dixon Line. A southern mentality prevailed in the city, as did Jim Crow laws, with many restaurants, theaters, and public venues strictly segregated. That was potentially a problem for the NFL. Many Washington fans did not want to cheer for black athletes, or so it was believed, but unlike baseball, which maintained a strict, if unofficial, "color line," NFL teams occasionally used black players. The owners feared that might cause problems in Washington. Still, Marshall tried to talk Carr into Washington, but the league president was adamant, mainly because of Boston's potential. Marshall finally gave in. At the Atlantic City meeting, which he attended with two members of his ownership group, the first order of business was admitting their team to the league. Tim Mara presented a motion. Halas seconded it. The vote was unanimous: Marshall was bringing a team to Boston.
He quickly struck a deal with Emil Fuchs, an attorney who owned the Boston Braves, the baseball team. The new football team would play at Braves Field, a roomier stadium than cramped Fenway Park, home of the Red Sox. With that deal done, Marshall decided to call his team the Braves, too. He figured he could use the Indian theme as a marketing ploy, but mostly he was just following the lead of other NFL teams: the Brooklyn Dodgers, Cleveland Indians, and New York Giants had all taken the names of the major league baseball clubs that played at their stadiums, hoping the association with the more popular sport would make them appear more legitimate and worthy of attention.
In their first season, the Braves fielded a young squad, with rookies making up more than half of the roster. The backfield included the incomparably named Honolulu Hughes, pro football's first Hawaiian-born player, and Cliff Battles, also no slouch in the name department. Battles was a promising rookie back from West Virginia Wesleyan, and Marshall, the West Virginia native, wanted players from the state on his team. He outbid several other clubs for Battles by offering him $175 per game, $25 more than any other team offered. The Braves' head coach was Lud Wray, Bert Bell's former Penn teammate and fellow assistant coach. The Braves played their first game on October 2, 1932, losing at home to Brooklyn, 14–0, before 6,000 fans. The outcome hinted at what lay ahead. After surprisingly defeating the Giants, 14–6, the Braves were shut out by the Cardinals on October 16 and played a scoreless rematch with the Giants at the Polo Grounds on October 23. The following week, the largest crowd of the year at Braves Field came to a game against the Bears, and after each team scored a touchdown in the first quarter, the fans witnessed a scoreless scrum over the final forty-five minutes, producing a 7–7 final score.
Marshall was increasingly frustrated. He believed in putting on a show for his customers, but the Braves were not exciting. They had scored three touchdowns in five games and played two ties. How could you expect fans to keep buying tickets to such dull shows? Marshall would soon become infamous for interfering in his coach's business, sometimes even demanding to call the plays, and Wray was the first to experience his meddling. Marshall wanted the Braves to pass more, but Wray stuck to the ground game. Cliff Battles would rush for more yards than any other NFL back in 1932, while Honolulu Hughes would toss just one touchdown pass and nine interceptions in his only NFL season. Marshall stewed.
Tensions briefly eased when the Braves engineered their version of an offensive explosion on November 6, defeating Staten Island, 19–6. But then the Green Bay Packers drummed them, 21–0, and the Portsmouth Spartans shut them out, 10–0. The Braves ended their season on the road, defeating the Cardinals and Dodgers by a combined score of 15–6. Their final record was respectable, four wins, four defeats, and two ties, but in those six hundred minutes of football, their offense had crossed the goal line just five times.
The lack of scoring was not limited to Boston. The Bears, who won the league title, played six ties out of fourteen games in 1932 while scoring just twenty-three touchdowns. On average across the NFL, teams scored just 8.2 points per game, a 23 percent drop from two years earlier. Marshall had recognized before the season that there was a problem. At the July 1932 owners' meeting where his franchise was formally approved, he had seconded a motion, introduced by the Giants' Dr. Harry March, to move the goal posts from the back of the end zone to the goal line. Intended to cut down on ties by making field goals easier to convert, the proposal "lost by a roll call vote after considerable discussion," according to the official minutes from the meeting. That "discussion" included the first on-the-record exhibit of Marshall's show-business sensibility, which would eventually produce profound changes in pro football. "I realize you men know your football inside and out," he told the other owners, "but the way I look at it, we're in show business. And when the show becomes boring, you throw it away and put a more interesting one its place. That's why I want to change the rules. I want to give the public the kind of show they want."
Months later, after his team's drab inaugural season, Marshall led a charge to enliven the game. From the outset, the NFL had simply followed college football's rules, which, among other things, required that forward passes originate from at least five yards behind the line of scrimmage. When the NFL owners met at the Fort Pitt Hotel in Pittsburgh in February 1933, Marshall gave another impassioned speech about the league needing to set its own rules rather than just follow the college game.
"Gentleman, it's about time we realized that we're not only in the football business; we're also in the entertainment business," Marshall declared. "If the colleges wants to louse up their game with bad rules, let them. We don't have to follow suit. The hell with the colleges! We should do what's best for us. I say we should adopt rules that will give the pros a spectacular individuality and national significance. Face it, we're in show business. If people don't buy tickets, we'll have no business at all."
When Carr opened the floor, Marshall was ready. Before the meeting he had talked with Halas, who loved football's brutal nature but was encouraged by Marshall's bold temperament to consider fundamental changes to the status quo. They had put together a list of amendments to the rules, and one by one, Marshall introduced them as motions. The first, and most important, was to allow forward passes from anywhere behind the line. Halas seconded the motion, and, in a fateful moment, it passed. College football still placed limits on the passing game, but now it was unrestricted in the pros. "Nagurski will pass from anywhere so why not make it legal?" muttered Potsy Clark, Portsmouth's coach, still bitter about the "indoor" title game in Chicago several months earlier. Marshall also introduced a motion to spot the ball ten yards in from the sideline after plays that ended with the ball either out of bounds or within five yards of the sideline. The idea was to bring more action into the middle of the field and give offenses more operating room. The motion passed, introducing hash marks on the field, an idea the colleges had long debated but declined to use.
The push for change became infectious. Tim Mara advocated doing away with the extra point and instituting a ten-minute overtime period to break ties. "In every sport but football, the authorities have sought to avoid a tie score," Mara said. Neither proposal passed, but Marshall reintroduced the idea of positioning the goal posts on the goal line rather than at the back of the end zone. Halas seconded the motion. It had failed a year earlier mostly because Nagurski was a strong kicker and the other owners believed Halas wanted primarily to help the Bears. This time, the rule change passed.
After the meeting, Carr told the press the owners hoped the new rules would make their game significantly more exciting. "We think we have overcome the balance previously held by the defense. In fact, if we can give the offense a slight edge, it doubtless would improve the game for both the players and the spectators," Carr said. "We are primarily interested in developing a spectacular scoring game. We haven't the pageantry associated with college games, hence as a substitute we must offer wide-open play with frequent scoring."
Five months later, at another owners' meeting at the Blackstone Hotel in Chicago in July, Marshall continued his assault on the status quo. It had been determined that the league would have ten teams in 1933. Marshall proposed that they be split into East and West divisions, and that the division winners play for the league title after the regular season. For years, the owners had discussed the idea of a postseason championship game patterned after the World Series, the biggest event on America's sports calendar. Determining the league title on the field was obviously preferable to using regular-season records, a method that often produced controversy. Hopefully, a single, decisive game would draw the attention of the national media and most of the sport's fans, whatever team they rooted for. The interest generated by the "indoor game" in Chicago convinced Marshall the time had come. His motion passed unanimously. The NFL would stage its first championship game at the end of the 1933 season.
Marshall had only been in the league for a year, and, already, he had turned it upside down. Many years later, Wellington Mara, Tim's son, would say, "Marshall was way ahead of everybody. He saw that pro football should be a family game. Anything to make it a show."
START-UP EXPENSES AND IN-SEASON COSTS HAD MOUNTED during the Braves' first season in Boston, and, by the end of the year, the operation was $46,000 in the red. Marshall's partners, concerned that the losses would not stop, expressed a desire to sell their interests. Marshall bought them out and became the team's sole owner. Although he lamented pro football's shortcomings in league meetings, he was still optimistic about its potential, both in Boston and elsewhere.
It was clear he needed to try a different approach in his second season, though, and, always unafraid of making big changes, he moved his home field to Fenway Park. That ended his association with the Braves, so he also needed to change the team's name. Keeping with the Native American theme, he selected Redskins. It appeared he wanted to continue using Native American imagery to help market the team. In 1932, his players had taken publicity photos in feathered headdresses. Marshall would later allude to several players having Indian blood, which was probably not true. In a broader way, he thought the theme gave his team an identity distinct from that of other teams in the league. The name also allowed him to keep the franchise's Indian-head logo.
When Lud Wray left after one season to coach his friend Bert Bell's new NFL team in Philadelphia, Marshall went as far as to hire a coach with a Native American connection. William "Lone Star" Dietz had played college football in the early 1900s with Jim Thorpe at the Carlisle Indian Industrial School in Carlisle, Pennsylvania. He had gone on to coach at Washington State, Purdue, and several other colleges, always selling himself as a Native American, born on a South Dakota reservation to a Sioux mother and German father. Although there remained a great deal of prejudice against Indians in America in the 1920s, Dietz embraced the identity, believing it set him apart in the coaching fraternity. Decades later, journalists would discover Dietz had, in fact, been born in Wisconsin to white parents.
From the start, Marshall denied hiring him because of his ethnicity. In an Associated Press article about the name change from July 6, 1933, Marshall said, "The fact that we have in our head coach, Lone Star Dietz, an Indian, together with several Indian players, has not, as may be suspected, inspired me to select the name Redskins." He just wanted to avoid any confusion with baseball's Braves, he said. He may also have selected Redskins to achieve a connection with the Red Sox, who also played in Fenway Park. Whatever his rationale, the new name and the switch to Fenway Park in 1933 did not bring much change in the team's fortunes. The Braves had drawn an average crowd of 15,500 per game in 1932. The Redskins averaged 15,619 in 1933. And with Dietz in charge, the team went 5-5-2, giving it a .500 record for the second straight season.
THE OPENING GAME OF THE 1933 NFL SEASON WAS A WEDNESDAY night affair between the Pittsburgh Pirates and Chicago Cardinals at Pittsburgh's Forbes Field. The midweek date was necessary because a referendum to ease Pennsylvania's blue laws was still a month away. Art Rooney's Pirates drew a small crowd of 5,000 fans to their franchise debut, and they won, 14–13, in a game that was forgettable except for one feature: it pitted the NFL's only African American players against each other. The Pirates had Ray Kemp, a tackle who had grown up in Pittsburgh, worked in the coal mines, and played for Duquesne and Rooney's semipro team. Joe Lillard, a speedy back, played for the Cardinals.
Their presence on the field was not deemed newsworthy. Black players suited up fairly regularly for NFL teams in the 1920s and early 1930s. Before he was the league's president, Joe Carr had covered black athletes as a sportswriter and welcomed them as competitors against his sandlot football team. Fritz Pollard, a black halfback, was one of the league's first stars, and nine black players had competed in the NFL in 1926. Although the number dropped after that, the league never went all white, like major league baseball. Duke Slater, a black offensive lineman, played for the Cardinals in 1927. Harold Bradley, another black lineman, played for the same team in 1928. Dave Myers, a black quarterback from New York University, played for Staten Island and Brooklyn in 1930 and 1931.
Lillard joined the Cardinals in 1932. Nicknamed "the Midnight Express," the six-foot-two, 195-pound back had starred at the University of Oregon until he was suspended for having played semipro baseball, a violation of his amateur status. Lillard said he had been paid only to drive the team bus, but, regardless, he was through with college football. In his third game with the Cardinals in 1932, he ran for gains, completed passes, returned kicks, and tallied an extra point on a drop kick against the Braves in Boston. The _Boston Globe_ 's headline read, "Negro Star of the Chicago Eleven Thrills 18,000 by Dazzling Runs as Cardinals Down Boston."
One can imagine George Preston Marshall stewing as he watched Lillard run circles around his Redskins. Marshall's racism, which he had first learned in segregated Grafton, West Virginia, was further hardened in segregated Washington. The otherwise shrewd businessman did not think blacks were good for business, on the football field or anywhere else. The official minutes from NFL meetings in the early 1930s do not reference discussions about forbidding teams from using African American players. But the owners' meetings often consisted of several hours of official business followed by long, boozy evenings at restaurants and hotel bars, where off-the-record business was conducted, and it seems clear in hindsight that race was a consistent topic on those evenings after Marshall became an owner in 1932. His quest to make pro football more pleasing to the public, in his view, included more than just rule changes aimed at increasing passing and scoring. Within two years of his arrival, the league no longer fielded African American players. In this respect, as with financial matters, the league's history is not one of continuing upward progress. It went backward before it went forward.
During the first half of the season-opening game between the Pirates and Cardinals at Forbes Field in 1933, Lillard was the best player on the field. "Great player, elusive as all outdoors. In the first half, he ran us crazy," according to Kemp. In the locker room at halftime, Kemp later recalled, the Pirates' player coach, Forrest "Jap" Douds, told his team, "We've got to get that damn nigger the hell out of there." Kemp said later, "I was mad, naturally. And as we were going back out, Jap pulls me aside and says, 'Ray, you know I didn't mean _you_ when I said that.'" Marshall was clearly not the only intolerant person in the NFL. It was no surprise, then, that the Pirates cut Kemp three games into the 1933 season. When Kemp complained to Rooney, the Pirates' owner refused to overrule Douds, who also played tackle, Kemp's position.
Kemp went back to a job at a steel mill until the Pirates asked him back late in the season. When he accompanied the team to New York for a game, he could not stay at the team hotel, which did not serve blacks. According to Kemp, Walter White, head of the National Association for the Advancement of Colored People, wanted to sue the hotel and the Pirates for discrimination. "He said, 'There's no reason this should be happening, you being a college graduate an all,'" Kemp recalled. "But I told him I'd prefer not to go to court. I said, 'I know Art Rooney. He invited me to play for his team. He just has a couple of guys running it, no doubt, who are racist. But give him a little time and he'll straighten all this out. He probably doesn't even know this is going on,' which he didn't." The New York trip culminated with Kemp starting against the Giants at the Polo Grounds. It was his final game as an NFL player. "It was my understanding that there was a gentleman's agreement in the league that there would be no more blacks," Kemp said later.
Lillard's career also ended unceremoniously. The Cardinals had suspended him in 1932, supposedly for clashing with the head coach and some teammates over missing practices and breaking team rules. He continued to be seen as a disruptive force in 1933, even though the real problem may have been that some white players resented that a black man was the team's best player. In any case, he did not start the Cardinals' season finale and was soon dumped from the roster, never to return.
Carr and the owners would always vehemently deny that they agreed to ban black players beginning in 1934. "For myself and most of the owners, I can say there never was any racial bias," Rooney said years later. In a 1970 interview, Halas said, "in no way, shape, or form" had the owners formally agreed to follow baseball's lead and exclude blacks. The record suggests otherwise. From 1934 to 1945, the NFL was completely white, a development many historians trace to the influence of Marshall, whose Redskins, infamously, would not integrate until 1961.
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# BENNY AND THE GIANTS
AFTER THE NEW YORK GIANTS STAGGERED THROUGH THE 1928 season, winning just four of thirteen games, Tim Mara had no trouble paying off the $40,000 debt the team accrued. Horse racing in New York was prospering, with crowds filling track grandstands and bettors wagering record amounts. Mara, one of the sport's most popular bookies, had become a wealthy man and used his profits to fund a stock portfolio and his lawbook bindery and coal company. He was not pleased to see the Giants losing money, but he could afford it.
That changed in 1929. The stock market crash liquidated his portfolio. Several of his businesses closed. He was still better off than many New Yorkers, who lost everything, but if his football team could not pay for itself, he would have to fold it. Mara knew that would devastate his sons, who loved that their father owned a team, but he felt as if he had no choice. Fortunately, the Giants engineered a dramatic reversal in 1929. Mara had taken charge of personnel matters during the offseason, reconfiguring the roster himself rather than letting his partner, Dr. Harry March, make decisions—as March, the more knowledgeable football man, had always done. Mara had joked about his lack of football knowledge, but it turned out he knew more than he thought.
His key move was acquiring Benny Friedman, a former University of Michigan backfield star who had played in the NFL for the Cleveland Bulldogs in 1927 and Detroit Wolverines in 1928. The five-foot-ten, 185-pound Friedman was a daring downfield passer who could also run for large gains and kick field goals. He had led the Wolverines to a 28–0 victory over the Giants early in the 1928 season, greatly impressing Mara. After the season, Mara told March, "We need Friedman. Spend what you have to spend, but get him."
March began negotiating with the Wolverines' coach, Leroy Andrews, who did not want to part with his talented young player. Detroit had finished third in the league in 1928, winning eight of ten games. But March kept haggling until Andrews agreed to one of the more unusual deals in NFL history, one that is unimaginable today. Mara would acquire every Detroit player, not just Friedman. The Detroit franchise would fold. Andrews would take over as the Giants' coach, replacing Potty Potteiger, a former baseball minor leaguer who had led New York to an NFL title in 1927. The scale of the deal indicated how badly Mara wanted Friedman, as did the $10,000 salary Friedman negotiated for the 1929 season. It was an unheard-of amount in an era when most players earned $125 a game. The other NFL owners were aghast. George Halas grumbled that Mara had lost his mind.
But Friedman was worth the money, Mara thought. The year before, as the Giants' debts mounted, Mara had asked his players to travel to road games on an old bus rather than in the private Pullman rail car they were used to. On one trip, they stayed at a YMCA rather than a hotel. If they wanted to become a first-class outfit, the Giants needed to sell more tickets. Mara, believing Friedman could make a difference, built a marketing campaign around him. Handsome and glib, the quarterback spoke to school and business groups all over New York before the 1929 season, extolling the virtues of pro football. Mara had bet on the right horse, it turned out. Red Grange was a bigger name, but Friedman was an exciting, unique offensive force, as well as a forward-thinking strategist. The idea of passing the ball in any situation other than third and long was deemed foolish by many coaches, but Friedman believed "the time to pass is on first or second down. Why wait until third down, when the defense is looking for it?" Fans flocked to see him and the Giants' new aerial attack.
Mara and March had surrounded him with former teammates from Detroit, a group of returning Giants, and several newcomers, including Ray Flaherty, a receiver from the New York Yankees, C. C. Pyle's franchise, which had folded. The Giants opened the 1929 season with a scoreless tie against a new team based in East Orange, New Jersey, that would collapse after one year. But, after the disappointing start, the Giants went on a long winning streak. They traveled to Rhode Island and defeated the Providence Steam Roller at the Cycledrome, then opened their home schedule a week later with a 19–6 win over Staten Island before 20,000 fans. The next week, 30,000 came to the Polo Grounds for a game against the Frankford Yellow Jackets. Friedman raced around the backfield, sidestepping defenders and hitting open receivers for touchdowns in a 32–0 rout. "Polo Grounds Crowd Watches Brilliant Aerial Display," read a headline in the _New York Times._
The sport's rules conspired against Friedman. In 1929, passes still had to originate from at least five yards behind the line, and, on top of that, two straight incompletions resulted in a 5-yard penalty. The league's official ball was so fat it was difficult to grab and toss. Undeterred, Friedman hurled passes all over the field. Fans stood in anticipation when he took the snap, and they were riveted when he threw the ball downfield. It was far more exciting than the usual war of attrition, mostly composed of short runs and punts, that constituted a football game, college or pro.
Three days after the win over Frankford, on October 23, a panic that had infiltrated the country's financial markets triggered a massive selloff that continued for almost a week. The country was plunged into an economic nightmare. It was the beginning of what would soon be called the Great Depression. But enthusiastic crowds continued to come to the Polo Grounds to cheer on Friedman. On November 24, the Giants hosted the Green Bay Packers in the most important game of the NFL season. Curly Lambeau's Packers were 9-0 and had given up only two touchdowns in total to that point. More than 25,000 fans arrived at the Polo Grounds. Although that was paltry compared to the nearly 80,000 that Army and Notre Dame would draw at Yankee Stadium a week later, it indicated a markedly higher level of interest in the sport in New York than just the year before.
The imposing Packers featured a pair of dominating interior players, Cal Hubbard and Mike Michalske. They also had a pair of nimble backs, Verne Lewellen and Johnny Blood, who helped Green Bay's offense bound down the field. They were too much for the Giants. Hubbard and Michalske harassed Friedman on pass attempts, while Lewellen boomed punts of more than 60 yards to keep the Giants stuck in their own territory. Somehow, the Giants kept the game close and pulled within a point on a Friedman touchdown pass in the third quarter. But the Packers' physical superiority prevailed, and they won, 20–6, before what the _New York Times_ called "the most enthusiastic professional crowd of the year."
The Giants played five more games in 1929 and won them all, mostly by wide margins, to finish the season with a superb record of thirteen wins, one loss, and one tie. Friedman finished with twenty touchdown passes, easily setting the league's single-season record. But the Packers finished with a 12-0-1 record, and there was no question the owners would vote them the championship. The Giants had to settle for second place. Mara lamented the lone defeat that had cost his team the title, but he was thrilled with the season. Owing to Friedman, the Giants had sold enough tickets to turn an $8,500 profit for the season. Mara could no longer count on his other business to keep the Giants afloat, but he hoped the team would no longer need help.
BY THE SUMMER OF 1930, MARA WAS CAUGHT IN A TANGLE OF legal cases. A bank was suing him to collect on a $50,000 note he had signed for his friend Al Smith's 1928 presidential campaign. He was suing Gene Tunney and Billy Gibson, his friends and former business partners, for money he believed he was owed for promoting a championship fight. Fearing he could lose control of the Giants if the cases went against him, Mara transferred ownership of the franchise to his sons. Although he still ran the team, his sons would eventually take command. Jack, who was twenty-two, had just graduated from Fordham and was headed to law school. He went on the team's road trips and enjoyed spending time with the players. But Wellington, who was fourteen, was the family's true football devotee. In 1930 he wrote a detailed scouting report on the Staten Island Stapletons before the Giants played them, his precociousness and knowledge leaving his father dumbfounded.
The move led to a major change in how the team operated. Within two years, Harry March sold his minority share to Mara and departed. March had worked alongside Mara since the Giants' inception, and though neither publicly commented on what caused their split, the timing suggests March realized, at this point, that he would never own the team. March took a job with the league office but soon lost that, too, after butting heads with George Preston Marshall.
The Giants, meanwhile, began the 1930 season with great optimism. Freidman was back, and Mara was trying to sign Chris "Red" Cagle, a former Army halfback whose slashing run so electrified fans that he had made the cover of _Time_ magazine. Rather than turn pro, Cagle had become a coach at Mississippi State. In the Giants' opener, Friedman ran for one touchdown, threw for another, and kicked two extra points in a 32–0 win over the Newark Tornadoes. One week later, the Giants lost at Green Bay, 14–7, before an overflow crowd of 13,000. Regrouping, they won their next eight games before losing to the Bears, giving them an 11-2 record heading into a home game against the Packers on November 23. More than 37,000 fans—the Giants' biggest crowd since the "Grange game" in 1925—trekked to the Polo Grounds, mostly to see Cagle, who had finally signed and was making his debut. Unlike in their home game against the Packers the previous year, the Giants built an early lead and held on to win, 13–7. The victory elevated the Giants to first place, but they lost their next two games, and, when the season ended, they had a 13-4 record and the Packers were 10-3-1. With ties excluded, the Packers had a miniscule advantage in winning percentage, .769 to .764. For the second straight year, Green Bay won the title with the Giants right behind them.
Despite that disappointment, the Giants were more profitable than the previous year, coming out more than $20,000 ahead. And, by December, the championship race seemed unimportant in comparison to a new event on the Giants' calendar—a charity exhibition game at the Polo Grounds against a squad of past and present Notre Dame stars, coached by the legendary Knute Rockne.
In the early 1930s, college football remained significantly more popular than the pro game. And no team embodied college football's preeminence more than Notre Dame, which had emerged as a powerhouse in the 1920s thanks to Rockne and his glamorous Four Horsemen backfield. National radio broadcasts and fawning newspaper coverage had turned the Irish into their era's "America's team," and, even though their campus was in South Bend, Indiana, their second home was New York, with its large Irish American population. After a roaring sellout crowd watched them upset Army at the Polo Grounds in 1924, the Fighting Irish played at least one game in the city every year.
Mara, with his Irish roots, supported Rockne's team. Seeking to raise money to help New Yorkers who had been ruined by the market crash, Mara proposed a game between the Giants and the 1930 Notre Dame varsity. Not only would it draw a crowd, but it also would give the Giants a chance to demonstrate that pro football was no longer a second-rate sport. Rockne liked the idea, but his team, on its way to another national title, had no room on its schedule. He proposed that a blend of former and current Irish players travel to New York for a game against the Giants. Mara readily agreed, and a date for the game was set: December 14, 1930.
Mara had no difficulty mounting a successful promotional campaign for the game. He took out newspaper ads that read, "See the Four Horseman Ride Together Again." Many football fans, especially those who rooted for Notre Dame, were not going to pass up such an opportunity. More than 50,000 tickets were sold.
Rockne's squad gathered in Indiana and practiced for four days before taking a train to New York. Mara was confident; his players were in better condition and physically larger, especially along the offensive and defensive lines. By the day of the game, Rockne had made the same realization. "Take it easy on us," he told Friedman when they met before kickoff to discuss the rules. Friedman was now the Giants' head coach as well as the quarterback, Andrews having been fired late in the season.
Sure enough, the Giants dominated. The Four Horsemen had nowhere to run. Friedman passed and ran for big gains. By halftime, the Giants led, 15–0, and Rockne was angry. When Harry March visited the Irish locker room, Rockne complained that he had scheduled the game for charitable reasons and was being embarrassed. The Giants played backups in the second half. The final score was 22–0.
The game raised more than $100,000. Mara and Friedman traveled to City Hall and presented a check to Jimmy Walker, the mayor of New York. Mara had never felt better about his team. The Giants had turned a profit during the season, won a slew of games, and contributed to the city. Their pummeling of Notre Dame sent a message to the country's sports public. Baseball and college football fans could no longer dismiss the NFL with a scornful laugh.
Best of all, the Giants were becoming a fixture in New York. The city's crowded sports landscape included baseball's Yankees and Giants, championship boxing matches, big college football games, and America's best horse racing. The Giants had sought a place among that company, and, after two seasons with Friedman, they were close to that goal. When the NFL's owners met after the 1930 season, they had plenty to fret about. Teams were losing money. Franchises were folding. The league's future had never seemed shakier as the effect of the Great Depression set in. But all the owners, not just Mara, found hope in the Giants' success in America's first city and largest media market. And as at other points in the NFL's early history, hope was about all they had.
LIKE MILLIONS OF AMERICANS, FRIEDMAN FOUND HIMSELF dealing with grave financial issues. Although he earned more than any other player in the league, he had invested in the stock market before the crash and suffered heavy losses. To make up for them, he took a part-time coaching job at Yale in 1930. Yale's head coach wanted him to show the team's backs how to mount a passing attack. During the 1930 season, Friedman left his apartment in Brooklyn early in the morning, took a train to New Haven, Connecticut, to coach at Yale, then took a train back to New York for the Giants' practice in the afternoon. It was an exhausting regimen. That Friedman played as well as he did for the Giants was somewhat miraculous.
Shortly after the season, in February 1931, Friedman was married at a Long Island country club, with Guy Lombardo and his orchestra providing the music. The guest list, composed of many of the most famous people in New York, was a testament to his celebrity, but marriage changed Friedman's view of his future. Even after the Giants' successful 1930 season, pro football was hardly a reliable way to make a living. Now that he had a wife to support, with kids surely on the way, he needed more stable and lucrative employment. He retired from the Giants, telling the _Brooklyn Daily Eagle,_ "I've got to build for the future. Professional football doesn't hold for me all the promise it might from a business angle. If I have a future in football, it's not as a player."
Yale offered him a full-time job as an assistant coach, and several of the school's alumni said they could try to find him a position on Wall Street, too. It was a major disappointment for Mara. Now he needed not only a new star player but also a new head coach. He hired Steve Owen, one of the team's linemen, as an interim head coach in 1931. A gravelly voiced, tobacco-chewing midwesterner, Owen played with uncommon intensity and worked as a foreman at Mara's coal yard during the offseason. The other players on the team respected him.
After opening the 1931 season with a win, the Giants lost three straight games, mostly due to a lack of offense. Mara had remained in contact with Friedman and tried to convince him to come back, especially after the promises of a Wall Street job came to nothing. Mara even offered to move the Giants' practices to the mornings so Friedman could continue to coach at Yale in the afternoons. Halfway through the season, Friedman agreed to return. The Giants won their first two games with him as attendance picked up, but then they lost three in a row. When the season ended, they had seven wins, six losses, and a tie—their worst record with Friedman—but had cleared a $35,000 profit.
Soon after the season ended, Friedman stopped by Mara's office. The two men were close, and their conversation that day was friendly until Friedman explained the reason for his visit. He wanted to invest in the Giants, to become a minority owner. He thought he deserved the opportunity after helping turn the team around. Mara delivered a sobering reply. "I'm sorry, Benny, but this is a family business," he said. "We've been friends and I like you a lot, but the Giants are for my sons. I'd like you back next year as a player-coach, but that's up to you to decide."
Friedman did not take the news lightly. He severed ties with Mara. "My timing was off," he said later. "If I had asked him in the years when the team was like a plaything to him, I probably would have gotten what I wanted. But at the time I asked him, it was his sole asset. He said, 'No, I'm keeping it for my sons.' That was that. I thought I deserved a piece of the club because I had played a big part of moving it from the red ink to black ink. And when Tim turned me down, I felt I should move along, that I couldn't stay with him."
George Halas wanted to sign Friedman and put him in the backfield with Grange and Nagurski, but Friedman's wife did not want to leave New York, so he signed with Brooklyn's struggling football Dodgers. They hoped he could help them gain on the Giants in the New York market, but it quickly became clear that Friedman could not be a one-man team; he needed talent around him, too, and the Dodgers did not have much. They ended the season with three wins and nine defeats, losing twice to the Giants.
The Giants, for their part, also endured a losing season in 1932, but Mara stuck with Owen, who would go on to coach the team for more than two decades. A year later, in 1933—the first year the NFL went with two divisions and a championship game—Owen had a lot to work with, including star players such as Mel Hein, a powerful center and linebacker who would play for the team for fifteen years without missing a game; Harry Newman, a young tailback from Michigan who could run and pass; and Ken Strong, an aptly named all-league fullback who had previously rejected the Giants to play for Staten Island. The Giants won the East division with an 11-3 record and played the Bears in the NFL's inaugural title game at Wrigley Field on December 17, 1933.
The game served as evidence that Marshall's new rules had enlivened pro football. As 25,000 fans watched, the Giants and Bears both moved the ball easily, utilizing deep passes and trick plays. The Associated Press described it as "probably the most spectacular game of the year" and "a brilliant display of offensive power." It was anything but a scoreless, muddy scrum. The Giants led by one point at halftime and by five early in the fourth quarter, but with less than two minutes to play, the Bears' Bronko Nagurski tossed a "jump pass" to a receiver who then lateraled the ball to a teammate. The resulting touchdown gave Chicago a 23–21 lead, and the Giants ran out of time on a final drive. They had fallen just short of the title for the third time in five years.
The next year, with many of the same players back, the Giants brought a 5-2 record into a regular-season rematch with the Bears in Chicago on November 4. The undefeated Bears humbled them, 27–7. When the teams met in New York two weeks later, a crowd of 55,000 packed into the Polo Grounds, offering the best proof yet that the Giants were no longer an afterthought, or an unsteady enterprise. The Bears outweighed the Giants by an average of fifteen pounds per man, but Owen had the Giants ready. With Hein dominating the interior, they took the lead with a second-quarter touchdown as their defense blunted Chicago's relentless attack. The immense crowd loosed a roar every time a swarm of red-clad Giants buried Nagurski or Grange.
It became clear in the 1933 championship game that rules changes made pro football more exciting. (Pro Football Hall of Fame)
Holding a 9–0 lead early in the fourth quarter, the Giants appeared on their way to an important win. But Chicago's physical superiority had worn them down. The Bears drove to a touchdown, got the ball back, and drove into field goal range. Their kicker booted a game-winner with less than a minute to play. "It was a game worthy of its surroundings, a game of savage tackling, of irresistible power and of spectacular ball-carrying. It was football at its best in a display that had the huge gathering limp with excitement," the _New York Times_ ' Arthur Daley wrote.
The Giants quickly recovered, winning two of their remaining three games to capture the East division again. For the second straight year, they would face the Bears for the league title, this time at the Polo Grounds. Though the teams had played a close game on the same field a month earlier, the matchup had all the makings of a rout. The Bears had finished the regular season with a perfect record, winning thirteen straight games, as Beattie Feathers, a rookie from Tennessee, became the first NFL back to rush for more than a thousand yards in a season. Halas's squad figured to dominate the Giants, who had finished the regular season with an 8-5 record after losing their finale to the weak Philadelphia Eagles. "I know it doesn't look good," Owen told reporters, "but we'll give them a battle."
Mara still anticipated another sellout, but, when a storm coated New York with ice several hours before kickoff, thousands of fans stayed home, preferring to listen to a live radio broadcast of the game. The Bears led, 10–3, after a first half in which players slipped around the field. At some point in the second half, though, the Giants changed their footwear. Ray Flaherty, a veteran end for the Giants, had told Owen before the opening kickoff that rubber-soled sneakers probably would provide better footing on the ice than metal cleats, prompting Owen to send a friend, Abe Cohen, on a search for enough sneakers for the entire team. Cohen, a diminutive tailor who helped on the sideline during games, tried several sporting goods stores, which were closed, before ending up at Manhattan College, where the athletic director gave him the basketball team's sneakers. The second half of the game was underway by the time he hurried back to the Polo Grounds. He handed out the shoes to the Giants' players on their sideline.
The Giants still trailed early in the fourth quarter, 13–3, but, after their footwear change, they were able to race around the field while the Bears still struggled for decent footing. In a stunning reversal, the Giants scored four touchdowns in the final ten minutes and won, 30–13. Halas was furious, almost inconsolable; the Bears' loss in what would become known as "The Sneaker Game" would forever rank among his bitterest memories. "It was a freakish way to lose, but it was legal and it cost us the championship!" he would write. Mara, though, would forever recall the surprising victory as one of his happiest moments as a team owner. After enduring several seasons ending in frustration, New York fans responded to the Giants' fourth-quarter rally with a show of support so wild it turned chaotic.
"Enthusiasm turned to delirium," the _Chicago Tribune_ wrote. "Hats spun down from the heights of the stands. Hundreds poured over the retaining walls and banked solidly around the gridiron. Only when a cordon of police, with the Giants' substitutes assisting, had lined up, could the crowd be controlled. After each touchdown, hundreds ran onto the field to slap the backs of their heroes." Mara could scarcely believe the scene. It was what he had always hoped for but feared might never happen. His city had lost its mind for his football team. There was, in his estimation, no sweeter sight.
#
# INSTITUTING A DRAFT
BERT BELL COULD NOT HAVE GROWN UP MORE DIFFERENTLY from Tim Mara, who quit school as a teenager, or Halas, a son of immigrant parents who worked hard just to get by. Bell attended elite schools and spent his summers at his family's country estate. "They had maids and butlers. He even had his own horse!" his son, Upton, would recall. But Halas, Mara, and the other NFL owners took to Bell from the day he joined the league in 1933. As they quickly discovered, he was a bon vivant who walked into rooms with a smile and a wink. "In those days, he was a man about town," Upton said. "He didn't have any money in his pocket, except his father's, but he knew how to live as if he did. In other words, he liked to party and he liked to gamble and he liked to have a drink."
His powers of persuasion would eventually help him attain the NFL's highest office; more than a decade later, his colleagues would elect him commissioner. But in 1933, he was failing in his efforts to convince one person in particular to see things his way. He had been courting Frances Upton, a willowy, dark-haired comic actress who had starred on Broadway. More than once, Bell had asked her to marry him. She always declined. "She was the only person who could ever say no to Bert Bell," Upton Bell would write. The daughter of a decorated New York police sergeant, Frances demanded that Bell give up drinking before she would consider marrying him. After Bell finally agreed to do it, they were married in early 1934. Bell was almost forty. The pieces of his life were coming together. He had married a woman he truly loved, not one his father had suggested was appropriate. Yes, he had wasted a small fortune and no longer had his family's financial backing—a fact of which the other owners were unaware—but he had a knack for getting by. When he decided to start a pro football team, his future wife loaned him the necessary money.
Surveying his circumstances after the 1934 season, he saw only one real regret. As much as he enjoyed being in the NFL, it had a fundamental problem. The league's franchises were split into two groups, those that consistently won and those that consistently lost. Bell's Philadelphia Eagles were just two years old but already entrenched as a "have not." It was going to be nearly impossible for them to join the Chicago Bears and New York Giants in the top tier, Bell believed. In the two years since they joined the league, the Eagles had won just seven games. They had experienced a few highs, including a 3–3 tie with the Bears in 1933 and a 6–0 win over the Giants in 1934. Bell found the tie especially satisfying because it was played on a Sunday in Philadelphia just days after the blue law referendum passed; Bell had campaigned hard for that outcome. But the Eagles' victories, whether moral or real, were few compared to the many defeats they had suffered.
Their first league game was a disaster, a 56–0 loss to the Giants at the Polo Grounds on October 15, 1933—a staggering blowout in a year when NFL teams averaged 9.7 points per game. Three days later, only 1,750 fans attended the franchise's first home game, a 25–0 loss to the Portsmouth Spartans. Late in the 1933 season, so few fans were coming to the Eagles' home games that Bell offered a free car wash to anyone who bought a ticket. In 1934, the Eagles lost five of their first six games before defeating the miserable Cincinnati Reds, soon to fold, before a crowd so sparse that no official attendance figure was announced.
Pro football was going nowhere in Philadelphia. The 80,000 fans Army and Navy drew to their game in the city on December 10, 1934, was more than the Eagles had drawn all season. The man once known as De Benneville Bell was unaccustomed to being second-class in any endeavor, but the Eagles were second-class NFL citizens along with other losing teams such as the Brooklyn Dodgers, Chicago Cardinals, and Art Rooney's Pittsburgh Pirates. It was hard to envision any of them competing with the Giants and Bears, whose larger crowds generated more revenue, providing an edge in the competition to pay for top college players turning pro.
All the owners were affected by their team's losses, but Bell, like Halas, was a former player and felt them almost viscerally. He had played in the Rose Bowl and later coached winning college teams. He simply hated losing, and not just because it meant he might sell fewer tickets to the next game. Determined to improve the Eagles' prospects after the 1934 season, he began recruiting a player he thought could help turn the team around: Stan Kostka, a burly fullback and linebacker from the University of Minnesota. The Golden Gophers had won college football's national championship that fall, earning accolades as one of the greatest teams of all time by going 8-0 and outscoring their opponents, 270–38. Kostka, a square-bodied, 210-pound bruiser, led the offense in touchdowns and leveled opposing runners as a defender. Bell envisioned him battling the formidable linemen who made the Bears and Giants so daunting.
Bell placed a call to Kostka. The young man told him the Dodgers, Giants, Bears, Packers, and Pirates also had contacted him. "I asked him point blank if he would sign with the Eagles if I came out there to Minnesota and offered him a contract for more money than any other team in the league would give him," Bell told the Associated Press. "He said yes so... I went to Minneapolis."
As Bell told the story, he and Kostka met at a hotel. Bell pledged to top the highest offer Kostka received, which, according to Kostka, was $3,500 in salary for the 1935 season. Bell offered $4,000. When Kostka asked for time to think about it, Bell gave him an hour. "I knew what was in his mind. He wanted to get to a telephone and call the club that had offered him $3,500 and see if they'd top my offer," Bell said. "Apparently, he couldn't make the connection, because when he came back he still hadn't made up his mind. I told him, 'Look, I'll give you $6,000 if you sign now and let me go home.' He hedged. So I left."
Kostka eventually signed with the Dodgers for $5,000. Bell was furious. That was more than Bronko Nagurski made, and Bell thought a rookie should not earn more than the league's best player. And even more ominous, in Bell's view, was that Kostka had all the leverage. When teams bid against each other, the player prospered, but the teams suffered. How was that good for the league?
Bell was not the only frustrated owner. The recruitment of another college star, Alabama's Don Hutson, created more bad feelings and underscored the need for change. Hutson, a speedy receiver, had put on a show in the Rose Bowl on January 1, 1935, catching seven passes, two for touchdowns, against Stanford. The Packers' Curly Lambeau attended the game in Pasadena, California, and contacted Hutson several days later, suggesting he come play in Green Bay. Other teams also reached out to him, and like Kostka, Hutson played them off one another, driving up his price. Eventually, only Lambeau and John "Shipwreck" Kelly, the Dodgers' twenty-five-year-old player-coach, pursued him.
"Finally, Curly sent me a contract and I just went ahead and signed it," Hutson would recall years later. The contract called for him to earn $300 a game. But, according to Hutson, on the day he put the contract in the mail, Kelly showed up at his home in Tuscaloosa and offered to match Green Bay's offer. "I told Kelly I couldn't do that because I had already signed with Curly and put the contract in the mail that morning because I hadn't heard from him," Hutson remembered. "Kelly said, 'Don't worry. Sign a contract with me, too, and let me worry about it.'" Hutson signed another contract, which Kelly immediately mailed.
Both contracts reached Joe Carr's desk at the league office on the same day. Carr could not believe Hutson had signed with two teams and tried to figure out how to resolve the situation. Glancing at the postmarks on both envelopes, he saw that Lambeau's had been posted seventeen minutes earlier. That informed Carr's ruling. Hutson belonged to the Packers.
Kelly and the Dodgers were frustrated, as was Art Rooney, who had lost out in the bidding to sign several other players. "Something has to be done," Rooney told a Pittsburgh sportswriter. "Our club lost a bit less than $10,000 last year, yet when we try to sign a new man from the college ranks, we find other clubs immediately jack up the price. It becomes a wild scramble with the players in the end getting ridiculous first-year salaries from the richer teams while the tail-enders, who need new talent most, get slim pickings."
After losing Kostka, Bell proposed the idea that would forever change pro football. Why not institute a draft? Pool the top college players and let teams select them one at a time, starting with the team with the worst record—which therefore needed the most help—and proceeding through the standings in inverse order, with the best teams picking last. That would be fairer and more orderly than the mad scramble each year for the top college players. The talent entering the league would now be spread around more equitably, leading to more competitive games, and, ideally, eliminating the class line between the Giants and Bears on one hand and teams like Bell's Eagles on the other. Just as important, in Bell's view, was that only one team would then own a player's rights, eliminating the battles driving salaries so high.
In the first months of 1935, Bell quietly sold his idea to the other owners. Some did not need convincing; Rooney and others in the lower echelon immediately saw it could help them. But what about Halas and Mara? As owners of the most dominant, profitable teams, they would be relinquishing one of their primary advantages over the other teams. It was a pivotal moment. Halas and Mara saw they would suffer if a draft was instituted, but they also understood the league would benefit. "I thought the proposal sound. It made sense," Halas said. "Tim Mara also approved. He and I had more to lose than any other team. With our support, the proposal was adopted."
Mara said the possibility of the Giants being less dominant "was a hazard we had to accept for the benefit of the league, of professional football, and of everyone in it." He grasped that the NFL, still in its relative infancy, needed to change. "People come to see competition," Mara said. "We could give them competition only if the teams had some sort of equality, if the teams went up and down with the fortunes of life."
On May 18, 1935, Carr and eight owners met at the Fort Pitt Hotel in Pittsburgh. Bell stood and addressed the group. "Gentlemen, I've always had the theory that pro football is like a chain," he said. "The league is no stronger than its weakest link, and I've been a weak link for so long that I should know. Every year, the rich get richer and the poor get poorer. Four teams control the championships, the Giants and Redskins in the East, and the Bears and Packers in the West. Because they are successful, they keep attracting the best college players in the open market, which makes them successful." He made his pitch for an annual draft. The other owners liked it, and, after Bell sat down, they hammered out details. A motion was proposed, seconded, and passed unanimously. The inaugural NFL draft was scheduled for the following winter, shortly after the 1935 season.
"Bert was a very persuasive man. You have to remember that he was a politician at heart," Art Rooney said later. "He had come from a political family. His father and brother were active in politics. That must have been where he acquired the finesse to work with strong men like George Halas and Tim Mara and George Preston Marshall and persuade them to work together for the common good."
IF ANYTHING, THE 1935 EAGLES ILLUSTRATED THE NEED FOR the draft that would follow that season. They played eleven games, lost nine, scored just 59 points, and didn't win a single home game. Bell tried various tricks to boost attendance. He announced that clergymen of varying faiths would sit on the Eagles' bench every Sunday. He signed a halfback who had been in prison, thinking the curiosity factor might sell a few tickets. His desperation was evident.
The prison halfback, Edwin "Alabama" Pitts, was a navy veteran who had been convicted with three accomplices of robbing a grocery store in New York. Though he had never played organized sports, he starred on the football and baseball teams at Sing Sing Prison in upstate New York, becoming a media sensation. Upon his release, he signed with a minor-league baseball team in Albany, New York, but lasted fewer than fifty games before being released. Turning to football, he signed a four-game, $1,500 contract with the Eagles.
As Bell hoped, the press jumped all over the story, which helped lure 20,000 fans, the Eagles' largest crowd ever, to their 1935 season opener. But Pitts never played in a 17–7 loss to Pittsburgh, not even when the fans chanted, "We want Pitts!" Lud Wray, the head coach, gave Pitts some snaps in the next few games, and he caught a few passes. But the team kept losing, and fans lost interest. When Pitts's contract expired after four games, he was gone. "Bert, the only thing you haven't done is hire a good football team. Have you thought about trying that?" Halas told Bell after the Bears routed the Eagles, 39–0, on October 13, 1935.
The Eagles' dismal season ended with a 13–6 home loss to the Packers before 4,000 fans. A week later, the Lions defeated the Giants in the league championship game in Detroit. Bell attended the game, returned to Philadelphia, and began to organize the draft. Because it was his idea, the other owners had put him in charge. He reserved a suite at the Ritz-Carlton, a hotel that Bell's father owned and Bell had once managed.
On February 8, 1936, the owners gathered at the hotel for a meeting set to start at 1:30 p.m. Bell directed them to his suite, which featured a conference table, piano, and chalkboard resting on an easel, which Bell had brought in for the occasion. Tim Mara was joined by his sons, twenty-seven-year-old Jack, by now the Giants' president, and twenty-year-old Wellington, more knowledgeable than ever about the talent in the college game. George Halas and Charles Bidwill, the owners of the Chicago teams, arrived together. Curly Lambeau represented the Packers by himself, as did Pittsburgh's Art Rooney and Boston's George Preston Marshall. Lud Wray, the Eagles' coach, was on hand to help Bell.
The men took off their jackets and went to work. Their first job was determining the group of college players they could select from. The owners and coaches volunteered the names of players who had exhausted their college eligibility. Someone—likely Bell or Joe Carr, who ran the meeting—wrote the names on the chalkboard. When the list swelled to nearly one hundred, the men agreed they should draft more than five each, the number they had agreed to initially. Bell offered a motion to raise the number of rounds to nine. Halas seconded the motion and it passed unanimously.
In the coming years, as the owners came to see the draft as one of the most crucial events on their calendar, teams would employ scouts and turn the study of college talent into a richly funded science. But the first draft involved little sophistication. To gauge the skill and talent of outgoing college players, the owners and coaches had done little more than read newspapers and magazines, check college media guides and All-American lists, and attend a few games. Their idea of advanced scouting was soliciting opinions from their friends in the college ranks. Their budgets included no funds for scouting.
When the nine teams were ready to start the 1936 draft, the Eagles went first, as they had the worst record. Bell picked Jay Berwanger, a darting halfback from the University of Chicago, who had won the Downtown Athletic Club Trophy, a new award given by one of New York's foremost sports organizations to the nation's top college player. It would become the Heisman Trophy a year later, in honor of John Heisman, the club's athletic director, after he died. Picking second, Marshall's Redskins selected Riley Smith, an Alabama quarterback who had thrown passes to Don Hutson. Art Rooney took Bill Shakespeare, a Notre Dame halfback nicknamed "the Merchant of Menace." The other six teams quickly made their first selections, with the champion Lions going _before_ the runner-up Giants because the Giants had a higher regular-season winning percentage.
The Eagles began the second round by taking John McCauley, a halfback from Rice Institute in Texas. After the other eight teams made their second selections, Bell started the third round by drafting Wes Muller, a center from Stanford. The meeting, which had started shortly after lunch, continued into the early evening and evolved into a football stag party. "There were plenty of cigars, and the liquor flowed," according to a Philadelphia sportswriter. The event featured none of the fanfare the draft would eventually attract. Without offering details, the Associated Press simply reported that the league had adopted a "new ruling" about how college talent would be dispersed. The _New York Times_ did not immediately report that a draft had occurred.
By the end, after teams had selected eighty-one players in total, the owners took the next step, negotiating with their picks to see whether they could agree on a price. The players had not agreed to this method of distributing talent, and it did not benefit them; now that one team "owned" their rights, they could not solicit multiple offers and pit bids against each other. It was the first example of the kind of broad differences between owners and players that would ultimately produce labor strife. The players selected in the inaugural draft had only one bargaining tactic: they could threaten not to play, and many did just that. The NFL was, after all, hardly a path to riches. Most players earned around $250 per game. Many prospects, even the best ones, went into business instead. Only twenty-four of the eighty-one players selected in 1936 suited up for a game that season.
Long before the Eagles made Berwanger the first overall pick, he publicly suggested he might not play. He wanted to finish his studies and graduate, he said, and wanted to maintain his amateur status so he could try out for the 1936 US Olympic team as a decathlete. "I haven't decided what I will do. I may play professional football next fall because of its practical advantages. I might take a coaching job, although it is my ultimate intention to enter business in preference to making a career in professional athletics," he told the Associated Press in the fall of 1935.
When he failed to make the Olympic team, he began considering the NFL more seriously. Bell contacted him and asked what he had in mind as a salary. Berwanger reportedly asked for $1,000 a game. Bell countered with $150. Seeing that a deal was unlikely, Bell traded Berwanger's rights to the Bears, receiving in return a tackle, Art Buss. Halas coveted Berwanger, a front-page sensation in Chicago. But Berwanger only raised his price after the trade, and, when Halas refused to meet it, he decided not to sign. He never played in the NFL.
"He asked me what I wanted," Berwanger said of Halas years later. "I said $25,000 for two years and a no-cut contract. We shook hands, said goodbye, and he and I have been good friends ever since. They just couldn't afford to pay that kind of money." Instead of playing in the NFL, Berwanger coached at his alma mater until it dropped its football program in 1939. After serving as a navy flight instructor during World War II, he founded a company that made plastic and sponge-rubber strips for car doors, car trunks, and farm machinery. It was grossing $30 million annually when he sold it in 1992.
Bell's frustrations with the Eagles' inaugural draft class went beyond his failed negotiations with Berwanger. None of the nine players he selected ended up signing with the team. John McCauley, the second pick, took a job with a tool company in Midland, Texas. Another back from Rice, Bill Wallace, also went into business. Harry Shuford, a back from Southern Methodist University, went to law school. Al Barabas, a Columbia running back, chose minor league baseball. John "Jac" Weller, an All-American guard from Princeton, opened a real estate and insurance business. Pepper Constable, a Princeton back, went to Harvard Medical School.
Other teams faced similar problems. Shakespeare, the third overall pick, opted to work for the Thor Power Tool Company in Aurora, Illinois, rather than play for Rooney in Pittsburgh. The Giants' first pick, tackle Art "Pappy" Lewis, played just one season with the team. The most enduringly famous name among the eighty-one draftees never played in the NFL. Paul Bryant, an Alabama end taken in the fourth round by the Brooklyn Dodgers, decided to go into coaching. Nearly a half century later, "Bear" Bryant retired as the most successful coach in college football history.
The point of the draft was to give lesser teams a better chance to compete, and that eventually happened, but the 1936 draft did not immediately produce parity. Mostly, the rich got richer. Of the four future Hall of Fame inductees selected, tackle Joe Stydahar and guard Dan Fortmann went to the Bears, and running back Tuffy Leemans went to the Giants. The fourth, Wayne Millner, an end from Notre Dame, went to Marshall's Boston club.
Sixty-four players were drafted before Millner, offering the owners an early example of what would become one of the great truths about the draft: outcomes for individual players are hard to predict. A player everyone regards as a future star can quickly become a bust, while a player taken in a later round, almost as an afterthought, can turn out to be one of the greatest of all time. It was true in the first draft and remains true today, even with teams now relying on detailed, time-intensive scouting practices.
When the draft was instituted, the owners saw it as a means of solving their own problems, and, while Halas and Mara graciously agreed to a plan that ended up undermining their own teams' dominance, what was absent from the owners' discussions was any sense of the players' interests. At the time, the owners cared little about what players might think. Indeed, one of the selling points of the draft was that it would keep player wages in check. That many would-be NFL players decided not to sign up under the new terms should not have shocked the owners, many of whom were savvy businessmen, but it did. The owners did not count on pushback from the players. But more of that, much more, was coming.
#
# BETTING BONANZA
ON THE FIRST SUNDAY OF THE 1936 SEASON, THE PITTSBURGH Pirates hosted the Boston Redskins at Forbes Field in Pittsburgh. Almost 16,000 fans came to the stadium, mostly to see whether Art Rooney's team demonstrated any signs of improvement. The Pirates had won just nine of thirty-five games in their first three NFL seasons.
Following his usual game-day routine, Rooney attended a morning mass before making his way to the game. He was optimistic, believing his team was in capable hands. Joe Bach, the Pirates' head coach, was a flinty midwesterner who had suited up for Notre Dame in the 1920s as one of the "Seven Mules," the blockers who opened holes for the Four Horsemen. Now thirty-five, he had worked as a college assistant after his playing days and then produced a winning team as a head coach at Duquesne. He was in his second year with the Pirates.
George Preston Marshall was also optimistic about what the Redskins might achieve in 1936, although when he spoke with Rooney before the game, he offered his customary lament about Boston's lack of interest in his team. It might force him to do something drastic one day, he warned.
When the game began, the defenses dominated. In the second quarter, a Boston halfback fumbled, and the Pirates' George Kakasic scooped up the ball and raced 26 yards for a touchdown. That remained the game's only score until Kakasic booted a field goal in the fourth quarter to finish off a 10–0 victory for the Pirates. Ten days later, they traveled to Brooklyn for a weeknight game at Ebbets Field and won again, 10–6, to give them a 2-0 record for the first time. That was all it took for the Pirates to pique the interest of fans in football-mad Western Pennsylvania. A crowd of 25,800 attended their next game at Forbes Field, against the New York Giants, on September 27. The Pirates had never beaten the Giants. The year before, the Giants had annihilated them in Pittsburgh, 42–7.
Rooney hoped his friend from the horse racing scene, Tim Mara, would accompany the Giants on their trip. Next to Bert Bell, Mara was his closest ally among the league's owners. Rooney remained cautious around Marshall and George Halas, large personalities who dominated league meetings. But he had known Mara for years and trusted him. Mara, though, did not travel to Pittsburgh. He had steadily ceded more and more authority over the Giants' affairs to his sons. Jack, the team president, was on the trip. When the game began, Jack was on the press box roof, running a film camera. The Giants had started filming their games, hoping to learn more about their players by studying the film afterwards.
New York had lost its season opener to the weak Philadelphia Eagles, a disappointing result, and now the Pirates struck first with a touchdown in the second quarter. The Giants answered with a touchdown in the third quarter, and the game was tied when the Pirates drove to the New York 4 yard line in the final minutes. Three plunges into the line went nowhere, so Bach called on his kicker, who booted an 11-yard attempt through the uprights for the decisive points that gave Pittsburgh the victory. After the game, Rooney bid farewell to Jack Mara with a handshake, asking the young man to convey greetings to his father. Then he retired to his office to count his gate, his biggest ever.
ROONEY'S FIRST YEARS IN THE NFL HAD BEEN ONE LONG LESSON in humility. His semipro teams had ruled Western Pennsylvania for many years, but he quickly found that NFL squads were bigger, faster, better coached, and considerably more skilled. Nonetheless, Rooney continued to field teams comprised of working-class Pittsburghers, the same kind of players who had filled his semipro rosters. Harp Vaughan and Warren Heller were two of Rooney's old friends from the Northside. Cap Oehler had worked in the coal mines. Dave Ribble carried a Teamsters card. Winning was important, but, with jobs scarce in a depressed economy, Rooney thought it was more important to help out the men he had played cards and sports with since his youth.
The quintessential early Pirate was Mose Kelsch, a running back who played without a helmet. He had grown up an orphan in Troy Hill, a Northside neighborhood, and received little formal education. But Rooney met him on the city's sandlots, and he became a fan favorite on the semipro circuit, directly challenging defenders in his path with a straight-ahead running style. When Rooney joined the NFL in 1933 and formed the Pirates, Kelsch, thirty-six, became the league's oldest player. Still playing without a helmet, as NFL players could do until 1943, he no longer ran over defenders, but he could kick field goals and extra points. In one of the Pirates' first games, he waddled onto the field in the waning minutes, bald head glistening in the sun, and booted a game-winning kick.
With Jap Douds as the head coach, the Pirates had gone 3-6-2 in their first season. The local talent on their roster helped sell tickets, but the Pirates were no match for the NFL's established teams. Their first-ever road trip produced a 47–0 loss to the Packers. The Giants defeated them twice by a combined 50–5 score.
Rooney tried a different coach, Luby DiMeolo, in 1934, and traded for Johnny "Blood" McNally, a hell-raising halfback who had been kicked out of Notre Dame. He had caused so much trouble while playing in Green Bay that the Packers finally traded him, even though he was one of their star players. Neither move worked. McNally barely played because of injuries, and DiMeolo's primary qualification was being a friend of one of Rooney's brothers. The Pirates lost ten of twelve games, and the fans even turned on Kelsch when he missed several key extra points.
Near the end of the season, Rooney and DiMeolo were having a conversation in Rooney's office when DiMeolo mused that football players were tougher than boxers. Rooney, a former ring champion, took offense. The argument escalated until Rooney suggested they settle it with their fists. Someone brought in gloves and Rooney proceeded to batter his coach. When the season ended, DiMeolo was out of a job and Rooney hired Bach. (Kelsch never had a chance to play his way back into the fans' favor. He died in an automobile accident in July 1935. Rooney served as a pallbearer at the funeral.)
Bach put a greater emphasis on conditioning, blocking, and tackling, and in 1935, his first season with the Pirates, they opened with a victory over the Eagles and won back-to-back games against the Cardinals and Redskins in late October. With a 3-4 record, they were just a game out of first place in the East division. But, when they suffered key injuries, Rooney lacked the funds to pay for capable replacements. They won just one of their last five games.
That season, the Pirates drew an average of 12,489 fans per game, slightly above the league average but not enough for Rooney to turn a profit. His tickets were among the league's cheapest. He received no money for radio broadcasts of his games; in fact, he paid a station to air them. He had to schedule a slate of exhibition games against semipro teams to stay in business, and the extra contests exhausted the players, as evidenced by their late-season swoon. "In those days, nobody got wealthy in sports," Rooney said later. "You got two thrills. One came Sunday, trying to win the game. The next came Monday, trying to make the payroll."
Always looking for different ways to bring in money, Rooney had accepted an unusual offer from Tim Mara before the 1936 season. Seeking to bring a semblance of order to the league schedule—there had been little before—the owners had instituted a set of protocols after they split the teams into two divisions in 1933. But the rules were flexible. If both owners wanted to change the date and location of a game, they could. They could even swap one opponent for another. Mara wanted to avoid playing the Bears twice in 1936, thinking the Giants' win-loss record would benefit. He offered to pay Rooney to take the Giants' place on the Bears' schedule. Rooney agreed to the deal, which meant the Pirates had to play the fearsome Bears twice in a three-week span, first in Pittsburgh on October 4, then in Chicago on October 18. With a 3-0 record going into their home game against the undefeated Bears, the Pirates sold out Forbes Field for the first time. The Bears toyed with them, building a 27–0 lead before the Pirates made the final result more respectable with a couple of scores in the fourth quarter. Two weeks later, before 20,000 fans at Wrigley Field, the Bears defeated the Pirates again, 26–7. Bach bristled about Rooney's deal with Mara slowing his team's momentum.
The Pirates righted themselves, though, and, after they defeated the Eagles, 6–0, in a Thursday night game in Philadelphia in early November, they had a 6-3 record and a grip on first place in the East. The Giants were having a down year. The Redskins were the only other winning team in the division. With three games to go, bookies listed the Pirates as 7–5 favorites to win the East and host the league championship game at Forbes Field. But their final three games were on the road, and they lost the first two, to the Lions and Cardinals. Their season came down to their final game against the Redskins on November 29 in Boston. The winner would take the East and play for the NFL title.
Rooney was optimistic because the Pirates had beaten the Redskins earlier in the season and had two weeks to prepare for the rematch. But he also had promised a friend in Los Angeles that the Pirates would come to the West Coast for an exhibition game in the interim. The players dutifully boarded a train for the cross-country journey, played the game, and returned, but the trip wore them down, and Bach was so incensed that he and Rooney came to blows during the ride home. The team's mood was grim heading into the big game in Boston, and the Redskins won easily, 30–0. The players each received a $65 bonus from the league for finishing second, but Rooney was disappointed, and Bach simply fled the scene, taking the head coach position at Niagara University. Rooney would say later that one of his worst mistakes was letting Bach go. His team would not win more than four games in a season again until the early 1940s.
IN HIS FIRST YEARS IN THE NFL, ROONEY WAS CAREFUL IN HIS dealings with the other owners. He was quite a bit younger than most of them and neither as accomplished in business as Marshall or Bidwill nor as savvy about football as Halas or Lambeau. But that did not stop him from courting them, a natural inclination for someone so innately sociable. He took them to his favorite restaurants, in Pittsburgh and elsewhere. He attended mass with the Catholic owners. The others found him funny, kind, and likeable. It helped that Mara vouched for him.
But he could see he was different. The others, especially Halas and Marshall, were deeply competitive by nature, willing to do almost anything to beat you or somehow take advantage of you. When Halas and Rooney were dividing up the gate after the Pirates played at Wrigley Field in 1936, Halas shortchanged Rooney by several thousand dollars. "Halas, mistrustful by nature, may have been testing this younger man," Rooney's biographers wrote. Rooney pointed out the error. Halas denied it. Rooney insisted he was owed more. Halas held his ground. Eventually, they stood within inches of one another, and a fistfight seemed inevitable. Then Halas backed down, smiled, and said he was glad they had not fought. "George, you were no sure thing to win that fight," Rooney declared.
Football and the affairs of their teams consumed the other men, or so it seemed to Rooney. He cared about the Pirates, but they were not his top priority, and that showed in their performance. "Aside from Halas, Marshall, Curly Lambeau and Mara, I guess I, like most of the other owners, didn't pay enough attention to football," Rooney said later. He was busy in local politics, even serving as Pittsburgh's Republican Party chairman in 1936. He had obtained a license to promote boxing matches. He still played some semipro baseball in the summers. And, of course, there was his primary source of income—gambling on horse racing.
In the midst of tending to his various affairs, playing baseball, and preparing for the Pirates' season (he had named Johnny Blood the team's player-coach) in the summer of 1937, he drove to Empire City, a racetrack in Yonkers, New York, to bet on the races one weekend. It was a social occasion; he was accompanied by Buck Crouse, a retired middleweight boxer. Once he was at the track, Rooney made his way to the betting enclosure, where a stable of bookmakers, including Tim Mara, held court. In the days before tracks managed gambling with pari-mutuel machines, legal bookies ran what amounted to small businesses; they set odds on the horses and agreed to wagers in individual transactions with their customers. Mara hailed the short, cigar-chomping Rooney, assuring the other bookies his credit was good.
Mara always had the scoop on which horses were running well; several months earlier, Rooney had turned a tip from Mara into a $7,000 score at Belmont Park. Now, after a conversation with Mara, Rooney went to another bookie and placed a $200 bet on the first race at Empire City. (He never bet with Mara, not wanting to compete with his friend.) His horse came in, earning $800. Feeling bad about taking so much from the bookie, he went back with more bets, giving the man a chance to even the score. But Rooney won "three or four" races to raise his winnings to $5,000, which he then bet on a 5-1 shot. When that horse came in, Rooney was up somewhere between $19,000 and $25,000.
Art Rooney (left) and Tim Mara study the horse racing odds. (New York _Daily News_ Archive via Getty Images)
He was not betting strictly on Mara's advice. Rooney was a keen student of horses' performance records, which were published in the _Daily Racing Form._ He also was unafraid to play a long shot on a hunch or back a favorite when he thought it was warranted. In the feature race that day at Empire City, he bet $10,000 on heavily favored Seabiscuit to win the Jerome Handicap, and Seabiscuit won, earning Rooney almost twice his original wager. He lost several late-day bets but still ended up well ahead. Seldom, if ever, had Rooney experienced such a profitable day at the races. Mara advised him to take his winnings and go home. "Stick that dough in your kick and forget about the horses. I should know. I'm a bookmaker. It's my business to take money from guys like you," Mara said.
Rooney planned to take Mara's advice. While eating a celebratory streak dinner at a Broadway saloon that night, his dinner companion, the saloon's owner, asked, "What's your next move, Artie?" Rooney replied, "Back to Pittsburgh." But the owner, a classic New York hustler, talked Rooney into heading north to Saratoga, where the summer racing meeting was set to open. Rooney arrived at the famous track early on Monday, July 20, 1936, and began to gather information before making his wagers. The weather was foul—lightning struck a barn, killing a horse and knocking eight others unconscious—but expected to improve later. Rooney found Mara in the betting enclosure and asked which horses were running well. He ate breakfast at the track kitchen with the backside clockers, who timed morning workouts.
Mara had advised him to wait several days before starting to bet because the track was sloppy and a batch of unfamiliar horses had arrived from California. Rooney paid no heed. He approached another bookie in the enclosure and bet on Taken, a 5–1 shot, in the first race. Taken, ridden by famed jockey Eddie Arcaro, won the race. Rooney then won the second race with a colt named Little Marty, and, after losing the third, won two straight with bets on "mudders," horses that enjoyed running on a sloppy track. Rooney did not stop there, but rather began to bet even larger sums. When his horse came in at 7–1 in the sixth race, he had brought a track cliché to life: he needed a wheelbarrow for his winnings. By the end of the day, Bill Corum, a sports columnist for the _New York Journal-American,_ estimated that Rooney hade made close to $100,000—nearly $2 million in today's dollars.
Corum, on hand to cover the races, had heard about Rooney's streak as word spread through the grandstand that a "plunger," racing's description for a high-risk gambler, was making a killing. He found Rooney and accompanied him as he bet. Corum wrote a column published the next day headlined, "It's Art but They Don't Like It," depicting Rooney as a heroic underdog, a canny native of hardworking Pittsburgh who had outmaneuvered the big-city bookies. Other New York columnists at the track picked up on the story and wrote about Rooney as his streak continued the next day with winning bets in the first three races. By now, crowds were following him around the grandstand and cheering him as he approached the betting window with fistfuls of cash. The publicity had turned him into a sensation. Rooney was suddenly the most famous horse player in America. He ended up far ahead for a second straight day.
When his hot hand finally began to cool, he took Mara's advice and headed back to Pittsburgh. His wife, Kass, had been holed up in their apartment with their two young boys and was pregnant with their third child. He told her their lives were about to change because they would never have to worry about money again. After a few days at home, he headed back to Saratoga and added to his winnings. An urgent phone call from home interrupted his run. Kass was going into labor. Rooney promised Mara that he would name the newborn for him, in honor of the touts Mara had supplied. Timothy James Rooney was born on August 8, 1937. Rooney returned to Saratoga later that month and kept winning. It was hard to know exactly how much he had won when the meeting ended, but Mara estimated it was between $250,000 and $380,000—a life's fortune in Depression-era America, between $4.3 million and $6.5 million in today's dollars.
As summer waned and football season approached, Rooney began to focus on the Pirates. The other NFL owners had read about his run in the newspapers. Several sent congratulatory telegrams. Never again would Halas test the younger man. Apparently, Rooney was not to be trifled with. Back in Pittsburgh, Rooney continued to field interview requests from journalists. One day, a New York columnist called and explained that Marshall had expressed concern about Rooney being both a gambler and an NFL owner. Rooney replied, "When George gives up the broads, I'll give up gambling."
Rooney would eventually become one of Pittsburgh's most beloved citizens, but he was not yet a legendary figure in the 1930s. Around his city, he was mostly recognized as a down-to-earth local entrepreneur who promoted boxing matches and owned a losing football team. Sports fans did not begrudge him his success. In fact, they were pleased to see one of their city's own receive national attention. They hoped his run at the betting window would translate into better days for the football Pirates. But they would soon discover that it made no difference at all.
#
# MOVE TO DC
LIKE BERT BELL, GEORGE PRESTON MARSHALL WAS COURTING an actress, Corinne Griffith, a lithe, dark-haired beauty who had been known as "the Orchid Lady of the Screen" during her heyday in Hollywood's silent-movie era. Marshall wanted to marry her and went all out to convince her to say yes. When he proposed early in 1936, he arranged a theatrical-style backdrop that included African American performers singing about slaves in the Old South and serving mint juleps in _Gone with the Wind_ costumes. When Griffith agreed to marry him, Marshall's engagement gift to her was a Confederate flag that had been in his family since the Civil War.
After marrying, the couple spent most of the fall of 1936 in Boston, where Marshall ran the Redskins from a hotel suite. Many of their conversations followed a similar course. Griffith told her his team's games were boring. Marshall admitted she was right. Though new to football, she knew the entertainment game. She certainly knew a spectacle from a flop, and, by any measure, the Redskins were the latter. They had fewer than five hundred season ticket holders after five years in business. They often drew just a few thousand fans to their games, which were quiet affairs, only slightly louder than Griffith's silent films.
Marshall had gone into pro football believing he could rule it. None of the other team owners could match his business acumen. Though they were good men and he got along well with them, they were bookies and gamblers for the most part, sports guys, while Marshall had built a lucrative laundry empire. The others knew football, but Marshall was sure he was the one who could make the NFL into a big enterprise, with his team on top.
From the outset, convinced he knew best, he had meddled with his team on such matters as which players made the roster, what plays to call, even whether the captain should call heads or tails at the coin flip before kickoff. Other owners watched games from the stands and press box, but Marshall stalked the sidelines, cursing officials and shouting plays and substitutions to his coach. To his surprise, the Redskins did not win in the manner that he had won in the laundry business—that is, efficiently and completely. They won some games but lost more. In 1935, they went 2-8-1. Marshall cursed his players, his coaches, the referees. He churned through three head coaches in the Redskins' first four years. In 1936, he made an effort to improve the team, spending more on player salaries and hiring Ray Flaherty, a respected former Giants player, as the team's latest head coach. But he also nearly doubled his ticket prices, giving Boston's sports fans another reason to ignore a team and sport they had never been excited about, anyway. The Redskins performed better on the field, building a winning record, but continued to draw puny crowds. Boston's sportswriters criticized Marshall, suggesting in print that his prices were too high, his meddling hurt the team, and his sport was dull. The football teams at Harvard and Boston College garnered more headlines, as did baseball's Red Sox and Braves. "There were times on game day when the papers played the Radcliffe girls' field hockey team above our game," Marshall groused later.
With his movie-star wife, stretch limousine, and full-length raccoon coat, Marshall believed he was much too big and important to be ignored. He began to consider moving his team to another city. In November he invited Joe Carr to a home game against the Packers, an attractive opponent, primarily to demonstrate why he was so upset. Seeing a crowd of just 11,220 fans, Carr understood Marshall's concerns. The owner snapped after the game, telling reporters, "The nice thing about owning a pro football team is that all you have to do to move is pack your trunks."
Quietly, he scheduled a scouting mission in Washington, his hometown. He had concocted a plan. If he moved the Redskins to the nation's capital, he could market them not only to sports fans there but also to fans in Virginia, his native West Virginia, and the entire Deep South, where the football-mad public only had college football and, thus, lacked a rooting interest on Sundays. It was a grand idea, Marshall thought. Washington was ready for pro football, he believed. He could build the team with players from popular southern college teams such as Florida, Georgia, Tennessee, and Texas. The Redskins could become the pro team for the entire Deep South. It meant he could not use African American players from schools with integrated teams such as Michigan State or UCLA, but Marshall wanted an all-white team, anyway.
Marshall's wife thought it was a great idea. Boston had all but given up on the Redskins, it seemed, especially after Marshall publicly threatened to move. On November 29, 1936, they pounded the Pirates at Fenway Park, 30–0. Suddenly, all they had to do was beat the Giants at the Polo Grounds on December 6 and they would win the East division and play in the league championship game. But only 4,283 fans attended the home game against Pittsburgh. That was truly pathetic. The low turnout convinced Marshall it was time for bold action. If the Redskins did win the division, he decided he would yank the championship game out of Boston. He had not run the idea past Rooney, Mara, or any of his friends, but because he would be hosting the game, he could do what he wanted. He decided the Redskins would play the Packers, who had won the West, in New York.
Griffith nodded when he suggested the idea. On autumn evenings in their hotel suite in Boston, the two began to plot the rollout of the team once it was in Washington. Marshall would court the city's sportswriters and win them firmly to his side, preventing a reprise of what had happened to him in Boston. The _Washington Times_ was looking for a publisher; if he took that job, he could control the paper's coverage and feature the Redskins at the top of the sports page. The longer Marshall discussed the idea with his wife, the better it sounded. They could start a team band and stage elaborate halftime pageants featuring music, jugglers, maybe even live animals. They would give the fans in Washington something besides football, perhaps even a Christmas extravaganza with a plane flying over the stadium and dropping a parachuting Santa Claus onto the field. One way or another, Marshall would make sure "the Orchid Lady of the Screen" never again complained that the Redskins' games were dull.
RAY FLAHERTY HAD BEEN WARNED ABOUT MARSHALL. CONFIDENT and purposeful, he demanded that his contract with the Redskins include a clause forbidding the owner from stalking the sidelines during games. Marshall reluctantly agreed to watch from a field box behind the bench, but he soon devised another way to continue to interfere. He had a pair of telephones installed, one by his seat and one on the bench. Whenever he had an idea, he called Flaherty... during the game.
Although Marshall's team may not have been able to win over many fans, his officiousness entertained the rest of the league. Before the Redskins played the Giants on December 6, 1936, with the East division title on the line, a reporter asked Giants coach Steve Owen whether Marshall's "coaching" bothered him. "Bothered? I hope George Preston Marshall is in good voice. It ought to be worth at least a couple of touchdowns to us," Owen replied.
Marshall got the last laugh. Playing in a driving rain, the visiting Redskins took the lead with an early touchdown while their mud-splattered defenders handily controlled New York's offense. In the fourth quarter, Boston's Cliff Battles splashed 80 yards for a touchdown. The Redskins earned their first division title and a place in the league championship game with a 14–0 victory. Unable to hide his delight, Marshall sent a telegram to the Bears' George Halas, his friend and nemesis, whose team had finished behind the Packers in the Western division:
george, stop
guess what, stop
you get to watch us in the big game, gpm, stop
After the game, when Marshall told Carr about wanting to move the championship game to New York, Carr did not attempt to dissuade him. The league announced that Boston and Green Bay would play at the Polo Grounds that Sunday. Marshall was done with Boston and its disinterested press and fans. "We'll get a much bigger gate in New York," Marshall told reporters. "We certainly don't owe Boston after the shabby treatment we've received. Imagine losing $20,000 with a championship club." Though the teams and the league had less than a week to drum up interest, the game drew 29,545 fans—unquestionably more than it would have attracted in Boston. New Yorkers rooted for the Redskins, their fellow East division team, but were disappointed as the Packers scored early on a 48-yard touchdown pass from Arnie Herber to Don Hutson and went on to win easily, 21–6.
After the game, Marshall told reporters he was uncertain where he would move his team, suggesting Newark as a possibility. But he was being coy. He had hosted a contingent from Washington at the title game, including Clark Griffith (no relation to Corinne), who owned baseball's Senators and the city's largest sports venue, Griffith Stadium. The two men discussed a lease arrangement after the game, and four days later, on December 16, 1936, Marshall announced he was moving the Redskins to Washington. The _Boston Globe_ buried the story. The _New York Times_ barely paid attention, printing a short blurb at the bottom of a sports page. But it was big news in Washington. "Marshall Moves Boston Redskins to District," blared a _Washington Post_ headline. It was understood that the other team owners and Joe Carr would officially approve the move at a later date; they were not going to interfere with Marshall's plans.
Even before that approval came several months later, Marshall began to sell his team and his sport to a new city. The Redskins' success was hardly guaranteed. Washington was not known as a sports town. Attendance for the Senators had plunged when they no longer challenged for the pennant every year, unlike in their heyday in the 1920s. The best local college football teams, Georgetown and George Washington, elicited modest support. Marshall certainly recalled the failure of his own Palace Five basketball team in the 1920s. But against the evidence, Marshall believed the Redskins could thrive. He had been an outsider in Boston, a stranger to the city's leaders, but in Washington he knew just about everyone there was to know. He was already a success in the city, owing to his laundry dynasty, and he was sure he could succeed again.
His timing was fortuitous. Washington would grow from 486,000 residents in 1930 to 663,000 by the end of the decade. Thousands of newcomers arrived every year, lured by federal government jobs generated by President Roosevelt's New Deal programs. That Marshall opposed the New Deal on principle did not stop him from benefitting from it indirectly. Long a relatively sleepy, southern-style outpost, Washington was evolving into a sophisticated metropolis.
In another stroke of good fortune, Marshall drafted Sammy Baugh, a star quarterback from Texas Christian University, days before the move to Washington was announced. Marshall hoped Baugh would energize the Redskins' offense. He would do that and much more, it turned out.
Marshall and Baugh did not get off to an auspicious start. Baugh held out, turning down the owner's initial offer of a $5,000 contract for the 1937 season. Utilizing his only leverage now that one team owned his rights, he threated to play baseball for the St. Louis Cardinals, with whom he had also signed, explaining to Marshall that he had dreamed of playing in the major leagues since he was a youngster in Sweetwater, Texas.
For his part, Marshall was too busy to focus strictly on Baugh. Aside from the Redskins, he still ran his laundries and had signed a $100,000 deal to produce the Greater Texas and Pan-American Exposition, a World's Fair–like event that took place in Dallas from June through October in 1937. Assisted by his wife, a native Texan, he staged a months-long variety spectacular that included an auto race, historical reenactments, nightly activities, and sports contests featuring athletes from twenty-one nations.
As Marshall's negotiations with his top draft pick dragged on, he brought Baugh to Dallas and squired him around the exposition. Baugh was impressed with Marshall's showmanship and bombast, but the stalemate continued. Finally, just before the Redskins opened their inaugural Washington training camp in September, Baugh signed for $8,000, becoming the NFL's highest-paid player. After they agreed to terms over the phone, Marshall asked Baugh to bring a Stetson hat and some cowboy duds to Washington when he arrived to sign his contract.
"What size do you wear?" Baugh asked, thinking Marshall wanted the clothes and hat for himself.
"They're not for me, son, they're for you!" Marshall exclaimed.
He planned to market Baugh as a gun-slinging Texas cowboy coming to the big city to play football. Never mind that Baugh had grown up in a town, not on a farm, and was too busy playing sports to ride horses or lasso livestock. Marshall wanted him in cowboy garb when he came to the nation's capital. Reporters gathered at the airport for his arrival, and Baugh stepped off the plane wearing a Stetson, checkered shirt, whip-cord pants, and a pair of high-heeled cowboy boots. "My feet hurt," he whispered to Marshall, who met him on the tarmac. Baugh limped to his welcome-to-Washington luncheon at the Occidental Hotel, the _Washington Post_ 's Shirley Povich wrote later. But the ploy worked. It would not take long for Baugh to become known as "Slingin' Sammy."
When he reported to training camp, Ray Flaherty put him in a passing drill and encouraged him to hit a receiver "in the eye." "Which eye?" Baugh drawled. He might not have been an authentic cowboy, but he possessed a quality every successful quarterback must have: supreme self-confidence. A new era for Marshall's franchise was underway.
SHORTLY BEFORE THE REDSKINS BEGAN TRAINING CAMP THAT summer, the telephone rang one evening in the suite at Washington's Shoreham Hotel, where Marshall and Corinne Griffith lived. She picked up. Barnee Breeskin, leader of the hotel's orchestra, was on the line. Washington's new team should have a fight song, he said, just like college teams do. In fact, Breeskin said, he had already written one, titled "Hail to the Redskins." When Breeskin played the tune over the phone, Marshall was initially unenthusiastic. But Griffith had the opposite reaction and quickly penned lyrics to go with the music. "Braves on the warpath," she wrote, would "fight for old D.C." Some of the lines required a clichéd Native American dialect: "Scalp 'um, swamp 'um, we will / Take 'um big score. / Read 'um, Weep 'um, touchdown, / We want heap more."
The Redskins had their fight song. Now they needed a band to play it. Marshall heard about a brass ensemble composed of milk deliverymen from the Chestnut Farms Dairy, located just over the Maryland line from the District, and he soon hired them. The band debuted at the team's first home game in Washington, a Thursday night contest against the Giants on September 16. Marshall was excited to see the matchup draw 24,000 fans to Griffith Stadium, and he put on a show. In a pregame ceremony, the players were introduced, and the band played "Hail to the Redskins." Jesse Jones, chairman of a powerful Depression-era government agency, the Reconstruction Finance Corporation, tossed a ceremonial first pass.
A defensive game unfolded. Although Baugh had set passing records at TCU, Riley Smith lined up under center with Baugh and Battles behind him in a double wing formation. The Giants' defense kept them in check. (The Redskins' top pick in the inaugural NFL draft, Smith had actually signed and proved useful on the field.) The score was 3–3 early in the fourth quarter, with a field goal by Smith providing Washington's only points. As the Giants tried to move into scoring range, Smith intercepted a pass and ran 58 yards for a touchdown. A few minutes later, he kicked another field goal. The Redskins won, 13–3, with Smith having scored every Washington point.
The Redskins followed their promising start with a home loss to the Chicago Cardinals, and their attendance soon fell off. Only 7,320 fans witnessed a 14–0 loss to the Philadelphia Eagles at Griffith Stadium on October 10. Marshall fretted. The meager crowd was reminiscent of what he had endured in Boston. So far, he had sold fewer than a thousand season tickets in Washington.
In the latter half of the 1937 season, though, the Redskins surged. Flaherty handed more of the offensive responsibilities to Baugh, who mostly lined up at halfback, alongside Cliff Battles and behind Smith, the quarterback. All three attempted passes in Flaherty's progressive scheme, but Baugh threw the most, befuddling defenses with sharp tosses that sliced through the autumn air to open receivers. The Redskins won three straight games, lost one, and won two more as the fans returned. Leading up to a home game against the Packers, the reigning NFL champions, on November 28, tickets sold so briskly that Marshall anticipated a capacity crowd. "Mark me, there will be a new record for football crowds in Washington," he told the _Post_ 's Povich, who wrote that Marshall "envisions the Green Bay crowd as the last convincing argument to fling into the teeth of the doubters who said pro football would not take root here. He would like to send a set of record figures back to Boston where fans avoided his ball team as if the Redskins were lepers with the black plague running interference."
When the gates to Griffith Stadium opened on the morning of the Green Bay game, hundreds of fans rushed inside and quickly filled the general admissions sections. The streets around the stadium were clotted with traffic, keeping thousands from their seats when John Garner, Roosevelt's vice president, tossed a ceremonial first pass just before kickoff. But soon enough, as Marshall had promised, a record crowd of 30,000 filled the stadium.
The game was a low-scoring affair. The Packers led at halftime, 6–0, but the Redskins took the lead on a run by Battles in the third quarter and sealed the victory when Baugh threw a touchdown pass. With the win, the Redskins improved their record to seven wins and three defeats. If they won their regular-season finale the following Sunday, they would capture the East division and play in the league championship game for the second straight year.
But their final regular-season game was a tough assignment: a rematch with the Giants at the Polo Grounds. With a 6-2-2 record, the Giants also would capture the East if they won the game. The contest was effectively a championship semifinal. Bookmakers favored the home team; a mixture of rain and snow was predicted, and the Giants' powerful squad was better suited to playing on a bad field. Ignoring the prognosticators, Marshall told reporters his team would "sweep the Giants aside like rubbish." Washington fans fed off his enthusiasm, immediately snapping up 350 tickets at the Redskins' offices. Another thousand tickets were ordered and quickly sold. The Pennsylvania Railroad scheduled special trains to run between Washington and New York on the Sunday of the game, arriving before kickoff and returning that evening. In the end, 8,000 Redskins fans traveled to New York by car, bus, plane, and train.
"The invading Washington rooters were much in evidence on the Eighth Avenue subway from Penn Station to the Polo Grounds. It wasn't difficult to distinguish them," _New York Times_ columnist John Kieran wrote. "They wore feathers in their caps and whooped. One hung up a big pasteboard sign in a subway car. It read: 'Redskins Special.'"
In a surprise that delighted the fans, the members of Marshall's band mustered on Seventh Avenue outside Penn Station. Marshall not only had brought them to New York, but he had outfitted them in "new costumes of burgundy and gold, with white feather head-dresses, imported straight from Hollywood. The leader and two drum majors wore chief's war bonnets with streamers of white feathers that fell all the way to the ground." As the band marched up Seventh Avenue toward Columbus Circle playing "Hail to the Redskins," hundreds of fans fell in behind it, roaring the lyrics. "They were simply full of loyalty and red feathers and other things," Corinne Griffith would write later, recalling the scene. Marshall, sporting a new raccoon coat, strode confidently in front of the band. "George Preston Marshall slipped unobtrusively into town today at the head of a 150-piece band and 10,000 fans," _New York Journal-American_ columnist Bill Corum wrote.
The traveling Washington supporters filled several sections of the Polo Grounds' seating bowl, but New York fans still dominated the crowd of 58,285, the second largest ever to watch a pro football game, behind only the massive gathering of curiosity seekers who had turned out to watch Red Grange in New York in 1925.
Once the game began, it became apparent that the Giants' defense was not prepared to check the Redskins' attack. With Battles rushing for large gains and Baugh hitting open receivers, the Redskins mounted a drive that produced a touchdown. Then Battles broke free for a 75-yard run down the sideline, setting up another score. In the second quarter, Baugh completed four passes on yet another scoring drive. With their team holding a 21–0 lead at halftime, the visiting Washington fans were almost delirious. Hundred stormed onto the field and "paraded in a wild demonstration," marching behind Marshall's band as it gave a halftime concert on the field.
But the Giants returned to the field with renewed purpose. They scored a touchdown on a 62-yard interception return, and, a few minutes later, their offense drove steadily until quarterback Ed Danowski hit Tuffy Leemans on a short pass for a touchdown. Washington's lead was reduced to seven, and the stadium "was in a frenzy," the _New York Times_ reported. "Complete strangers slapped one another on the back. The Giant benchwarmers came perilously close to rushing on the field and parading their mates around the gridiron on their shoulders. Pandemonium hit the Polo Grounds with a lusty hand." But the Redskins "hauled out their tomahawks and went to work again," according to the _Times._ Baugh completed four straight passes, the last to a wide-open Ed Justice for a touchdown. The rally had been blunted, and the Redskins overwhelmed the Giants in the fourth quarter. Danowski dropped back to punt near his goal line, but "the gargantuan form" of the Redskins' 258-pound Turk Edwards was "on him in a flash." Edwards blocked the punt, and a teammate fell on the loose ball in the end zone.
New York fans remained in their seats, mesmerized by the Redskins' performance. "There is not a superlative in the English language that can quite describe the magnificence of the Washingtonians," Arthur Daley would gush in the _New York Times._ "There was no Cliff Battles or Slingin' Sammy Baugh in the New York lineup. The way Battles carried the ball had to be seen to be believed." Shortly after the blocked punt and resulting touchdown, Battles intercepted Danowski at the Redskins' 24 yard line and headed in the other direction, weaving between lunging Giants trying to bring him down. Exhausted after 75 yards, he was tackled one yard short of the goal line. Riley Smith bulled into the end zone on the next play, and the Redskins later added yet another touchdown. The final score was stunning: 49–14. The Giants had only allowed 60 points all season before this game.
When the last whistle blew, the 8,000 Washington fans "joyously stampeded onto the field," the _Washington Post_ reported. "Then, fighting off police who attempted to defend the goal posts, the wildly cheering contingent seized the uprights, rent them in splinters and bore the remains on the field in a triumphant procession. Long into the darkness the wild celebration continued until the Capital fans were forced to scurry downtown to board special trains back to Washington."
Marshall was euphoric. Not only had his players backed up his pledge to "sweep the Giants aside like rubbish," they had scored more points in a game against the Giants than any opponent in New York's franchise history. When the Redskins returned to Washington, 5,000 fans greeted their train at Union Station. The city had fallen in love. The Redskins' season ticket total would soar from 958 in 1937 to 10,951 in 1940 and 31,444 by 1947. To this day, the team's fan base remains one of football's largest and most loyal.
In the 1930s, the league championship-game site alternated every year between the homes of the East and West division winners. Having "hosted" the game in New York the year before, the Redskins now traveled to Chicago to face the Bears for the 1937 title at Wrigley Field. Unable to stop himself, Marshall again pledged a victory, and, again, his players backed him up. The Redskins won, 28–21, with Baugh tossing touchdown passes of 55, 78, and 35 yards.
The bizarre "indoor" title game between the Bears and Portsmouth Spartans had been played in the same city just five years earlier, but already it seemed like an event out of football's distant past. There had been just one touchdown in that game, which was dominated by the defenses. But the league had instituted important rule changes since then, hoping to open up the pro game, and the changes had worked. In 1937, the Redskins and Bears combined for seven touchdowns and more than 800 yards of offense in the championship game. Football's future had arrived, ushering Marshall to the pinnacle of the pro game—right where he had always thought he belonged.
# **PART THREE**
#
# BROTHERHOOD OF RIVALS
IN THE SECOND QUARTER OF THE 1937 CHAMPIONSHIP GAME between the Bears and Redskins at Wrigley Field, Sammy Baugh absorbed a brutal hit and limped to the sideline with a hip injury. He missed more than a quarter but returned in the second half. In the final minutes, Baugh, playing defense, tackled a Chicago halfback, Dick Plasman, near midfield. Plasman, one of the last NFL players still performing without a helmet, believed Baugh was playing too rough and punched him as they tumbled out of bounds. A fight between the teams broke out, and George Preston Marshall leapt from his field box to join it, eventually finding himself jaw-to-jaw with George Halas. They exchanged obscenities and insults and nearly came to blows.
When tempers finally cooled, Marshall returned to his box. His wife was livid. "That man Halas is positively revolting!" Corinne Griffith sputtered.
Marshall roared back at her, actually shaking a finger under her nose. "Don't you dare say anything against Halas! He's my best friend!"
For Griffith, who was still relatively new to football, it was a startling introduction to the curious brotherhood of men who governed the NFL. Even though they fought at league meetings, and even occasionally on the field, all was quickly forgotten amid their efforts to see their sport survive and prosper. "They were the most unique set of men in American sports history. They argued and fought like crazy, but the air was always cleared the next day," Bert Bell's son, Upton, said. "Through it all, they developed respect for each other and became the closest of friends."
Halas and Marshall had known each other since the 1920s, when they owned teams in the same pro basketball league. Each was headstrong, intensely competitive, and wanted desperately to beat the other. At league meetings, neither took a bathroom break out of fear that the other might take advantage of his absence and pass a rule favoring his own team. But they also were "drawn together" in what amounted to "love at first sight," Corinne Griffith later wrote. Within days of their near-fight at the 1937 championship game, Halas and Marshall were on the phone, exchanging jokes while they arranged postseason exhibition games between their teams in Dallas and Miami.
Texas and Florida were populated by zealous college football fans who had never seen a pro game. Marshall wanted to convince them not only that pro football was a quality product but also that they should support the Washington Redskins. Halas had a more immediate reason for wanting to schedule extra games. He needed the money. Just a few years removed from giving his players IOUs instead of their salaries, Halas, unlike Marshall, was not a wealthy man. The Bears always walked a thin financial tightrope. The proceeds from exhibition games might keep Halas from having to take out a loan.
The Redskins and Bears split the two reenactments of the championship game, with the game in Miami disintegrating into a brawl that led to eight player ejections. When the other NFL owners read about the games in the newspapers, they were dismayed. The Redskins and Bears were making money. It could create a competitive advantage for what were already two of the league's best teams. When the owners convened at the Ritz-Carlton Hotel in Philadelphia for a league meeting in late February, they quickly passed a resolution banning offseason games for every team except the champion, which could only play one—a late-summer contest against a team of college all-stars, which had already become a popular annual event.
As always, much of the meeting was given over to finalizing the schedule for the upcoming season—an exhausting debate. Every owner had issues, either stadium conflicts or the desire to play certain opponents on certain dates. Satisfying everyone's agenda was impossible. The owners had put a scheduling protocol in place after they split the league into two divisions in 1933. Every season, a team played two games against each of its four in-division opponents (one in each city) and faced two opponents from the opposite division on a rotating basis. Another opponent from the opposite division was selected out of a hat, completing an eleven-game schedule for each team. Scheduling had been haphazard since the league's earliest years, but, finally, it made a modicum of sense. Still, even in 1938, the situation was flexible. If both owners wanted to change the date and location of a game, they could, with permission from the league office. They could still even swap one opponent for another if all three teams agreed.
Year after year, the schedule generated more ill feelings among the owners than all other matters combined, with the debates inevitably becoming heated and personal. Halas, Marshall, Rooney, Bell, and Mara had different goals. As the owners of losing teams, Bell and Rooney cared more about their bottom lines than their win-loss records and did not mind giving up home dates; they needed to play before larger crowds on the road just to stay afloat. Halas and Marshall, as the owners of winning teams, were always looking to add home games they could win, even if it meant playing a lesser team and selling fewer tickets.
Year after year, no one made out better than Mara. Every other team was always happy to come to New York because the visitors' take of the Giants' gate was the largest in the league. The Giants wound up playing more home games, which helped them continue to dominate on the field. Between 1936 and 1941, they faced the Bears and Packers eight times during the regular season, and all eight games were at the Polo Grounds; a game in Green Bay, especially, would not produce nearly as much revenue for the teams to split.
No matter where they were situated in the league hierarchy, though, the influential owners knew it was important to attend meetings and fight doggedly for their teams' best interests. "The owners with the staying power were the ones who came away with the decent schedules," Rooney said. "The guys who snuck out to get some sleep or go night-clubbing wound up getting murdered the next season because when they weren't there to defend themselves, we'd give them all the dates we didn't want."
On the first day of the Philadelphia meeting in February 1938, a tentative schedule for the upcoming season was put on a chalkboard. So many issues ensued that the session did not adjourn until two in the morning. As usual, Marshall's voice was the loudest in the room. He was not pleased that the Redskins were scheduled to return to Chicago to play the Bears. Washington had just played the championship game in Chicago, and, though Marshall had won, he did not want to go back that fall. He was still trying to sell pro football to a new city, and he believed a home game against the Bears, a championship rematch, would help immensely. Marshall and Halas had argued about it during their teams' postseason exhibition tour, and Marshall brought up the issue at the league meeting. "It is absolutely vital to us, as far as the press and public are concerned, that the Chicago Bears play a game in Washington this year," Marshall thundered. "We have played the Bears in the (title) game in Chicago. We have played them in several exhibition games. We have been, naturally, as we should be, as good members of the league, very reasonable with Mr. Halas, and we expect him to be so with us."
The other owners suggested Marshall was putting his own interests first and did not deserve an extra home game. He explained that this was not about him getting an extra home game; he believed a rematch of championship-game opponents from the prior season should always take place in the city that did not host the title game. The fans in that city deserved to see the top teams play.
One of Halas's favorite tactics was to say little at certain times, and he did that now, believing the other owners would not side with Marshall, who continued to speak. "I don't think there is a member here who would think it unreasonable if I offered that idea as a resolution," Marshall said. "I don't think my request is unreasonable. But I am perfectly willing to abide by the judgment of the league and put it to a vote."
Tim Mara could stay silent no longer. "I don't think that is a legal form of procedure," the Giants' owner said. He had never cared for Marshall, even before their teams became rivals for East division supremacy. Marshall's loud officiousness set off Mara's temper. Art Rooney would later recall watching the two "get redder and redder as they yelled each other at league meetings. Maybe it was the schedule, or a change in the rules. It didn't make any difference. They just liked to fight." Now, after listening to Marshall propose a vote on switching the site of his game with Halas, Mara snapped. "There is no use putting to a vote something that is not right," he said, staring at Marshall. Taken aback, Marshall appeared to relent. "I didn't say I think there should be a vote on it. I did not mean to put it in that form, Mr. Mara," he said. "But I think it ought to be a question of whether it is acceptable to Mr. Halas."
After being prodded by Carl Storck, the league secretary, who was running the meeting, Halas finally spoke: "I don't see any reason why he should have six games at home and the Chicago Bears only have four. I think the public of Chicago is entitled to an even split. Why should he not have five home games in Washington and we have five home games in Chicago? The fact that he won the pennant does not mean a thing. The pennant has been won before by the Bears, and it was won by New York, and by the Packers and Lions, and they never asked for the best of it."
Storck finally asked for a vote on Marshall's resolution that would make it compulsory to reverse the site of any championship-game rematch played the next season. Mara, Bell, and three other owners supported Halas, giving him a majority. Rooney and three others sided with Marshall. "The motion is lost," Storck said.
Hearing that, Bell asked to change his vote. He felt the issue should be decided in private, between the two owners, not by a vote. Now the tally was five against and five for. Storck declared a recess so that Halas and Marshall could settle the dispute, which was holding up the scheduling process for the whole league. But Halas and Marshall had been arguing over the matter for several months, and there was no hope of either changing his mind. Halas had the NFL law on his side, but he liked Marshall and wanted his rival to feel any decision was fair. He offered to flip coin, a magnanimous gesture from a fierce competitor with the upper hand. Marshall agreed, and a coin was produced.
Halas won. That fall, the Redskins traveled to Chicago and played the Bears on November 13 at Wrigley Field. The Bears, in the midst of a down season, came into the game with a .500 record, while the Redskins held first place in the East—but the Bears won the game easily, 31–7.
AFTER THE DECISIVE COIN FLIP AT THE PHILADELPHIA MEETING in February 1938, the owners spent an entire afternoon trying to finalize a schedule tolerable to each of them. But they failed and finally just tabled the matter so they could turn to others before the meeting adjourned.
Their first piece of other business was addressing a letter from Damon Runyon, the famous writer, who was presenting an offer to the league from a business group in Miami. The group wanted to move the NFL championship game to their South Florida city for the next five years, and it was offering attractive financial terms—a guaranteed $40,000 payout every year, with a percentage of gate receipts beyond that also going to the teams. The owners were tempted. The championship game had never generated that much money, and it was seldom played in good weather because most of the teams in the league were in the Northeast or Midwest. Wintry conditions had hurt the gate for several of the championship games, including the most recent one in Chicago. Only 15,878 fans had braved frigid temperatures to watch the Redskins and Bears.
Nearly three decades later, pro football's owners would approve the idea of playing their championship game at a warm-weather neutral site. The game would quickly become known as the Super Bowl. But in 1938, the owners still believed the drawbacks outweighed the upside, primarily because each of them could not imagine abandoning his fans for such an important game. "I move that the president be directed to thank Mr. Runyon for his kind offer," Mara said, "and advise him that it would be impossible for the teams in this league to play the championship game in Miami for the reason that it would be unfair to the fans who support our games during the season."
Rooney second the motion, and it passed unanimously. The meeting soon turned to weightier matters. Halas stood, and the room fell silent. He said Runyon's offer indicated that their championship game was growing in stature. Obviously, the league had taken a step in the right direction when it established the two-division setup and postseason title game. Those changes had instilled order where chaos once ruled. But although its seasons were better organized now, the NFL still had problems, Halas said. One of the biggest, in his opinion, was the continuing disparity between the "have" and "have not" franchises. Bert Bell's draft should eventually level the playing field, he said, but at this point, the predraft status quo endured. The same teams won year after year—Packers and Bears in the West, Giants and Redskins in the East. With their superiority assured, it was no surprise, Halas claimed, that some teams had strong attendance while others could not get anyone to come to their games.
The Giants were in a class by themselves, having drawn an average of 35,717 fans to their home games over the course of the 1937 season. Their total season attendance of 250,025 represented more than a quarter of the entire league's attendance for the season, more than double any other team's total. Halas did not need to point out how auspicious these facts were. If the Giants did not yet match the stature of baseball's Yankees and Giants in New York, they were gaining ground.
After the Giants, there was a tier of teams that were at least not failing at the gate. The Bears had averaged 22,752 fans per game in 1937, while the Redskins averaged 18,837 and the Lions averaged 18,830. Those were decent if unspectacular figures. Aside from those teams, though, the news was depressing. None of the other six teams was faring well. After eight years in Brooklyn, the Dodgers still played in the Giants' shadows, drawing less than half as many fans. Pittsburgh's Pirates had averaged 13,089 fans per game in 1937, not enough to make a profit. The Packers, though winners on the field, averaged just 12,888 fans per game, almost solely because of their stadium's limited capacity. The league's newest team, the Cleveland Rams, had flopped in 1937, averaging just 11,160 fans per game, but they still outdrew the Chicago Cardinals and Philadelphia Eagles. One of the league's oldest teams, the Cardinals had drawn just 25,812 fans all season. Bert Bell's Eagles had attracted just 23,698.
The absence of parity was a problem, Halas said, but an even more pressing one, he believed, was the way the game itself was played. Although loosening the rules to promote more passing and scoring had made pro football more entertaining, NFL games were still dogged by issues that could serve only to repel fans. Many games seemed to drag, lasting more than two and a half hours, with long lags between snaps. The pace was too slow. The officiating also needed to be addressed, Halas said. The owners strived to pick competent officials and educate them about the rules, but almost every game was marked by disputes and controversies. That was bad for the league. Fans needed to have faith that the officiating was unbiased and competent.
Several other owners surely smirked at his last suggestion. Throughout the league, it was widely believed that the Bears received favorable treatment because of Halas's relationship with Joe Carr. Officials who either lived in Chicago or were intimidated by the famously imperious Halas always seemed to work the Bears' games. Exhibit A was the jump-pass touchdown that decided the indoor championship game in 1932. It almost surely was illegal, but the officials had let it stand. The next year, Carr even allowed Halas's own brother, Walter, to officiate a Bears game.
More evidence of Halas's sway had come at a 1934 league meeting. Some owners had proposed making a dropped lateral a live ball, a change Halas feared would inhibit his T-formation offense, which relied on laterals. "You gentlemen will destroy me and the modern T-formation," he cried. Wellington Mara would recall that Halas "was bitterly opposed" and "gave one of his most passionate speeches. He really cried. Real tears." The owners voted in Halas's favor. They could not bear to cross him.
Wellington Mara also remembered a minor incident at Wrigley Field that, he believed, spoke volumes: "An official went to retrieve a punt that had gone out of bounds. He dropped his cap to mark the spot. George took his foot and moved it a foot or so in favor of the Bears. The distance meant nothing, but the action was typical. Halas just couldn't resist getting every possible advantage for the Bears."
As he spoke at the 1938 league meeting in Philadelphia, though, Halas seemed to truly have in mind the league's best interests, not those of the Bears. The men in the room were his partners in the pro football business. Their game, their product, needed help. And Halas believed he knew who could provide that help: Hugh "Shorty" Ray, an official and rules aficionado from Chicago.
Halas and Ray had both attended Chicago's Crane Tech High School and the University of Illinois. Like Halas, Ray had played football for the Illini, even though he stood just five feet six. After studying mechanical engineering in college, Ray took a job as a mechanical drawing instructor at a Chicago high school. He also became a high school football official and found his calling. In 1917, he started an association that oversaw the training and licensing of high school officials throughout Illinois. When college football became popular in the 1920s, he officiated Big Ten games.
Halas respected Ray. He was aware that Illinois _high school_ football possibly had better officiating than the NFL. At the 1938 league meeting in Philadelphia, Halas suggested to the owners that they bring in Ray as a consultant. The officiating was bound to improve, Halas said. The other owners agreed to the proposal. Although Halas exasperated them at times, they bowed to his knowledge and ideas about football; aside from Bell, he had the most storied career as a player and coach.
Ray did not seem like a man who would significantly change pro football. He was fifty-four years old, short, and nebbish, wore horn-rimmed glasses, and spoke in a high-pitched monotone. But he would leave a lasting mark on the NFL. Within two years, he had organized four-man teams of "followers," as he called them, who traveled to every game with stopwatches in hand, studying penalties, timeouts, and other fine-point mechanics of the game. After reviewing the data his teams produced, Ray proposed changes both big and small. He noticed that seconds were wasted almost every time the ball went out of bounds and prompted the owners to add sideline crews tasked with retrieving the ball quickly and getting it to the officials. Ray also discovered that many controversies resulted from the officials not clearly signaling their rulings. A set of hand gestures was already in place, but Ray encouraged the officials to gesture with greater clarity and enthusiasm.
In the coming years, Ray would become a fixture around the league and a major influence. He changed the shape of the pro ball, streamlining the more rugby-ball-like original. He helped make the officiating more professional. Every summer, Ray would give his officials a written test, demanding that they correctly answer 95 percent of his rules questions. "He pounded the rules into his officials," said Mark Duncan, the NFL's supervisor of officials, in a 1966 interview. Ray also transformed the game itself. With less time wasted, a given game had more plays, more action. The pace improved, and scoring rose, in part because of new strategies implemented by forward-thinking coaches, but also because teams simply had more time with the ball.
Every year, Ray traveled to training camps and presented the latest rule changes to the players and coaches. Some snickered while he spoke; he had none of the bravado of most men in football. Some coaches believed he had made the game too complicated. But, as Halas would later put it, hiring Ray was "my great contribution to the National Football League. Every team in the league has benefitted from his efforts." Indeed, although Halas, Marshall, and the other large personalities deserve the most credit for putting the league on firm footing, unsung figures such as Ray and Joe Carr also helped make the game what it is today.
#
# A STEP FORWARD
AFTER THE GIANTS' LOPSIDED LOSS TO THE REDSKINS ON the last Sunday of the 1937 season, Tim Mara did not want to attend the league meeting in Chicago a few days later, knowing he would encounter George Preston Marshall. But he knew he needed to be present at the Sherman Hotel for the gathering, scheduled for a day before the championship game between the Bears and Redskins. The league's annual college draft was on the docket.
Mara traveled to Chicago with his sons, Jack and Wellington. Now a twenty-one-year-old Fordham University graduate, Wellington Mara had talked his father into allowing him to skip law school to work for the Giants. Given the title of secretary, he was in charge of everything from arranging travel to purchasing equipment to negotiating player contracts. He also handled the team's scouting efforts, and it was in this role, as a talent evaluator, that he truly distinguished himself. The league's other football men relied mostly on newspaper articles to learn more about notable college talent, but Wellington spent his fall Saturdays in the stands at college games. Then he contacted administrators, coaches, and even professors to get the inside scoop on his favorite prospects. He had maintained files on players since his middle school days.
In 1935, while at Fordham, Wellington took a train to Washington one Saturday to watch George Washington play Alabama. He was there to see Tuffy Leemans, a fullback for George Washington. They arranged to meet in front of the school's gym after the game, with Wellington having signed his father's name to the telegram to increase the chances that Leemans would show up.
"When I got there, he thought I was a kid who wanted his autograph. He looked at me strangely suspicious," Wellington recalled later. Leemans protested that he was supposed to meet with Tim Mara, "but I was able to convince him that I was in fact a legitimate emissary, and he did listen to me," Wellington remembered. The Giants eventually selected Leemans as a second-round pick in the 1936 draft, and he became an immediate contributor, leading the league in rushing as a rookie before settling in as a vital offensive "triple threat" who piled up yards rushing, passing, and receiving.
Two years after Wellington's first meeting with Leemans, when he was on his way to Chicago for the draft in December 1937, Wellington shared with his father the extensive files he had amassed on that year's prospects. None of the other teams had nearly as much information. In the parlance of the racetrack, which the elder Mara understood, the Giants were lengths ahead of their rivals coming down the stretch. Nonetheless, Mara insisted that his son share his research with the others. When the owners and coaches met to select players at the Sherman Hotel, Wellington unveiled his list of the top 166 prospects on a chalkboard. To his father, Wellington protested that teams that failed to pay attention to the college game did not deserve the help, but Tim Mara was adamant, heeding an ethos that Joe Carr had preached and that Halas also subscribed to and embodied: They might be enemies on the field, but the owners were partners in a business. They needed to strive for the betterment of the group, even if those on top suffered in the process. As they had understood during the debates over scheduling, a few successful teams would not make for a successful league. They all needed to do well. "The thinking was, 'If you don't all stand together, you're going to die,'" said Upton Bell, Bert's son.
"It was a pretty remarkable thing, when you think about it," said Virginia McCaskey, Halas's daughter. "They were all very strong-minded, strong-willed individuals, but they understood they had to give up personal considerations if they were going to make it. The draft, no league had ever done that. I remember hearing my mother questioning my father on some things, 'Why are you doing that when it might hurt the Bears?' His response was what happens on the field was different from the business of the league."
The draft began at the Sherman Hotel shortly after noon when Carl Storck, the league's secretary-treasurer, called the meeting to order. Originally instituted to promote competitive balance, the draft had been only marginally effective so far. The additions of Baugh and Riley Smith had helped turn the once-lowly Redskins into winners, but the perennially strong teams still dominated, and neither the Eagles nor the Pirates, losing teams both, had signed any of their top picks. Frustrated, Rooney opened the Chicago meeting by proposing that losing teams receive twice as many picks as winning teams, but the motion failed. The powerful owners were not willing to go that far.
With the fourth pick in the first round, the Pirates selected Byron "Whizzer" White, a speedy halfback from Colorado regarded as the most naturally gifted player in the draft. But he also was a top student and was competing for a Rhodes Scholarship, which would take him to Oxford University in England. The teams drafting ahead of the Pirates had avoided White for that reason, but Rooney, always a gambler, picked him anyway. His bet paid off when Oxford allowed White to postpone his studies for a semester, enabling him to play for the Pirates in 1938. White's $15,000 contract immediately made him the league's highest-paid player, and, when he signed it, the ceremony was covered in a live national radio broadcast, a rarity for the Pirates. White proved he was worth the investment in the short term, leading the NFL in rushing as a rookie. But the Pirates still finished last in the East, winning just two games. Shortly after the season, White left for England to begin his studies at Oxford and never again played for Pittsburgh. When he changed his academic track a year later and returned to the United States to attend Yale Law School, he played for the Detroit Lions for two seasons, leading the league in rushing once more, before joining the navy in 1942.
The Chicago draft did help several teams in more substantial ways. The Lions selected Alex Wojciechowicz, a sturdy two-way lineman who would become an All-Pro and later gain induction to the Hall of Fame. The Packers found a new tailback, Purdue's Cecil Isbell, who would become a league-leading passer and part of a championship squad. The Dodgers added Frank "Bruiser" Kinard, a tackle from Ole Miss who would earn all-league honors in six of his nine pro seasons.
In all, the teams combined to pick 110 players, and when the process ended late that afternoon, the owners joined in applause in the room for Wellington Mara, who had helped guide their selections. But, ironically enough, the Giants did not fare well in the draft. Their high picks, Gonzaga back George Karamatic and Northwestern back Fred Vanzo, failed to contribute to the team. Quietly stewing over those failures, the young Mara continued to amass information on college players during the 1938 season and again filled a chalkboard with prospects' names at the next draft meeting, held in New York on December 9, 1938. But when it was the Giants' turn to pick in the first round, they drafted a player who was not listed on the board. Asked about the omission, Wellington shrugged. "I didn't think I had to put every name on that list," he said. The all-for-one philosophy had its limits.
NO ONE WAS GETTING RICH OFF PRO FOOTBALL IN THE LATE 1930s. Many owners continued to rely on other businesses to offset the losses from their teams. "They would gather for league meetings, get their business done, and get back home to their other work," Virginia McCaskey said. Marshall still ran a laundry chain. Rooney still promoted boxing matches and gambled. Halas was still a partner in a commercial laundry. Tim Mara was invested in coal and liquor, but his bookmaking operation required more of his time than anything else. He had been a fixture at New York's racetracks for nearly two decades, fearful of delegating his business to underlings even for a day. With horse racing making front-page news almost year-round, the public still knew him as a bookie more than as the Giants' owner.
By the late 1930s, Mara believed the Giants' present and future were stable enough for him to step back from their daily operations. Jack and Wellington Mara ran the team adeptly, in his view. The Giants were championship contenders, and their attendance was the envy of the rest of the NFL. When the 1938 season began, Mara was especially optimistic. The Giants appeared to have another winning team—and they had vanquished a New York team from a rival league.
The American Football League had kicked off in 1936, in the hope and belief that the public's appetite for pro football could support two leagues at once. It amounted to a personal attack on Mara. Doc March, his cofounder and longtime assistant with the Giants, had dreamed up the idea of the AFL and brought it to life. March had soured on the NFL after Mara turned the Giants' future over to Jack and Wellington, and then, after he joined the league office, he clashed with Marshall, leading to his ouster. Seeking revenge, he gained the backing of Wall Street investors, solicited franchise bids from fifteen cities, and announced a new league with eight teams would kick off in 1936.
The AFL's New York franchise, the Yankees, immediately declared war on the Giants. They hired a former Giant player as their head coach and signed three players from the existing roster, including Ken Strong, a back who had been the team's leading scorer. The Yankees were offering more money. Harry Newman, the Giants' quarterback, also departed for the AFL, signing with a Brooklyn franchise.
But the challenges that starting a new league entailed were more daunting than March and his backers imagined. It turned out American sports fans did not want more pro football. Franchises in the AFL began folding before the season began. In the end, six took the field in 1936. Two moved to different cities within weeks. Playing at Yankee Stadium, the Yankees averaged around 14,000 fans per game, easily the best in the league. With a 5-3-2 record, they finished third in the standings behind the Boston Shamrocks and Cleveland Rams. March left the league after the season in the wake of contentious arguments with several owners. The NFL quickly annexed the Rams, choosing Cleveland as its tenth franchise, over Buffalo and Los Angeles. The AFL picked up the Los Angeles team and hung on for another season, but key players defected from the Yankees, whose attendance dropped precipitously, and the league itself folded after the 1937 season.
The threat gone, Mara was pleased that the Giants had Manhattan to themselves again. After losing two of their first three games in 1938, they faced the Redskins for the first time since Washington's epic rout the previous December. The matchup drew a sellout crowd of 37,500 to Griffith Stadium in Washington, and the Giants won, 10–7, on a late touchdown pass. Both teams continued to dominate the East division through the fall, and, for the second year in a row, they concluded the regular season by playing at the Polo Grounds in early December, with the division title at stake.
For the practices leading up to the game, the Giants' coach, Steve Owen, wrote a simple message on the locker room chalkboard: "49–14." Owen wanted the players to remember how badly the Redskins had beaten them in New York the year before. He did not have to worry.
On Sunday morning, eleven special trains from Washington arrived at Penn Station bearing Redskins fans and the hundred-piece Redskins Band. Marshall had given the band an official title. The league's other owners were incredulous that he had spent thousands of dollars on uniforms for a _band._ But it was Marshall's favorite toy. Repeating the scene from the year before, the owner and his band mustered outside Penn Station and marched through the streets of Manhattan toward the Polo Grounds, with hundreds of fans trailing them and shouting the words to "Hail to the Redskins." Marshall's intent, clear enough, was to show himself and his team to be conquerors.
From the outset, though, it was clear this game would be markedly different. The Redskins' first possession was halted when the Giants' Ward Cuff intercepted Baugh and returned the ball 32 yards to the Washington 42. On the next play, Giants fullback Hank Soar dashed through a gaping hole and sprinted to the end zone for a touchdown. A few minutes later, the Giants recovered a Redskins fumble and drove to another touchdown.
The Redskins were not the same team as the year before. Cliff Battles, their magnificent back, had retired before the season and taken a job as a college coach when Marshall refused to give him a raise. (He had made half as much as Baugh in 1937.) They also were without Riley Smith, their quarterback, who had suffered a major knee injury halfway through the season. Focusing on Baugh, Giant defenders intercepted an incredible six passes, denying the Redskins any chance to build momentum. The Giants increased the lead to 17–0 in the second quarter and did not hold back in the second half. With the score 36–0 in the waning minutes, Marshall's bandsmen marched out of the Polo Grounds. "The band had seen enough," the _New York Times_ ' John Kieran reported.
Eddie Reeves, a vice president in the Redskins' front office, congratulated Wellington Mara after the game. "A great game," Reeves said, "but what you need is a band like we have." The young Mara smiled and said, "Eddie, we don't need a band. We have a football team."
THE NFL HAD INSTITUTED A POSTSEASON CHAMPIONSHIP GAME aiming to establish a major event on the American sports calendar, on par with the World Series. After five years, though, the comparison was still impossible to justify. The first five title games had drawn a disappointing average crowd of just 24,295. Moreover, the failure of the AFL in 1937 served as a reminder to the NFL owners that the continued existence of a pro football league was not assured.
The Giants stop the Packers' Clarke Hinkle just short of the goal line in the 1938 championship game. (Associated Press)
But the championship game between the Giants and Green Bay Packers at the Polo Grounds on December 11, 1938, indicated that the faith the owners had placed in the sport and clung to for years was not misguided. The game drew 48,320, easily the largest crowd in the event's brief history. The fans witnessed a mesmerizing exhibition of the drama, skill, and violence that pro football alone could offer. The college game had remained more popular until now largely because it was viewed as an endeavor that helped turn boys into men—a process that transcended sports. But pro football's fan base would increase exponentially over the next quarter century, and it would eventually become the more popular version of the sport, in part because of its sheer brutality. Pro players were older, more physically developed, and thus their collisions were more breathtaking than those in college football. Long fascinated with violence in all forms, Americans lusted to see bodies crunching, and as pro football developed, they found it hard to turn their heads away.
The 1938 championship game between the Giants and Packers hinted at what lay ahead. It was an "absolutely ferocious" event, according to the _New York Times_ ' Arthur Daley. Early on, the Giants blocked two punts and took a 9–0 lead. But Green Bay's Arnie Herber tossed a long touchdown pass to start a rally that culminated with the Packers going ahead, 17–16, in the third quarter. "No such blocking and tackling by two football teams had ever been seen at the Polo Grounds," Daley wrote. "Tempers were so frayed and tattered that stray punches were tossed all afternoon."
The Giants took an uncommonly brutal beating. One player went to the hospital with a spinal contusion. Another suffered a fractured sternum. Mel Hein, New York's All-Pro lineman, suffered "a contusion of the brain that left him temporarily bereft of his memory," but Hein returned to the field after the Giants regained the advantage and led a defensive stand that denied Green Bay on several late drives. There was no thought given to the possible detrimental effect of his playing with what obviously was a concussion; a connection between football and serious brain trauma would not be made for decades. After the final gun sounded with the Giants ahead, 23–17, Daley intimated in the nation's foremost newspaper that the game had been compelling not in spite of its violence but because of it. "This was the gridiron sport at its primitive best," he wrote, adding that the display had gone so far as to legitimize the NFL: "Professional football, once a shabby outcast among sports, has become a dignified and honored member of the American athletic family."
On the field, the Giants' players lifted their coach, the 265-pound Owen, onto their shoulders in celebration. In the stands, Tim Mara shook hands with Joe Carr and reflected on how far the Giants had come. They had endured difficult times in the late 1920s and early 1930s, losing so much money at times that Mara could imagine the team failing. More recently, he had weathered the challenge posed by a rival league. There was always something. But while some of the NFL's other teams still struggled financially, the Giants would turn a $200,000 profit in 1938—an inconceivable sum. Mara would have to spend many days in the betting enclosures to make that much. For the first time in the NFL's history, someone was making real money in pro football. That it had happened in New York was perhaps little surprise to the other owners, and Mara deserved the credit, even if his main skill as an owner was knowing precisely when to let the true football minds, including his sons, take over.
#
# THE GREATEST ROUT
VIRGINIA MCCASKEY WAS AROUND TWELVE YEARS OLD ON the day in the mid-1930s when George Halas took her, her brother, and her mother to Riverview, a sprawling amusement park on Chicago's North Side. They were out with Arch Ward, sports editor of the _Chicago Tribune,_ and his family. "I was about the same age as their daughter, Ruth, and [my older brother] Mugs was about the same age as their son, Tom," Virginia recalled. "Our parents were friends and we lived in the same parish, a few blocks from each other. We did a lot of things together."
Spread over acres and acres of land and featuring massive wooden roller coasters as well as other rides that whirled and dropped, Riverview drew large crowds. But no one bothered the Chicago Bears' owner and coach as he walked the grounds with his family while talking with Ward and munching on one of the park's signature foot-long hot dogs. "No one asked for his autograph or bothered him. No one knew who he was," Virginia recalled. "It would have been a nice problem, having people recognize him and interrupt our day, but the Bears were not a big deal. We were just another family at the park."
Today, pro football's prominent figures are celebrities, as familiar to the public as entertainers and politicians. The head coach of a successful team would need a security detail to enjoy a day at an amusement park. In the 1930s, though, pro football's coaches and players did not enjoy any measure of renown. Boxers, college football stars, and major league baseball figures could cause a commotion when out in public, but not a pro football coach—not even a good one.
In Chicago, baseball's Cubs riveted sports fans. They had led the National League in attendance for six straight years beginning in 1927, selling more than a million tickets in each of the first five seasons. Babe Ruth's Yankees were the only other major league club that drew comparable crowds, and the Cubs even outdrew them in 1928, 1929, and 1930. The Cubs' popularity was partly attributable to the tradition of excellence they established while winning five National League pennants and one World Series between 1906 and 1918. But their crowds had remained relatively modest until their forward-thinking owner, William Wrigley, began broadcasting the team's home games on the radio beginning in 1923.
Radio's popularity soared in the 1920s. The number of radios in use in America rose from 60,000 in 1922 to 3 million in 1924 to 16.6 million by 1932. The number of radio stations also rapidly grew, from 382 in 1922 to 681 in 1927. Those stations needed programming, and Wrigley had what they wanted—hours of baseball, day after day.
The other major league owners were terrified of live game broadcasts, fearing the practice would destroy attendance, their primary source of revenue. Why would fans buy a ticket when they could stay home and follow a game for free? Eleven of the sixteen major league owners were skeptical enough to consider banning all radio game broadcasts in 1931. That never happened, but in 1934 the Yankees, Giants, and Dodgers did agree on a five-year radio ban in the New York market.
William Wrigley saw the new medium differently, as a promotional opportunity, not a threat. In 1925, he allowed WMAQ, a major Chicago station, to broadcast the Cubs' home games, hoping that fans who listened to games might be encouraged to come to the ballpark and buy tickets. Stations and networks eventually would pay for broadcast rights, but in 1925, before radio's power became evident, Wrigley gave his games to WMAQ for free. It was not an exclusive deal, either; by the end of the decade, most major Chicago stations would also broadcast the Cubs' home games, creating an overwhelming presence on the AM dial.
Just as Wrigley predicted, the broadcasts prompted his team's attendance to soar, not sink. The Cubs' gate rose 140 percent between 1925 and 1929. In 1927, they became the first major league club other than the Yankees to draw more than 1 million fans in a season. In 1929, they drew almost 1.5 million, more than any club would draw in a season until after World War II. Radio created loyal fans in Chicago and throughout the Midwest, and many wrote letters to the club thanking it for the broadcasts. One farmer rapturously wrote, "Don't stop it. I have a radio in the field with me. I plow one turn, sit down for a cool drink out of the jug and listen to the game. It's grand."
Halas was still a baseball fan. He had played the game adeptly enough to receive at-bats with the Yankees in 1919 and had followed the Cubs since he was a boy. "He loved them," Virginia said. So did the boys at her coed middle school. "It wasn't a big deal to them that my father was with the Bears. They were all Cubs fans," she said.
Halas did not seriously believe the Bears could become as popular as the Cubs. He believed in pro football's future, but he was a realist. The Bears were among the NFL's best franchises, and they struggled for attention. He did what he could to change that. After witnessing Wrigley's brilliant use of radio, he found a station that would broadcast the Bears' games in the 1920s. But the arrangement did not last, and the Bears were absent from Chicago radio in the years when the Cubs dominated it.
Finally, in 1933, Halas found a radio partner when WGN agreed to broadcast the home games of the Bears and Cardinals, the city's other NFL team. Using his newspaper connections, Halas made sure the broadcasts were promoted. He still believed print was the best way to win new fans to his team. He did not have time to run a newspaper and thereby guarantee the Bears better coverage—a stunt George Preston Marshall had pulled in Washington—but he did become friendly with sports editors, above all the _Chicago Tribune_ 's Don Maxwell. "I remember him having dinners with us," Virginia McCaskey said of Maxwell. "Don realized he needed something for his Monday morning sections and that helped the Bears." When Maxwell was elevated to the paper's city editor in 1930, he turned the sports section over to Arch Ward, an Iowa native who had served as Knute Rockne's first publicist at Notre Dame before joining the _Tribune_ sports staff in 1925. Having risen through the ranks, he now authored the iconic In the Wake of the News column, a daily compendium of notes and opinions covering sports across the country, with a focus on Chicago and its teams.
But Ward was an impresario more than a journalist, more interested in staging events than writing about them. In 1933 Chicago put on a world's fair celebrating its centennial, and the mayor asked Ward to find a sports event that could be included. Ward convinced major league baseball to hold an exhibition contest between the best players from the American and National leagues. Dubbed "the Game of the Century" by the _Tribune,_ it was held on July 6, 1933, at Comiskey Park, home of the White Sox, and drew almost 50,000 fans. Babe Ruth hit a home run, the American League won, and baseball's All-Star Game was born.
The next year, Ward conceived the idea of a late-summer football exhibition pitting the NFL champions from the previous year against a team of college stars who had graduated. Halas and the other NFL owners eagerly went along. Many fans still believed college football was superior to the pros—it certainly remained more popular—and the pros jumped at the chance to dispel what they saw as a myth. The first game drew 79,432 fans to Chicago's Soldier Field on August 31, 1934. The college team had been selected by a fan vote, orchestrated by the _Tribune,_ and featured well-known players. They faced off against the Bears, who had won the NFL title the previous December. The game ended in a disappointing scoreless tie.
Like baseball's All-Star Game, football's College All-Star Game quickly became a staple on the national sports calendar. It was much more popular than the NFL's championship game, another relatively new event. In 1935, the Bears, subbing for the NFL champion Giants, defeated the college stars, 5–0, before a crowd of 77,450. In 1936, the Detroit Lions and All-Stars tied, 7–7, before 76,000 fans. The results helped the pros' campaign for respectability. Many fans remained dubious, but more and more top college players were continuing their careers in the NFL, raising the league's caliber of play.
Ward named his event the College All-Star Game, with no reference to the pros, for a simple reason: he wanted to sell tickets. Pro teams still were not especially attractive commodities in the wider sports marketplace. The Bears enjoyed playing before giant crowds in the exhibition game, but they did not draw nearly as well on their own, without being associated with an opponent from the college ranks. Averaging 22,752 fans per game during the 1937 regular season, they were championship contenders, but still afterthoughts in Chicago, at least when compared to the Cubs.
AT A BANQUET IN 1935, CLARK SHAUGHNESSY, THE HEAD coach at the University of Chicago, approached Halas and introduced himself. Halas knew who he was. Shaughnessy, a cerebral Minnesota native, had replaced Amos Alonzo Stagg, the legendary coach who built the University of Chicago into a national power during a forty-year tenure that ended when the school administration believed he had grown too old for the job.
Shaughnessy wanted to talk to Halas about the Bears' T formation. With its pre-snap man in motion, end split wide, and quarterback lined up directly under center, it had helped the Bears win NFL titles in 1932 and 1933 and complete an undefeated regular season in 1934. When Shaughnessy began asking questions, Halas could see he possessed a keen strategic mind. Within two years, Halas was paying Shaughnessy a consultant's fee even though Shaughnessy still coached at the University of Chicago.
Over the years, as the two men discussed how to make the T more effective, the need for Halas and the Bears to do _something_ became evident. The balance of power in the NFL's West division shifted after the Packers signed Don Hutson, the speedy receiver who "roamed the ball field, pulling down impossible passes," according to Halas. The Packers won three division titles and two league titles in a four-year span beginning in 1936. The last NFL game of the 1930s was Green Bay's 27–0 victory over the Giants in the 1939 championship game.
The Bears still fielded winning teams in these years. In 1939, they went 8-3 and their offense was one of three in the league that produced an average of more than 300 yards per game. It was clear the pro game was becoming more offensive-minded—before 1939, only one offense in league history had averaged as much as 300 yards per game during a season—and the Bears were at the forefront of the evolution. Still, Halas was tired of losing enough games to finish behind the Packers. The league's better defenses had adjusted to his T, he believed, by widening their alignments, which prevented the Bears' halfbacks from getting around the edges of the line. He decided it was time to introduce a new T, one that he and Shaughnessy had designed over the course of several years of conversations. In the new version, the quarterback assumed a larger role. Before, he was mostly a traffic cop whose job it was to take snaps and pitch to tailbacks, who in turn threw the passes. Now, he would become more of a centerpiece, throwing passes himself while making sure the offense ran smoothly.
Halas scouted the college ranks for a quarterback who could handle the job. He found Sid Luckman, a Columbia University star with a strong passing arm and the intelligence to run an intricate offense. Luckman was expected to be taken by the time the Bears picked in the first round of the 1939 draft, but, in a trade with Rooney's Pirates, Halas obtained the second overall pick and took Luckman. A year later, Halas again moved up in the first round, this time in a trade with Bell's Eagles, and used the second overall pick to draft George McAfee, a Duke halfback whose 165-pound frame belied his uncanny knack for breaking big gains. Some other owners rolled their eyes at how Halas manipulated the draft process, obtaining the best players even as the Bears continued to win. That went against the spirit of the draft, which had been designed to level the playing field. But Halas did not care. He wanted to win, and he was sure he had put together a powerful team. "When the 1940 season began, I felt we were fit for anything or anybody," he would write.
In their season opener, the Bears routed the Packers, 41–10, in Green Bay—a promising start. The Cardinals upset them the next week, but they rebounded with five straight wins, the last another victory over the Packers. Believing they were nearing a division title, the Bears carried a 6-2 record into a game against the Redskins at Griffith Stadium in Washington on November 17.
The Redskins, who led the East division, were ready with a 5-3-3 defensive alignment that stunted Luckman and the Bears' attack. The Redskins led at halftime, 7–3, and that was still the score when Luckman drove his offense deep into Washington territory in the final minute. After McAfee ran the ball to the 1 yard line, he faked an injury to stop the clock and give the Bears time for one more play. Luckman tossed a pass toward Bill Osmanski, his fullback, who had circled the defense and was open in the back of the end zone. But the Redskins' Frank Filchock wrapped his arms around Osmanski, denying the receiver a chance to make a catch. The ball hit Osmanski in the chest and fell to the ground for an incompletion.
Halas screamed about what he thought was an obvious pass interference penalty, but no flags fell, and the Redskins celebrated a victory. "I was ready to tear the referee limb from limb. I knew his ruling of no interference must stand, but I wanted to make my feelings known," Halas later wrote. "He popped into a dugout. All I could do was shout abuse after him. I probably used all of the words I had learned in the Chicago streets and in ball parks and training camps and maybe even made up a few new ones."
Hearing of Halas's complaints, George Preston Marshall responded with his own loud criticism. "The Bears are a bunch of crybabies. They can't take defeat," Marshall told reporters. "They are a first-half club. They are quitters. They are the world's greatest crybabies." Marshall never minded needling Halas. The two spoke regularly on the telephone during the season, mostly about league affairs, but the intense competition between their teams brought out the nastiness in both.
The Bears finished the regular season with two lopsided wins to earn the West division title and set up a rematch with the Redskins in the 1940 championship game at Griffith Stadium. "I did not let the players forget" what Marshall said, Halas later wrote. "You can understand why the game for the championship took on special importance."
Marshall did not back down, telling reporters the Redskins had beaten the Bears before and would do so again. He also sent a bombastic telegram to Halas after the Bears secured the division title: "Congratulations. I hope I will have the pleasure of beating your ears off next Sunday and every year to come. Justice is triumphant. We should play for the championship every year. Game will be sold out by Tuesday night." Seldom had an NFL championship game generated more anticipation, in part because of the public exchanges between Marshall and Halas. Although the league owners, as a group, believed in harmony, this was one instance where animus paid off. More than 36,000 tickets were sold, more than 150 press credentials issued. The Mutual Broadcasting System paid $2,500 for the right to broadcast the game nationally on the radio.
The game was set for December 8, 1940. Shaughnessy, now coaching at Stanford, traveled from California to Chicago to help Halas prepare. Shaughnessy's Stanford team, also wielding the updated T, had gone undefeated and would play in the Rose Bowl on New Year's Day. In Chicago, Halas and Shaughnessy devised a plan for challenging the Redskins' defense. Halas's preparations also included motivational tactics. In the locker room before the game, Halas hung newspaper clippings of Marshall's negative comments about the Bears. "When we were ready to go out, he pointed to the clippings and said, 'That's what the people in Washington are saying about you gentlemen. I know you are the greatest football team ever. Now go out and show the world.' We almost broke down the door," Osmanski recalled.
Before the kickoff, Halas huddled with Luckman and gave the quarterback three plays to run to begin the game. "They will show you whether the Redskins are staying with the defense they used in the last game against us. If they are, you will attack it as we have worked out," Halas told him.
The Bears won the toss and began the game with the ball. Luckman called a fake reverse with a man in motion. The Redskins reacted as they had three weeks earlier and held McAfee to a 7-yard gain. Yet Halas was thrilled, now certain his reconfigured offense would work. On second down, after McAfee went in motion to the right, Osmanski headed in the opposite direction, and Luckman pitched him the ball. The Redskins were fooled, and a hole opened. Osmanski straight-armed a linebacker and broke into the clear down the sideline. With help from a final clearing block, he ran 68 yards for a touchdown without being touched. "I could see this was going to be a great day for the Bears," Halas wrote.
After a long kickoff return put the Redskins in scoring range on their first possession, Sammy Baugh dropped back to pass and spotted a receiver open at the 4 yard line. But the receiver, Charley Malone, dropped the perfect pass, possibly because the sun got in his eyes. The Redskins settled for a field goal attempt and the kick flew wide. With the ball again, the Bears moved steadily downfield, entirely on the ground. A 27-yard run by Osmanski put them near the end zone, and Luckman plunged over the goal line for the score. "Our adjusted plays had them confused. They didn't know where the runner was going," according to Halas.
Minutes later, a partially blocked punt put the Bears in position for another score. Halas sent in a play that befuddled the Redskins more than any other to that point. The right halfback went left. The left halfback went right. Luckman lateraled to the fullback, Joe Maniaci, who ran to the left with the right halfback blocking for him. Without being touched by a defender, Maniaci ran 42 yards for a touchdown. The Bears had a 21–0 lead, and the first quarter was not over. The score was 28–0 at halftime, and somehow the second half was worse for Marshall and his team. The Bears' Hamp Pool intercepted a Baugh pass and ran it back 15 yards for a touchdown. Minutes later, McAfee also ran an interception back for a score. Before the end of the third quarter, yet another Washington pass was intercepted and returned for a touchdown.
The Bears' Bill Osmanski races 68 yards for a touchdown on the second play of the 1940 championship game. (Associated Press)
The score was 54–0 by then, and, though Halas and Washington coach Ray Flaherty used backups in the fourth quarter, the rout continued with the Bears scoring one more touchdown, another, a third. The supply of new balls for the game ran out because the Bears had kicked them all into the stands on extra points. (Teams had not yet thought of putting up nets.) In the final minutes, the teams played with old practice balls, and, to avoid running out of those, the Redskins asked Halas to attempt the Bears' final two extra points on plays from scrimmage rather than on kicks. Halas complied.
When the final gun sounded, the Griffith Stadium scoreboard reflected a score that astonished sports fans across America: 73–0. "We wanted revenge and we got it," Bears tackle George Musso said. Actually, Halas and the Bears had done more than just exact revenge. With the most lopsided victory in league history, they had humiliated Marshall beyond measure—on his home turf, no less.
The Redskins' fans, furious with Marshall for having riled up the Bears, heckled him in his box seat throughout the second half. When Marshall ordered the stadium announcer to promote 1941 season ticket sales with the Redskins trailing by 60 points, the crowd booed. After the game, Washington's players were crestfallen, some near tears and barely able to respond to reporters' questions. When it was suggested to Baugh that the outcome might have been different if Malone had not dropped that sure touchdown early in the first quarter, Baugh shook his head. "If Charley had caught it, the score would have turned out 73–7," he said.
The Redskins admitted they had played poorly, but the Bears deserved credit, as they saw it, for a brilliant performance bordering on perfection. Some newsmen picked up on the theme. Arthur Daley began his _New York Times_ story with a simple declaration: "The weather was perfect. So were the Bears."
The winning locker room, meanwhile, was crammed with reporters seeking an explanation. One reporter wore an official's uniform. The head linesman that day had been Irv Kupcinet, a Chicago sportswriter who was a friend of Luckman's and covered the Bears for the _Chicago Daily Times._ Destined to become a popular Chicago media personality, Kupcinet moonlighted as a football official. Although it was not unusual for sportswriters to officiate NFL games in the 1930s, the fact that it happened in a championship game, with a writer who covered the Bears, was precisely the kind of sly maneuver that Halas often employed, pushing ethical boundaries and infuriating the other owners. But Kupcinet's judgment was not a factor in the result. The Bears' lopsided victory was honest and deserved. The _Chicago Tribune_ 's Wilfrid Smith wrote that the rout was attributable to the Bears being "the greatest team professional football has ever produced." The _Washington Post_ 's Shirley Povich wrote, "The Bears were wonderful, weren't they? The T formation is really dread stuff and Coach George Halas comes pretty close to being the No. 1 offensive genius in the land."
For two decades, Halas had struggled to colonize the minds of Chicago's sports fans. The 73–0 game ushered the Bears into the limelight, almost by itself. Their attendance spiked the next season, with crowds at Wrigley Field routinely surpassing 40,000 for meaningful games against other strong teams. Chicago's sports tastes were changing. The University of Chicago had dropped football. The Cubs had fallen on hard times, their attendance dropping by more than 50 percent as years of losing mounted. Two radio stations now broadcast the Bears' home games. Never again would Halas stroll anonymously through a Chicago amusement park.
#
# SAME OLD PIRATES
AFTER ART ROONEY MADE HIS FORTUNE AT THE BETTING window, he let his wife pick out any house she wanted as long as it was in the Ward, the Pittsburgh neighborhood they had grown up in. In 1939, they moved into a rambling three-story home with a center entry hall and enough space for the Rooneys' growing brood of young boys. It was not on a fashionable street and cost just $5,000. Though pleased about the purchase, Rooney quietly fretted about paying for its upkeep. His luck had turned. No longer did he return from the races with cash bulging his pockets. The ponies were beating him. Meanwhile, his football team continued to lose games and money. In 1938, the Pirates finished $35,000 in the red, pushing Rooney's deficit since he joined the NFL to more than $100,000.
His losing streak extended to politics. In 1938, a friend talked him into running for the registrar of wills in Allegheny County. He did not truly want the job but campaigned as only he could, donning suits, smoking cigars, and speaking honestly. He told one crowd he did not even know what the registrar of wills did. A victory in a crowded primary led him to believe he might win, but he lost in the general election. His ballot-box defeat was actually a relief. He had enough other responsibilities and needed to focus on his finances. Never lacking for ideas, he noticed boxing had reached a new peak of popularity in Pittsburgh, where the stable of local fighters included Billy Conn, a light heavyweight world champion. Rooney began promoting fight cards at Forbes Field, running the business out of his office at the Fort Pitt Hotel. The new business helped his overall bottom line.
He held out hope that his football team would also eventually become successful. Few in the city shared his optimism. The University of Pittsburgh's Panthers, a national power coached by Jock Sutherland, completely dominated the local football scene. The Pirates were rightfully seen as pitiful in comparison. Even with Whizzer White as the NFL's leading rusher, they won just two games in 1938. That fall, the United Press International polled the nation's newspaper sports editors on whether they thought Pitt could beat an NFL team. Forty-six percent of the editors responded yes, and, no doubt, many envisioned the Pirates as that NFL team losing to Pitt.
Part of the Pirates' problem was that their player-coach, Johnny Blood, was not only a mediocre coach but completely unreliable. He forgot to show up one Sunday to his team's game. Instead, he went to the Bears' game in Chicago and was sitting in the press box when a reporter asked why he was not with his own team. "We're not playing this week," Blood replied just as the stadium announcer gave the Pirates' score. In Blood's defense, sometimes it was difficult to know where the Pirates were playing. In 1938, they took on the Philadelphia Eagles in Buffalo, New York, and Charleston, West Virginia, because of lagging tickets sales. Rooney then moved the final game of the season, against Cleveland, from Forbes Field to New Orleans in hopes of luring a bigger gate; again, he had sold few tickets to the game, which he had postponed earlier in the season because the Pirates had so many injured players. (The Rams were furious, but Joe Carr allowed it.) When Rooney asked the mayor of New Orleans for promotional help upon arriving in the Big Easy, the mayor admitted he had thought the Pirates were a college team in town to play Tulane.
Every year, Rooney began the season with a full roster, but, as the losses mounted, he shed players to save expenses and the outmanned Pirates absorbed savage beatings, both figuratively and literally: there was often not a quality substitute on the bench, so the injured player had to stay in the game. Sportswriters lambasted him for failing to field competitive teams. He was too kind, they suggested, and it was true: he was loyal to the local players who needed the work, even if they were not helping the Pirates win. The gregarious Blood was good company at the racetrack, which kept him employed even though he set a terrible example. "On most teams, the coach worries about where the players are on the night before a game; on our team, the players worry about the coach," Rooney said.
After the 1938 season, Rooney seized on an opportunity to turn the Pirates around. Suddenly, Pitt's Sutherland was available. The tall, commanding coach had won 111 games while losing only 20 during a fifteen-year run at the school. His tenure had been marked by sold-out home games, undefeated seasons, and trips to the Rose Bowl; he was seen as sporting royalty in Pittsburgh. But Pitt's administration, increasingly uncomfortable with football's growing importance to the school, had instituted a series of changes that reemphasized academics, prompting Sutherland to resign after the 1938 college season.
Rooney praised Sutherland publicly, telling reporters he had "felt for a long time that Sutherland was the best coach in the profession." The two men knew each other, and Rooney wooed Sutherland, but Sutherland elected not to coach at all in 1939. Instead, Rooney brought Blood back. Fortunately for all concerned, Blood quit early in the 1939 season, after a 32–0 loss to the Bears that dropped the Pirates' record to 0-3. Walt Kiesling, a former player also frequently found alongside Rooney at the racetrack, took over, and he fared no better. By late in the season, the Pirates were 0-8-1 and on a fifteen-game winless streak. Only two games remained in their season, both against the Philadelphia Eagles, owned and coached by Bert Bell, Rooney's closest friend in the league and partner in football misery. The Eagles were 0-7-1.
PEOPLE WHO HAD KNOWN THEM BOTH FOR A LONG TIME laughed at the idea: Bert and Art, the best of friends? It could not have happened when they were younger. Bell was raised in opulence as a scion of America's ruling class. Rooney grew up over a bar, among gamblers and steel workers. "In that sense, they were opposites," Bell's son, Upton, said. But, by the 1930s, they were more alike. Bell had rebelled against his sniffy upbringing, even rejecting the name his parents gave him. And Rooney retained a certain personal modesty even after his famous run at Saratoga in 1937. That day, after he finished placing his bets, he walked the halls of the fabled track selling dollar raffle tickets to benefit his brother's church.
Both had been successful athletes as young men. Both worked their political connections to overturn Pennsylvania's blue laws and clear the way for games on Sunday and for Pennsylvania teams in the NFL. Their differences receded, and a role reversal of sorts occurred. As Rooney's gambling winnings soared, Bell, having wasted his fortune, needed his wife's money to start the Eagles. But nothing brought them together more than their shared misfortune in the NFL. By the end of the 1930s, even after the institution of a draft, it seemed as though the Pirates and Eagles would never compete with the Bears, Giants, Redskins, and Packers.
Like Rooney's Pirates, Bell's Eagles had never produced a winning season. After absorbing $90,000 in losses in their first three seasons, they went bankrupt, and Bell had no choice but to offer them for sale at a public auction house in downtown Philadelphia in 1936. Bell himself made the only, and thus winning, bid—$4,500. No one else wanted the team. That year, Bell added the title of head coach to his duties as general manager, ticket manager, trainer, scout, and publicist. His debut season on the sidelines did not go well. The Eagles threw a total of thirty-six interceptions while winning just one of a dozen games. Bell would coach the team for five years and register just ten victories against forty-four defeats. At one point, he lost fourteen straight games. Convincing his city's fans to buy tickets became all but impossible. On September 21, 1937, a meager crowd of 3,107 attended the Eagles' game against Cleveland at Philadelphia's Municipal Stadium, a massive edifice that could seat 100,000, as it did when Army played Navy.
In 1939, Bell tried to postpone a game against the Brooklyn Dodgers because of slow ticket sales and a forecast of driving rain. But Dan Topping, who owned the Dodgers, was already in town with his girlfriend and future wife, the Olympic figure skater Sonja Henie. Topping demanded that the game go forward as planned. Bell brought the fifty or so diehards who attended the game into the press box and served them free coffee and hot dogs while the teams splashed to a sodden, scoreless tie on the field. "It's days like that when it takes a very good sense of humor and an utter lack of regard for your bank balance to stay in professional football. I'm glad I had both," Bell said later. If the Eagles led the league in any category, it was financial struggles. The other owners were well aware of Bell's plight. Despite facing his own issues, George Halas offered to loan Bell $2,500 to help him get through the 1938 season. Bell accepted the loan, which he repaid the following year. Rooney likewise offered to loan Bell money.
The Eagles managed their best-ever season on the field in 1938, winning five games. Then, for the first time, they signed their first-round draft pick, Davey O'Brien, a star quarterback from Texas Christian University. Bell gave him a $12,000 bonus and a two-year contract, and O'Brien immediately showed that he was worth it, leading the league in passing as a rookie in 1939. But the Eagles fell apart around him and sank back to the bottom of the standings, forcing Bell to resort to extreme measures to keep from having to disband the team. Instead of taking trains to away games, the Eagles traveled on an old bus and spent nights at rooming houses rather than hotels. Bell told the players to pack lunches for their trips. As the bus motored down the road, Bell would spot flat farmland from his front seat and bellow at the driver to stop. "Everyone out, time for practice!" he shouted. Though the NFL had been in business for nearly two decades, it still retained much of the haphazardness of its early decades.
LED BY O'BRIEN, BELL'S EAGLES WON THE FIRST OF THEIR TWO meetings with Rooney's Pirates near the end of the 1939 season. When the teams met again three days later at Forbes Field, Rooney partnered with the Polish Refugee Relief Fund to make the game a fundraiser benefitting Poles fleeing the Nazis, who had invaded Poland that fall. That resulted in a much larger crowd than originally expected, and this time the Pirates prevailed. They and the Eagles both finished the season with one victory.
The Pirates had lost $8,000 during the season, but that was good news, relatively speaking; they had lost more during other seasons. Nonetheless, sportswriters speculated that Rooney could not afford to back his dismal franchise much longer. Fans filled high school stadiums across Western Pennsylvania on Friday nights and avidly supported Pitt, Duquesne, and Carnegie Tech on Saturdays, but little of that enthusiasm carried over to Pirates games on Sundays.
Offering his friend a way out after the 1939 season, George Preston Marshall found a wealthy Washingtonian willing to buy 50 percent of the Pittsburgh franchise. The offer was fair, but the man wanted to move the team to Boston, and Rooney, against the evidence, still believed he could succeed in Pittsburgh. "They tell me around here that I'm fighting a losing battle, that I'll never be able to make a go of it against the three college teams we have in Pittsburgh, and all of those fine high school teams. But I know different," Rooney said. But he did admit he was near his breaking point. "I'm definitely going to keep the team in Pittsburgh for another season," he told the press. "I hope I can always keep it here. But I can't go on losing money with the team here. I'll try it once more in Pittsburgh. But if I lose for the seventh time in eight seasons, I guess I'll have to take one of those offers."
Seeking a fresh start in 1940, he held a contest to change the team's nickname. Three thousand entries were submitted, and Rooney announced the winner in March. From now on, in a nod to the city's primary export, his team was the Pittsburgh Steelers. But sportswriters doubted the change would make a difference. "No matter what you call a grapefruit, it still squirts in your eye," Chet Smith wrote in the _Pittsburgh Press._ Rooney also took another stab at hiring Jock Sutherland, who was ready to return to coaching. Rooney had no doubt the move would boost attendance and change the team's fortunes. But he offered Sutherland only a $7,500 annual salary, which Dan Topping easily doubled. "I wish Art Rooney all the luck in the world," Sutherland said as he became the coach of the Brooklyn Dodgers.
Rooney still hoped his team could begin to establish itself in 1940. The schedule provided an opportunity, with four of the first five games at home. Rooney spent a little more money than usual acquiring talent, and when Halas brought the powerful Bears to Erie, Pennsylvania, for a preseason game, planning to easily dispatch Rooney's squad as they usually did, the Steelers did not quickly fold.
Shortly before the kickoff in Erie, as Halas exhorted his players in the visiting locker room, the door creaked open, and in walked Rooney with his eight-year-old son, Danny. Halas was stunned to see his rival in his team's locker room just before a game. It was a breach of basic football protocol. "Say, George, I hope you're giving them that keep-the-score-down talk," Rooney said. A few players chuckled. Then Halas smiled. Eventually, the entire locker room dissolved in laughter. The practical joke "broke the Halas spell," the _New York Times_ ' Art Daley wrote later, and the Steelers surprised the Bears that night, 10–9, further bolstering Rooney's hopes for the 1940 season.
They opened with a 7–7 tie against the Cardinals before 22,000 fans at Forbes Field, then also tied the Giants, 10–10, before 18,000. After winning in Detroit, they hosted the Dodgers and Sutherland. Rooney believed Pittsburgh fans would fill his stadium to get a look at the revered coach, but there were empty seats, and Sutherland's team won. The next week, the undefeated Redskins visited, bringing their band and a thousand fans along with Sammy Baugh, and they routed the Steelers, 40–10.
By early November, it was clear to all that it had been a fantasy to think a new name would make any difference. Rooney's team carried a 1-6-2 record into a rematch with the Redskins in Washington. Rooney indulged his habit of saving payroll expenses now that his team was out of the division title race. The Steelers dressed only twenty-five players, eight below the maximum limit, while Washington dressed the full thirty-three. After watching the Redskins win by four touchdowns, the _Washington Post_ 's Shirley Povich criticized the shorthanded Steelers as a "woeful gang" that "made a mockery of themselves and the league." Povich estimated that Rooney had saved $2,000 but damaged the NFL's credibility.
For the second straight year, the season concluded with the Steelers and Eagles playing a pair of games. Bell's team was in even worse condition than Rooney's, winless in 1940 and playing to sparse home crowds. The Eagles' few remaining fans had given up on them, it seemed, after they suffered the worst possible indignity in late October, losing an exhibition game to a minor-league team, the Wilmington (Delaware) Clippers. Bell had scheduled the game to make extra money, but the result embarrassed the entire NFL.
Every Sunday night, Bell and Rooney commiserated on the phone, comparing their latest league defeats and lamenting their prospects. But although Rooney was struggling, he knew his friend was losing more money and asked whether Bell needed help. "After I turned him down three times in a row, I got a special delivery letter the next Monday. There was nothing in the envelope except a check for $5,000," Bell told the _New York Times_ later.
Both men enjoyed being in the NFL and had earned the respect of the other owners. After proposing the draft, Bell had gained a seat on the league's executive committee, which handled major decisions. Rooney, a calm voice in a group dominated by headstrong competitors such as Marshall, Halas, and Mara, was "more effective resolving NFL matters than he was in addressing the Steelers' woes," Rooney's biographers would write. By 1940, both Rooney and Bell understood that it was time to act. No longer could they tolerate the losing on the field, or the expenses they incurred.
In late November of that year, Bell heard from the East-West Sporting Club, an organization formed by Alexis Thompson, the grandson of the founder of Republic Iron and Steel. A twenty-six-year-old sports-loving Yale graduate, Thompson had inherited millions as a teenager and bolstered his fortune selling eye-care products in New York. He wanted to buy the Eagles and move them to Boston, where his family was from. Bell did not want to sell but told Rooney about the offer. Rooney authorized Bell to serve as his agent in a potential sale of the Steelers to Thompson. If Bell could negotiate a sale within thirty days, he would receive a 25 percent commission. On December 9, 1940, Rooney and Thompson agreed to a complex deal. Thompson would pay Rooney $160,000 for the Pittsburgh franchise and the contracts of twenty-four players—seventeen Steelers and seven Eagles. The Steelers would send eleven players to the Eagles. Bell would receive a $32,000 commission.
The news broke at a league meeting in Washington the day after the Bears' 73–0 rout of the Redskins in the 1940 championship game. Most Pittsburgh sportswriters did not criticize Rooney for selling after so many years of losses. "You can't blame the guy," the _Pittsburgh Sun-Telegraph_ 's Harry Keck wrote. But Pittsburgh fans feared the sale meant they would lose the Steelers. Loyal as ever to his hometown, Rooney quickly set out to fix the problem. Aided by the proceeds from his sale of the Steelers, he bought a 50 percent stake in the Eagles; he and Bell were going into business together. While fans in Philadelphia cheered the move, hoping Bell could straighten out the Eagles with the large sale commission and Rooney's infusion of cash, Rooney quietly rooted for Thompson to move the Steelers to Boston. He and Bell could then realize their ultimate goal: to own a franchise together that played home games in _both_ Philadelphia and Pittsburgh.
The other owners quickly scuttled the plan, telling Thompson they did not want a team in Boston so soon after Marshall's disastrous experience there. They also told Rooney and Bell that they could not abide two cities sharing a team. After several weeks of uncertainty, Thompson announced in February 1941 that his team would stay in Pittsburgh with a new name—the Iron Men.
Rooney plotted another move. When Thompson missed a March deadline to open team offices, Rooney took him out for an evening at a popular Pittsburgh saloon, plied him with drinks, and suggested they exchange franchises. Thompson could have Philadelphia and the Eagles. Rooney and Bell would take Pittsburgh and the Steelers. Though shocked at first, Thompson listened intently as Rooney explained that Philadelphia was more Thompson's kind of town with its arts scene and the high society of the Main Line. By the end of the night, Thompson agreed to swap teams. The three men presented their unusual idea to the other owners. To their surprise, it was approved. Thompson's East-West Sporting Club now owned the Eagles. The Bell-Rooney partnership, which was now officially called the Philadelphia Eagles Football Club, Inc., owned the Steelers. That was awkward, but Bell and Rooney would not change their partnership's name for another three years.
For a head coach, Thompson hired Greasy Neale, who had played with Jim Thorpe years earlier and coached at Virginia and West Virginia. Neale would bring championships to Philadelphia by the end of the decade. Bell and Rooney contacted several notable names about coaching the Steelers, but none wanted the job. In the end, Bell became the head coach. He did not fare as well as Neale.
Between the exchange of Philadelphia and Pittsburgh players in Thompson's original purchase and the subsequent franchise swap, it was almost impossible to know which players belonged where. In the spring of 1941, Neale, Thompson, Bell, and Rooney met at the Racquet Club in Philadelphia to divide up the players on the two teams. After that meeting, Bell thought he and Rooney had ended up with better players. As he prepared the Steelers for the 1941 season at a training camp in Hershey, Pennsylvania, he declared, "This is the finest squad I've ever worked with in the National Football League." But Rooney disagreed. Stopping at Hershey for a day on his way to Saratoga to bet on the races, he sat in the bleachers and watched practice. A Pittsburgh sportswriter asked what he thought. "Those new uniforms they're wearing threw me off a bit, but once I saw them practice a couple of minutes, I could see they were the same, old Pirates," Rooney said.
The comment was a tacit acknowledgement that the Steelers simply were not good at football. Rooney would long regret what he said. The sportswriter quoted him in the next day's paper, and Pittsburgh's fans picked it up as a refrain with only a slight alteration. In the coming years, whenever their frustration boiled over as their team's losses mounted, they would simply utter three letters, SOS—"same old Steelers."
Though he had not played and coached as much as his partner, Rooney proved more adept than Bell at gauging the team's prospects. The Steelers went 1-9-1 in 1941 while the Eagles went 2-8-1 in their first year with Thompson as their owner. Bell's tenure as the Steelers' coach did not last long. They opened the 1941 season with a loss to the Rams in Cleveland, then lost their home opener to the Eagles, a particularly demoralizing result.
"We have to do something. At this rate, no one is going to come see us play," Bell lamented to Rooney after the loss to the Eagles.
"I know what we have to do, but you won't go for it," Rooney replied.
"Name it," Bell said.
"You have to quit!" Rooney roared.
Bell announced his resignation three days later; he would never coach in the NFL again. In a surprise, his replacement was Duquesne's head coach, Aldo "Buff" Donelli. It was not a surprise because Donelli was unknown; he was one of college football's more successful coaches. The surprise was Donelli would continue to coach Duquesne while also leading the Steelers. Yet again Rooney and Bell had come up with an unprecedented and highly unusual scheme. It seemed to be a coup for the Steelers, but Elmer Layden, the NFL's new commissioner, was appalled. Layden, who had been hired before the 1941 season, was a fabled former player; he had been the fullback in Notre Dame's Four Horseman backfield in the 1920s. More recently, he had coached the Fighting Irish. But he had coached at Duquesne before that—in fact, Donelli had played for him—and he believed it was unprofessional for Donelli to simultaneously coach pro and college teams. He forced Donelli to choose. Donelli agreed to coach the Steelers while serving as an "advisor" to his top assistant at Duquesne. That temporarily appeased Layden, even though it was clear Donelli was still effectively coaching both teams.
The Steelers briefly improved under Donelli; they did not win a game but nearly beat the Redskins. Meanwhile, Duquesne built an undefeated record. Donelli was able to make every game for both teams until a conflict arose. The Steelers were due to play the Eagles in Philadelphia a day after Duquesne played St. Mary's in California. Donelli could not make both games. Layden interceded again, telling him that he could no longer coach the Steelers if he was not in Philadelphia for their game. Donelli chose to go west with Duquesne, which served, in effect, as his resignation from the Steelers.
Rooney was not happy in the least that Donelli was no longer coaching his team. He blamed Layden, whom he had supported as a candidate for commissioner. "He could have helped us and helped the league, too," Rooney groused. Seeing little choice, Rooney tapped Walt Kiesling to coach the team for the rest of the 1941 season. Kiesling had been the head coach the year before and an assistant under Bell and Donelli; he was a favorite of Rooney's from the racetrack. As the 1941 season wound down, Kiesling performed what some in Pittsburgh regarded as a minor miracle. Somehow, he coached the Steelers to a victory over the Brooklyn Dodgers—their only triumph in yet another disappointing season.
#
# POLITICAL WINDS
WHILE THEY JUGGLED FRANCHISES AND PLAYERS IN EARLY 1941, Bert Bell and Art Rooney joined their NFL colleagues in finishing off a crucial piece of league business—hiring a commissioner. Before the owners settled on Elmer Layden, the job was open for almost two years. Joe Carr had run the league office since 1921, but his title was president, not commissioner. Carr was a level-headed, effective executive who often wielded great influence on important matters, but when he died in May 1939 after suffering a heart attack, the owners sought to hire a bigger name, their version of Kennesaw Mountain Landis, major league baseball's imperious commissioner. A credible sports league needed a credible leader, they thought.
Carr's death gave them no choice but to settle for a fallback plan in 1939. Carl Storck had been Carr's lieutenant and the league's secretary-treasurer from the beginning, since 1921. He was the opposite of a high-profile hire. In fact, football was his second job; he worked full time for General Motors. But he knew the league's business and could keep things running well enough. The owners gave him a one-year contract.
After the 1939 season, they renewed their search. In Washington, George Preston Marshall had a conversation about the job with J. Edgar Hoover, the director of the Federal Bureau of Investigation. But Hoover was not interested. George Halas tried to hire Arch Ward, offering the _Chicago Tribune_ 's innovative sports editor a ten-year contract worth $25,000 a year—a staggering amount. But Ward turned Halas down, saying he "could not overlook the splendid opportunities in my position with the _Chicago Tribune_." The owners pledged to make the hire when they met in New York in April 1940, but, lacking a candidate, ended up giving Storck another one-year contract. Marshall, though, was no fan of Storck, who had refused to overturn a controversial call that denied the Redskins a division title in 1939. In comments to reporters, Marshall made it clear Storck's tenure would not last much longer. "I think Storck is a fine executive, but I can name a better one," Marshall said. "However, I know of no available candidate now."
During the 1940 season, Halas again offered the job to Arch Ward, who again said no. This time, Ward himself suggested another candidate, Layden, who was also Notre Dame's athletic director as well as its football coach. Halas loved the idea. Although Layden had limited administrative experience, he was a famous sports figure who would generate good press. But other owners also had candidates in mind. Bell favored Jack Kelly, a wealthy Philadelphia contractor who had won three Olympic gold medals in rowing as a young man; Bell and Kelly had been friends since they served together in the Great War. Frank McCormick, athletic director at the University of Minnesota, was also under consideration.
At a meeting in Chicago on January 17, 1941, the owners amended the league constitution, inserting a clause enabling them to create the position of commissioner. They assigned Halas and Bell to interview Layden and Kelly by the end of the month. After conducting the interviews, Bell left for a vacation in Florida, believing a decision would not be made until the third candidate, McCormick, also had been interviewed. On the first day of his vacation, though, he received a shock. When he opened his morning newspaper, he read that Layden had been hired.
Knowing that Bell preferred Kelly, Halas had waited until Bell was in Florida and unavailable and spoke with the other owners who lived in Chicago, the Lions' Fred Mandel and the Cardinals' Charles Bidwill, selling them on Layden. Halas then asked Art Rooney to help him. Working the phones, Rooney obtained support for Layden from Marshall, Tim Mara, Curly Lambeau, and Cleveland's Edward Bruch. Emboldened, Halas offered Layden a five-year contract with a $20,000 annual salary. Layden accepted.
In interviews with the Associated Press, Bell, Alexis Thompson, and Brooklyn's Dan Topping accused their colleagues of skirting the league constitution in hiring Layden. (Thompson would swap franchises with Bell and Rooney weeks later.) The owners never voted as a body, Bell pointed out, adding that the announcement "came from Chicago, which is where Halas lives." Bell obviously believed Halas had manipulated the process. "Well, that's one thing Bell got right: I do live in Chicago," Halas snorted to the AP. He denied going behind Bell's back. "Bell knew all about the progress of negotiations. We interviewed Layden together last week in Pittsburgh. Then we talked to Thompson and Topping by phone. Layden's appointment was strictly legal," Halas said. "No announcement was made until Layden was handed an official binding agreement containing the signatures of a majority of our club owners."
Thompson explained to the AP that Bell and Halas were supposed to interview all three candidates before making a decision, but they "also were given authority to make an offer to one of the three and report back to the league." Halas had hijacked that authority while Bell was out of town, according to Thompson. "Bell wasn't even in on the signing of Layden," Thompson said. It was what some recognized, by that point, as a classic Halas maneuver. No one, including the other owners, doubted that he effectively ran the league. He always received unwavering support from Bidwill, who still cheered for the Bears despite owning the Cardinals. Halas also had arranged for Mandel, a young Chicago store owner, to buy the Lions when their prior owner, George "Dick" Richards, was forced to sell. That guaranteed Halas the support of three of the NFL's ten franchises on any issue—a powerful base.
The Lions' sale had been made possible by another Halas scheme. Richards, a flamboyant radio executive, had bought the Portsmouth Spartans in 1934, moved them to Detroit, and renamed them the Lions. They had developed a following and even won an NFL title in 1935 while Richards, a millionaire, bankrolled them through the Great Depression and became an influential owner, constantly pushing for bold measures, including firing Joe Carr, hiring a big-name commissioner, and putting games on the radio. But Richards irritated Halas, who was loyal to Carr, and Halas eventually orchestrated Richards's exit from the league.
When the Lions' owner fired his coach, "Gloomy Gus" Henderson, in 1940, Henderson took revenge, providing the other owners with letters proving Richards had bet large sums on the Lions. Fearing a gambling scandal, Halas leapt into action. He told the owners to keep the story quiet, then located a buyer, the thirty-one-year-old Mandel, who offered Richards $165,000, then a record price for an NFL team. Mandel did not have the cash, but Halas arranged for the ever-willing Bidwill to write a check making up the difference. Richards wanted to keep the team, but Halas was adamant, believing the Lions' owner was potentially toxic now. The sale of the Lions for a sizable profit bought Richards's silence.
Layden's hiring and Richards's exit exemplified one of the league's fundamental commandments: thou shalt not challenge George Halas. When Bell expressed concern about Layden's lack of executive experience—a fact that would soon enough prove problematic—his concern was drowned out by Halas's support. Marshall chimed in, calling Layden's hiring "the most constructive and finest move ever made" by the NFL. Rooney also offered praise. Storck was stunned. Other than Halas, no one had been associated with the NFL longer than him. He thought he had served the owners well since taking over for Carr. But the owners had other ideas, bigger plans. When they asked Storck to stay on as president under Layden, he resigned, criticizing his replacement as he departed. "I am convinced Layden is not qualified to handle the job, mostly due to his lack of administrative experience in professional sports," Storck said. "Layden was steamrolled into his job when George Halas and Arch Ward saw an opportunity."
Shortly thereafter, Storck suffered a stroke, which was followed by a series of health issues that he battled for almost a decade before dying in 1950 at age fifty-six. When his failing health drained his savings in his final years, Tim Mara alerted the owners, and they pitched in with several thousand dollars a year. But Storck's daughter said she believed her father's bitterness over his abrupt departure from the NFL led to his death. Halas may have been among the league's first owners and, among them, the most dedicated to the sport, but he was not the only person involved in the NFL's early history who saw pro football as a calling.
IN THE FALL OF 1941, CHARLES BIDWILL ADMITTED TO HALAS that owning the perennially mediocre Cardinals was not especially exciting. Bidwill asked Halas about the possibility of moving the team to Los Angeles. The NFL had been flirting with putting a team in Southern California, which was becoming an attractive sports market as its population exploded around midcentury. Five years earlier, the league had granted a "probationary franchise" to a Los Angeles group with the idea that it would develop a team that would, in turn, eventually join the league. The Los Angeles Bulldogs developed quickly, winning three of six games against NFL squads that traveled west for exhibitions in 1936. But the league broke its promise, establishing a new team in Cleveland rather than adding the Bulldogs in 1937. Most owners were against the idea of regular travel to the West Coast. Joe Carr, still in charge at the time, supported the idea of a team in Ohio, his home state.
After being turned down by the NFL, the Bulldogs joined the American Football League, Harry March's brainchild, then in its second and final season, and won the title with an 8-0 record in 1937. After that, they returned to independent status and continued to play exhibitions against NFL teams, then changed their name to the Hollywood Bears and joined a lesser league.
As sports teams on the West Coast played to larger and larger crowds, it was evident the NFL had to consider a franchise in Los Angeles. If Bidwill wanted to move the Cardinals there, Halas would not attempt to stop him. Halas certainly owed Bidwill, who had helped the league in many ways over the years; he had arranged for Halas to obtain a loan when Halas was on the verge of losing the Bears in 1932, and, more recently, he had provided money to help the sale of the Lions go through.
Bidwill's lukewarm interest in his own team was a source of amusement in league circles. In 1938, a reporter had asked whether he would be in New York to watch his Cardinals take on the Giants. No, Bidwill said, he would be in Chicago to watch the Bears. By the early 1940s, the gap between Chicago's two teams was widening. Halas had built a powerful squad that played to large, enthusiastic crowds. The Cardinals continued to lose and shrink further into the Bears' shadow. Moving them to the West Coast was one solution. But Halas asked Bidwill to keep the idea between them for the time being. The Los Angeles situation was delicate, as several West Coast groups also were interested in obtaining an NFL franchise. Hopefully, Halas told Bidwill, we can make it happen sooner rather than later. That pledge would cause more trouble than either man could have imagined.
IN 1939, FOR THE THIRD YEAR IN A ROW, THE REDSKINS AND Giants concluded the season by playing at the Polo Grounds for the East division title. Each team sported an 8-1-1 record. They had played a scoreless tie in October at Griffith Stadium. The rematch drew 62,404 fans on a gray December afternoon, another indication that the Giants had become a marquee sports attraction in their city, especially when the Redskins visited.
The defenses dominated. Neither offense produced a touchdown in the first three quarters as the Giants inched ahead with three field goals from two different kickers. But just when it appeared the 9-point lead would hold up, the Redskins rallied. They blocked a punt, quickly scored a touchdown, forced another punt, and drove the ball into scoring range. As the crowd fell quiet, the Redskins' Bo Russell lined up a 15-yard field goal attempt to win the game in the final seconds. The snap and hold were perfect. Russell put his right foot into the ball. Half of the Redskins Band, seated behind the end zone, erupted in celebration, thinking the kick was good. The other half groaned, believing the ball had flown wide of the uprights.
On the field, standing behind the offense, Bill Halloran, a veteran referee, signaled that the field goal was no good. His was the only opinion that counted. It produced bedlam. Washington coach Ray Flaherty rushed toward Halloran, furious. A half-dozen Washington players surrounded the 135-pound referee, shouting at him. As Halloran and the other officials tried to leave the field, one Redskin chased after them and threw a punch. A team of policemen had to form a wedge to protect the officials.
A few hours later, Tim Mara and George Preston Marshall shared a lavish dinner at a Manhattan restaurant. Marshall was livid; he was sure Halloran had robbed his team of a division title. But, still, he could joke about it. Noting Mara's luck that afternoon, he asked, "Tim, just tell me one thing, what church do you go to?" Marshall often infuriated Mara, but the two understood that the rivalry between their teams was good for each of their businesses, and for the league in general.
Both men quickly forgot about their conciliatory dinner, however. Marshall went on a rampage. First, he tried to convince Carl Storck, at that time still the league president, to overturn the call; Storck refused, which probably cost him his job a year later. In the meantime, Marshall saw to it that Storck was relieved of an important duty, the assigning of referees to games. Starting in 1940, a committee of owners, led by Marshall, handled the assignments. Halloran's load was reduced. Mara believed Marshall was acting childishly, and their feud escalated. They began arguing over everything, including the hiring of the commissioner, the schedule, rules changes, and more. "The two moguls were squaring off," according to Rooney's biographers. Rooney had to calm them down with the reminder that the league's future required cooperation off the field.
Mara and Marshall were not the only owners whose relationship veered from friendly to acrimonious and back again. Halas and Mara "were so often on opposite sides that I grew up looking upon Halas as an enemy," Wellington Mara said. But they also could shake hands and work together. Halas and Lambeau had battled on and off the field for two decades, but the rivalry between the Bears and Packers helped keep both teams afloat. Bell was infuriated by Halas's hiring of Layden as commissioner, but Halas had great respect for Bell and for Rooney, especially after he tried to short the upstart Rooney on a game check in 1936 and was challenged to a fight. "Their relationship was one of great warmth," Virginia McCaskey said of Halas and Rooney. "Art's personal warmth may have gotten in the way of his having a good team at times, but it also benefitted the league. Helping people get along. He just wanted to be a good friend to everyone."
Months after Layden's hiring seemingly drove a wedge between them, Halas asked Bell for a favor. Virginia was attending college, having left Chicago for Drexel University in Philadelphia, and now she was dating a University of Pennsylvania student named Ed McCaskey. "Would you please check up on him and let me know what you find out?" Halas asked Bell, the Penn grad and lifelong Philadelphia resident. The request was a sign of the immense trust between the two owners. Halas's older brother, Walter, had been a coach and athletic administrator at Drexel since the late 1920s, but Halas asked Bell to "scout" his potential son-in-law.
McCaskey was on a partial scholarship that covered his tuition but left him constantly scrambling to pay for his meals, books, and rent. A resourceful young man, he took extra jobs waiting tables and working in Penn's athletic ticket office. The ticket manager, Bill Lenox, liked him and offered to help. Penn was a national power in football, drawing big crowds to its home games at Franklin Field. The demand for tickets was always high. Lenox let McCaskey sell cheap, obstructed-view seats and keep the proceeds. Bell knew Lenox and asked what he thought of McCaskey, explaining that the young man was dating Virginia Halas. Lenox said he thought highly of the diligent McCaskey.
Bell's scouting mission was not over. One day McCaskey reported for work at a restaurant near Penn's campus. His boss told him two men were waiting to speak to him. He was directed to a table occupied by Bell and Rooney. "Ed sat down with them. They asked how he was doing," Virginia McCaskey recalled. "The conversation went on for a while and finally ended when Bert said, 'Well, if you're OK with Bill Lenox, you're OK with me.'"
Bell contacted Halas to tell him the same. Halas remained unconvinced, but that changed after McCaskey married Virginia a year later and eventually became part of the NFL's fraternity of owners. McCaskey, it turned out, fit right in. "He and Art Rooney both loved horse racing," Virginia said. "They got to be real close."
#
# DOG MEAT
THE STADIUM ANNOUNCER'S VOICE ECHOED THROUGH THE Polo Grounds shortly after 2 p.m., during the first quarter of a game between the Giants and Dodgers on December 7, 1941.
"Attention, please. Attention, please. Here is an urgent message," the announcer stated. "Will Colonel William J. Donovan call operator 19 in Washington immediately?"
Few in the crowd of 55,051 thought much of it. The Polo Grounds routinely reverberated with announcements during games. Season tickets were for sale. A car outside the stadium was parked with the motor running and the doors locked. A man's wife had gone into labor; please call home. Some fans surely recognized that this announcement was unusual, however: "Wild Bill" Donovan was widely known as a Great War hero and now headed the Office of the Coordination of Information, a forerunner of the Central Intelligence Agency. In attendance at the Polo Grounds because he rooted for the Giants, he surely was dealing with an important matter if he had to make an urgent call to Washington.
The NFL was concluding its season with a slate of Sunday games, including this one in New York, where the Dodgers were surprisingly ahead of the Giants early. In the Polo Grounds press box, a Western Union operator studied his news ticker and told the sportswriter next to him that the Cardinals also had gone ahead of the Bears in Chicago, another surprise.
A few minutes later, still looking at his ticker, the Western Union man said, "Oh, my God."
"What, Cardinals score again?" the sportswriter asked.
"No," the wire man said, "the Japs have attacked Pearl Harbor."
While the game went on, everyone in the press box gathered around the ticker as more details came through. _U.S. fleet in ruins. Thousands dead. President Roosevelt to meet with cabinet. Declaration of war imminent._ The news spread rapidly through the crowd, even without a stadium announcement. A team chaplain informed twenty-five-year-old Wellington Mara on the sidelines. "I didn't even know where Pearl Harbor was," the young Mara would recall.
The Giants' head coach, Steve Owen, told his players at halftime. "He gave us such a bad account of all the bad things that happened there, it was like we didn't want to go back out on the field," said Jim Poole, an end. Jock Sutherland, the Dodgers' coach, elected not to inform his players, fearing they would lose interest in the game. But they already knew. "What do we do now?" asked halfback Ace Parker as he paced the locker room. The teams played a listless second half. Near the end of Brooklyn's 21–7 victory, the public address announcer's voice rumbled through the stadium's loudspeakers again. "Attention, all officers and men of the Army and Navy are to report to their stations immediately. Repeat, all armed forces personnel will report to their stations immediately."
Tim Mara left the stadium deeply conflicted. Although the Giants had lost, they had already secured the East division title, earning them a place in the upcoming league championship game. That normally would have been cause for celebration, but it felt meaningless now. Thousands of Americans were dead and the country surely was going to war. At fifty-four, Mara was the elder statesman among the NFL's brotherhood of owners. As the son of Irish immigrants who had fled dire conditions in their homeland for a better life in America, Mara had strong feelings about his country. Though he was too old to serve, he would aid the impending war effort however he could. The fate of the Giants and the NFL seemed trivial in comparison.
Yet Mara could not help but worry about his team and the league. Two years earlier, New York had legalized pari-mutuel wagering, effectively putting the state's racetracks in charge of the gambling on their premises. Wagers were now placed with the house, not on a man-to-man basis in a betting enclosure. Legal bookmakers had been put out of business. In 1939, Mara's career as a bookie came to an end, cutting off what had been his steadiest source of income for many years. He still owned a fuel company (technically, his wife owned it, in the same way his sons owned the Giants) and had other interests, but the Giants were now the backbone of his business empire.
The Giants had become popular and profitable, owing to their consistent success on the field. But the continued existence of the league overall was far from assured. Even after two decades in business, the league was constantly held back by teams that were neither successful on the field nor profitable at the gate.
Recently, after barely surviving the economic depression of the 1930s, the NFL had finally started to gain a measure of security. Interest was growing, attendance surging. Now, though, the league faced another challenge. At the very moment its business appeared to be stabilizing, a war was beginning. Mara was old enough to remember life during the Great War. It had been a time of great uncertainty, when Americans were asked to conserve resources to support the war effort. If rationing was mandated again, Mara wondered, would the NFL be able to endure?
IN CHICAGO, THE STADIUM ANNOUNCER AT COMISKEY PARK broke the news from Pearl Harbor to the crowd of 18,879 that had gathered to watch the Bears play the Cardinals. "They announced it over the loudspeakers. It was a tremendous shock to everyone," recalled Sid Luckman, the Bears' quarterback.
The game was vitally important to the Bears, who needed to win to set up a one-game playoff with the Packers for the West division title. The Cardinals, concluding another losing season, had less to play for, but they always wanted to beat their heralded crosstown rivals and had taken an early lead. After the announcement, "the teams just didn't have the same emotions knowing our country had been attacked," Luckman said. There was talk of stopping the game. "I didn't know what to do. We decided the game should go on. Very few people left," Halas wrote later. His team continued to trail for most of the game, but finally took the lead in the fourth quarter when George McAfee caught a 39-yard touchdown pass from Luckman. McAfee then sealed the win with a 70-yard touchdown run.
Halas was briefly elated, but his thoughts quickly turned to the impending war. As a young man, he had volunteered for naval service during the Great War and requested that he be assigned duty at sea. He was disappointed when the navy instead installed him in the sports program at the Great Lakes Naval Training Base. After his discharge, he pledged to see more purposeful action if America ever went to war again. It was time to uphold that commitment. In the midst of his preparations for the playoff game with the Packers, he drove to the Great Lakes base, north of Chicago, and asked the commander, an old friend, if he could be "sent to sea." The commander told him he was too old. Halas was forty-six. "I'll send your name to Washington. Maybe someone will pick you up," the commander said.
Halas returned to Chicago and coached the Bears. Their game with the Packers drew 43,425 fans, a sizable figure, to Wrigley Field; it seemed people needed a respite from the grim war news in their newspapers. The Bears routed the Packers, then also routed the Giants, 37–9, in the 1941 championship game a week later. Few would dispute that Halas had put together the finest pro football team ever. The Bears had now won back-to-back NFL titles. But only 13,341 fans attended the title game at Wrigley Field. The public's interest in sports already was waning.
In the coming months, dozens of NFL players volunteered for military duty, leaving rosters depleted. When training camps opened in 1942, almost half of the NFL's players, more than 150, were in the service. The Giants had lost more than half of their 1941 division-winning squad. Twenty rookies made New York's roster in 1942. "I took one look at the squad and I felt like crying," fullback Tuffy Leemans said. The Steelers had lost so many players that they dressed just sixteen for their first preseason game. There was some talk that the league should suspend operations. But in early 1942 President Roosevelt penned a "green light letter" to Kennesaw Mountain Landis, suggesting he "keep baseball going" because the war effort would be taxing and people "ought to have a chance for recreation and for taking their minds off work." The NFL owners took that as a rationale to continue operating normally. When Bell and Rooney lobbied the other owners to at least shorten the 1942 season to nine games, their proposal was dismissed.
A powerful squad to begin with, the Bears lost fewer key players than other teams did and dominated their opponents once the 1942 season began. Led by Luckman and McAfee, they beat the Packers by 16 points, the Rams by 14, the Cardinals by 27, the Giants by 19, and the Eagles by 31. Their home attendance remained strong, with 38,000 fans attending the Cardinals game, and 32,000 paying to see the championship-game rematch with the Giants. At times, it was hard for Halas to tell the country was at war. But midway through the season, Halas finally received his military call-up; the navy reactivated him as a lieutenant commander and assigned him to a base in Norman, Oklahoma, where aircraft mechanics were trained. He wore his uniform on the sidelines of a home game against the Lions on November 1, 1942, his final contest before leaving. At halftime, players from both teams gathered around him at midfield, and an induction officer presented him with a sword. Halas also inducted his son into the navy as part of the ceremony. After the Bears won, 16–0, Halas departed for Oklahoma, leaving his top assistants in charge of his undefeated team. There was no immediate falloff in the Bears' performance. They scored 162 points and gave up just seven while winning their next four games.
Halas arrived in Norman to find he was third in command at the base, with "many duties," he later wrote. Still, the assignment discouraged him. "I would not have chosen it," he wrote. "The duty I wanted was in the Pacific, fighting the Japs. I hoped an early transfer could be arranged."
In December, he wrangled a temporary leave and took a military flight to Washington to watch the Bears play the Redskins in the 1942 league championship game at Griffith Stadium. The Redskins had gone 10-1 during the regular season, finishing with nine straight wins after an early loss to the Giants. They still had Sammy Baugh at quarterback and a strong squad around him, but the undefeated Bears were favored to win. Chicago had scored 376 points and allowed just 84 during the season. The Redskins, however, were eager to avenge the 73–0 humiliation Chicago had dealt them two years earlier. Their fans felt the same. Meanwhile, the Bears had grown overconfident after winning eighteen straight games over two seasons. "We were beginning to think of ourselves as unbeatable. Coach Halas never would have allowed that," Luckman recalled.
A packed house of 36,006 crammed excitedly into Griffith Stadium but fell quiet when a burly Chicago tackle, Lee Artoe, picked up a fumble and rumbled 50 yards for the game's first touchdown. But the rout many expected did not happen. Eighteen Redskins were playing their final game before beginning their military deployments. Washington's coach, Ray Flaherty, was joining the navy in forty-eight hours. Displaying the passion one might expect in such circumstances, the Redskins stymied Luckman and the Chicago offense, which was accustomed to scoring easily.
The Redskins took a 7–6 lead on a stunning touchdown pass before halftime. Baugh dropped back and heaved the ball 50 yards, seemingly beyond the reach of his receivers. But Wilbur Moore caught up to it and grabbed it on a dead sprint for a score. The Redskins then scored another touchdown in the third quarter. Halas, seated on the Bears' bench, was shocked. Sensing victory, many Washington fans stood through the fourth quarter, encouraging the home team. In the final minutes, Luckman led a drive to the Washington 2 yard line, but several runs fell short of the goal line, and a fourth-down pass fell incomplete. Washington's fans flooded the field after the final gun. "The once mighty football empire of the Chicago Bears was forever crushed and ground," the _Washington Post_ wrote the next day.
George Halas, in his navy uniform, on the Bears' bench during the 1942 championship game. (Associated Press)
Disconsolate at first, Halas soon recovered, at least outwardly, wearing his naval uniform to the owners' post-championship meeting the next day. Marshall, in the mood to gloat, punctured his calm. "George, you're too old to fight a war. Why don't you take off the uniform and let a younger guy do the job?" Marshall said. Halas had to be pulled off his "best friend" who owned the Redskins. "I thought Halas would kill Marshall," Art Rooney recalled.
WHEN PEARL HARBOR WAS ATTACKED, ROONEY WAS FORTY, with five sons and several businesses to run. He was hardly an ideal candidate for combat. But after arguing with Kass, he went to a recruitment center and signed up. As he turned in the paperwork, though, an official sneered, "You're no big shot now!" Rooney tore up the duty application papers and walked away. His friends had suggested his energies would be better spent at home, helping people in need, boosting morale with his football games and boxing cards. He realized his friends were right. That winter, he staged patriotic-themed boxing cards at Duquesne Gardens, Pittsburgh's largest indoor venue. Servicemen received free admission, and Rooney sold war bonds between bouts. Months later, 19,000 fans came out for what sportswriters called the best boxing card ever staged in Pittsburgh, headlined by a bout between Ezzard Charles and Joey Maxim.
Rooney remained troubled that he was not fighting for his country. Several of his brothers and friends had volunteered, as had a booking agent in his boxing business who was two years older. Rooney sought to assuage his guilt by tending to the needs of those left behind. "He found people waiting for him every morning in the Fort Pitt Hotel lobby. Many counted on Art to intercede on their behalf or reach into his pocket," his biographers wrote.
He had hoped the NFL would cancel its 1942 season; too many players were in the service, he believed, and too many fans did not have enough money for tickets. After reading Roosevelt's "green light letter," he knew the league would remain open for business, but he still disagreed with that implicit decision and initially staged a quiet protest by failing to field a full roster of players. After watching the outmanned Steelers lose miserably to the Cleveland Rams in a preseason game, however, he changed his mind and went on a recruiting binge. The Steelers wound up fielding the most competitive team in their history.
Rooney also benefited from some good fortune. Months earlier he had drafted Bill Dudley, a supremely talented halfback from Virginia. Dudley promptly signed up to fight—typical Steeler luck, many observers lamented. But, over the summer, he received a furlough enabling him to play in 1942. He scored all four of the Steelers' touchdowns in their first two games, both defeats. Rooney sensed another losing season on the way, but Dudley was more confident. "This team is going to win some games," the young man told the owner.
Dudley was prescient. The Steelers won their next three games, helping lure a sellout crowd to their next home contest, against the Redskins. One sportswriter enthusiastically declared pro football finally had arrived in Pittsburgh. The Steelers lost, but it was clear they were vastly improved. The next week, they went to New York and beat the Giants as Dudley broke a 65-yard touchdown run to seal the victory. It was the start of a four-game winning streak, their longest run of success since they joined the NFL. For the first time, Pittsburgh ended a season with a winning record. But the war effort remained Rooney's priority. In the middle of the winning streak, the Steelers played a military team in a benefit exhibition game and raised $35,000, which went toward building a USO canteen in downtown Pittsburgh.
After the season, Rooney again suggested to his fellow owners that the NFL suspend operations, even though he had enjoyed his team's winning campaign. When the owners voted to keep playing, Rooney groused that his franchise would "go through the motions" in 1943. He did not think it was a tenable situation. By April, a third of the players on his roster had enlisted, and more were leaving every week. Bert Bell had sent recruiting letters to 250 prospects, but none signed up. Rooney feared offering a cheap product to the public. Fans might lose faith in what was still a fledgling league, at least compared to major league baseball.
His concerns gained support. By April 1943, the Cleveland Rams had only a handful of players under contract and petitioned the league to be allowed to suspend their own operations for the rest of the year. The owners approved the request. By June, Rooney and Bell were in a similar position, with just five players under contract. The rosters of the Eagles, Bears, and Cardinals also were thinning. At a league meeting in June, Rooney proposed that the Steelers and Eagles merge their squads for the 1943 season. The Bears and Cardinals also asked to merge. Fearing the power of a single Chicago team, the other owners passed a rule forbidding such mergers. But they quickly relaxed several conditions of the rule before voting on whether the Steelers and Eagles could merge.
Rooney had proposed a permanent merger of the league's two Pennsylvania franchises two years earlier, when he, Bell, and Alexis Thompson were negotiating their complex franchise sale and eventual swap. The other owners did not like the idea then, but it made sense now. Thompson, like Halas, was in the military, leaving the Eagles without an owner. But they did have sixteen players under contract, far more than Bell and Rooney in Pittsburgh. There also were larger issues to consider. The league needed eight teams to put on a season, and Cleveland was already out. If neither Philadelphia nor Pittsburgh could field squads, the 1943 season might have to be abandoned.
Some owners remained against the merger. George Preston Marshall feared that a combined Philadelphia-Pittsburgh squad would deny his Redskins a division title. Tim Mara also expressed doubts. When the proposal finally was put to a vote, it passed, but barely, by a 5–4 margin, and it included the stipulation that the merger expired at the end of the regular season. The other owners did not want the Philadelphia-Pittsburgh squad eligible to play in the championship game.
Though it had been his idea, Rooney was unhappy from the outset with the merger arrangement. It was decided that the team would wear green and white uniforms, the Eagles' colors, and practice in Philadelphia, which had a naval yard and more defense department jobs than Pittsburgh had, giving it access to more players. The home schedule would be split between the cities, but Philadelphia would host four of the six games. It almost seemed Pittsburgh had been cut out of the league. But Rooney kept his dissatisfaction to himself. He had agreed to the merger because the league needed it, not because it was in his or his city's best interests.
During training camp, it was hard to be optimistic about the "Steagles," as sportswriters quickly dubbed them. Pittsburgh's head coach, Walt Kiesling, and Philadelphia's head coach, Greasy Neale, were supposed to run the team together, but they did not get along, so Kiesling ran the defense, Neale ran the offense, and they spoke as little as possible. The team dressed just twenty-five players, eight below the limit. Most of the players were available because they were ineligible for military service. A tackle had bleeding ulcers. Another lineman was deaf in one ear. A receiver was blind in one eye. The situation appeared so bleak that Bell called Steve Owen, coach of the Giants, near the end of camp.
"Please help me, Steve," Bell said. "I hardly have enough men here to field a team. I'll take anyone you cut from your squad."
"Sorry, Bert," Owen replied. "I don't have anyone I can spare. All I have here is dog meat."
Surprisingly, though, the Steagles opened their season by winning a pair of home games over the Dodgers and Owen's "dog meat" Giants before decently sized crowds at Philadelphia's Shibe Park. That was followed a pair of lopsided road losses to the Bears and Giants, in which they allowed a combined 90 points. But their first game in Pittsburgh brought a win, and the Steagles held their own down the stretch, even defeating the Redskins in Washington. They finished with a 5-4-1 record and, more impressively, drew 34,294 fans to their last home game at Shibe Park.
Attendance was similarly strong in several other NFL cities. When the Giants and Redskins met in a playoff at the Polo Grounds to determine the East division title, the game drew 42,800. A week later, 34,320 came to Wrigley Field on the day after Christmas to watch the Bears win the league title over the Giants. Overall, some 1.1 million fans attended NFL games during the 1943 season, just short of the all-time record. It seemed that Americans wanted to watch football in wartime. There had always been, in the eyes of many, an undeniable connection between the two—the brutal sport and real battle—that underscored its appeal. Teddy Roosevelt had praised the game as an ideal training ground for military leaders. Author Stephen Crane had said he used his experiences as a football player and coach to help him write his acclaimed Civil War novel, _The Red Badge of Courage._ "I believe I got my sense of the rage of conflict on the football field," Crane said. Not long after Pearl Harbor, as the United States entered what became known as World War II, Commander Thomas J. Hamilton of the navy asserted that football was "the nearest thing to actual war."
Perhaps sports fans at home, being so far from the front, felt that supporting football was one way of connecting with the troops overseas. Attendance lagged at major league baseball games, which seemed peaceful by comparison. A game of football, however, reflected the general American experience of the early 1940s. When major college programs such as Alabama, Auburn, Stanford, Harvard, Michigan State, and many others elected not to field squads during the war, the NFL became one of the few places where fans could watch football. Even though many of its best players were overseas and its product was diluted, the NFL was thriving during the war. In fact, it was thriving _because of_ the war.
ROONEY, BELL, AND THOMPSON ALL TURNED A PROFIT WITH their merged squad in 1943, with Rooney making out the best because he had invested the least in the Philadelphia-based operation. At a league meeting in January 1944, though, Rooney said he would not merge the Steelers with the Eagles again. With Bell's help, he planned to field a team in Pittsburgh that year. Three months later, though, he only had five players under contract. The other owners came to Rooney with a request: Would he merge the Steelers with Charles Bidwill's Chicago Cardinals, who had gone winless in 1943 and badly needed help?
Reluctantly, Rooney assented, mostly because, again, it was what the league needed. Cleveland was back in for the 1944 season. The Eagles also were back, hoping to build on the unexpected success of pro football in Philadelphia the year before. A new team in Boston, known as the Yanks and owned by Ted Collins, a millionaire radio entrepreneur, was kicking off in 1944. That meant the league had eleven teams, but it wanted ten, a number that made scheduling easier. If the Steelers and Cardinals merged, the problem was solved. Thus was born the team known as Card-Pitt. "If we don't watch it, we could get arrested for polygamy," Steelers coach Walt Kiesling joked after the merger announcement.
After his success with a merged team the year before, and despite his reservations, Rooney was hopeful about the combined team's prospects. "We could put a weak team on the field and so could Chicago, but together, we are sure to be strong," he said. From the outset, though, this second merger was an abject disaster. Card-Pitt opened the season with a competitive loss, but the quarterback was drafted into the army before the next game, and the team never recovered. A handful of players were fined for not playing hard during a loss to the Bears, and the fined players almost quit the team entirely before meeting with Rooney and agreeing to pay what they owed. A loss to the Redskins featured a brawl so violent that police had to break it up. Rooney, the former boxer, ended up in the scrum and came close to throwing punches.
As the season unfolded, Card-Pitt lost so miserably that one sportswriter joked they should be called the "Car-pets" because everyone walked all over them. A star running back, Johnny Grigas, simply abandoned the team late in the season, explaining to Rooney that he was mentally exhausted after playing for the winless Cardinals the year before and now this winless team. In the end, Card-Pitt played ten games and lost them all, in the process tossing forty-one interceptions, a single-season league record. "We just didn't have it," Rooney lamented. Sportswriters lambasted him for merging with other teams in back-to-back seasons, depriving Pittsburgh of its own squad and of a quality product. Rooney did not even try to defend himself.
#
# TWO WARS
AFTER TRAINING AIRPLANE MECHANICS AT THE BASE IN Norman, Oklahoma, for six months, George Halas received what he saw as a more desirable assignment in the spring of 1942. Finally, at age forty-seven, he went to war, joining the Seventh Fleet, the immense naval force supporting General Douglas MacArthur in the South Pacific.
Upon connecting with the fleet in Brisbane, Australia, he found he was a welfare and recreation officer, in charge of shipboard movie viewings and overseeing the construction of baseball diamonds, beer halls, and rec centers on bases. "I would have preferred a place on a warship, but looking back, I can see my years with the Bears did make me more useful in the duty the navy allocated to me," he later wrote. MacArthur personally asked him to accompany comedian Bob Hope and other celebrities on USO tours. Near the end of the war, the fleet's commander would award him a ribbon for "contributing to high morale."
While in uniform on the other side of the world, Halas managed to stay informed about the Bears, later recalling that Luke Johnsos, his coaching stand-in, would send a cable when they won and write a letter when they lost. "I think sometimes he put the letter in a bottle and dropped it in Lake Michigan," Halas wrote. When the world war ended, Halas came home to find himself immersed in a different conflict—a war in professional football that threatened the league he had worked so hard to build.
The conflict could be traced to Halas's actions before he rejoined the navy in 1942. He had all but promised a Los Angeles franchise to his friend, Charles Bidwill, who had grown tired of running the No. 2 team in a two-team town. When Bidwill suggested moving the Cardinals to the West Coast, Halas pledged to make it happen but asked Bidwill to keep the idea private while Halas cleared the way with the other owners. Then Arch Ward proposed a different plan for pro football in Los Angeles. Ward, the influential _Chicago Tribune_ sports editor, was so respected by the owners that they had twice sought to hire him as their commissioner. Ward turned them down but remained in the league's inner circle. He convinced a powerhouse West Coast group to invest in pro football, and, at a league meeting in Washington on December 9, 1942, that group, led by Don Ameche, the popular movie actor, applied for a franchise for Buffalo, planning to move it to Los Angeles and begin playing when the war ended.
The day before the meeting, the Bears had played the Redskins in the championship game and lost, 14–6, at Griffith Stadium. Halas, already in the navy, had taken a brief leave to attend the game, but the real purpose of his trip was to wield his influence at the league meeting the next day. "I had promised Charley [Bidwill] I would back him when Los Angeles opened," Halas would remember. "I told Arch I could not go back on my promise to Charley. The league did not approve his [Ameche] application. Arch was furious. His anger was to prove costly."
Much like Harry March a few years earlier, Ward took revenge by forming a rival league. The timing was right, in Ward's view. No longer was the NFL widely dismissed as a poor imitation of the college game. The Bears, Redskins, and Giants were popular and profitable. Wealthy men in other cities wanted in. If he waited for the end of the war to start his league, Ward figured, Americans would be ready to spend on entertainment when the peace began, and a new league could prosper.
Helping his cause, the NFL moved cautiously without Halas present, fearful of taking a misstep. The owners were well aware that other cities wanted franchises and also knew that, structurally, their sport should eventually be able to support a second league; baseball had two leagues, after all. But the owners were skeptical of letting anyone into their exclusive club. With the country at war and several existing franchises still barely surviving, they tabled almost all expansion plans. The new franchise they approved for Ted Collins in Boston was an unusual case. When they licensed the franchise in 1943, to begin play in 1944, they did so to achieve an even number of teams and prevent scheduling headaches.
The owners' caution was apparent at a league meeting in Chicago in 1944. Prospective ownership groups from five cities made pitches. Four were so confident of receiving approval that they paid a $50,000 nonrefundable deposit, which the league had demanded. Bing Crosby headed Buffalo's group; the practice of attaching a celebrity face to an ownership group—still relatively common—has a long history. Anthony Morabito, a wealthy lumber magnate, led San Francisco's bid.
The owners turned them all down. They regarded the Buffalo market as too small because it did not have a major league baseball franchise. "Buffalo is not ready for the league," Tim Mara declared. George Preston Marshall advised Morabito to forget about pro football entirely. "We've got 10 clubs operating now. Only four have ever shown a profit. More than 40 other franchises have gone broke. Stay in the lumber business. You'll be better off," Marshall said. As the meeting ended, commissioner Elmer Layden told reporters, "We feel there is no hurry in deciding which way we want to go." But that did not satisfy Morabito. Before leaving Chicago, he met with Ward. He had heard the sports editor was recruiting prospective owners for a new league. Morabito's interest helped convince Ward it was time to launch the endeavor.
At the initial meeting in St. Louis on June 4, 1944, a name for the new league was decided on: it would be the All-America Football Conference. The form of the AAFC began to crystallize at a meeting in New York in September. The Ameche group, spurned by the NFL, would back a team in Los Angeles. Gene Tunney, the retired boxing champion, would start one in Baltimore. Morabito would have his San Francisco franchise. Arthur McBride, a taxicab entrepreneur in Cleveland, would field a team in that city. (His attempt to buy the NFL's Rams had failed.) Chicago, Buffalo, and New York also would have teams.
A few months later, the AAFC followed the NFL's lead and hired a member of Notre Dame's famed Four Horsemen backfield as its commissioner. Its choice, Jim Crowley, had gone on to coach winning teams at Michigan State and Fordham. A young lineman named Vince Lombardi had played for him at the latter school. Initially, the AAFC hoped Crowley and his former college teammate, Elmer Layden, could work together in what it called "a spirit of cooperation and friendliness," replicating baseball's arrangement with its American and National Leagues. But the NFL owners did not want to cede the monopoly they had worked so hard to build over a quarter century. Layden refused to meet with his former teammate or anyone from the AAFC and offered a tart public reply to the new league's handshake offer. "All I know of a new league is what I read in the newspapers. There is nothing to talk about as far as new leagues are concerned until someone gets a football and plays a game," Layden said in 1945. Meanwhile, Halas returned from naval duty to discover he was positioned opposite Ward in a conflict of escalating tensions and expanding size. "The rival league spoiled their friendship," Virginia McCaskey recalled. "That was such a sad development."
OTHER NFL OWNERS BESIDES HALAS ALSO FOUGHT IN THE war—the real war. Brooklyn's Dan Topping, just twenty-eight when Pearl Harbor was attacked, served in the Marines for forty-two months, twenty-six of which he spent out of the country, mostly in the Pacific. Wellington Mara enlisted in the navy as a lieutenant in early 1942 and served until the war ended, earning medals as a radar officer on aircraft carriers in both the Atlantic and Pacific theaters. Both of the Cleveland Rams' co-owners, Dan Reeves and Fred Levy, joined the Army Air Corps.
Their absences meant fewer people around the table at league meetings. Marshall, by now among the longest-tenured owners, became an even more dominant figure without Halas around, voicing his opinions so loudly he almost shook the walls. The wartime restrictions that shaped the lives of so many Americans had little impact on Marshall. He continued to spend and spend to keep the Redskins popular and successful, and he still lived extravagantly with Corinne Griffith.
Some insiders had thought the absence of hundreds of players due to the war would finally level the playing field, bringing losing teams such as the Eagles and Steelers more even with the Giants and Redskins. But the Redskins remained a power and still drew larger crowds than any team except the Giants. In 1943, when they won the East in a playoff before losing to the Bears in the championship game, they sold 206,540 tickets to six home contests, setting a franchise record.
Their head coach that year was Arthur "Dutch" Bergman, formerly the coach at Catholic University, which had discontinued football. Bergman replaced Ray Flaherty, who had gone into the navy after leading the Redskins to the league title in 1942. Marshall had never been afraid to interfere with his coaches, tell them who should be on the field, even call plays, but he had refrained with Flaherty, an authoritative former player who did not tolerate such meddling. Once Flaherty was gone, though, Marshall quickly resumed his invasive ways. Bergman lasted just one year. His replacement, one Dudley DeGroot, was a brainy Stanford graduate who held a doctorate in education and was a recognized expert in ornithology, the study of birds. He was the Redskins' sixth head coach in their thirteen-year existence and the easiest for Marshall to push around. "He would drive his limousine right out on the practice field and say, 'Change this guy over here,' like that,'" former Redskin Jack Doolan told sportswriter Dan Daly years later. "And DeGroot would say, 'Yeah, OK.' That's the kind of coach George wanted."
Playing defense, the Redskins' Sammy Baugh (33) closes in on a tackle during a game in 1943. (Bettmann)
DeGroot put up with it in part because he had never coached such talent before. In 1944, the Redskins' backfield featured two star quarterbacks, Sammy Baugh and Frank Filchock. Baugh, now thirty, had received a military deferment with orders to produce beef at his Texas farm, deemed vital to the war effort. He spent his weeks in Texas and his weekends with the Redskins, a schedule that proved problematic when DeGroot, at Marshall's request, switched offenses, installing the T formation. Filchock, rejoining the team after two years in the navy, was around for practice and more able to learn the offense, but DeGroot was not about to bench Baugh. The quarterbacks split snaps on Sundays, shuttling back and forth between the sideline and field.
With Baugh flying between his Texas ranch and Washington so frequently, Marshall took out a $100,000 insurance policy on the quarterback, fearing he might die in a plane crash. Ever mindful of promotional angles, Marshall also sought to use the situation to generate headlines. The owner parked a plane by the Redskins' practice field and identified it for the press as the one Baugh used on weekends. That was just a ruse, though; the plane was a rudimentary "trainer" plane, incapable of traveling far. "I wouldn't go near that thing on a bet, let alone fly in it. It's just another of George's promotions," Baugh said with a laugh when reporters asked about the plane.
The Redskins started fast in 1944, winning five straight games after opening with a tie. Another division title seemed likely. On Sunday nights, after the latest win, Marshall and Griffith would make a grand entrance at the Blue Room of the Shoreham Hotel, where bandleader Barnee Breeskin performed. Breeskin and Griffith had cowritten "Hail to the Redskins" in the late 1930s, and now, when Breeskin saw Marshall and Griffith enter the Blue Room, he would stop his orchestra mid-song, tap his baton, and lead a rousing rendition of the city's beloved football fight song. Beaming, with his hair slicked back and a beautiful woman on his arm, Marshall appeared like a king, his mood as buoyant as ever even with America at war.
It did not last. Though they took an early lead over the Eagles before 35,540 fans at Griffith Stadium on November 19, the Redskins were crushed for the rest of the day and lost, 37–7. Suddenly, it felt like a burden to have two quarterbacks operating a new offense. Baugh's arrangement came under scrutiny and criticism from the parents of soldiers wondering why the quarterback was allowed to flout the travel restrictions in place during the war. The Redskins ended the season with a pair of losses to the Giants, who took the East title. The biggest surprise, perhaps, was that Dudley DeGroot survived Marshall's ire and kept his job.
ARCH WARD WAS NOT THE ONLY SPORTS ENTREPRENEUR WHO believed America would be ready for another pro football league after the war. Two other leagues, the Trans-America Football League and the United States Football League, also appeared, with plans to begin play when the war ended.
The TAFL boldly proposed a merger with the NFL that would result in a sixteen-team league—eleven from the NFL and five from the TAFL. The NFL owners immediately dismissed the idea. Though their league was still not on firm footing, they did not see the benefit in merging with a league composed of teams that had never played a down. In the end, the TAFL folded before a game was played.
The USFL lasted somewhat longer, having received a flurry of attention after announcing Red Grange as its commissioner. Now an author and broadcaster, Grange was still football royalty. But his league's demise was effectively sealed on the day it announced it had eight teams and planned to kick off in 1945. "Our club owners are all good businessmen, not millionaires," Grange told reporters. He did not realize that a new league needed millionaires. Lacking the necessary backing, the USFL never got off the ground.
Ward's AAFC was in much better shape with an ownership group that included millionaires such as McBride and Morabito, as well as James Brueil, an oilman from Buffalo; Ben Lindheimer, a developer and race track owner from Chicago, who was Ameche's coinvestor in the Los Angeles franchise; and John Keeshin, a Chicago trucking magnate. The AAFC had the resources to present a serious challenge to the NFL.
On February 13, 1945, the new league announced the signing of Paul Brown, a highly regarded thirty-seven-year-old coach who had won at Ohio State and, before that, at a high school in Massillon, Ohio. During the war, he had coached at the Great Lakes Naval Training Base, where Halas served during World War I. Most fans had expected Brown to return to Ohio State, but McBride lured him to Cleveland's AAFC franchise with an unprecedented offer, a five-year deal worth $25,000 per season, which was more than the league's commissioner made. Now no one in the NFL could doubt that the AAFC was a true threat.
Two months later, in early May, the real war in Europe ended with Germany's surrender. Japan surrendered in August, days after American planes dropped atomic bombs on Hiroshima and Nagasaki. As the rhythm and rituals of normal American life slowly resumed, NFL players returned from military service to find the landscape of professional football changed. Though the AAFC would not begin playing until 1946, Crowley told reporters that the league already had 150 players under contract, including some from the Redskins and Bears.
For its part, the NFL experienced a strange season in the fall of 1945. Dozens of players returned from the war and put their football uniforms back on, and the status quo exploded. The Giants, Bears, and Packers—three of the four teams that had long dominated on the field—fell out of playoff contention. Alexis Thompson's Eagles rose up and challenged the Redskins for the East division title. The Rams shot to the top of the West division behind Bob Waterfield, a rookie quarterback from UCLA whose pro debut had been delayed by an injury and the war.
Some things remained the same. After two years of shotgun mergers with other teams, Art Rooney brought the Steelers back to Pittsburgh, determined to go it alone. But with an assistant coach in charge of a no-name roster, the team won just two games. The Redskins shut them out twice. Marshall's team still controlled the East. After beating Pittsburgh a second time, the Redskins just needed to defeat the Giants in their season finale at Griffith Stadium on December 9 to wrap up their fifth division title in nine years in Washington.
But, several days before the game, Marshall and the other owners received a shock. On December 6, 1945, Dan Topping, who had owned the league's Brooklyn franchise since 1931, called a press conference in New York to announce he was abandoning the NFL and jumping to the AAFC starting in 1946. Now the new league _really_ had the NFL's attention. Though just thirty-three, Topping was wealthier than Halas, Bell, Rooney, and the NFL's other decision-makers—perhaps wealthier than all of them combined. Topping's grandfather, Daniel Reid, had amassed a fortune in the tin-plate business; started the American Can Company; invested in railroads, tobacco, and banks; and left most of his estate, valued at between $40 million and $50 million, to Topping's mother. Topping could do as he pleased. Earlier in 1945, he and two partners had spent $2.8 million to buy baseball's New York Yankees, the most storied and probably the most valuable franchise in the sport.
The sale had included Yankee Stadium, the majestic ballpark in the Bronx where the Yankees had played since 1923. That meant Topping now owned a stadium, a claim no other NFL owner could make; they all rented their home fields. That only increased Topping's desire to change his football team's status quo. He was tired of owning a Brooklyn team that played in the long shadow of Tim Mara's Giants. A handsome playboy who would marry six times, Topping thought he deserved better. He had more money than Mara. He owned the Yankees. He thought _he_ belonged in the spotlight, not Mara.
But there was a problem with his grand vision. Mara had held the NFL's territorial rights to New York since the 1920s. Any league matter involving the city had to go through him. The other NFL owners were sympathetic to Topping's plight. His Brooklyn franchise had lost what little following it had during the war. Brooklyn and Ted Collins's Boston Yanks had been forced to merge for the 1945 season. Chafing at the situation, Topping had told the owners he was set on moving his team from Ebbets Field to Yankee Stadium in 1946. Reluctantly, Mara had agreed to work with him to find a peaceful way forward. They met at Mara's office in late November 1945 to divide up home dates for the next season, so Mara's Giants and Topping's Yanks—the name he wanted to use—would never play at home on the same day. Each wanted as many home dates as possible later in the year, after the baseball season ended, when football attendance always picked up.
Mara took some dates and offered Topping others. The Giants' owner thought the meeting went well and expected to hear soon that Topping had submitted prospective home dates to Elmer Layden for league approval. But the next time Mara and Topping spoke was a few minutes before the December press conference at which Topping announced he was leaving the NFL for the AAFC. Topping wanted to give Mara the news personally before making it public.
At the press conference, held in the Yankees' offices at Yankee Stadium, Topping issued what amounted to a declaration of war. He announced he was hiring Ray Flaherty, the former Giant who had won two NFL titles as the Redskins' coach, to coach his New York Yanks in the AAFC. The team would be filled with players from his defunct NFL team, he said. He reminded all present that Yankee Stadium could hold as many as 90,000 fans for football games, and he planned to fill it.
The NFL had previously faced competition from rival leagues such as the "Grange League" in 1926 and the American Football League in the 1930s. Every time, the new league had attempted to establish itself initially in New York, turning Mara and the Giants into the NFL's first line of defense. In the previous instances, Mara and the Giants had held their ground, prompting the rival league to fold. This latest challenge appeared far more formidable, however. According to the _New York Times,_ "It had been the contention of observers ever since the AAFC was first conceived that it could not quite attain the status of a major football circuit until it operated a franchise in New York. Now that this has been achieved, and with the vast Yankee Stadium and its proposed 90,000 capacity providing the setting, the path of the new league to a major ranking seems assured." The _Times_ added, "Everything is set for a war to the hilt for local patronage."
Mara was among the NFL's most respected owners, but his colleagues were perturbed with him now. Topping would not have bolted, they thought, if Mara had granted him more late-season dates at Yankee Stadium. Asked to comment on Topping's defection, Mara launched into an emotional defense of his franchise, as if he and it were under attack. "We've spent years of time and heaps of money building up the Giants to where they are today," he declared. "I wouldn't take a million dollars for the franchise. It may not be worth that much but it is to the Mara family." He sought to downplay the significance of Topping's defection. "All it has done has been to balance our league better," he told the _Times,_ explaining that it would have proved awkward to have two teams in Manhattan and eleven overall. Marshall made a similar claim, telling the paper the move "will help our league by clearing things up all around." Marshall added dryly, "I hope that Topping does better in the new league than he did in the old one."
Halas did not comment. He had just reentered civilian life in November, having received a Bronze Star from the navy. With his return, all seats at the NFL's ownership table finally were filled for the first time since 1942, and important league business could once again be decided.
The war years had scarred certain teams in the NFL. To survive, five had been forced to merge with another for at least one season, and another had skipped a season altogether. None could pledge to their fans a rosy future. Once again, the trajectory of the league was not one of constant ascent but, rather, of advances followed by challenges and setbacks. Overall, though, the decision to continue playing during the war years could not have worked out better. If the NFL had halted operations, it might have lost many fans who simply forgot about pro football and never returned; the country was hardly obsessed with the sport at the time, after all. Resuming play after such a prolonged hiatus, the league could well have been fatefully diminished. At a minimum, it would have begun its conflict with the AAFC on almost equal footing, a dangerous proposition.
The AAFC, with its millionaire owners and big plans, had loosed a counterproductive line of thinking among the NFL's owners. They had always grasped that they needed to work together, that the good of the league should supersede their own interests. But, with the AAFC looming, that focus on the collective had given way to the idea that it might be time for them to look out for themselves. Topping certainly had done that. In the coming weeks, Bert Bell, a true insider, would meet with Jim Crowley, commissioner of the AAFC, and discuss the possibility of putting a team in Philadelphia, Bell's hometown. Dan Reeves, the Rams' owner, would demand that he be allowed to move his struggling franchise from Cleveland to Los Angeles. If the other owners did not allow it, he said, he was through with them.
Suddenly, it seemed everything was up for grabs. Although the NFL had survived the real war with palpable momentum in many cities, it was under siege like never before, both from outside and from within. With Halas back, though, it was fully armed for the looming conflict with the AAFC—a conflict that, indeed, would test the strength of the collaborative instincts the NFL had developed over the years.
#
# THE RIGHT GUY IN CHARGE
DAYS BEFORE THE RAMS PLAYED THE REDSKINS FOR THE league championship on December 16, 1945, eighteen inches of snow fell on Cleveland. Another front moved in on the day of the game. The temperature was eight below zero in the morning and around zero at kickoff. Dan Reeves, owner of the Rams, had hoped for a crowd that demonstrated Cleveland had arrived as a legitimate pro football town. The Rams had mostly struggled since joining the NFL eight years earlier and had even suspended operations for a season during the war. Now, though, they had a winning team and a marketable young quarterback, Bob Waterfield, who was married to Jane Russell, the sultry Hollywood actress.
Cleveland's fans had gone wild for Waterfield and the Rams, prompting Reeves to move the site of the championship game. His team normally played at League Field, a deteriorating brick bandbox with 30,000 seats. Anticipating a much larger crowd with a title on the line and the powerful Redskins visiting Cleveland for the first time, Reeves rented Municipal Stadium, the cavernous home of the Indians, the city's major league baseball team. It could hold more than 80,000 fans.
Some 40,000 tickets had been sold, a record for the Rams, but Reeves was disappointed not to sell more, and now, given the weather, some of those 40,000 fans would surely stay home and listen to the game on the radio rather than venture outside. Many streets across Cleveland still had not been plowed. When George Preston Marshall and his wife, Corinne Griffith, arrived at the stadium and took their seats before kickoff, they were surprised to see fans departing. The stadium was adjacent to Lake Erie. Brutal winds howled around the bowl. "I didn't think I could take it," Griffith would later write. "Icy gusts of wind, leftovers from the recent blizzard, swept frozen bits of snow high in the air and held them there to diffuse an already pale winter sun. Other stray blasts, roaring through the stadium, blew in relentless spasms against the early arrivals."
Marshall and Griffith did stay, and, in the end, 32,178 fans witnessed a dramatic contest. Reeves had thought of an ingenious way to protect the field before the blizzard arrived. He ordered bales of hay and paid a crew of city workers to spread the straw on the turf before the storm hit. The workers returned hours before kickoff and shoveled the snow and hay off the field. The process left slush piled high behind the benches and end zones, but the playing field was relatively clear. Even with the whipping winds, Waterfield and the Redskins' Sammy Baugh could operate as normal.
The Rams scored first on a fluke play. With the ball on the Redskins' 5 yard line, Baugh took a snap and retreated into the end zone to throw a pass. He saw an open receiver and fired the ball in his direction, but it hit one of the goalpost uprights and fell to the turf in the end zone. According to the rules, when a pass fell incomplete without crossing the goal line, the defensive team was awarded a safety. Cleveland led, 2–0. In his seat, Marshall cursed the little-known rule. He and the other owners had moved the posts to the goal line to enhance scoring by making field goals easier to convert. That change had worked, but this "safety" rule, an addendum, was in Marshall's sights now. It would be gone from the rulebook by the start of the next season. From then on, a pass that fell to the turf in the end zone was just another incompletion.
Baugh soon left the game with bruised ribs, but his replacement, Frank Filchock, threw a 37-yard touchdown pass to give the Redskins the lead in the second quarter. The Rams regained it before halftime on a Waterfield touchdown pass. Waterfield's extra point attempt—he also kicked and played safety—was partially blocked, but it fluttered to the goal posts and landed on the crossbar for a tantalizing second before rolling across, giving the Rams a point that eventually proved decisive.
Waterfield hurled another touchdown pass in the third quarter, but he missed the extra point, leaving the Rams ahead, 15–7. The Redskins rallied before the quarter ended, with Filchock leading a long drive that ended with a short touchdown pass. Trailing by a point, the Redskins threatened to score throughout the fourth quarter, but Waterfield saved a touchdown by tripping up a Washington back in an otherwise open field, and the Redskins' kicker, Joe Aguirre, missed field goal attempts of 46 and 31 yards. When the final gun sounded, a few fans stormed the field to celebrate the Rams' victory—but most headed for home or the nearest bar to warm up.
Reeves had mixed emotions. It was exhilarating to win, particularly against a league standard-bearer such as the Redskins, but between the stadium rental and hay purchase, he had invested so much in the game that he ended up losing money; not even the largest pro football crowd in Cleveland history could save him. He also had lost money on the season—a _championship_ season. And now the AAFC was bringing a team to Cleveland, and, with Paul Brown as its coach, the competition for the city's fans would be formidable. Meanwhile, Reeves had coveted the possibility of moving to Los Angeles for several years, expressing his desire to his fellow owners. They had denied him. Now, emboldened by his championship and his celebrity quarterback, and unenthused by the prospect of a turf war in Cleveland, he was determined to go.
Marshall himself also was weighing a change, though of a different kind. Despite the defeat in Cleveland, the Redskins were winners, and consistently profitable, too. Marshall was having so much fun and making so much money that he no longer wanted to run a team _and_ a chain of laundries. Within months, he would sell his controlling interest in the Palace Laundry and Dry Cleaning Corporation to his partner, an old friend named John Chevalier.
When the Redskins opened training camp the next summer, they were favored to win the East again. Marshall could focus solely on his team. At fifty, he was known now as a sportsman, not a laundryman. Baseball's Washington Senators had descended into mediocrity, drawing puny crowds. In less than a decade, the Redskins had come to rule Washington. But World War II was over, and society was changing in ways he did not—could not—comprehend. Marshall and his team would be left behind. Indeed, the game he had just witnessed in Cleveland was the last championship contest he would see his beloved Redskins play.
THE NATION'S NEWSPAPERS REPORTED THAT THE NFL OWNERS had decided to meet in a special session at the Commodore Hotel in New York in early January 1946. But, in reality, only one owner thought the meeting was necessary. With the AAFC threat looming, Halas believed the league could not hesitate to move on what he saw as a series of critical issues.
Most sportswriters covering the session did not expect fireworks. The owners needed to strike a new deal with Elmer Layden, whose five-year contract as commissioner was expiring. But it was widely assumed Layden would keep the job. Halas had other ideas. He got along well with the mild-mannered Layden, but he thought the league needed a more combative leader if it was going to beat back the AAFC. Layden was friendly with Arch Ward and hesitant to confront him. Layden also had bungled the Dan Topping situation, Halas believed, by neglecting to treat Topping's festering dissatisfaction. A more able commissioner never would have allowed Topping to defect, Halas believed. Working the phones before the special session began, Halas garnered support for a change. It turned out the other owners also were not happy with Layden. His hiring had brought attention to the league five years earlier, but Marshall and Art Rooney wanted a more imposing personality to lead the league. When the owners gathered informally the night before the New York meeting began, Marshall remarked that Layden would continue as commissioner "over my dead body."
Shortly after Layden opened the meeting the next morning, a vote was taken on whether to approve extending his contract. Only three owners voted for him. Layden, surprised and saddened, was told to leave the meeting and wait in his hotel room. Once the former Notre Dame fullback was gone, a discussion commenced on who should replace him. Halas asked Bert Bell to leave the room, too. Halas wanted to make Bell the commissioner.
Some of the other owners expressed doubt, wondering whether Bell, with his ready smile and gregariousness, had the necessary gravitas. His record in the sport certainly did not shine. He had lost money and games as an owner and coach in both Philadelphia and Pittsburgh. How did that make him a viable candidate to run the league?
But Halas saw him differently, believing Bell was one of the few men with the right vision for professional football and for the NFL in particular. It had been Bell who proposed a draft to make the league more competitive—a goal that was finally being realized. Bell also had sat on the league's management council, so he had a hand in numerous major decisions. From his role in the various franchise swaps and mergers that had enabled the Eagles and Steelers to survive during the war, it was clear he was a skilled dealmaker. "Bell's mission in life was football. He had a sure instinct for conducting the business of the game," Halas said later. Halas held Bell in such high regard that he had even asked for a scouting report on a prospective son-in-law.
But most important, in Halas's view, was that Bell was a member of the small fraternity of men who had run the league for several decades. "There were other guys in the room, but Halas, Marshall, Bell, Rooney, Mara, and Bidwill were in charge. It was a crucial moment for the league and they thought it was time for one of their own to become the commissioner," Rooney's son, Dan, recalled. "And Bert could do it. Halas couldn't do it. Marshall couldn't do it. But Bert could."
Halas called for a vote. Seven owners supported Bell—a majority. Still, Halas asked for another vote, thinking it was important that the league show its unanimous support for Bell. A second vote produced just that.
Returning to the room, Bell was overjoyed at the decision. He had long ago wasted his fortune, and, though he and his family were comfortable, he had typical financial concerns. The commissioner's job, with its $20,000 salary, would provide security for his wife and three children. He also would make money selling his half-interest in the Steelers to Rooney—a stipulation of his taking the new job.
In a session with reporters after the owners' meeting, he mused about changes he wanted to make. He wanted to start the season earlier, so it could end in early December. Never again, he said, should a title be decided in wintry conditions such as those the Rams and Redskins had just endured in Cleveland. He also thought that more night games would boost attendance and that NFL radio announcers should be taught to emphasize to their audiences what was different and special about the pro game, drawing a starker contrast to college football. The pro game held up well in such comparisons, Bell told reporters, as it boasted more passing, scoring, and excitement.
Most of the other owners were excited about Bell. "Now we have a pro running our league and they have an amateur," Marshall said, referring to the AAFC's Jim Crowley, whose main qualification was that he had been one of the Four Horsemen. (Layden, of course, had been another.) The football press also gave the hiring its approval. Bell "speaks the pro football language," the _New York Times_ wrote, and "is aware of the problems of each and every owner, as well as the league itself. He seems admirably equipped for the job, even though he takes over in a time of crisis. It's almost as if the NFL said to the AAFC, 'OK, you asked for a fight and we'll give it to you because Bert Bell is the best scrapper we have.'"
Left to right, seated, at a league meeting after World War II: Art Rooney; Wellington Mara; commissioner Bert Bell; Curly Lambeau, Packers; Fred Mandel Jr., Lions. Standing: Dan Reeves, Rams; Walter Halas, Bears; Jack Mara, Giants; Roy Benningsen, Cardinals; George Preston Marshall; Al Ennis, Eagles; Ralph Brizzolara, Bears. (Associated Press)
Privately, Bell marveled at the twisting path he had taken to reach this moment. His father had helped found the NCAA, which oversaw college football. Bell had championed the college game as a young man, disdaining the pros. But now he was a pro league's most prominent and capable defender. At age fifty, the former quarterback and Philadelphia socialite had a sizable paunch, but he had not lost any of his passion for the sport.
When he banged the gavel to open his first meeting as commissioner on January 12, 1946, he was immediately greeted with an epic crisis. Dan Reeves had not relented on his demand to move the Rams from Cleveland to Los Angeles. Reeves's general manager, Chile Walsh, stood by the head table and argued passionately for moving the team while Reeves sat quietly, listening. He needed eight votes for approval. Six owners supported him. Leading the opposition was Halas, who argued that travel to the West Coast would be unaffordable for the rest of the teams, an argument he had made many times to keep Los Angeles vacant. A vote was scheduled. Reeves stood up to leave. Before he departed, he turned and spoke solemnly to the group. "Gentlemen," he said, "you who know me know that I never bluff. I am not trying to force you into any action you might consider detrimental to the league. But when I return to this room after you have voted on my proposal, I am announcing that unless you go along with me, all of my stock in the Cleveland club will be for sale. I am getting out. No bolting, understand, for I do not expect to go with the All America Conference. But I am leaving the National Football League."
Los Angeles's pro football vacancy had caused the fissure between Arch Ward and Halas, so upsetting Ward that he started another league. Now it appeared the Los Angeles issue might produce more unsettling headlines. Bell called a recess and told Halas, Marshall, and Bidwill to go speak to Reeves. Bell wanted to figure out a way to satisfy Reeves, even if meant allowing him to move. Bell was not opposed. The AAFC was starting a franchise in Los Angeles, and whatever costs the move would impose on the NFL's other teams, the necessity of competing with the upstart league in one of the country's largest markets seemed to outweigh them.
Halas had known that his fellow owners would eventually turn against him on this issue. He had prepared himself for this moment in two ways, by accepting its inevitability and by persuading Bidwill to back away from the idea of moving to Los Angeles. Halas had told his longtime friend that the Bears and Cardinals needed to work together to defeat the well-funded AAFC team that was coming to Chicago with the intent to win over the city. Halas exhorted Bidwill to redouble his effort to make the Cardinals flourish in Chicago. Ever amenable, Bidwill agreed to try. That meant Halas could bless the move of another owner into Los Angeles, and he did not have any particular objections to that owner being Reeves.
Sitting in Reeves's hotel room, Halas, Reeves, Marshall, and Bidwill negotiated the terms for the Los Angeles team. League rules stipulated that home teams guaranteed visitors $5,000 for regular-season games. Reeves agreed to guarantee $10,000 for his home games, which would help defray the visitors' travel costs. That allowed the deal to go through. On Bell's first day as commissioner, he had helped orchestrate the most momentous franchise move in league history.
THE OWNERS' SPECIAL SESSION TURNED INTO A MARATHON LASTING almost a week. Bell's agenda grew and grew. He brought in travel agents to explain the air and rail options for trips to California. One day was devoted to the draft. Bell advised teams not to reveal their selections to anyone outside the room so they could negotiate with their players without interference from the AAFC.
The owners and their new commissioner girded themselves for war. They announced a five-year ban of players who signed with the AAFC. They ratified an amendment to the league constitution limiting the NFL to ten franchises—the current number—in the belief that that would discourage any AAFC owners who secretly hoped to end up in the NFL if the leagues merged. Instinctively, Bell decided on an approach for dealing with the AAFC in public. He would ignore it. In the coming years, he would seldom comment on any aspect of the rival league, even when reporters prompted him.
When the marathon meeting finally adjourned, Bell took a train home to Philadelphia. By the time he walked in his front door, another crisis had erupted, this time with him in the middle of it. Jim Crowley, commissioner of the AAFC, had told the Associated Press that the NFL's new commissioner had recently considered jumping to the new league. Crowley and Bell had met in Philadelphia to discuss the possibility, Crowley claimed. Two other men were part of a potential ownership group for an AAFC team in Philadelphia, according to Crowley, and Bell was involved because—this was a bombshell—he had taken out a lease on the football rights to Shibe Park, one of the city's main sports venues. The lease deal seemed to support the allegation that Bell truly had considered joining the AAFC. Why else would the Pittsburgh Steelers' co-owner take out a stadium lease in another city?
Following up, the New York _Daily News_ intimated that Bell was interested in the AAFC until George Halas heard about it and came up with a solution. One AAFC owner told the paper "it is pretty plain" that Halas guaranteed Bell the commissioner's job to ensure he did not jump leagues. That claim was debatable. In fact, the NFL owners had hired Bell for a multitude of reasons, one of which was that he could think on his feet. He now put that skill to use trying to stamp out the story. It was true he had spoken to Crowley, he said, but he denied any interest in owning an AAFC team, claiming the other prospective owners had brought him into their conversation with Crowley only because he held the Shibe Park lease.
One of those other prospective owners corroborated Bell's story. "Bert at no time represented us," said Walter Donovan, owner of Garden State Park, a racetrack. But why had Bell leased Shibe Park? He had an answer: he wanted to keep an AAFC team from playing there. "There was no secret about it. The whole [NFL] knew," Bell said. He also denied that Halas had promised him the commissioner's job to keep him in the NFL.
The story lingered for several days, with one Philadelphia paper suggesting that Bell had considered trying to run the Eagles out of business by refusing to allow them to continue to play in Shibe Park, where they had averaged 30,804 fans for six home games in 1945. Then Bell's Steelers could move to Philadelphia, the paper suggested. But this accusation made little sense. The Eagles, after struggling for years, finally were winning games and drawing crowds. Why would Bell want to kill off the team he had founded? In any case, the Eagles themselves supported Bell's version of the story. "We knew Bert was talking to Crowley," the team's general manager said. "We thought it was smart to have him find out as much as possible about the new league. Everyone in the NFL has the highest respect for Bert."
The story died. Bell went to work. He moved the commissioner's office from Chicago, where Layden lived, to New York but quickly tired of commuting. The owners let him operate out of Philadelphia. He opened an office in a second-floor space over a men's clothing shop near the Penn campus. A sportswriter visiting him there said customers in the men's shop could easily hear the NFL's most powerful man conducting the league's business in his booming voice. Bell later moved the office to Center City.
Both at home and wherever he worked, Bell had a telephone in his ear as he conversed with owners, coaches, and other league officials. "There was a phone in the bedroom. A phone on the landing. A phone on the first floor. A phone in what he called his office. You could just about kill yourself on those long extension cords he had running all over the place," his son, Upton, would later write, describing the scene at home. "He'd be walking back and forth, a cigarette in his left hand and a phone in his right, talking to owners like George Preston Marshall."
His immediate priority was finalizing the schedule for the 1946 season. The owners had failed to agree on one at the meeting in Philadelphia; as always, various stadium conflicts and individual requests, as well as personal jealousies, had prevented a solution. "All of the clubs were very jealous of the schedules and no one trusted anyone. After a while people started walking out of the meetings and saying 'Let Bert do it,'" Wellington Mara would recall. Bell sat down with the list of conflicts and requests. He decided to build the schedule around the idea that the weaker teams should play each other early in the season, enabling some of them to win games, stay in contention longer, and hopefully sell more tickets. He drew up a schedule, tested it with different owners, and made corrections. After settling on a version that seemed to satisfy everyone, he sold it to the owners at a league meeting in April. Bell called it the most harmonious meeting he had ever attended. "Only once did anyone raise his voice. That was George Marshall," Bell commented. "I told him, 'Keep your shirt on, George.' He apologized."
By the end of the year, the owners would raise Bell's annual salary to $30,000 and add two more years to his original three-year deal. He would receive another extension soon enough. From a most surprising place—the lower echelon of its franchises—the NFL had found its ideal commissioner. Indeed, Bell would keep the job for the rest of his life, becoming one of the most important and influential figures in league history.
# **PART FOUR**
#
# BACK ACROSS THE COLOR LINE
AMERICANS WERE READY TO ENJOY THE PEACE THAT FOLLOWED their country's military victory. The war effort had provided jobs for millions, and, with restrictions lifted and triumph in the air, people crowded into bars, restaurants, movie theaters, and ballparks, ready to spend their money.
Sports experienced a soaring renewal. On May 4, 1946, the Kentucky Derby, America's foremost horse race, drew more than 100,000 spectators for the first time, according to the race's organizers. A colt named Assault won, and then he also won the Preakness Stakes and Belmont Stakes to capture the sport's Triple Crown as millions listened on the radio. In June, boxers Joe Louis and Billy Conn fought for a title at the Polo Grounds in another event that captured headlines, with Bert Bell among the celebrities sitting ringside.
No sport was seen as more distinctly American than baseball—during the war, Japanese soldiers had taunted US soldiers with cries of "Fuck Babe Ruth!"—and no sport came back stronger. Dan Topping's Yankees drew 2.265 million fans to seventy-seven home games in 1946, smashing their season attendance record. The Brooklyn Dodgers, Detroit Tigers, and Boston Red Sox also set records for season attendance. Overall, major league crowds nearly tripled compared to three years earlier. The radio rights to the World Series sold for $150,000, a record fee, and the Red Sox and St. Louis Cardinals played a taut series that mesmerized the nation.
College football rosters had been so gutted by the war that some schools could not field teams. But the sport returned in 1946, and so did its fans. Notre Dame twice drew more than 70,000 to games and never played before fewer than 50,000. Michigan and Illinois drew 85,938 to an October game in Ann Arbor, Michigan. Southern Cal and UCLA played before 93,714 at the Los Angeles Memorial Coliseum in November. For the second year in a row, the college football season peaked with what the media dubbed "the Game of the Century." A year earlier, Army and Navy had been ranked No. 1 and No. 2 when they played in a sold-out Municipal Stadium in Philadelphia; it was such an event that President Harry Truman had attended. Now, a year later, Army and Notre Dame were No. 1 and No. 2 when they met at the Polo Grounds, with war heroes General Dwight Eisenhower and Admiral Chester Nimitz in the crowd.
The NFL owners believed they could take a similar leap forward. Although they now had to contend for gate receipts with the AAFC, the NFL had the advantage of a quarter century of tradition, and, though the league had experienced various troubles during the war, there had been positive signs as well. The strongest teams—the Giants, Bears, and Redskins—had drawn large crowds, and formerly lesser teams such as the Eagles and Rams had finally become competitive. The Bears' Sid Luckman had commented at one point during the war that so many players were missing that the NFL had become a semiprofessional league, but with dozens of popular players back now, that was no longer the case. The owners expected their product to become more exciting and interesting.
But pro football still lagged behind baseball, horse racing, boxing, and college football. The NFL's 1945 championship game had drawn a crowd of 32,178, a pittance compared to the teeming throngs that gathered for major horse races and boxing matches and important games in other sports. The radio rights to the NFL championship game had sold for a fraction of what the rights to the World Series sold for. Outside of Chicago, New York, and Washington, sports fans still—after twenty-five years—paid comparatively little attention to the NFL. Part of the problem was the league was still very much a regional enterprise, confined to the East Coast and Midwest. Much of the country simply never saw pro games. That would change with Dan Reeves's move to Los Angeles, as would another longstanding feature of the NFL: its all-white racial composition.
THE RAMS WANTED TO PLAY AT THE LOS ANGELES MEMORIAL Coliseum, a massive public venue. The team's general manager, Chile Walsh, appeared at a meeting of the nine-man commission that ran the stadium on January 15, 1946, asking for a lease deal. Haley Harding, a sports reporter for the _Los Angeles Tribune_ , a black weekly newspaper, took the floor at the meeting and pointed out that no NFL team had employed a black player since 1933. Harding suggested it was wholly inappropriate to use a taxpayer-funded stadium to effectively sanction segregation. The commission agreed. Pledging that no player would be barred from the Coliseum because of his skin color, it approved a lease deal with the Rams on the condition that they attempt to integrate.
Walsh promised they would grant tryouts to black players. Two months later, on March 21, they signed Kenny Washington, a black receiver who had earned All-American honors while playing for UCLA before the war. Now twenty-seven, he had played for semipro teams and worked as a policeman to make ends meet. "I have heard many fine things about Washington, both as a player and as a man, and I feel certain he will be a credit to our ball club and to his race," Chile Walsh said. "I look for other teams in the league to accept him in good grace, just as he has always been given fair treatment and won the respect of all who have played with him and against him in intercollegiate football and in his professional play on the West Coast during the past five seasons."
Walsh's comment amounted to a warning to the other NFL owners and teams to accept the signing of Washington. It was a delicate subject, to put it mildly. The league had fielded entirely white rosters for more than a decade. But the Rams had no choice but to integrate. Within weeks, they reached a deal with Woody Strode, another black receiver who had played at UCLA.
Bob Snyder, the Rams' backfield coach, later conceded that financial concerns, rather than tolerance or even special concern for the situation of black Americans, guided the Rams' decision making. They needed Washington and Strode to obtain a lease on the Coliseum. "I doubt we would have been interested in Washington if we had stayed in Cleveland," Snyder said. If the Rams hoped the rest of the league would understand, they were quickly disappointed. "All hell broke loose," Snyder said. Although the owners would always deny they had agreed to exclude black players for more than a decade, it seems clear in hindsight that they had an understanding. Several dozen black players had suited up for NFL teams from the league's first year in 1920 through 1933, but rosters had gone entirely white starting in 1934.
This was not unusual at the time. Many major American institutions were still segregated or otherwise governed by Jim Crow–era attitudes in 1946. Major league baseball would not integrate until Jackie Robinson debuted with the Brooklyn Dodgers a year later. America's military forces had been segregated for decades and would remain so until 1948, when President Harry Truman signed an executive order forcing their integration.
If, in fact, all hell did break loose in the NFL after the Rams leapt across the league's color line, it is likely George Preston Marshall voiced his displeasure most vehemently. He had impacted the NFL in many positive ways during his fifteen years as an owner, pushing for rules to promote scoring, for the owners to make their games more of a show, and for the league to be divided into two divisions with the season culminating in a championship contest. But his position on integration was a negative influence. The Redskins' owner was, simply, a racist. Blacks belonged in their place, he believed, and that place was not the NFL. Although Marshall seldom discussed his attitude publicly, when he did, his distaste for the idea of integration was manifest. "In ordinary conversation, Marshall refers to Negroes in a manner which leaves little doubt that his objection to them is based purely along racial lines," _Sport_ magazine would write about him.
Years earlier, Marshall had told another interviewer it was a bad idea to mix black and white players on a team because the whites might harm the blacks. Indeed, in the 1930s and 1940s, college football in the South remained strictly segregated and some southern players now in the NFL were opposed to playing with and against African Americans. But the majority of professional-caliber white players had no problem with it. After Kenny Washington played for the College All-Stars against the Green Bay Packers in 1940, a New York columnist urged Tim Mara to sign him. "He played on the same field with boys who are going to be scattered throughout the league. And he played against the champion Packers. There wasn't a bit of trouble anywhere," Jimmy Powers wrote in the _Daily News._
Marshall was resolute. He also maintained a business rationale for keeping NFL rosters white. His team in Washington was the league's southernmost franchise, and, from the start of his time there, he had sought to profit from the situation, selling the Redskins as the South's pro team. They had a regional network of radio stations that broadcast their games deep into the South. Marshall encouraged his coaches to sign players from southern colleges, reinforcing the bond between the Redskins and the region. Marshall had long assumed that fans of his team, both in Washington and beyond, preferred not to see African Americans playing for _either_ team in an NFL game.
By 1946, however, racial strictures and attitudes were beginning to change, at least in some parts of the country. President Franklin Roosevelt had integrated the defense industry during the war, a prelude to the integration of the military that would soon occur. Baseball's Dodgers had signed Robinson in October 1945, anticipating that he would need a year of grooming in the minor leagues before braving the majors, where, indeed, he was greeted with fury and contempt by many fans.
George Halas had considered integrating the Bears before the war, after watching Kenny Washington play in the College All-Star Game in 1940. Washington had led the nation in total offense as a senior at UCLA, and, after he made several sparkling runs against the Packers, Halas asked that he stay in Chicago after the game, perhaps while Halas tried to talk the other NFL owners into letting him sign Washington. But Washington eventually went home unsigned.
Art Rooney also had contemplated signing black players after watching several perform for a military team against the Steelers in a wartime charity exhibition game. Rooney's attitude on race was far different than Marshall's. Rooney "practiced civil rights before it became fashionable," said a relative of Cum Posey, a black sports entrepreneur who owned the Homestead Grays, Pittsburgh's powerhouse team in baseball's Negro leagues. Rooney and Posey had developed a close friendship after meeting in the early 1920s. Both were former athletes who had turned to the business side of sports. Rooney's semipro baseball teams barnstormed with the Grays for many years. Posey, a decade older, advised Rooney on organizing and operating teams. Later, Rooney lent Posey money that kept the Grays afloat.
Around Pittsburgh, Rooney was viewed as a progressive on race. He had never hesitated to put black players on his semipro rosters in the 1920s and early 1930s. The Steelers were one of the last NFL teams to field a black player before the league went all-white starting in 1934. In the end, though, Rooney cooperated with the NFL's unwritten all-white dictum—probably out of "deference to the league and his coaches," according to his biographers. Even after the Rams reintegrated in 1946, he hesitated to follow their lead; the Steelers did not sign a black player until 1952. The _Pittsburgh Courier,_ the city's black newspaper, praised Rooney's many shows of tolerance in an editorial in 1947 but also chided him about the Steelers' all-white roster. "What about the Steelers, Mr. Rooney?" the _Courier_ asked.
Rooney's slow response to the Rams' reintegration was typical of the entire league's reaction. After the Rams signed Washington and Strode in 1946, two years passed before another black player joined the NFL. In 1951, the Bears, Steelers, and Redskins still fielded all-white teams.
The AAFC's Cleveland Browns were the only other pro football team to integrate in 1946. As they opened training camp that summer, Paul Brown signed Bill Willis, a black defensive lineman who had played for him at Ohio State. After Willis quickly proved in practice that he deserved a starting spot, Brown signed another black player, fullback Marion Motley, who had starred for Brown's Great Lakes Naval Training Base team during the war.
Willis and Motley performed so well for the Browns in 1946 that they were named to the all-league team. Their teammates accepted them, and the Browns certainly did not suffer at the gate because of them. Cleveland went wild for Paul Brown's team in a way it never did for the Rams. On their way to capturing the AAFC title, the Browns drew an average of 57,000 fans per game—far more than any NFL team had ever averaged in a season. The Browns' success was a rebuke to any NFL owner who feared turning off fans by using black players.
That is not to say the integration of the Browns passed without incident. Motley and Willis had to stay apart from their teammates on the road whenever the Browns stayed at segregated hotels. Both players endured racist taunts from opponents. They could not play in a game in Miami, where municipal law prohibited integrated sports events.
Washington and Strode had similar experiences with the Rams in 1946. Their teammates accepted them, and their presence did not offend fans; the Rams drew an average crowd of more than 41,000 at the Coliseum. But some opposing players and fans in other cities taunted them, and they could not stay at segregated hotels on trips to Chicago, New York, Green Bay, Detroit, and Boston. According to author Thomas Smith, "Strode did not relish being a racial pioneer. As Washington's roommate on the road, he had to share the humiliation of eating and staying overnight at separate establishments from their teammates. 'If I have to integrate heaven,' Strode told a reporter, 'I don't want to go.'"
The Los Angeles Rams reintegrated the league with Kenny Washington (standing, left) and Woody Strode (on his knees, far right). (Associated Press)
Unlike Willis and Motley, Washington and Strode were veterans with ebbing skills. Washington had undergone multiple knee surgeries and lost his quickness. Unable to use him at halfback or receiver, the Rams gave him a shot at quarterback during the 1946 preseason. He threw an interception and was tackled for a safety. They tried him at fullback once the regular season began, and he caught some passes out of the backfield, but he suffered another knee injury. Eventually, Washington did not play much at all. Neither did Strode, who was thirty-two and had been signed mostly so Washington would not have to live alone on the road.
In many respects, Washington and Strode faced the same obstacles as Jackie Robinson did after he debuted with the Dodgers on April 15, 1947. And they stared down the challenge with the same stony calm as Robinson, who had played football and baseball with Washington and Strode at UCLA. Why did Robinson attain far greater renown as a symbol of racial progress? It helped that he was a fantastic talent who came to the majors in his prime. Just as importantly, though, he played America's favorite sport, its national obsession. The story of Washington, Strode, and the reintegration of the NFL would gain more attention after the fact, but the collective shrug that greeted it at the time was, if anything, an indication of pro football's secondary place in American sports.
ART ROONEY COULD HARDLY WAIT FOR THE 1946 SEASON TO begin. The Steelers had seldom won since they joined the league, but Rooney had finally achieved one of his longstanding goals and hired Jock Sutherland as the team's head coach. Rooney was confident that would make all the difference.
Sutherland was a football god in Pittsburgh, owing to his magnificent run as coach of the Pitt Panthers between 1924 and 1938. Sutherland's teams had won seven eastern championships, made four Rose Bowl appearances, and played before sellout crowds at home. When the school's administrators instituted tighter controls on his program, he resigned and eventually took a job with Dan Topping's Brooklyn Dodgers. He had left the Dodgers after two years, though, to serve in the navy during the war. Now, Sutherland finally was ready to come back to Pittsburgh.
Knowing how badly Rooney wanted him, Sutherland did not sign a deal until Rooney gave him a lucrative package that included a $12,500 salary, 25 percent of the team's profits _plus_ stock options. But Rooney got his man and was so elated he effectively handed the franchise over to his new coach. Sutherland was given control of scouting, drafting, negotiating contracts, promoting the team, and selling tickets. A notorious micromanager, Sutherland wanted no less.
The hiring accelerated a shift in the makeup of the city's football fans that was already underway. Pitt was no longer a power. Duquesne, which had fielded ranked teams in the 1930s, was deemphasizing the sport. The Steelers had a chance to take over, and, with Sutherland as their public face, they began doing just that. During the spring and summer of 1946, Sutherland traveled around Western Pennsylvania giving speeches about how he expected to turn the Steelers into winners. He always returned to Rooney's office at the Fort Pitt Hotel with a stack of season-ticket pledges.
Rooney's only job was to sign the checks that paid for whatever Sutherland wanted, which Rooney gladly did in most cases. At times, though, he hesitated over the checks for player salaries. The price for football talent was rising sharply now that AAFC teams also were bidding for players. The new league's cadre of wealthy owners knew how to compete for college stars. They signed forty of the sixty-six players on the College All-Star squad that took on the Rams, the reigning NFL champions, in the exhibition game in August 1946. Dozens of former NFL players also signed with the new league, despite the NFL's pledge to permanently ban players who jumped. (A pledge the league did not keep when it proved impractical.) Although NFL owners insisted to one another and to the football public that AAFC teams would play inferior football, it was becoming clear the new league would put a decent product on the field.
Rooney had always needed to limit his payroll because the Steelers did not win enough games or draw enough fans to cover his large costs. But he was not going to cut corners after finally hiring a coach who could turn the team around. Sutherland, a shrewd judge of talent, put together a solid team heading into training camp. The offense was built around Bill Dudley, the elusive tailback who had led the NFL in rushing as a rookie in 1942 before heading off to war. Back in shape after returning to the team, he appeared ready for a strong season. Sutherland drove the players hard during training camp in Hershey, Pennsylvania. The Steelers practiced in pads for two hours in the mornings and three hours in the afternoons, sometimes scrimmaging during both sessions. Sutherland spiked the drinking water on the sidelines with oatmeal to make it unpalatable; at the time, drinking water while playing was thought to make a player "soft." After working out with the team one day, a Pittsburgh sportswriter who had played at Alabama wrote, "There will only be two kinds of men on the Pittsburgh Steeler roster this year—those that are in shape and those that are dead."
To help the team get off to a good start, Sutherland asked Rooney to lobby Bert Bell to move the date of a game between the Steelers and Cardinals, scheduled for December at Forbes Field. Make it the season opener, Sutherland suggested. Rooney agreed to ask Bell, who approved of the idea and convinced Charles Bidwill to go along. Fans snapped up tickets to Sutherland's debut. The Friday night contest sold out several days beforehand. "First time anything like that has happened out there," Bell told reporters. By the day of the game, Rooney had sold $185,000 worth of tickets to the opener and to other games later in the season. That was far more than he had ever sold before any season. "I've never seen anything like it," he said. "We've had them waiting in line for days, and I remember, not so long ago, when we used to be happy to deliver two tickets to any customer, just so he would buy them."
A steady rain that fell on the day of the season opener did not dampen the city's enthusiasm. Baseball's Pirates were finishing up a losing season. Pittsburgh was focused on pro football. Almost thirty-three thousand fans crammed into Forbes Field that night. Rooney, scarcely believing his eyes, watched scalpers outside the stadium selling tickets for more than their face value.
As evident from his training camp, Sutherland preached toughness as the key to winning. His offense employed the single wing, a bruising alignment from football's yesteryear. His defense beat up opponents. The Cardinals featured a daunting lineup of offensive stars such as Marshall Goldberg, a fleet halfback who had played for Sutherland at Pitt, but the Steelers shut them down. Dudley tossed an early touchdown pass, then set up another score with a long run before halftime. Goldberg caught a touchdown in the third quarter, but the Steelers held on to win, 14–7. When the final gun sounded, the fans loosed a roar and filed out into the streets, not caring in the least that they were soaking wet. They would fill Forbes Field all season, turning a Steeler ticket into such a valued commodity that the city agreed to add seats on the field, expanding the stadium's capacity to nearly 40,000.
Rooney had been right about Sutherland's ability to turn the franchise around. The change was instantaneous and profound. After barely surviving the war years, the Steelers battled the Eagles, Giants, and Redskins for the East division title in 1946.
On November 3, the Redskins visited Pittsburgh. A record crowd of 36,995 fans came to see the Steelers take on an opponent that had dealt them much misery over the years. The Steelers brought a 3-2-1 record into the game. They badly needed to win. Their scoring had dropped off since their opponents realized Dudley constituted most of their offense and focused on him. The fans roared when Dudley intercepted a Sammy Baugh pass and returned it 80 yards for a touchdown in the first quarter. That was the game's only score until the Steelers again reached the end zone early in the fourth quarter. Baugh directed a touchdown drive a few minutes later, but the Steelers won, 14–7.
Unlike some owners, Rooney had rarely squabbled with George Preston Marshall. Nonetheless, he relished the victory over the Redskins and their loudmouth owner. The Steelers followed it up with another home win over the Eagles, putting them in control of the division race. If they won their final two games, they would capture the division title. But those final games were on the road, and the players were exhausted after four months of Sutherland's challenging practices. The Giants beat them, 7–0, and then they lost to the Eagles, 10–7. The Steelers finished tied for third behind the division-winning Giants.
Sutherland was undaunted, telling reporters it took five years to develop a consistent winner. The Steelers were well on their way, he claimed, and Pittsburgh's fans believed him. They would buy more than 21,000 season tickets in 1947, doubling the total from the year before. It seemed that pro football finally had arrived in Pittsburgh.
Rooney was not as sure about that, though. The Steelers had lost money in 1946 despite their improved attendance. The problem was player salaries, which had risen sharply because of competition from the AAFC. The rising payroll had offset Rooney's higher revenues. Rooney was constantly in touch with his fellow owners during the season, and they offered the same lament. They were not coming out ahead. League-wide, the player payroll had risen 250 percent from 1945. No business could survive for long in such a situation.
Some teams had fared worse than others. The Lions and Boston Yanks had lost a lot of money. Failing to draw as well as they hoped in their first year in Los Angeles, the Rams also ran a sizable deficit. The Eagles lost less, but they sold out almost every game now that they had a competitive team, and their owner, Alexis Thompson, was disturbed by the absence of a profit. The only NFL teams that made money in 1946 were the Giants and Bears, who won the division titles, and the Redskins. And Tim Mara was not comforted by his slim profit. His player payroll had been under $100,000 in 1945 and now it was close to $300,000. He feared what might happen if he had to continue to compete with the AAFC and Dan Topping in New York.
The owners had hoped the new league would collapse quickly. That was what happened to the "Red Grange league" in 1926 and the American Football League a decade later. But if the AAFC's inaugural season was any indication, the latest upstart league was not going to fold. Its championship team, the Browns, had drawn massive home crowds and probably could have competed against the NFL's best squads. Tony Morabito's San Francisco 49ers had fared reasonably well at the gate, as had Topping's Yankees despite their ill-advised idea of playing home games on Saturday nights.
But every AAFC team other than the Browns had lost money, quite a bit in some cases. Their player payrolls were just as high as the NFL's, and they had given away tickets to cultivate interest in their product. Most teams had lost at least $100,000. The Miami franchise went under. The Chicago franchise was a disaster. Still, there was enough strength in the AAFC's coalition to assure its continued existence. It was a thorny reality the NFL owners would have to confront. When they met in New York in April 1947, Bert Bell spoke rapturously to them and to reporters about the record attendance the league had achieved in 1946 and his belief that interest in the NFL was on the rise. It sounded great. But, when speaking privately, the owners grumbled that this was no way to run a business. Art Rooney was the primary example in their minds. He finally had a competitive team and a devoted fan base but still faced the same financial problems that had threatened individual franchises, and the league, from the beginning. That was not encouraging.
#
# SCANDAL
EVEN WITH HIS PLAYER PAYROLL SOARING, TIM MARA surely saw a lot to like when he contemplated the Giants' circumstances on the eve of the 1946 championship game. His son Wellington, now thirty, was back from the war and again in charge of scouting college talent, drafting players, and negotiating contracts. The Giants had started the 1946 season with four wins in their first five games and, after slumping at midseason, finished strong to earn a division title. By sundown on December 14, 1946, the day before the title game, they had finished preparations and were ready to play the Chicago Bears before what was likely going to be a record crowd at the Polo Grounds. The NFL championship game had never drawn more than 49,000 fans, but New Yorkers had stood in long ticket lines all week, and Mara was going to be disappointed if Sunday's crowd did not surpass 60,000.
The Giants had never been more popular. Bert Bell had permitted them to host an extra home game in 1946—only one of their last eight contests was on the road—so they could compete with the AAFC's Yankees for local headlines and fans. The Giants had taken full advantage, generating increasing excitement in the city with their winning season. They had averaged 51,705 fans per game, easily their highest attendance figure ever. The AAFC's Yankees had also fielded a division-winning team that fall, but they averaged just 27,800 fans per game at the cavernous stadium where baseball legends Babe Ruth and Lou Gehrig once played—an impressive figure for a new team, but still far behind the Giants. For Tim Mara, building the Giants into a viable concern, in a city that was the capital of major league baseball, had been a daunting challenge. But, in 1946, it was clear his Giants had carved out a sizable niche.
Best of all from his point of view, it seemed they were poised for a long run of success. Before the season, the Giants' longtime coach, Steve Owen, had asked Mara to trade for Frank Filchock, a dual-threat tailback on the Redskins whose opportunities were limited because of Sammy Baugh. Owen thought Filchock had the right skills to run his unusual "A formation" offense; the agile twenty-eight-year-old from Pennsylvania's coal country could throw a deep pass and was also a gifted runner. Mara made the trade, and Filchock had delivered for the Giants just as Owen envisioned, passing and rushing for a total of 1,633 yards during the season. No player had contributed more to the team's success, and it seemed Filchock was in New York to stay, having signed a three-year contract before the season. "He's going to be a Giants star for a long, long time," Owen told reporters.
But, after sunset on the eve of the championship game, Mara received a phone call that soured his optimistic view. His son, Jack, who ran the Giants, was on the line with ominous news: William O'Dwyer, the mayor of New York, wanted to see them both at City Hall—immediately. Tim and Jack arrived to discover O'Dwyer also had summoned Bert Bell and several of the city's top law enforcement officials. O'Dwyer explained the urgency. Undercover detectives working in the Giants' security detail had discovered that Filchock and a teammate, Merle Hapes, had a relationship with a gambler, Alvin Paris, who was well known to New York police. The men had spent several evenings together with their wives, and according to the police, Paris had offered the players bribes to intentionally lose the championship game.
Filchock and Hapes, a fullback from Ole Miss, were contacted and also told to come to City Hall. O'Dwyer questioned them separately as Bell listened. Soon, "both were in tears," according to Bell's biographer. Hapes admitted Paris had offered him a bribe. Filchock denied it.
After midnight, the mayor was notified that Paris had been arrested and taken to a precinct on West Fifty-Fourth Street. The entire party, included Filchock, rushed to meet him there. Hapes was permitted to leave. Near dawn, Paris signed a statement admitting he had offered the players $2,500 apiece to throw the game. In an unusual dark-of-night press session, Bell announced Hapes was suspended for the championship game later that day, but Filchock could play. Reporters, who had arrived after listening in on police radio chatter, asked why one could play but not the other. Bell responded that Filchock was "absolutely in the clear" but Hapes had delayed telling Owen about the bribe offer, raising doubts about his intentions.
Tim Mara did not sleep that night. He went home, showered, changed, attended morning mass, and headed to the Polo Grounds. He was worried. Although he had been involved in legal gambling for decades, he was familiar with the underbelly of that world. It was no secret that gamblers and bookies targeted athletes and tried to influence games. Major league baseball had nearly fallen apart as a result of the "Black Sox" gambling scandal in 1919. More recently, New York police had uncovered a betting ring involving Brooklyn College's basketball varsity.
Mara was not naïve. He knew a betting scandal would generate headlines and could linger, threatening a team's business and even its survival. He hoped the story would die quietly. His players had rebuffed Paris, after all. By the start of the game that afternoon, though, the story's impact was evident. The crowd did not surpass 60,000, as Mara had expected. And the fans at the Polo Grounds voiced their opinion, giving Filchock—a popular player who had led the team all season—a nasty welcome. A chorus of boos echoed through the stadium when he jogged onto the field before kickoff.
The Bears took an early 14–0 lead as Filchock's troubles continued with a hit that broke his nose. Doggedly playing on, he tossed a pair of touchdown passes that tied the score by the middle of the third quarter. But the Bears' Sid Luckman led two late-scoring drives, and, when the final gun sounded, the visitors celebrated a 24–14 victory.
The gambling story did not die there. In fact, it took a darker turn. At Paris's trial several weeks later, Filchock testified that he had lied to the mayor the night before the title game. Yes, Paris had offered him a bribe. Paris was a front man for three New Jersey bookies, it turned out. Mara was dismayed, as were the other owners. Bert Bell was outraged. He had been commissioner for only a year, but he had been in the league since 1933 and seen it through the challenges of the Great Depression and World War II. This, though, was the gravest threat the NFL had faced, he believed. Even though they had not taken a bribe, Filchock and Hapes had undermined the league's credibility by consorting with a gambler.
At a league meeting in late January 1947, Bell warned the owners that he was embarking on a crusade. The NFL needed to take a strong position against gambling. Bell, like Mara, was no innocent on the subject; he had lost a fortune betting on horse racing years earlier and had even bet on himself as a player at Penn, losing a new car in the process. But his youthful foolishness bore little resemblance to a mobster trying to change the outcome of a championship game. The league needed to make clear to its fans, Bell told the owners, that NFL games were legitimate.
At the meeting, the owners approved a measure allowing Bell to ban for life "without appeal" any player or team official who withheld knowledge of a plot to fix a game. He could also ban anyone he deemed "undesirable" from a locker room or stadium. The commissioner feared "city slicker" gamblers taking advantage of "country boy" players, believing Paris had done that to Filchock and Hapes. Before the meeting adjourned, the owners added a warning about gambling to the league's standard player contract and agreed to put the warning on posters that hung in locker rooms.
Bert Bell (right) hands suspension papers to Frank Filchock. (Associated Press)
Continuing his crusade a few months later, Bell enacted a league rule forcing teams to publicize all news about player injuries. Coaches had previously sought to keep such information out of the papers, thinking, rightly, that they benefitted from keeping their opponents in the dark. But injury news was what prompted gamblers to try to infiltrate locker rooms in the first place; armed with insider knowledge, a gambler could beat a point spread if, for instance, he alone knew that an important player on a given team was unlikely to play. Making injury news public would eliminate the desire for the information, Bell believed, and deny gamblers the potential edge.
In early April, Bell announced Filchock and Hapes were suspended indefinitely from the NFL. He had wanted to trigger his new lifetime ban option but, in the end, decided that would not be fair because the ban was not in effect when Filchock and Hapes received bribe offers. Some fans and sportswriters were surprised by the penalty's severity; the players had not actually accepted bribes, after all. But Bell shrugged off the distinction. "Professional football cannot continue to exist unless it is based on absolute honesty," he explained. "The players must be not only absolutely honest, but above suspicion."
Filchock never played again for the Giants. He spent the rest of his career in the Canadian Football League except for a few games in 1950 after Bell lifted his suspension. Hapes also played in Canada and never returned to the NFL, although Bell lifted his suspension in 1954.
As it turned out, Mara was right to suspect that the scandal would have a grave impact on his team. Stripped of their starting backfield, the Giants went into a nightmarish decline. Early in the 1947 season, they lost seven games in a row for the first time in the franchise's history. They had never finished a season in last place, but they achieved that dubious franchise first in 1947 with a record of two wins, eight defeats, and two ties. Many fans simply abandoned them. Their total ticket sales dropped almost by half, from 361,937 the year before to 190,173. Their December showdown with the Redskins drew just 25,594 fans after attracting more than 60,000 the year before.
As Mara's revenues declined, his player payroll continued to increase. Suddenly, his team was operating at a deficit. Meanwhile, Dan Topping's Yankees fielded another division winner that fall, and thousands of fans appeared to have adopted the new team.
Topping and the football Yankees were formidable rivals. New York fans approved of the Yankees' coach, Ray Flaherty, a former Giant. The Yankees also had a dynamic running back, one Orban Eugene "Spec" Sanders, a former University of Texas star who, with Filchock gone, became New York's premier pro football figure in 1947, rushing for 1,432 yards and eighteen touchdowns. As the Yankees drove toward a division title, more and more fans came to their games. On November 23, while the Giants hosted Green Bay before 27,939 fans at the Polo Grounds, the Yankees hosted the Cleveland Browns, the AAFC's top team, before more than 70,000 at Yankee Stadium. Those fans witnessed a classic contest. The Yankees scored the game's first 28 points. The Browns responded with 28 straight of their own. After the game, which ended in a tie, supporters were spent from hours of shouting. Although the Yankees gave away tickets to boost attendance, they were gaining on the Giants.
Mara was anxious, and he was not alone among the NFL owners in this respect. Other members of the league's ruling class also experienced challenging seasons in 1947. The Redskins won just four games. The Packers went a month without a win and slipped from contention. The Bears won eight straight games at one point, but they lost the first two and final two games on their schedule, and those defeats denied them a division title. The NFL's world had been turned upside down. Now, the teams on top were the ones that had spent years being humiliated by the Giants, Bears, Redskins, and Packers. Those four teams had combined to win sixteen of the past eighteen NFL championships, but in 1947 the Cardinals, long entrenched as Chicago's No. 2 team, won the West division, and the Eagles and Steelers tied for first in the East. None of the three had ever come close to winning a division title.
The tie in the East meant the Eagles and Steelers met for a one-game playoff on December 21 to determine who would play the Cardinals for the league championship. The Eagles won, 21–0, disappointing a sellout crowd at Forbes Field. A week later, the Eagles and Cardinals played for the title before just 30,759 fans at Comiskey Park on Chicago's South Side. It was the smallest crowd for a league title game in six years, well short of the stadium's capacity. More than twice as many people attended the AAFC title game at the Polo Grounds and watched the Browns defeat the Yankees. Although the AAFC, like the NFL, was operating in the red because of high player salaries, it was clearly appropriating a significant slice of the pro football pie. The new league actually seemed more popular at times than the NFL. No NFL team had ever encountered anything like the Browns' success on and off the field.
In the end, though, the Browns' impressiveness damaged the league. Quite simply, they were _too_ good. In the AAFC's first two seasons, they won twenty-four of twenty-eight regular-season games and a pair of championships. In 1947, they defeated the Baltimore Colts, 42–0; the San Francisco 49ers, 37–14; the Brooklyn Dodgers, 55–0; and the Buffalo Bills, 28–7. The league lacked suspense, and if the Browns were removed from the calculations, it clearly was struggling. The other seven teams in the AAFC were hemorrhaging money, losing an estimated $1.5 million between them in 1947 alone. Jim Crowley, the AAFC's original commissioner, had resigned after one year to take over the Chicago franchise, called the Rockets; he had been a winning college coach. But the Rockets went 1-13 while playing in mostly empty Soldier Field. The AAFC's Baltimore and Brooklyn teams also were foundering.
Strangely, the sudden decline of the NFL's ruling class worked in the older league's favor. Although fans of the Bears, Giants, Redskins, and Packers bombarded their teams' offices with unhappy letters and phone calls in 1947, those franchises could count on their histories and traditions to sustain them through dismal seasons. Their owners might lose money in the short run, but the teams could return to profitability. It was more important to the NFL's health that its lesser franchises become more competitive. Leveling the playing field had long been a goal of the men who ran the league, and that goal was being realized. The Cardinals, Eagles, and Steelers were winning and drawing crowds. Although the NFL still had several troubled franchises, most of its teams were now capable of winning a championship. The AAFC could not credibly make the same claim.
The Cardinals' success was exactly what the owners had envisioned when they instituted a draft in 1936. In 1947 the Cardinals relied on what sportswriters dubbed the "Million Dollar Backfield," a group of big-name former college stars. Players of that caliber never would have signed with the lowly Cardinals before a draft existed, when any player could sign with any team. But the Cardinals had secured their rights by drafting them, and then offered them enough money to sign. Marshall Goldberg, the halfback from Pitt, had been the No. 12 overall selection in 1939. Paul Christman, a quarterback from Missouri, was the No. 13 overall pick in 1941. Pat Harder, a fullback from Wisconsin, went No. 2 overall in 1944. Charlie Trippi, a halfback from Georgia, was the very first pick in the 1945 draft. Elmer Angsman, a Notre Dame halfback, was the No. 16 overall pick in 1946.
When World War II ended, and the players returned from military duty, each became the subject of a bidding war with an AAFC team. The Cardinals seemed unlikely to sign them all, or even just one. Dozens of players were decamping for the AAFC. The Cardinals, perennial losers, were not a glamorous option. But when the AAFC put a team in Chicago, Charles Bidwill uncharacteristically became motivated to win. He knew John Keeshin, the trucking magnate who was backing Chicago's AAFC team. Both men operated horse racing tracks. Keeshin irritated Bidwill when he told him that three pro football teams were too many for Chicago and the Cardinals should just leave for another city. Bidwill had seemingly never minded seeing his team lose, but now he wanted nothing more than to win games and put Keeshin out of business. Bidding aggressively, he landed all five players, including Trippi, who had seemed likely to sign with Dan Topping's Yankees until Bidwill offered him a $100,000 contract, by far the largest any pro player had received. Trippi joined the Cardinals, and, in the 1947 championship game against the Eagles, he scored touchdowns on a 44-yard run and a 75-yard punt return, all while wearing tennis shoes for better traction on an icy field.
Sadly, Bidwill did not get to see his new signings lead the Cardinals to the title. In the spring of 1947, after he had signed the players but before the NFL season began, he contracted pneumonia and died on April 19. He was just fifty-one. His fellow owners raised a toast to him at the first league meeting after the Cardinals won the title. They also toasted the lamentable state of the AAFC's Chicago franchise. Keeshin had sold it after one disastrous season. Bidwill had won that contest, too.
AS THEY LOOKED AHEAD TO 1948, THE GIANTS NEEDED TO reverse course—and quickly. They had won just two games the year before. The Yankees had stolen their headlines. Now, yet another New York–area AAFC team was offering a challenge. Branch Rickey, the forward-thinking baseball executive who had integrated the major leagues by signing Jackie Robinson, had followed the AAFC's rise. He believed the franchise-building fundamentals that worked in baseball could also work in pro football, and he convinced the board that ran baseball's Brooklyn Dodgers to buy the AAFC franchise with the same name. It had floundered in 1946 and 1947, but Rickey believed he would have the football Dodgers winning games and drawing fans to Ebbets Field in 1948.
A showdown occurred early in 1948, long before the football season. The Dodgers had the AAFC rights to Charlie Conerly, a quarterback who had set passing records at Ole Miss during the previous two seasons after returning from the war. The Giants also wanted Conerly. Wellington Mara believed he could make Owen's offense hum and, hopefully, lure New York fans back to the Polo Grounds. Wellington asked his father to approve a trade with the Redskins, who had drafted Conerly while he was in the service. Tim Mara told his son to go ahead, and the Giants sent Washington two players in exchange for Conerly's rights. Now they had to sign him.
A master showman, Rickey made headlines when he offered Conerly a $110,000 deal. The baseball man was sure he had landed a quarterback who could turn the Dodgers around. Tim Mara contemplated his response. The Giants would not get into a bidding war, he decided. He believed Conerly was skeptical about the AAFC. Mara also understood that it would offend the Giants' veterans to pay a rookie as much as Rickey was offering. He instructed his son to offer a $62,500 deal. Conerly signed with the Giants.
Furious, Rickey predicted the Giants would have "a morale problem" because Conerly had taken the lesser offer. "It seems un-American to me," said Rickey, who was known for making lowball offers to his best baseball players, including Ralph Branca, a twenty-one-game winner in 1947. "Maybe the kid figures he'll have greater security with the Giants than with an organization that puts such a [low] price on a 21-game winner," Mara replied dryly. "Or maybe he looked over the All-America conference and realized we've been here 24 years, whereas Brooklyn has had three, four owners. I don't know where this guy [Rickey] gets off talking about morale problems and stuff, considering the business he's in."
The Dodgers opened the 1948 season with six straight defeats. Baseball savvy did not translate to football, it turned out. Rickey's team was a laughingstock. His recruits included Pepper Martin, a forty-four-year-old retired baseball star. The Dodgers ended the season with two wins and a dozen defeats, playing in a nearly empty stadium. O'Malley gave up the franchise after the season, having lost $300,000. The AAFC's Yankees also struggled badly in 1948. After beating the Dodgers to open the season, they lost four games in a row. A trip to Cleveland resulted in a 35–7 loss to the Browns, who would go undefeated and win a third straight league title. The Yankees now played before smaller crowds. Their final game drew less than 19,000 fans.
The Giants did not fare that much better, comparatively. Early in the 1948 season, they lost successive road games in Washington and Philadelphia by a combined 86–10 score. Owen's signature unit, his bruising defense, had fallen apart. Another losing season was soon assured. Fans wrote letters demanding Owen's firing. But the signing of Conerly would eventually make the fans' suffering well worth it. Resembling a young Sammy Baugh, he tossed twenty-two touchdown passes and piled up 2,175 passing yards in 1948. The Giants' defense was weak, but they now had one of the league's most exciting offenses. Conerly would wear their uniform for thirteen years, winning three East division titles and a league championship before he retired.
The Giants also added Emlen Tunnell in 1948. An African American who had played halfback at Iowa, he had not signed with a team by that summer; although the Rams and Browns had broken pro football's color line two years earlier, no other black players had been signed since then. Tunnell, from near Philadelphia, simply showed up at the Giants' offices in New York one day.
"I'm looking for a job," he told Wellington Mara.
"What kind of a job?" Mara asked.
"Playing football. I'm a football player and I think I can make your club," Tunnell replied.
The team's scouts had heard of him, and the Giants signed him. The southern players on their roster embraced him when training camp began, easing a fear that may have discouraged other owners from integrating. Tunnell became the Giants' first black player, and, as a rookie in 1948, he ran back punts and emerged as a star defensive back, intercepting seven passes.
Toward the end of the season, Tunnell returned an interception 43 yards for a touchdown against the Packers in a game the Giants won, 49–3. Two weeks later, Conerly dropped back on almost every down against the Steelers in Pittsburgh, attempting fifty-three passes and completing thirty-six, three for touchdowns. The Giants rolled up thirty-one first downs and 463 offensive yards, mostly through the air. Although they lost, 38–28, Conerly was the talk of the town in New York the following week.
His performance in Pittsburgh was indicative of important changes occurring in the NFL. Passing offenses were evolving; it was no longer just Sid Luckman in Chicago who could march a team downfield through the air. Conerly could. The Rams' Bob Waterfield could. And, because an effective passing offense was hard to stop, a talented quarterback could make all the difference. Where once a team needed reliable players at many positions, more and more the focus would be on the quarterback. With players like Conerly and Waterfield, the modern game was coming into view.
For decades, football's appeal had rested on its ability to build character, its inherent violence, its approximation of war. Those elements were not ebbing in the eyes of fans, but as the sport evolved, becoming as much about skill and speed as toughness, other elements became equally paramount, none more than the sheer brilliance of the talent—in the NFL, especially. In the coming decade, as it became a league of quarterbacks, the pro game's capacity to entrance sports fans, to _dazzle,_ would catapult it to heights not even the most optimistic insider ever envisioned.
#
# EVERYONE LOSES
AFTER WATCHING JOCK SUTHERLAND COACH HIS TEAM FOR two years, Art Rooney believed the Steelers were on the cusp of glory. They had tied for the East division title in 1947 with an 8-4 record. Other owners in the league now saw them as a power. In March 1948, Sutherland left Pittsburgh for an annual driving trip through the South to scout talent and reconnect with his college contacts. In early April, the Steelers received a call from a Kentucky sheriff whose deputies had found Sutherland wandering through a field, disoriented. He had a headache, he said, and could not account for his recent whereabouts. Several Steeler assistants flew to Kentucky, collected him, and brought him back to Pittsburgh, where he underwent surgery to determine what was wrong. The surgeon found an inoperable brain tumor. Sutherland died on April 11 at age fifty-nine.
It was a fateful development for the Steelers. Sutherland had planned to coach until 1950 and then hand over the team to a young assistant he was grooming. That handoff now took place sooner, before the assistant was ready. The Steelers' rise abruptly halted, and they descended into mediocrity again. More than two decades would pass before their fortunes significantly changed.
But although Rooney simply could not manage to push his team into the NFL's upper ranks, he continued to wield influence in the league's inner circle. He had been an owner for fifteen years when Sutherland died, making him one of the longest-tenured men at the owners' table. The commissioner was his former business partner and one of his closest friends. Halas and Marshall, who together practically ran the league, trusted his instincts and relied on him to mediate their disputes. Tim Mara, his friend from the horse racing world, felt similarly about him. With his kind nature and calm demeanor, Rooney could be counted on to sort through the clutter and render sound judgments that benefitted the league.
In 1948, a furious internal dispute arose over how to deal with the AAFC. Weary of losing money, the Eagles' Alexis Thompson suggested the NFL should at least cooperate with the new league on a draft, which would eliminate the outrageous bidding wars that were driving salaries so high. Halas and Marshall vehemently disagreed. The war with the AAFC was personal to them, especially Halas, whose feud with Arch Ward had started it. Halas and Marshall wanted to put the AAFC out of business, not cooperate with it, and Mara agreed. As usual, their opinion was all that mattered. When Thompson's general manager raised the possibility of a common draft at an owners' meeting, the idea was rejected with little discussion and no vote.
But, other than Halas and Marshall, everyone in the NFL, including Mara and Rooney, was operating in the red. They wanted to end the war, even if it meant working with the AAFC. Although they dismissed Thompson's idea this time as a show of solidarity, they actually were open to it.
The AAFC's owners also wanted to negotiate. Except for Cleveland's Mickey McBride, they were all losing money, too, and no longer able to deny that their league faced significant problems. Trying to make games more competitive in 1948, they engineered a dubious personnel swap in which winning teams simply gave players to losing teams. It was a ridiculous exercise that, predictably, failed. The Browns won fourteen games without a loss during the 1948 season and easily defeated the Buffalo Bills in the championship game, 49–7. The Browns and San Francisco 49ers were the only teams that posted winning records. The Yankees faltered. Branch Rickey's Brooklyn experiment had come to nothing. Chicago's franchise stayed afloat only because the Los Angeles Dons' owner, Ben Lindheimer, underwrote it.
But the NFL's owners did not exult in the AAFC's woes. They had problems of their own in 1948. Dan Reeves sold a minority share of the Rams to keep from going under. After losing several hundred thousand dollars in six years, Fred Mandel sold the Lions for $40,000 less than he had paid for them. The Eagles defeated the Cardinals in a Philadelphia snowstorm to win the championship game, but Thompson continued to lose money and preach cooperation with the AAFC. "We'll either get smart and make peace, or we'll all go bust," he said.
The Steelers won just four games in 1948. The enthusiastic crowds that flocked to Forbes Field the year before vanished. Rooney still sold enough tickets to gross $900,000 in revenues, but he ended the season $40,000 in the red and did not expect that to change in 1949 as long as the AAFC still existed.
Rooney occupied a unique seat in the league's hierarchy. Although he was close with Halas, Marshall, and Mara, he understood the plight of teams that lost games and money season after season. For years, he had demanded that the owners guarantee the road team a sizable cut of the attendance receipts at every game—a safeguard that kept some losing teams from folding. Bell, who was commissioner now but had endured terrible seasons in Philadelphia and Pittsburgh, had a similar firsthand grasp of what it was like to run a losing team. In their daily phone conversations, Rooney and Bell agreed on the need for a solution that ended the war. Halas and Marshall had to be talked out of trying to obliterate the AAFC. It was time to shake hands and make peace. Too many people were losing too much money. If Halas and Marshall could not relate to the less successful owners, they needed to be convinced that a truce was in the NFL's best interests.
From his office in Pittsburgh, Rooney orchestrated a campaign. As always, he also had other businesses to tend to; he still promoted fight cards and had bought a horse farm in Maryland, where he bred his own thoroughbreds for racing. But in phone conversations with Halas and Marshall during the 1948 season, he pointed out that virtually every other team was suffering and a truce with the AAFC was imperative. He had little trouble convincing Halas, who had originated the principle of putting the league's best interests ahead of your own when the situation demanded it. Marshall was more reluctant, but, once Halas was swayed, he began to relent, too. "The time is ripe for peace. Certainly we can sit down and work out a sensible solution," Halas told the Chicago media.
The AAFC took Halas's remark as a signal that the NFL was open to talks. Within days, a group from the rival league met with Bell. The commissioner made a stark proposal: the NFL would take on the Browns and 49ers, but the other AAFC teams would disband without a settlement of any amount from the NFL. The owners of the AAFC's Buffalo and Los Angeles franchises would have the option of investing in an NFL team as minority owners.
Most of the AAFC owners were ready to accept Bell's terms. But the AAFC's Baltimore franchise, the Colts, scuttled the deal. The Colts wanted to join the NFL, and almost every NFL owner was ready to allow it. The lone holdout was Marshall, who believed a team in nearby Baltimore would infringe on his market. Marshall eventually softened his position, saying he would accept $200,000 from the Colts' owner, Abraham Watner, in exchange for letting the Colts join the NFL. But Watner said that was too high a price, leaving the situation unsettled. Meanwhile, the AAFC owners had said they would sign off on the deal only if every team approved it. With the Colts in limbo, the AAFC chose to continue operating in 1949.
Mike McGee, a horse trainer whose father conditioned Rooney's thoroughbreds starting in the late 1940s, recalled a conversation with Rooney about Marshall. "We would talk about things. He told me Marshall was the most cantankerous man he'd ever met," McGee said. "Rooney told me that 'everyone would agree on something, except George. You couldn't do a lot of things until he came around, and he was very bullheaded, hard to deal with.'"
But, though initial negotiations between the NFL and AAFC failed, largely because of Marshall, they provided a starting point for dialogue. Talks continued through the spring and summer of 1949 and intensified during the football season. The need for a deal became obvious. Attendance in both leagues declined. Teams continued to lose money. Rooney took a public stand, saying the Steelers would not field a team in 1950 unless the NFL and AAFC struck a compromise to end the war.
By December 1949, the AAFC was ready to capitulate. It only had seven teams, most of which were losing money. Lindheimer, whose money supported two franchises, had suffered a heart attack and lost interest. The Browns were about to win their fourth straight title, but even they were losing money now because their home attendance had dropped; their fans were bored with watching them roll over overmatched opponents. But, even though both sides were ready to deal, relationships among the principals held the negotiations back. Cleveland's Paul Brown criticized Marshall for blocking a merger. Marshall fired back, insisting he would be open to one. Bell and the AAFC's third commissioner in four years, O. O. "Scrappy" Kessing, a retired navy admiral, found little common ground.
Finally, a baseball man interceded. Horace Stoneham owned baseball's New York Giants and the Polo Grounds, which made him a football landlord. The football Giants had played at the Polo Grounds since 1925, and, in the 1949 season, another NFL team also played there after Ted Collins moved his downtrodden Boston franchise and rechristened them the New York Bulldogs. Stoneham watched both of his tenants lose money in 1949, and he knew Dan Topping's football Yankees were doing no better. Fearing that pro football in New York was about to fail and end one of his sources of revenue, Stoneham arranged for Bert Bell to meet with George Weiss, the baseball Yankees' general manager. Bell agreed to try to negotiate a settlement with a lone representative of the AAFC, J. Arthur Friedlund, general counsel for the baseball and football Yankees.
Bell and Friedlund met at the commissioner's office in Philadelphia. Bell presented an offer similar to the one he had made a year earlier. The NFL would take the Browns and 49ers, and it would also take the Colts if Watner could agree with Marshall on a price. The rest of the AAFC would go out of business. Not wanting to block a deal, Marshall lowered his asking price to $150,000. Watner, who had already lost a great deal of money on the Colts, continue to negotiate and eventually paid Marshall just $50,000. But that finalized the deal. A series of other details were worked out. The NFL's Bulldogs would buy out Topping's Yankees, change their nickname to the Yanks, and play their home game at Yankee Stadium rather than the Polo Grounds. The players on disbanding AAFC teams would be dispersed in a draft, separate from the annual college draft. Bell, seeking to ensure the Browns' support, quietly agreed to give Cleveland three of Buffalo's best players—a side deal that enraged Halas and Marshall when they learned of it.
On December 9, 1949, Bell and Friedlund called a press conference in Philadelphia and announced the two leagues were merging into an entity known as the National-American Football League. It would have thirteen teams, with the divisional alignments to be determined. Bell would be the commissioner.
The war was over. It had cost millions, pushing the owners and the two leagues to the brink. Finally, though, there was peace again in pro football—of a sort.
TWO DAYS AFTER THE MERGER ANNOUNCEMENT, THE NFL completed its 1949 regular season with a slate of games on December 11, a Sunday. The Eagles, who had already clinched a third straight East division title, defeated the Giants to finish with an 11-1 record, best in the league. The Rams routed the Redskins to win the West and secure a spot in the league title game for the first time since they moved to Los Angeles.
Bert Bell made plans to travel to California to attend the championship game on December 18 but canceled his trip several days beforehand. He had barely slept while hammering out the merger deal, and his doctor told him he needed to rest. Bell reluctantly stayed home. At fifty-four, he was not in the best physical shape, and his job was increasingly stressful.
He still became embroiled in a controversy over the championship game, even though he was at the other end of the continent. The Rams had hoped to sell 70,000 tickets, but a hard rain fell in Los Angeles in the days before the game, and, according to forecasters, it was not going to stop in time for kickoff. With a much smaller crowd anticipated and the Los Angeles Memorial Coliseum field a muddy mess, the owners of the Rams and Eagles wanted to postpone the game for a week in hopes of better weather and better attendance. But Bell said the game had to be played on the scheduled date. He had negotiated deals for national radio and regional television broadcasts, and the networks did not want to change their schedules at the last moment. The Los Angeles press crucified Bell after 27,980 fans sat through a driving rainstorm as the Eagles defeat the Rams, 14–0, on a field that was barely playable. "Bertie sat back there in his Philadelphia apartment and... pulled one of the biggest bloomers of his career," the _Los Angeles Times_ wrote.
Whether or not he was right to force the game to be played, Bell was right to skip the long trip. He was going to need all his energy and savvy for the owners' meeting, the first since the merger, scheduled to begin on January 19, 1950, in Philadelphia. Many aspects of the reconfigured league remained undecided. With strong-willed men from two leagues coming together for the first time, there were certain to be acrimonious disputes.
A mix of snow and rain was falling outside when Bell banged a gavel to begin the meeting at the Bellevue-Stratford Hotel in Philadelphia's City Center. It was a Thursday, shortly after noon, and the familiar cadre of NFL owners had gathered, led by George Halas, Tim Mara, George Preston Marshall, and Art Rooney, who, along with Bell, Curly Lambeau, and Charles Bidwill, had guided the league's affairs through most of the 1930s and 1940s. "We owners were a tight little group," Halas would write. "We had gone through a lot together. We had helped one another. We had to the best of our abilities become professionals dedicated to the game of football."
By 1950, though, Bidwill had died, and Lambeau was being forced out in Green Bay. His purchase of a year-round training facility had strained the Packers' finances just as salaries escalated. Unable to keep pace with wealthier teams in larger markets, the Packers had sunk to the bottom of the West division. The team's board of directors also was quietly unhappy that Lambeau was on his third marriage and spent his offseasons in California. Without Bidwill and Lambeau, the "tight little group" was even tighter. Bell was in charge, with four men constantly whispering in his ear: Halas, whose tenure dated to the league's birth; Mara, who had doggedly fought for and defended his New York franchise since 1925; Marshall, whose innovations and prejudices had shaped the league in fundamental ways; and Rooney, the affable peacekeeper.
That they still controlled the league soon became evident. Within weeks of the Philadelphia meeting, the owners would toss out the awkward name they had come up with, the National-American Football League, and return to the more familiar National Football League.
But during the meeting, the newcomers made their presence felt. Paul Brown, the Cleveland Browns' head coach, was not only one of the sport's best strategists, but also a shrewd boardroom tactician, unafraid to voice strong opinions, and he never let anyone take advantage of him. Brown could not stand Marshall. It irritated him that Marshall was so determined to keep African Americans from playing for the Redskins. Marshall also had not hidden his scorn for the AAFC throughout the league's four years. In 1947, the AAFC's commissioner at the time, Jonas Ingram, a retired navy admiral, had proposed that the champions of the two leagues play, with the proceeds going to charity. Marshall haughtily responded that Ingram should have the AAFC winner play Navy's varsity. Now, in Philadelphia, Brown observed Marshall at a league meeting for the first time and found him "obnoxious." What really bothered Brown, he said later, was Marshall's "habit of sleeping most of the day" after carrying on in nightclubs all evening "and showing up at the meetings late in the afternoon. By that time all of us were pretty tired and ready to adjourn, but he was rested and mentally sharp. That was when he tried to work some of his little deals." Brown's personal and professional opposition to Marshall represented the start of a decline in Marshall's power—an ebbing that would continue through the 1950s.
On the first day of the meeting, prospective ownership groups from Buffalo, Houston, and Oakland lobbied to join the league. Although the initial merger agreement had provided for a total of thirteen teams, some owners wanted to let in one more. Making out the schedule would be easier, and several cities were viable candidates, it seemed. Buffalo had more than 14,000 season ticket pledges. Houston was proposing to build an 110,000-seat indoor stadium. But most of the "tight little group," led by Halas, was dubious about letting anyone else in. "As with most organizations, we were perhaps too unresponsive to newcomers wanting to join our league." Halas would write. "We liked things the way they were. We did our best to keep things that way." Bell announced that a vote for adding another team had to be unanimous. That was not going to happen. "Plans here are the proverbial dime-a-dozen. There is a Marshall Plan, a Mara Plan, and three or four other plans," the _New York Times_ reported. When a procedural voice vote fell short of unanimity, Bell called off the whole process. There would be thirteen teams in the NFL.
The next item on the agenda was organizing those thirteen teams into two divisions. Everyone agreed there would be two six-team units and a "swing" team that would alternate between competing in one division one year and the other division the next year. But whenever one owner proposed a particular alignment, an argument erupted. When Marshall suggested the Browns should be the swing team, Brown glared at him and threatened to pull out of the league. Rooney, as was his custom, took the floor and preached for calm. Bell offered a threat: if the owners did not settle on a plan soon, they could find a new commissioner. "I banged down the gavel and started for the doors," Bell would recall. "Someone stopped me. I cooled off for the minute and they put the action through."
The owners voted on a two-division setup with Baltimore as the swing team. The motion passed, 12–1, with Bell casting the dissenting vote on behalf of Marshall, who, according to Bell's biographer, had "left the meeting in a huff when he realized he couldn't put through a motion to have any team other than Baltimore named the swing team." The Associated Press would credit Bell for negotiating "the most important decision in the new league... a decision that seemed impossible until Bell waved his gavel and threatened direct action. From all indications, the owners would have been in conference, arguing, until next week, if Bell hadn't called a halt."
Another complex matter was how to distribute the players from the disbanding AAFC teams. The situation was hopelessly complex. Everyone agreed that there was going to be a draft, but should the NFL allow its weaker teams to select more players, seeing as they needed more help? And should the AAFC teams entering the league get to keep all their players, include those on their developmental "reserve" list? That did not seem fair, as the NFL teams were only going to be able to "protect" so many from being eligible for the dispersal draft.
After arguing for almost five hours on January 21, the owners threw the problem to Bell, who retreated to his hotel room for an entire afternoon before returning with a proposal. The three teams entering the NFL from the AAFC could protect thirty-two active players and three on reserve. The Packers and Colts, as the weakest teams in the merged league, would receive five extra selections. New York's two franchises, the Giants and Yanks, could split up most of the talent from the AAFC's Yankees. It was not an entirely equitable solution, but there did not seem to be an alternative. The men in the inner circle had always instinctively known when to prioritize the league's best interests ahead of their own, and this surely was such a moment. Marshall, who was back at the table, seconded Bell's plan, and Halas "never kicked," Bell said, despite getting "the worst of it." The proposal passed easily.
The owners also conducted a college draft, approved several rules changes, and gave Bell a ten-year contract. When the commissioner wrapped up the meeting on January 24, he was described by the _Times_ as "shirt-sleeved and dead tired." The "portly" Bell had somehow navigated a minefield of conflicting agendas and opinions without blowing up the fragile coalition he now oversaw.
WHILE NEWS FROM PHILADELPHIA CONCERNING FRANCHISE BIDS, divisional alignments, and drafts generated headlines across the country, a seemingly minor rule change barely made the papers: after experimenting with allowing teams to make unlimited substitutions during games in 1949, the NFL was making the rule permanent. The AAFC had permitted unlimited substitutions throughout its four-year history, and the owners and coaches from that league believed the freedom to move players in and out of huddles markedly improved the game. The NFL was adopting its former rival's inventive stance on the issue.
Restrictions on substitutions had been in place from the very start of the sport. In 1922, the NCAA mandated that a player who came out of a game in the first half could not return until the second half, and a player who came out in the second half was finished for the day. Deferring to the college game, far more popular at the time, the NFL simply utilized the same rule. At both levels, it became routine for players to have roles on both offense and defense, and seldom leave the field. Don Hutson became famous as the Packers' brilliant receiver, but he also accumulated thirty interceptions during his eleven-year career as a defensive back. The Giants' Mel Hein was a center on offense and a linebacker on defense.
The endurance required to play "both ways" was seen as an essential burden the game placed on players, part of the physical challenge that made football so compelling for spectators. When players suddenly were in scarce supply during World War II, however, both college and pro football were forced to adapt. The NFL went with unlimited substitutions. In the college game, a player who left the field had to sit out at least one play before returning. When the war ended, the NFL reinstituted limits on substitutions, allowing only three players to enter a game at a time. The college game continued with a freer approach, allowing teams to switch out as many players as they wanted on possession changes. But the purists in the college game believed this violated the game's nature, changing it beyond recognition. Robert Neyland, a former army brigadier general who coached at Tennessee, famously referred to football with unlimited substitutions as "chickenshit football."
In 1953, the NCAA would reinstitute limits on substitutions. A player could enter a game only once per quarter. The doughty two-way player, a staple of the game's past, was valued again. But the college game was making a mistake, looking backward instead of ahead. The unlimited-substitution rule was a cornerstone of football's future. It led to teams developing two separate units, an offense and defense. Now, a strong-armed quarterback just played offense; he did not have to risk injury playing defense, too. Coaches could separate their teams into units, enabling players to remain fresher and to become true specialists, thereby raising the quality of play across a single team and the entire sport. The Giants' Charlie Conerly was a case in point. He was born to play quarterback, and, under the new rules, he could focus on developing the skills necessary for succeeding at that position.
Not surprisingly, Paul Brown had already figured out how to take advantage of the unlimited substitution rule—indeed, it had been central to his team's success in the AAFC. Throughout the sport's history, players on the field had always called the offensive signals, but Brown was able to exert more control; he called his offense's plays from the sideline, sending in his instructions via a pair of guards who shuttled between the sideline and huddle on every play. College football was more storied, but the pro game had become more innovative and dynamic. With one rule change that received almost no attention at the time, the NFL had set in motion a fateful inversion. By the time the college game recognized its mistake and moved to unlimited substitutions in 1965, the NFL had surpassed it and pro football was well on the way to becoming America's most popular sport.
#
# THE LITTLE BLACK BOX
ONE DAY IN EARLY 1947, GEORGE HALAS DROPPED BY THE _Chicago Tribune_ newsroom to visit Don Maxwell, the newspaper's city editor. The two had been friends since the 1920s, when Maxwell edited the sports section and Halas wanted coverage for his new pro football team. Halas found Maxwell staring at "a little black box, about two feet square, with a glass front on which fuzzy pictures were moving about," Halas would write.
"There it is, George—television," Maxwell said.
Halas was not impressed. "The picture is so small, Don, and so fuzzy," he said. "Will it ever be anything more than a toy for adults?"
Maxwell smiled and said, "George, that little box with the fuzzy picture is going to change the American way of life." He explained that the picture quality would soon improve, and the ability to transmit a picture "miles away" to sets in living rooms would transform the news, sports, and entertainment industries.
"Television is coming, George," Maxwell said. "What are you going to do about it?"
Halas had no answer. But after listening to Maxwell, he began "asking questions." Within weeks, the NFL owners addressed the issue "for the first time" during a meeting in Chicago. Though focused on the Filchock gambling scandal, the owners voted to permit teams to sell the television rights to their home games in 1947. It was not deemed a significant matter. The rights to local radio broadcasts of NFL games had grown to the point that teams now received between $15,000 and $35,000 per year. But that amount, although not a pittance, did not significantly impact a team's business, and there was no reason to believe television income would, either; just 44,000 sets were in use in America in 1947, compared to 40 million radios.
Halas approached Chicago's single television station about broadcasting the Bears' home games in 1947. The station agreed to do it, paying the team $900 per game for the rights. "I could not believe it. The money was an unexpected bonus," Halas wrote. He viewed the arrangement less as a driver of profits than as an experiment. The Bears were coming off a championship season in which they averaged 42,291 fans per game. Halas wondered whether his customers would stop buying tickets once they could watch the Bears for free, on television, either at home or in a bar. Sure enough, even with a fuzzy picture and few sets in use, his attendance dropped 9 percent in 1947. Nonetheless, he signed another deal to televise his games the following year, in the belief that the broadcasts helped publicize the team. The Bears fared better at the gate that season, with an average crowd of 43,672. Their attendance was actually up after two years of televised home games.
During the 1948 season, though, Halas soured on the experiment. He realized Maxwell had been right about television's impact. Radio industry powerhouses such as the Columbia Broadcasting System and National Broadcasting Company had launched TV divisions that were off to promising starts. The American Broadcasting Company and DuMont Television Network were also airing programming. Meanwhile, the country was buying TV sets in greater numbers. There were 350,000 sets in use in America early in 1948, and the total would rise to 2 million within a year and 7.7 million by 1950.
As Maxwell had predicted, television was changing Americans' habits. Instead of going to movies or listening to the radio, more and more people just turned on their sets for entertainment. Television was becoming so prevalent so quickly that Halas believed his fear would be realized—fans would stop coming to see the Bears if given the option of staying home and watching for free. "So many sets were coming into Chicago homes that I lacked enthusiasm for having our games televised," he wrote.
The success of a comedy show, the _Texaco Star Theater,_ revealed TV's potential to influence a sizable portion of the public. The program, which starred Milton Berle, a rubber-faced former vaudevillian, debuted on ABC in 1948, and a year later, when Berle jumped to NBC, the _Texaco Star Theater_ became a phenomenon, drawing 80 percent of the television audience during its Tuesday night slot. It was rumored that restaurants and movie houses began closing that night because so many of their customers stayed home to watch Berle. On May 16, 1949, the comedian made the cover of _Time_ magazine.
Several sports also thrived in these early years of television. Broadcasts of boxing matches proved popular, sparking renewed interest in a sport that had declined. Broadcasts of major horse races turned thoroughbreds into household names. If Berle was television's first superstar, a gray colt named Native Dancer was the second.
Of all the sports, however, baseball was the biggest draw on television. Major league teams quickly struck deals with local stations and networks, and, suddenly, the national pastime was available for free. The viewing experience was far from optimal, with the small ball difficult to see on a small screen, and, thus, the action difficult to follow. But it was still a revelation. Many fans began to stay home and watch games rather than buy tickets. Major league attendance, which had spiked after World War II, declined sharply. The average crowd for a game was 16,447 in 1949. Within four years, it was 11,831. Halas and the football owners saw that as a reason to avoid embracing television, but, surprisingly, most major league club owners did not mind seeing their attendance plummet. In 1946, the New York Yankees became the first club to sell their local television rights, receiving $75,000 for that season. The market for rights fees quickly escalated. Within a decade, the Brooklyn Dodgers received $800,000 for the rights to televise one hundred games per year.
But baseball's owners were the only ones profiting. The televising of major league games crippled minor league baseball, long a popular diversion in smaller American cities. Millions of minor league fans simply gave up on their teams, choosing instead to follow major league clubs on television. The number of minor leagues would shrink from fifty-nine to twenty-one within a decade as attendance dropped 65 percent. College football also suffered once games were televised. The sport's overall attendance dropped 5 percent in 1950 and another 5 percent in 1951. Though that was not as precipitous as baseball's decline, it was enough for the NCAA to act. In 1951, it passed a regulation limiting the number of games that could be shown on television—seven per season in each region of the country.
Most NFL owners experienced similarly ominous results with their initial television broadcasts. Attendance dropped throughout the league in 1948 and 1949, significantly in several cases. Teams in the AAFC also televised games and saw their attendance drop. The war between the leagues did not help, but NFL owners believed the televising of games was the root of the decline.
Halas permitted just one game at Wrigley Field to be broadcast in Chicago in 1949. The $5,300 he received in return constituted his entire television income for the year. "I, a most cautious man with no outside income to speak of, was most careful to preserve ticket sales," Halas later wrote.
Most of his fellow owners followed his example. Although they recognized television's increasing prominence, they still feared its impact on ticket sales. They also could not envision their rights fees soaring as high as baseball's; their sport simply was not as popular. In 1950 the owners of the newly merged league continued to adhere to an informal agreement the NFL owners had reached the year before: teams would not televise home games.
The Rams were granted an exemption. Their owner, Dan Reeves, was so bullish on television's potential that he had arranged for all his team's games, home and away, to be televised in 1949. The Rams fielded a talented team led by Bob Waterfield, won a division title, and their attendance rose. Reeves negotiated the same deal for the 1950 season, with one important, new provision: if his attendance did drop, the Rams' television sponsors would reimburse him for the lost revenues. The new provision soon went into effect. Although the Rams won another division title in 1950, their attendance declined precipitously, and Reeves's sponsors had to pay him $200,000.
Halas and the other owners were not surprised by such an outcome. It seemed there was no doubt about the correlation between television broadcasts and lower attendance. Yet so many Americans were buying TV sets now that more than half of the homes in the country would have one by 1953. The NFL owners knew that could not be ignored. "I determined to increase our effort to make it work for the Bears," Halas wrote later. But how?
THE HARDEST TASK THE COMMISSIONER FACED EVERY YEAR WAS setting the regular-season schedule. For weeks, sometimes months, Bell sat at his kitchen table, smoked cigarettes, and scribbled versions, then called owners for their reactions. Marshall always took issue with Bell's proposals. Halas was seldom lacking objections. It was impossible to satisfy everyone's idea of what was fair. In the end, Bell went with the schedule that made the most owners the least angry.
Whether it was a skill he developed or an innate talent, Bell was a superb scheduler. That was never more apparent than in 1950. To open pro football's first post-merger season, he chose the game that fans across the country had yearned for: the Philadelphia Eagles, two-time defending NFL champions, would host the Cleveland Browns, winners of the AAFC every year the league existed.
Fans had debated the merits of the rival leagues since the AAFC kicked off. Several columnists had suggested the champions should meet on the field at the end of the season and put an end to the arguments. The leagues never got along well enough for that to occur, but now that Bell controlled the situation, he addressed it immediately. No one could accuse him of lacking a showman's touch.
The demand for tickets was high enough in Philadelphia that the Eagles switched the site from Shibe Park, the 33,000-seat baseball park where they usually played, to Municipal Stadium, the 100,000-seat behemoth that hosted the Army-Navy game. That famous college rivalry always sold out, and the Eagles-Browns game did not—an indication, perhaps, that college football still commanded more interest. But the crowd of more than 71,000 was easily the largest in Eagles history, and _that_ was an indication of what lay ahead for pro football.
The Eagles expected to win, perhaps easily. Led by Steve Van Buren, a relentless running back, they had rolled through the NFL for two years. The NFL's owners, players, and fans had no doubt their football was superior to the AAFC's. "The worst team in our league could beat the best team in theirs," Marshall had said. That remark—representative of a general smugness in NFL circles—served to motivate Paul Brown and his Cleveland squad, which contained five future Hall of Fame inductees, including Marion Motley and quarterback Otto Graham. Anticipating the showdown, Brown had scouted the rainy 1949 NFL championship game between the Eagles and Rams. The Eagles' coach, Greasy Neale, never deigned to scout the Browns. "I would say that there was never another team in the history of sports, anywhere in the world, that was as prepared, physically and emotionally, to play a ballgame. We would have played the Eagles for a keg of beer or a milkshake," Graham said.
Bell was in the large crowd that stood and cheered when the opening kickoff flew through the air on a warm September evening in Philadelphia. Midway through the first quarter, the Eagles' veteran quarterback, Tommy Thompson, led a long drive. Van Buren, holder of six NFL rushing records, was out with a broken toe, but his backup gouged Cleveland's defense for gains and the Eagles kicked a field goal for a 3–0 lead. Late in the first quarter, Graham retreated to pass, scanned the field, and saw a receiver running behind the defense. His long pass hit Dub Jones in stride, and the receiver raced to the end zone to complete a 59-yard scoring play.
Fullback Marion Motley carries the ball during the Browns' season-opening victory in Philadelphia. (Associated Press)
A tight, back-and-forth game developed. Trailing 7–3, the Eagles drove to a first down at the Cleveland 2 yard line in the second quarter. It appeared the home team would regain the lead. But Motley—so useful he still played both ways, despite Brown's emphasis on specialization—led a defensive stand that kept the Eagles out of the end zone on four plays. That galvanized the visitors. Graham threw a touchdown pass before halftime and another in the third quarter. The Eagles finally reached the end zone in the fourth quarter, but the Browns kept adding to their lead. The final score was 35–10, an unimaginable result for the NFL. "We whetted our appetite for that game for about three years," said Brown, unable to hide his immense satisfaction.
Bell was noticeably subdued after the game, but he soon received some encouraging information. A coaxial cable had been laid that could carry a television signal from the East Coast as far west as Omaha, Nebraska. (The cable would reach the West Coast in 1951, making "national" broadcasts possible.) Bell had tried to coax NBC and CBS into televising the Eagles-Browns game as far as the cable could carry the signal. Those networks passed, but DuMont, the struggling fourth network, was desperate for programming and signed a deal to televise the season-opening game, several other regular-season contests, and the NFL championship game. The viewing audience for the opening game was large, it turned out.
The contract with DuMont was Bell's second national television deal of the year. ABC had already agreed to televise fifteen regular-season games across the coaxial cable. The money was minimal: teams earned just $8,000 apiece from the ABC and DuMont deals. But the quasi-national broadcasts introduced pro football to areas of the country where college football had long ruled and, in some cases, pro results barely made the newspapers.
The timing was exquisite. With unlimited substitutions and daring offenses led by strong-armed quarterbacks and speedy receivers, pro football was becoming a spectacle. Meanwhile, many college coaches still relied on slow-moving ground games.
Although the Browns-Eagles contest was one-sided, Bell and the rest of the NFL learned that it was surely the most-watched league game ever. The next year, DuMont released data showing that national broadcasts of NFL games attracted 17.1 percent of the television audience in their time slot. By 1954, that figure had had risen to 36.1 percent on Sunday afternoons. That meant millions were watching. For Halas and the other owners who had feared television might ruin them, the Browns-Eagles game was a watershed. Here was the way to make the new medium work for them. Yes, if given a chance, thousands of fans in their home cities would stay home and watch games for free. But by televising games in other cities and states, particularly those that did not have teams of their own, franchises could expand their reach and attract new fans.
Halas contacted stations in eight cities in Chicago's orbit. He rented coaxial cable space on Sunday afternoons and struck a deal with WGN, a Chicago station, to televise his home games as well as those of the Cardinals. WGN's broadcasts of Chicago pro football were shown in Omaha, Minneapolis, Cincinnati, Louisville, Nashville, and several other cities. The Bears paid for the broadcasts, but the out-of-town stations sold advertising to help defray the team's costs. "It was quite an operation. We took a big gamble," Halas wrote. When 1951 season ended, the Bears had lost $1,750 on the venture. "But more people have seen the Bears play this year than the first 30 years of our existence put together," Halas said. The next year, stations in fifteen cities wanted the signal, and Halas picked up a major advertiser when Standard Oil paid $30,000 for 50 percent of the commercial time.
Several other owners adopted the same strategy. The Giants sold game broadcasts to stations throughout the Northeast. The Redskins developed a network of affiliates in the football-mad South, which did more than anything to realize George Preston Marshall's long-held ambition to make his team the South's team. By the end of the decade, the Bears' network would consist of seventy-seven stations in nineteen states, the Redskins' network of thirty-seven stations in nine states, and the Giants' network of fourteen stations in seven states.
Inevitably, problems arose. Some teams either were not as adept at selling themselves or could not match the interest that the Bears, Redskins, and Giants generated. By the end of the decade, the Eagles' network would consist of just three stations beyond Philadelphia. The Steelers and Lions had six stations apiece. There were "have" and "have not" television franchises, and the differences often translated to the field as certain franchises became much wealthier and thus had more to spend on players.
The league also had to go to court to protect its television policy. After the Rams' disastrous experiment in 1950, the league enacted a rule that games could not be televised within a seventy-five-mile radius of the home city—an obvious attempt to preserve ticket sales. But a station in Erie, Pennsylvania, sued the league for restraint of trade when a game between the Eagles and Browns in Cleveland was "blacked out" in Erie, seventy miles from the game. After more than two years of legal wrangling culminating in a federal trial in Philadelphia, the league was found guilty of three antitrust violations. But the judge upheld the legality of the seventy-five-mile blackout policy, giving the league an important victory. The owners had protected their ticket sales and gained control of their television broadcasts. They unanimously voted not to appeal the decision.
Between regional broadcasts and Bell's network deals, television income soared. In 1951, NBC paid $100,000 to broadcast the league championship game from "coast to coast," a first. In 1957, CBS offered $1 million for the broadcast rights to the entire NFL season. The league declined the offer, mostly because Halas, Mara, and Marshall were reluctant to break up their lucrative regional networks. Even with their television money growing from a pittance to a pile, the inner circle still operated with the instincts honed in the 1920s. They were protective of any gains, distrustful of outsiders, and watchful of one another's best interests.
BY THE MID-1950S, THE GREEN BAY PACKERS HAD BECOME A nuisance to the rest of the league. They were a historic franchise, but they still played in a high school stadium with just 26,000 seats, and with their winning days just a memory, they rarely sold out even that small venue. As a run of losing seasons mounted in the 1950s, they could not build a viable regional network of television and radio affiliates. Other owners, especially those relatively new to the league, no longer saw the romance in having a team in "little Green Bay." Art Rooney had rammed through a 60-40 gate-split rule, ensuring that visiting teams received 40 percent of the gate receipts for every game, but after playing profitable games before large crowds on the road, the Packers could not reciprocate when opponents came to Green Bay. The visitors' take was virtually nothing.
The Packers' future seemingly rested on the fact that they now played several games a year in Milwaukee. The city, much larger than Green Bay, was having a sports boom. It had built a new multisport stadium with 54,000 seats, and that had attracted a major league baseball franchise, the Braves, who set attendance records and became a pennant contender soon after moving from Boston in 1953. Although the Packers did not draw nearly as well in Milwaukee, the other NFL owners broached the idea of the team moving there permanently. The last of the NFL's small-town franchises, a holdover from the days of sandlot and semipro teams, looked as though it might fail and bring an era to an end.
But Halas and his "tight little group" did not want the Packers to move. When Bell was struggling in Philadelphia in the 1930s, the board of directors who oversaw the Packers had loaned him money. He never forgot it, later telling a Green Bay sportswriter that there would always be an NFL team in the city. Halas was loyal to Green Bay, too. The Packers had been the Bears' primary rivals for more than three decades, and the enmity between the franchises ran deep. But Halas knew a rivalry was good for business; fans love to hate. Halas also knew that Green Bay had steadfastly supported its team through many years when other cities showed little interest in professional football.
Bell suggested to the Packers' board that the team needed a new stadium. The funding for one was floated as a bond referendum in Green Bay in April 1956. Halas drove up from Chicago and stumped for the project, and the referendum passed. Seventeen months later, the Packers upset the Bears at City Stadium, their new home venue, before a sellout crowd that included Bell and Richard Nixon, the US vice president, a noted pro football fan.
With the completion of the new stadium, the Packers' future in Green Bay was ensured. Although they would hit a low point with an 0-11-1 season in 1958, that miserable performance was followed by a fateful coaching change. Out went Raymond "Scooter" McLean, who played cards with his players on road trips. In came a strict, little-known Giants assistant coach named Vince Lombardi.
At that critical moment in the mid-1950s, when the members of the league's inner circle were deciding whether to continue to support a team in Green Bay, they were also considering what would happen next with television. They were far more encouraged by its possibilities now. Although they were still cutting their own deals with regional networks, Bell was negotiating network contracts from which all teams profited. As viewership and rights fees spiraled upward, the owners could envision the wealth that would result—and how that wealth, properly shared, would benefit the entire league. It was a remarkable prospect for them to consider, but a team in Green Bay could make just as much as a team in New York.
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# ALL-WHITE REDSKINS
THREE YEARS AFTER THEY REINTRODUCED AFRICAN AMERICAN players to the NFL in 1946, the Rams crossed another threshold, becoming the first team in the league to sign a player from an all-black college. Paul "Tank" Younger, a halfback and linebacker from Grambling College in Louisiana, was not among the 251 players selected in the 1949 draft, but the Rams had scouted him—in itself a progressive act—and liked him. They signed him shortly after the draft.
The press ignored the move, as did the rest of the NFL. Many pro scouts and coaches still believed _all_ black players, even those on integrated major college teams, were not equipped to play in the pros. Players on historically black college teams such as Grambling, Bethune-Cookman in Florida, and Morgan State in Baltimore were widely dismissed as inferior.
When the Giants and Lions finally followed the Rams' example in 1948, they signed black players from integrated major college teams. The Giants, with Tim Mara's blessing, added Emlen Tunnell, a defensive back from Iowa. The Lions signed Melvin Groomes, a halfback from Indiana, and Bob Mann, a receiver from Michigan. Tunnell and Mann earned starting jobs as rookies and demonstrated they belonged on the field with the league's best white players.
Questions about race were at the forefront of America's sports culture in the late 1940s and early 1950s. After Jackie Robinson broke in with baseball's Brooklyn Dodgers at the start of the 1947 season, four other black players were called up to the major leagues that year. By the end of the 1940s, almost a dozen were in the majors. In 1950, Althea Gibson became the first African American to play in the United States Lawn Tennis Association's national tournament. That same year, a court order forced the American Bowling Congress to remove a clause in its constitution restricting membership to whites. The National Basketball Association integrated in 1951 when the Boston Celtics drafted Chuck Cooper, a black forward from Duquesne.
Once the NFL allowed a few black players in, most of the owners examined their biases. Playing both ways as a six-foot-three, 225-pound rookie in 1949, Younger totaled more than 300 rushing and receiving yards, forced four fumbles, leveled opposing halfbacks with fierce tackling, and helped the Rams win a division title. Scouts began to look differently at black players, especially those from historically black colleges. The 1950 season brought more irrefutable evidence that black players belonged in the league. Marion Motley and Bill Willis had helped the Browns dominate the AAFC, but the NFL was dubious of the brand of football played in its rival league. Once the Browns joined the NFL, though, they won the championship in their first year with Motley and Willis performing well enough to earn All-Pro honors.
On November 25, 1951, George Halas brought his Bears to Cleveland to face the Browns for the first time. The Bears still had an all-white team, as did Art Rooney's Steelers and George Preston Marshall's Redskins. Marshall, descended from Confederate soldiers, was unambiguous on the subject of integration. "I have nothing against Negroes but I want an all-white team," he told the _Pittsburgh Courier,_ that city's black newspaper, in 1950. At the very least, the end of the color line in other sports had led him to make his stance on the issue public. By contrast, it is not clear why Halas and Rooney failed to integrate their teams.
Halas certainly was not opposed to having African Americans play for the Bears. In 1940, he had tried to talk the other owners into letting him sign Kenny Washington. In 1949, the Bears had become the first NFL team to draft a black player when they took George Taliaferro, a halfback from Indiana. But Taliaferro turned Halas down to play for the AAFC's Los Angeles Dons, and the Bears were still an all-white squad when they traveled to Cleveland to play the Browns two years later.
Perhaps Halas and Rooney did not integrate their teams because they were not under pressure to do so. Even as America's racial laws and attitudes began to change in the early 1950s, segregated institutions and public venues remained commonplace. Few in the mainstream press—the white press—expressed anything close to outrage. Halas would always deny that the absence of blacks from his roster in these years was purposeful. Much later on, he would point out that scouting was in its infancy and teams had little information on players from all-black colleges—an incomplete explanation at best. At least one of Halas's biographers said he was influenced by his friendship with Marshall.
Whatever caused Halas to hesitate, his trip to Cleveland in 1951 resulted in a humbling the likes of which he had not often experienced, and it changed his mind. The game between the Bears and Browns was not only a battle of first-place teams but also Halas's first opportunity to make a statement with his team about the caliber of the AAFC relative to the NFL. "He really tried to get us up that week. I don't think I ever saw him want to win a game more," said Don Kindt, one of the Bears' defensive leaders. But in front of a howling crowd of 40,969 at Municipal Stadium, the Browns—faster, quicker—dismantled Halas's squad. Cleveland led by two touchdowns at halftime and built a 42–7 lead before settling for a 42–21 victory. Browns halfback Dub Jones, who scored six touchdowns, took the next day's headlines, as did the officials, who flagged the teams for thirty-seven penalties combined, but the Browns' three black players all played central roles in the victory. Willis disrupted Chicago's offense from his middle guard spot. Motley rushed for gains. Horace Gillom, a punter, continually pinned the Bears deep in their territory.
It was clear now to Halas that he was hurting his team by not employing black players. Two months later, he made Eddie Macon, a black halfback from College of the Pacific, his second-round pick and the twentieth overall selection in the 1952 draft. A year after that, the Bears used their first-round pick on Billy Anderson, another black halfback, from Compton Community College in Los Angeles.
Neither Macon nor Anderson fared well. Macon fumbled eight times as a rookie in 1952 and was released after two seasons. Anderson, the son of a famous actor, Rochester Anderson, was a bust. But it seemed that Halas had left behind whatever biases or even prejudice that had characterized his earlier thinking. With a second-round pick in 1955, he selected Bobby Watkins, a black halfback from Ohio State, who became a starter. The next year, he drafted Willie Galimore, a halfback from Florida A&M, and J. C. Caroline, a defensive back from Illinois, both of whom also became valuable starters.
By the time the Browns humbled Halas and the Bears in 1951, Rooney and the Steelers had already grown accustomed to Cleveland embarrassing them. The teams had been assigned to the same division after the merger, which meant they played twice a year. In 1950, the Browns won in Pittsburgh, 30–17, and in Cleveland, 45–7. In 1951, the Steelers, still fielding an all-white team, lost both games of the home-and-home series by a combined 45–0 score.
Why did Rooney, otherwise a man of principle and substance, wait so long to integrate his team? It could be that, like Halas, he was loyal to Marshall. He may not have wanted to overrule his coaches, who either doubted that black players were skilled enough for the pros or did not want to deal with the locker room tension that might arise between a black player and white southerners from segregated colleges. Whatever the explanation, the Steelers, like the Bears, finally integrated in 1952. Joe Bach, just hired as the team's head coach, told reporters that jobs would go to the best players, period, regardless of skin color—a clear indication that a new era was coming into view. It was long overdue, embarrassingly so. Pitt, the city's foremost college team, had integrated seven years earlier.
In the 1952 draft, hours after Halas took Eddie Macon in the second round, the Steelers drafted a black player for the first time, Jack Spinks, a 235-pound fullback from Alcorn State, a historically black college in Mississippi. He went in the eleventh round, and fourteen rounds later, the Steelers took Bill Robinson, a halfback from Lincoln, a historically black college in Missouri.
With a rare blend of speed and strength, Spinks was a promising prospect. But the Steelers' assistant coaches eyed him suspiciously during training camp. One lamented that Spinks did not even own a sports coat to wear on the road, as if that were a reason to cut him. After hearing that, one of Rooney's brothers loaned Spinks a coat.
Robinson, a Pittsburgh native, was a long-shot prospect. The Steelers' coaches thought so little of him that they did not even want to bring him to training camp. "We're wasting our time with him," Walt Kiesling said. But Rooney intervened; his son Dan had played on youth teams with Robinson. In the end, Robinson was invited to camp, but he played little. Rooney requested that he at least be given a shot. "All I'm asking is that you put him on the kickoff and we'll see what he can do," he said before a preseason game against the Giants. The owner then called Steve Owen, the Giants' head coach, and asked, "Would you see that your guy kicks the ball to him?"
Owen said he would happily kick to Robinson. "Do you want him to go all the way?" the coach joked.
During the game, the Giants' kicker drove the ball to Robinson, standing deep in the end zone. One of Robinson's teammates urged him to down the ball, but Robinson brought it out, thinking this might be his only chance to make an impression. A few yards past the goal line, he realized he had made a mistake and tried to return to the end zone to down the ball, but the Giants tackled him for a safety. "I told you he couldn't play!" Kiesling told Rooney.
Robinson did not make the team, but Spinks did, becoming the Steelers' first black player since Ray Kemp in 1933. And indeed, as some people affiliated with the team no doubt expected, several of his white teammates resented him. In _Ruanaidh,_ his book on his father, Art Rooney Jr. wrote that, after Spinks ran over a white defensive back in practice one day, the white player cursed him with racial slurs and threw a football in his face from point-blank range. Mimicking Jackie Robinson, who had responded to racial abuse with a steely, dignified silence, Spinks returned to the huddle without speaking. According to _Ruanaidh,_ Art Rooney either saw the incident or heard about it, and counseled Spinks, "Jack, the guy who threw that football at you is a good kid, but the next time that happens, I want you to punch him out."
Another rookie, Ed Modzelewski, beat out Spinks for the starting fullback job. Spinks carried the ball just twenty-two times during the 1952 season and was cut from the team the next year. The Cardinals picked him up, and he continued to draw a paycheck in the NFL through 1957, also playing for the Packers and Giants and switching positions to offensive guard before his career came to an end.
After their "experiment" with Spinks in 1952, the Steelers were cautious about black players. The next year they drafted Jack "Cy" McClairen, an end from Bethune-Cookman, in the twenty-sixth round. But an army stint kept McClairen out of pro football until 1955, and, in the intervening years, the Steelers remained entirely white.
IN 1949, THE LAST YEAR BEFORE THE MERGER WITH THE AAFC, five black players had jobs in the NFL. In 1950, after the merger, there were nineteen. The total would steadily increase over the decade. But, despite those gains, black players were pro football's second-class citizens. They faced taunts from opponents and fans. They stayed apart from their teammates on the road, in lesser accommodations, when their teams stayed at segregated hotels.
In 1951, the Giants and Redskins played a preseason game in Birmingham, Alabama, that was sponsored by the local Chamber of Commerce and benefitted an all-white hospital. Birmingham's city leaders made it known that they did not want black players in the game. Rather than stand up for their players, the Giants acquiesced, telling Tunnell and Bob Jackson not to suit up. Teams received sizable payments from cities to stage these preseason games, and neither wanted to lose the paycheck.
Teams also routinely signed blacks that played the same few positions, usually offensive end, defensive back, and offensive tackle or guard, then made them compete for jobs, ensuring that there would only be so many on the final roster. The originator of this practice, known as "stacking," has never been identified, but teams seldom had more than three or four black players at a time, and many players were sure an off-the-books quota existed. "I doubt it was written, you couldn't prove it in court, every owner would deny it, but it was there," said Jim Brown, who joined the Browns in 1957.
By the time Brown was drafted, though, fans had at least become accustomed to seeing black NFL players take the field for their teams, which represented progress over the previous decade. The Cardinals had drafted Ollie Matson, a running back from the University of San Francisco, with the third overall pick in the 1952 draft; a future Hall of Famer, he scored eight touchdowns as a rookie. Dick "Night Train" Lane, an agile defensive back, also with the Cardinals, led the league as a rookie with fourteen interceptions in 1952, then led the league again in 1954. Lenny Moore, a halfback-receiver from Penn State, earned the league's Rookie of the Year award in 1956 after the Baltimore Colts made him their first-round pick. When the Giants reemerged as a power that year, a pair of dominating black linemen anchored their interior play. Moore's former college teammate, Rosey Grier, a defensive end, had been a third-round draft pick in 1955. Rosey Brown, a gigantic offensive tackle from Morgan State, had been picked in the twenty-eighth round of a thirty-round draft in 1953. He was the league's best tackle. Ever so slowly, teams were moving in the right direction on a sensitive issue—with one glaring exception.
THE FIRST BONA FIDE EPIDEMIC OF PRO FOOTBALL FEVER HAD broken out in Washington, DC, after the Redskins came to town in 1937. Within a few years, Griffith Stadium hosted enthusiastic sellout crowds as Sammy Baugh led them to five division titles and two championships in their first nine years in the nation's capital. The Redskins' success had helped stabilize the NFL. But, by the mid-1950s, they had regressed. They had not won a division title since 1945. They no longer drew sellout crowds at home. George Preston Marshall still rolled out a marching band and staged elaborate halftime shows, but what the fans really wanted was winning football, and they were not getting it. Starting in 1946, the Redskins finished under .500 six times in an eight-year span.
"I went to a game in Washington in the late 1940s. It wasn't very crowded, nothing like it is today," recalled Mike McGee, a thoroughbred horse trainer whose father worked for Art Rooney starting in the late 1940s. "Rooney had given me a pass to get into any NFL game. I walked in there. They had a cyclone fence around back on one side. There was a crowd, but I thought, 'Jeez, this isn't a big deal.'"
Marshall took solace in the fact that his profits were up even though his gate receipts were down; his regional television network produced more and more income in the form of rights fees and advertising profits. Only Halas and the Bears had a larger network than Marshall and the Redskins.
As for the team itself, Marshall, with typical bombast, insisted it was only a matter of time until the Redskins reigned again. When pressed to explain their years of defeat, he fell back on a set of convenient excuses. Baugh had retired. Several coaches had failed to do the job expected of them. The draft had not brought relief. His rationale omitted the fact that, first, he made many important personnel decisions himself, and, second, he often selected players based on promotional value, not their value to the team. Ever focused on winning newspaper headlines and selling tickets, he used high draft picks on prospective offensive stars, largely ignoring the blockers and tacklers that served as a team's foundation. Almost every year, the Redskins drafted a quarterback or running back with their top pick.
Marshall also thought he could sway the public with "name" coaching hires, such as Curly Lambeau, the fading Green Bay legend, whom he brought to Washington in 1952, and who won ten games with the Redskins over two years before he was fired, never to coach again. It did not help that Marshall continually harangued and second-guessed whoever coached his team. He continued to pick up the private phone line connecting the owner's box and the sideline during games and suggest substitutions or play calls. The coaches and players tried to ignore him. "We had those big capes for cold weather, and sometimes we'd hang one over the phone at the bench, to muffle the sound," running back Jim Podoley told the _Washington Post._ "When Marshall saw what was happening, he'd send his chauffeur down to take the cape off the phone."
An equally if not more daunting problem was Marshall's steadfast refusal to employ black players. Even as they emerged as role players and stars on other teams, Marshall stuck to an all-white policy. His fondness for an older world, one in which the hierarchies of his youth were still in place, was readily apparent. His beloved halftime shows occasionally featured entertainers in blackface. In the late 1950s he briefly changed a lyric in his team's fight song from "fight for old D.C." to "fight for old Dixie." Surely, he abhorred the idea of paying blacks to play football and truly detested the thought of granting them leverage in salary negotiations.
At first, he attempted to avoid making news on the subject by obfuscating. Although he had told the _Pittsburgh Courier_ in 1950 that he wanted an all-white team, he told a Washington columnist in 1953 that he "would like very much to sign a colored player. But it seems the other guys always beat me to them." It helped him that the Senators, Washington's baseball team, also had not integrated by the end of the 1953 season. Soon, though, his intentions became too obvious to ignore. In the 1954 draft, other teams combined to select thirteen black players, but the Redskins spent all thirty of their picks on white players. Then, on September 6, 1954, five months after the Supreme Court declared segregation in public schools unconstitutional, the Senators broke their color line with Carlos Paula, a black outfielder from Cuba. Now Marshall had the only all-white team in Washington.
That fall, the Redskins won just four games. On November 21, Ollie Matson scored four touchdowns against them in a 38–16 win for the Cardinals in Chicago. It was evident the Redskins were falling behind by ignoring black players. The pressure on Marshall began to build. Sam Lacy, an influential black sportswriter for the _Baltimore Afro-American,_ called for black fans to boycott the team. Lacy had traveled with Jackie Robinson in 1947, the year Robinson integrated the major leagues. A DC native, he had stopped covering the Redskins in 1950 because of Marshall.
But Marshall paid little attention to criticism from Lacy or from other reporters, including the _Washington Post_ 's Shirley Povich. In 1955, the Redskins had the NFL's only all-white team and surprisingly went 8-4 to finish second in the East. Dick McCann, their general manager, proclaimed it "the greatest reconstruction job since the Civil War," a comparison his boss surely enjoyed. The next year, Washington finished 6-6.
Whenever the subject of race and football came up, Marshall insisted fans in Washington wanted an all-white team. But his rationale was dated. It was true that Washington had been imbued with a southern sensibility when Marshall brought the team to town in 1937. (Ironically, though, Griffith Stadium was one of the few public facilities open to blacks at that time.) But the city was undergoing a dramatic transformation. Its population had soared to 1.5 million, and, after discrimination in federal hiring was outlawed in 1950, African Americans flooded the capital in search of work. Between 1938 and 1956, the percentage of blacks in the federal workforce grew from 3 percent to 24.4 percent. By the mid-1950s, Washington's public schools, Catholic schools, restaurants, and theaters were no longer segregated, and it was much harder to claim that its sports fans desired an all-white team.
Marshall was apt to point out that the Redskins' fans in the Deep South still had a strong bias against black players. In 1956, the team's games were broadcast on sixty radio and twenty-nine television stations, covering Virginia, the Carolinas, and even Florida, where the top college teams remained all white. The Redskins barnstormed through the region every summer, playing preseason games in stadiums with separate seating for blacks and whites. Marshall did not want to tamper with a profitable arrangement.
Opposition to his position was growing, though. In January 1957, when the NFL owners met at the Bellevue-Stratford Hotel in Philadelphia to conduct the final rounds of that year's draft, they were surprised to find anti-Marshall protestors picketing the building. The Washington branch of the National Association for the Advancement of Colored People had organized the protest.
The owners rallied around their colleague, unanimously passing a resolution in his honor: "George Marshall, having completed 25 years in professional football, is the greatest asset sports has ever known with his honesty, integrity, and his perfect frankness in expressing what he believes." The resolution remains a blemish on the records of Halas, Bell, Rooney, Mara, and the entire NFL. Povich, a longtime critic of Marshall's, was appalled by it. "There are those who will contend," he wrote, "that a more debatable statement has never been uttered in the entire history of the spoken word."
IN THE FIRST ROUND OF THE 1957 DRAFT, THE BROWNS SELECTED Jim Brown, who had played at Syracuse. The Colts selected Jim Parker, a tackle from Ohio State. Both were African Americans, destined for the Hall of Fame. The Redskins selected Don Bosseler, a fullback from Miami, who was white and destined for a solid if workmanlike eight-year pro career. After Bosseler, they drafted twenty-nine more white players. That fall, they went 5-6-1 to begin a run of nine straight losing campaigns.
The 1958 season brought more indignity for Marshall and his team. After Brown rushed for 152 yards and several scores in a victory for the Browns in Washington, Povich wrote that the powerful running back, "born ineligible to play for the Redskins, integrated their end zone three times yesterday." Povich would later note that the Redskins' colors were "burgundy, gold and Caucasian." The Redskins finished that season 4-7-1 and then fell off badly, going 3-9 in 1959 and just 1-9-2 in 1960. "There were only so many good players, and when you eliminated half of them, it was tough. Very tough," recalled running back Jim Podoley, who played for the Redskins from 1957 to 1960. But Marshall was defiant. "We'll start signing Negroes when the Harlem Globetrotters start signing whites," he said.
On December 27, 1960, the owners gathered in Philadelphia for the annual college draft. Owing to their recent failures, the Redskins were in a prime position, holding the second and third picks in the first round. After the Minnesota Vikings, an expansion team, selected Tommy Mason, a white halfback from Tulane, with the first overall pick, it was the Redskins' turn. The pool of draftees included future stars such as Bernie Casey, a speedy back from Bowling Green; Herb Adderly, a cornerback from Michigan State; Houston Antwine, a guard from Southern Illinois, and Ernie Ladd, a massive lineman from Grambling—all African Americans.
The Redskins took two white players: Norm Snead, a quarterback from Wake Forest, and Joe Rutgens, a tackle from Illinois. Both would play well in the pros, but they could not change the fortunes of the all-white Redskins, who went 1-12-1 in 1961, reaching an embarrassing nadir. "In modern pro football, Marshall is an anachronism, as out of date as the drop-kick," Povich wrote. "The other club owners have passed him by. Marshall, with his dedication to white supremacy on the football field, is still hearing a cry that doesn't exist."
Marshall dismissed Povich's criticism as a publicity stunt—for whom, it was not clear. His colleagues at the owners' table knew better, but they could not dissuade him. Marshall was going to run the Washington Redskins as he damn well pleased.
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# FORTY MILLION VIEWERS
AT SOME POINT IN THE 1930S, TIM MARA HAD PLEDGED TO treat the Giants' office staff to lunch every workday. He was still doing it more than two decades later even though it had become an expensive proposition as pro football became a bigger business, and the Giants' staff swelled with coaches, scouts, and administrators. Mara also had promised to take care of the Giants' head coach, Steve Owen, who, remarkably, had never signed a contract for longer than one year since first taking the job in 1930. Though the succession of one-year contracts may have suggested otherwise, Mara trusted Owen, who had won two league titles as the Giants' coach.
By the end of the 1953 season, though, Mara was weary of being the patient, rational owner who preached trust and continuity. The Giants, one of the oldest and most successful franchises in the league, had stopped winning, and he needed to make changes. It had been seven years since their last division title, a severe drought for a team that had played in eight league championship games between 1933 and 1946. After a low point in the late 1940s after the Filchock gambling scandal, the team briefly recovered; they tied for a division title in 1950 and posted winning records in 1951 and 1952. But in 1953, the Giants won just three games. And it was not just that they lost but _how_ they lost that bothered Mara. Everywhere he looked, he saw teams playing more sophisticated and effective football. The league championship games of 1950 and 1951 had featured spectacular aerial duels between the Browns' Otto Graham and the Rams' Bob Waterfield. The Detroit Lions had won the league title in 1952 with another daring quarterback, Bobby Layne, leading the way. Those teams mixed old-fashioned power running with innovation and deception. The Giants, meanwhile, still ran Owen's A formation attack, in which the primary deception was the center snapping the ball to one of three players lined up in the backfield. They looked predictable and slow in comparison to the other teams. The Browns had embarrassed them, 62–14, near the end of the 1953 season.
Mara feared that fans were losing interest. The Giants had developed a loyal following after nearly three decades in business, but baseball had always been a more popular sport in New York, and that was truer than ever in the 1950s. The three major league teams in the city had launched something of a golden age of New York baseball. By the fall of 1953, the Yankees had won five straight World Series titles. In four of those five years, another New York–area team, either the Giants or Brooklyn Dodgers, had won the National League pennant before losing in the Series. With luminous stars such as Mickey Mantle, Willie Mays, and Jackie Robinson hitting home runs and stealing bases, baseball was dominant. In 1953, the Yankees, Dodgers, and Giants combined to sell 3.51 million tickets, even with many games televised. That fall, Mara's Giants sold just 147,056, an average of 24,509 per game—their lowest figure in several decades. Although the availability of games on the team's regional television network likely was a factor, it was just as likely that the product on the field was the primary problem.
When the Giants had fallen apart in the late 1940s, Mara went to his sons, who still ran the team, and asked whether Owen was the problem. As fond as Mara was of the coach, he was willing to replace him. His sons assured him the problem was not Owen but the talent, or lack of it, on the squad. Their opinion seemingly was validated when the Giants began winning again with Owen still in charge.
By late in the 1953 season, though, Mara's sons thought otherwise. Their roster featured promising young players, all recent draft picks, such as Kyle Rote, a receiver from SMU; Frank Gifford, a triple-threat halfback from Southern Cal; and Rosey Brown, a tackle from Morgan State. Their veteran quarterback, Charlie Conerly, could still play at a high level. The Giants had talent. But their whole approach seemed dated. Cleveland's Paul Brown and Detroit's Buddy Parker were mastermind coaches, always inventing new schemes. Owen had devised a new defensive alignment, a 6-1-4 setup known as the "umbrella" defense, to blunt opposing passing attacks, but the league had already figured out how to beat it. Sports columnists in New York called for Owen's ouster, and "as much as the Maras hated to admit it, they had to agree that the gridiron parade had passed by their old warhorse," wrote Don Smith, the team's director of publicity, years later.
A day after the 62–14 loss in Cleveland, Tim Mara and his sons summoned Owen for a meeting. "What's up?" Owen asked as he sat down in Tim's office. He listened silently, shocked, as his bosses informed him that his long run was over; he was being fired. Jack Mara later described it as "the toughest thing I ever had to do; Steve was like family." Owen coached the Giants' 1953 finale, which was his last game with the team. He did not speak to the Maras for years afterward.
But, though the firing of Owen was personally difficult for the Mara family, it was the correct move. The Maras replaced Owen with Jim Lee Howell, an easygoing native of Lonoke, Arkansas, who had played receiver and defensive back for the Giants before and after World War II. Howell put one of his assistants in charge of the offense and another in charge of the defense—a relatively new practice, one that followed the unlimited substitutions rule. To run the offense, Howell hired Army's backfield coach, Vince Lombardi, a tenacious former Fordham classmate of Wellington Mara's. The defense was handed to an active defensive back, Tom Landry, a tall Texan with a sharp strategic mind.
Of course, Lombardi and Landry would become head coaches, win championships, and make the Hall of Fame. As young assistants in the mid-1950s, they worked together to orchestrate a drastic turnaround for the Giants. Landry designed a defensive alignment featuring four linemen and three linebackers in front of a four-man umbrella of defensive backs, an update on Owen's approach. Lombardi designed a methodical offense built around Gifford, a nimble natural athlete who could run for gains, catch passes, and throw. The Giants posted a 7-5 record in 1954, in their first year under Howell, with Conerly throwing seventeen touchdown passes. The quarterback had considered retiring, not wanting to play another losing season, but now that the Giants were headed in the right direction, Conerly would play for them into the early 1960s.
In 1955, Conerly alternated with a young quarterback, Don Heinrich, while Gifford made All-Pro and fullback Alex Webster regularly plowed up the middle for chunks of yardage. The Giants started slowly, losing four of their first five games, but, by late in the season, no one wanted to play them. They went unbeaten in their final five games. On the Sunday after Thanksgiving, the Browns visited the Polo Grounds, and an epic game unfolded. The Giants went ahead, 14–0. The Browns, destined to win the league title, rallied to lead, 21–14. The Giants then staged a rally of their own, going up 28–21 as Conerly fired completions and Gifford twisted away from defenders to move the ball downfield. Back and forth the offenses went, with Conerly and Otto Graham matching big plays, until Graham moved his unit into position for a short field goal that would win the game in the final seconds. But the Giants blocked the kick. The final score was 35–35. The teams had combined for 770 yards of offense. Two years after Owen's firing, the Giants were playing thrilling football. They had drawn just 7,000 fans for a home game against the Cardinals earlier that season, but 45,699 watched them play the Browns.
That fall, Bert Bell phoned Tim Mara with some surprising news. A pair of Texas oilmen had offered to buy the Giants.
"But... the Giants aren't for sale," Mara sputtered.
"I know that," Bell responded.
Curious, Mara asked what the oilmen were offering.
"They'd pay $1 million," Bell said, "but they want to move the home games to Yankee Stadium."
Mara was amazed, both by the amount of the offer and the proposed venue change. "You know," he told his sons, "if we're worth $1 million in Yankee Stadium and they don't want any part of us in the Polo Grounds, maybe we ought to think about moving to Yankee Stadium."
Until that point, Mara had little interest in moving to Yankee Stadium because of his poor relationship with Dan Topping, who still owned the Yankees and the stadium. Mara remembered with some bitterness how Topping had cut off negotiations over home dates for their respective teams and jumped to the AAFC a decade earlier. But, as he had with Owen, Mara saw that necessity dictated that he put aside his personal feelings. The Polo Grounds had served the Giants well, but it was originally built in 1890 and, perhaps not surprisingly, starting to fall apart. The baseball Giants had stopped drawing big crowds to the stadium even though they had winning teams. Yankee Stadium was larger, which meant the Giants could sell more tickets, and it featured wider concourses and better sight lines. Fans also equated it with success, owing to the Yankees. Mara turned down the Texas oilmen, but, with Bert Bell's encouragement, he moved out of the Polo Grounds. The Giants signed a lease to begin playing in Yankee Stadium in 1956.
That year, they added another player who would prove vital, when Sam Huff, a ferocious rookie from West Virginia, joined the defense. They already had a stout unit with Rosey Grier and Andy Robustelli anchoring the line, and Emlen Tunnell leading the secondary. Tom Landry devised another new scheme around a third linebacker stationed in the middle of the defense, behind the line and in front of the secondary, responsible for stopping both runs and passes. Previously, most defenses had used two linebackers, one on each edge of the line, but with Huff roaming the field as a newfangled "middle" linebacker, Landry's defense yielded the fewest yards in the NFL in 1956.
The Giants began the season with three road games, winning two, as baseball preoccupied the city's sports fans. Contesting the sixth all–New York World Series in eight years, the Yankees and Dodgers played seven games before a winner was determined. (Yankees, again.) By the time the football Giants hosted their first game at Yankee Stadium on October 21, though, baseball was over, and the city was ready to turn its attention to them. The Giants promptly routed the Steelers, 38–10, before 48,108 fans. Three weeks later, they defeated the Cardinals, 23–10, in front of 62,410. It was their fifth straight victory.
The Browns had won six straight East division titles since the merger, but the Giants were now the superior team. Although they showed some weakness down the stretch, at one point winning just once in a month, they claimed the division title, their first in a decade, before the final Sunday of the season.
A throwback championship-game matchup was finalized when the Bears routed the Lions on the final Sunday to win the West. The Giants and Bears had met in the NFL's first two championship games, in 1933 and 1934, after George Preston Marshall had proposed the idea of a title game; and they had played again in 1941 and 1946. Now, after a decade in the wilderness for both teams, they were meeting again for the title.
George Halas had coached the Bears in their previous championship games against the Giants, but in 1956 he had handed the head coaching duties over to his friend and longtime assistant, Paddy Driscoll. Halas still effectively ran the team (and the league, though to a lesser extent than before), conducting meetings and putting sixty-four-year-old Clark Shaughnessy, his favorite football strategist, in charge of the defense.
Early in the week leading up to the title game, Tim Mara announced that he wanted to speak to the players, a rare request. After practice, he came to the locker room, still a commanding figure at age sixty-eight, over six feet tall, always dressed as if he were headed to the opera. The weather in the city had been frigid for weeks, and the forecast for Sunday was for more of the same. "Boys, we played the Bears for the title back in '34 in weather this bad, and we nearly lost," Mara told the players. He explained how the Giants fell behind on a frozen field, then rallied to win after they changed into sneakers after halftime. "We're going to do the same thing this year, only we don't have to steal the sneakers," Mara said.
He pointed to Robustelli, who owned a sporting goods store. "Andy, can you fill an order for a good pair of sneakers for every man on the team by the end of week?" he asked. "You betcha, Mr. Mara," Robustelli said.
As predicted, the weather on game day was below freezing and blustery. An hour before kickoff, Howell put one player in cleats and another in sneakers and asked them to test the field. It was an easy choice. "We all go with sneakers!" Howell exclaimed.
The weather limited the Yankee Stadium crowd to 58,836, but the fans were rewarded for braving the conditions. The Giants scored an early touchdown and led by 13 points at the end of the first quarter. Near the end of the second quarter, they blocked a Chicago punt in the end zone and fell on the ball for a touchdown that gave them a 34–7 lead. Shaughnessy's defense could not stop Lombardi's varied attack. Conerly tossed a pair of touchdown passes. Gifford totaled 161 rushing and receiving yards. Webster also went over 100 yards from scrimmage. The final score was 47–7. A national television audience, watching on CBS, saw a caliber of football no college team could possibly reach. The Giants were almost frighteningly fierce on defense. Their offense dazzled the Bears. Like rubber-faced Milton Berle a decade earlier, New York's football Giants had become must-see TV.
ALTHOUGH THEY HAD BECOME FAMOUS LARGELY FOR LOSING time and time again to the Yankees in the World Series, baseball's Brooklyn Dodgers were popular and profitable. Ebbets Field was sold out for many of their games. They shared a lucrative local television contract with the Yankees and Giants. Baseball fans around the country knew their lineup and rooted for them to topple the widely reviled Bronx Bombers. Nonetheless, Walter O'Malley, who owned the club, was restless by 1956. Ebbets Field was small, with just a 32,000-seat capacity. A few years earlier, the worst team in the National League, Boston's Braves, had left behind a cramped, empty ballpark and moved into a large new stadium in Milwaukee. Now they were winning, drawing big crowds, and generating profits. O'Malley was jealous. Brooklyn supported his team, but he wanted a new place to play.
Various New York City politicians had different ideas about the best site for a new ballpark. There was a lot of discussion but no decision making, and O'Malley began to look elsewhere. Los Angeles beckoned. The West Coast metropolis was now larger than all but three cities with major league teams. It already had a successful NFL team, and the city's elected officials wanted a baseball franchise. O'Malley quietly began negotiating with politicians in Los Angeles, who offered to build him a new stadium if he moved the Dodgers. When the media learned of the talks, O'Malley at first denied that he would leave Brooklyn. But when New York officials still did not react as he wanted, he offered a warning early in 1957: "Unless something is done within six months, I will have to make other arrangements."
O'Malley called Horace Stoneham, owner of baseball's Giants, who was in a similar position. His attendance was plummeting. After drawing 1.16 million fans with a pennant-winning team in 1954, the Giants had drawn just 824,000 in 1955 and a paltry 629,000 in 1956. The Polo Grounds, like Ebbets Field, was dated. Tim Mara had moved out, taking the football Giants to Yankee Stadium. O'Malley asked Stoneham whether he, too, was pondering a move, and Stoneham said yes.
In May 1957, the other National League owners gave O'Malley and Stoneham permission to leave New York as long as they confirmed their intentions by October, which they did. New York sports fans were heartbroken. They had lived at the epicenter of the baseball world for decades, their clashing loyalties energizing the city. Now, though, they would only have one major league team.
The 1957 baseball season was solemn in New York. On September 24, the Dodgers played their final game at Ebbets Field. Between innings, the stadium organist played such songs as "Don't Ask Me Why I'm Leaving" and "Thanks for the Memories." Within a week, the Giants played their last game at the Polo Grounds.
Less than three weeks later, Tim Mara's Giants, the reigning NFL champions, were welcomed with a roar when they routed Pittsburgh in their first home game of the 1957 season. A palpable transformation was underway. No longer the capital of professional baseball, New York was turning to pro football. The Giants of the mid- to late 1950s were ideal objects of such affection. Gifford, glib and handsome, was destined for magazine covers and a career as a broadcaster. He began receiving the endorsement offers that had previously gone to baseball stars, as did Conerly, the drawling quarterback, and Huff, the fierce defender with an incongruously sunny personality. Football players had long been lesser figures in the city than baseball players, but that was shifting. Now, when a Giant drank at Toots Shor's, the iconic New York City watering hole, or dined at 21, it made the tabloid gossip columns.
The football Giants' season ticket sales grew quickly, as did their overall attendance. The 290,667 tickets they sold for six home games in 1957 was nearly double the amount they had sold just four years earlier. And the number of fans watching in person was small compared to the television viewership. Although the Giants' games were blacked out in the city, their regional network reached throughout the Northeast. Fans in the city drove to Connecticut, Long Island, and New Jersey on Sundays to watch games on stations outside the seventy-five-mile radius.
For much of the 1957 season, it appeared the Giants would win a second consecutive league title and launch a dynasty. When they defeated the Cardinals on November 24, they had a 7-2 record and trailed first-place Cleveland by just a half game in the East. But they faltered in December, losing their final three games. The division title went to the Browns.
Despite that disappointment, the Giants remained New York's darlings. In 1958, they played to even larger crowds and again battled Cleveland for the division title. After a midseason slump, they trailed by one game heading into their final regular-season contest, against the Browns at Yankee Stadium. Before 63,192 fans, they won, 13–10, on a field goal in the final minute. That meant the teams had to play again a week later, also at Yankee Stadium, to decide the division, and the Giants won again to advance to the league championship game for the second time in three years. They would play the Baltimore Colts, a new team in the league's championship mix.
The Colts were a Bert Bell creation, palpable evidence of the commissioner's vision and influence. The Baltimore franchise that joined the NFL from the AAFC in 1950 had lasted just one year before folding. Two years later, when a team in Dallas failed, Bell moved it to Baltimore and put a new owner in charge, Carroll Rosenbloom, a wealthy clothing manufacturer whom Bell had coached on the football squad at Penn in the 1920s. Rosenbloom quickly put the franchise on solid footing.
But the central figure in the Colts' rise was their quarterback, Johnny Unitas, a crew-cut Pittsburgh native whom Art Rooney already saw as one of his biggest mistakes. The Steelers, forever struggling, had given Unitas a tryout at their training camp in 1955, but they cut him without letting him throw a pass in the preseason. After playing semipro ball in Pittsburgh for a year, Unitas received a tryout offer from the Colts in 1956. He won the starting job and now, in his third pro season, operated the league's most dangerous passing attack.
Much like the revived Giants in New York, the Colts played before sellout crowds—fans so enthusiastic a Chicago sportswriter would label the scene in Baltimore "the world's largest outdoor insane asylum." Seven thousand Baltimore fans bought tickets to the 1958 championship game against the Giants and traveled to New York to cheer on their team. For the third straight Sunday, Yankee Stadium was brimming with pro football diehards.
When the game began at 3 p.m., fans across the country settled in to watch NBC's live broadcast from New York. Other sports that had initially benefitted from television's power were now struggling. Interest in boxing had plummeted because of overexposure. Horse racing had simply balked, refusing to televise many major races out of fear that attendance at tracks would drop. Baseball had made inroads, but the game was not always easy to follow on a small, black-and-white screen. The union of pro football and television, however, amplified the power of both the sport and the medium.
By using blackout rules and regional networks to control their television audience, the NFL's inner circle—Halas, Bell, Marshall, Rooney, and Mara—had boosted interest outside of their home cities while protecting their attendance figures and thus their gate receipts. The ratings for NFL broadcasts were up, and so was attendance. In 1950, the average crowd for an NFL game was 25,356. By 1958, it was 43,167. The inner circle had always believed in their game and their league and hoped that one day it would reach the same heights of popularity and influence as baseball and college football. Now, through television, pro football appeared poised to do just that.
The game itself was chiefly responsible for the surge in interest. For years, the prominent owners had tinkered with the rules, always with an eye toward making the game more accessible and exciting. In 1933, they had eliminated restrictions on the forward pass. Three times, they had voted to move the hash marks nearer the middle of the field. In 1950, they permitted unlimited substitutions. By the late 1950s, their game was a wide-open blend of brute force, athleticism, and daring. It was ideal for television. The 100-yard stage offered a tighter focus than baseball's. It was easy to see the hits and follow the significantly larger ball on the screen. The 1958 championship game introduced a final, and necessary, ingredient: high drama.
The Colts led at halftime, 14–3, with costly Giant fumbles having wasted one scoring chance and set up one for Baltimore. Unitas seemed in total control of the flow of the game, his pinpoint passes allowing him to move the Colts against Tom Landry's vaunted umbrella defense. Yet the Giants rallied. Rote fumbled near midfield after catching a pass, but Alex Webster scooped up the loose ball and raced to the Baltimore 1 yard line before being tackled. That set up a New York touchdown. Early in the fourth quarter, the Giants drove deep into Baltimore territory on a long pass from Conerly to receiver Bob Schnelker, and another pass, from Conerly to Gifford, produced a touchdown. The Giants now led, 17–14.
The game was decided by a late Baltimore drive. Starting at his 14 with two minutes to play, Unitas moved the ball forward with completions to Raymond Berry, a spidery wide receiver and future Hall of Fame inductee whose precise footwork enabled him to shake free from defenders. The drive penetrated deep into New York territory as the clock ticked down. The fans screeched, barely able to watch the tense scene.
With seven seconds to play, the Colts lined up for a 20-yard field goal that would tie the score. Bell, watching from the Yankee Stadium stands with Rooney and other league officials, knew what was at stake, but few fans and players did. The league had a "sudden death overtime" rule for its championship game. In the event of a tie after four quarters, play would continue until one team scored to win the game. The league had passed the rule more than a decade earlier, but it had never been used.
After the Colts' kicker, Steve Myhra, booted the ball through the uprights to tie the score at 17–17, players on both teams initially thought they would simply share the title. A few even shook hands and headed for their locker room until an official intervened, explaining that the game would continue.
A coin flip at midfield determined who would get the ball first. The Giants won the flip, but their offense could not pick up a first down, leading to a punt. Now Unitas had the ball again. The big crowd quieted when he threw passes to Berry and Alan Ameche, his fullback, for first downs. Ameche picked up 22 yards on a run. A completion to Berry moved the ball to New York's 8 yard line. Any score would win the game, but, rather than settle for another field goal, Unitas wanted a touchdown. He completed a pass to an end, Jim Mutscheller, moving the ball to the 1. Now Unitas called a running play, and Ameche took the handoff and bulled into the end zone for a touchdown. The Colts had won.
"Up in the grandstand, a man was crying tears of joy. It was Bert Bell," columnist Frank Graham wrote in the _New York Journal-American._ The commissioner immediately and fully comprehended the significance of the moment. The NFL had staged a championship contest that was more than just another game. It had been a dramatic, unpredictable spectacle, just as compelling on television as it was in person. Ratings experts would estimate that 40 million people had watched the Colts and Giants on NBC. Forty million! That was roughly one-fifth of the country's population.
George Halas watched the game on a black-and-white television set in his den in Chicago. George Preston Marshall also watched from his home. Tim Mara was in his seat on the Giants' side of the field, distraught over how the game ended but aware that the show had been a success. Art Rooney sat in the stands next to Bell, his great friend. The five of them had worked together and encouraged one another for several decades even as their teams competed ferociously on the field. They had made many poor choices but many more good ones. With their determination to cooperate, their relentless, often unfounded optimism, and their skill as both football men and businessmen, they had built out of nothing something that was substantial and profitable, something millions now cared about. In that sense, their job was done.
# EPILOGUE
BY THE FALL OF 1957, THE NFL'S PLAYERS WERE WELL aware of the league's television bonanza and knew the owners could no longer cry poverty in salary negotiations. The players wanted to form a union and collectively bargain for a minimum salary, preseason pay, and support for injured players. The owners were split on how to respond.
George Preston Marshall led the opposition to a union, which was no surprise. A staunch political conservative, he had fought against the New Deal and opposed unionization in any context. And his stinginess was legendary. He was furious when he heard the Lions had started paying players fifty dollars to participate in preseason games. George Halas also opposed the union, unwilling to give up the leverage he had always wielded in salary talks.
Marshall and Halas had fought with each other through the years, but when they aligned on a league issue, they usually got their way. This time, though, they did not. Art Rooney lived in a union town and had a softer heart. He believed the players needed the help and could unionize without putting the owners out of business. Bert Bell's first instinct may have been to side with Halas and Marshall, but the commissioner understood that unionization probably was inevitable and that it would be better for business than the alternative, given the political climate. A congressional antitrust subcommittee was investigating restraint of trade in pro sports because the leagues had been so slow to expand. Bell had told the subcommittee that he was not opposed to the players forming a union, then filed a statement with the subcommittee in August 1957 saying he planned to formally recognize the players' nascent union as legitimate.
The night before Bell released the statement, Marshall lectured him over a meal in Washington. "You're going to get fired, Bert. What are you going to do? You can't get a job anywhere," Marshall said. Bell shrugged and replied, "If I get fired, I get fired." He was accustomed to threats. A year earlier, Tony Morabito, the volatile lumberman who owned the 49ers, was so upset by an officiating call that went against his team that he said he would "try to get Bert Bell's job." Morabito called Bell "a dictator." But that potential revolt never materialized after Halas defended the commissioner, and now, though Marshall envisioned another revolt, Bell actually had broad support on the issue. Other than Marshall and Halas, no owner was vehemently opposed to the players forming a union. After Bell said he would recognize it, the other owners stood by him. "There's no doubt Bell has the right to negotiate any differences between the players and owners," Jack Mara said.
The NFL officially dealt with the matter at an owners' meeting in Philadelphia on December 2, 1957. According to Art Rooney's son Dan, who attended the meeting, Halas and Marshall still did not want to recognize the union. "My father was the guy who got up and said, 'You have to vote so the players can have a union,'" Dan Rooney said. "Marshall and Halas were yelling at him and he said, 'Listen, Bert went before Congress and said he would get this done. If you don't do this, his effectiveness as commissioner is finished.'" Rooney forced a vote and the issue carried by a 10–2 margin, the minimum required for passage.
Halas, who had long acted as a shadow commissioner, was accustomed to getting his way, but he had been overruled. He grudgingly said he would support the union as long as players from every team belonged, but in a demonstration of his stubbornness and lingering power, the Bears' players did not join until 1962.
The conflict over the union was the last great debate between Halas, Bell, Marshall, Rooney, and Mara.
On February 16, 1959, six weeks after the Giants' loss to Baltimore in the overtime championship game that had been televised across the nation, Tim Mara suffered a heart attack and died at his Park Avenue apartment. Though his health had declined and his death was not unexpected—his family, the Giants' team doctor, and a priest were by his side—it was still a shock. Until recently, Mara had still been arriving at the Giants' offices every day at 7 a.m., as he had for years. In fact, at age seventy-one, he had never been more optimistic about the team. Season tickets were selling briskly after two championship-game appearances in three years. "We're going to sell out next year!" Mara exclaimed.
His death made national news. "Pro Football Pioneer Dies," read a banner headline in the _Chicago Tribune._ Although Mara's sons had effectively run the team for years, Mara had founded the franchise that gave the NFL a credible presence in New York, the country's largest media market. He had kept the Giants afloat through the stock market crash, the Great Depression, World War II, and a gambling scandal involving the team's quarterback. Only George Halas had been associated with the NFL longer than Tim Mara. Art Rooney had regarded Mara as a wise older brother, both in football and at the racetrack, going so far as to name a son after him. Rooney and the other owners traveled to New York for Mara's funeral. According to Rooney's biographers, Rooney was stoic at the funeral, "finding solace in his faith." But Bert Bell, who was anything but stoic, became agitated and suffered a minor heart attack during the event.
After that scare, a doctor advised Bell, who was sixty-six, to stop attending NFL games; it was possible his heart could not take the stress, the doctor said. Bell dismissed the warning. "I'd rather die watching football than in my bed with my boots off," he said. He would get his wish. Seven months later, while taking in a game between the Eagles and Steelers at Franklin Field in Philadelphia on October 12, 1959, Bell suffered a fatal heart attack.
It happened after the Eagles, headed for victory, scored an insurance touchdown with less than two minutes to play on a pass to Tommy McDonald, a young wide receiver destined for the Hall of Fame. McDonald would recall looking up and seeing the fans cheering except for those in one section, who were calling for help. Bell had slumped after seeing his beloved team score.
His son, Upton, was also at the game, seated across the stadium. "There was a commissioner's box, which he never sat in. He always moved around, talking to people," Upton said. "I remember looking across the field and seeing a guy wearing a tan suit down. He always wore a tan suit in the summer and a blue suit in the winter.
"I said to my friend, 'Give me the binoculars.' He was gone by the time I got to him."
Though devastated, Upton Bell understood that it was a fitting end for his father, the lifelong football man whose devotion to the city of Philadelphia, and to the NFL, was unrivaled. "What better way was there for him to go out? He was watching an NFL game between the two teams in the league he had owned. The Eagles had just scored the winning touchdown," Upton Bell said. A sportswriter would later characterize it as "like Caruso dying in the third act of Pagliacci."
The news of his death startled the rest of the league. Rooney, who also attended the game, said later he was so dazed he wandered in front of a streetcar as he left Franklin Field and was nearly killed. The Packers' first-year head coach, whom Bell had helped steer to Green Bay, had to take a seat and compose himself when reporters told him about Bell after the Packers' game. "I don't know how we'll replace him," Vince Lombardi said.
It would not be easy. Bell's record as an owner and coach in Philadelphia and Pittsburgh had been lamentable, but almost from the day he joined the NFL in 1933, he had been a central figure in league circles. It had been his idea to stimulate competitive balance with an annual draft of college talent. "That move alone probably saved the league," Upton Bell said. As commissioner since the end of World War II, Bell had fended off and co-opted the AAFC and deftly steered the league through the reintegration of rosters, television's rise, and the start of a players' union. Over the course of his tenure, he had taken the league from uncertainty to security, from a tenuous financial state to clear profitability, and from the lowly status of a secondary sport to the game of the television age.
After his death, the tributes rolled in. "There is no such thing as an indispensable man. But Bert Bell came closer to it than most in his role as commissioner," Arthur Daley wrote in the _New York Times._ Edwin Anderson, the Lions' team president, remarked that Bell "has done more for professional football than any other man," quite a statement given that he worked alongside Halas.
"He's certainly the only commissioner in sports history who played the game, coached the game, owned a team, and became commissioner. No one else in sports history has ever had that background," Upton Bell recalled. "If there was a problem with a player, he knew what it felt like to have his nose broken and his face kicked in. If there was a problem with an owner, and there were many, he'd done that so he could tell them off."
More than a half century later, Upton Bell said his father was preparing to give up the commissioner's job when he died. "He was going to buy the Eagles back. He had a deal for $900,000," Upton said. That went unreported at the time, probably because it was not widely known. Bell had been the commissioner for so long that the owners could not imagine anyone else in the job. They battled through twenty-three ballots at the next league meeting before they finally agreed on a replacement: Pete Rozelle, the Rams' general manager.
A thirty-three-year-old, perpetually tanned former public relations man, Rozelle would attain legendary status as he guided the NFL through an era of exponential growth. As the league became a slick, wildly profitable corporate entity, the pre-Rozelle years would become something of a curiosity. It seemed impossible that the commissioner of America's preeminent sports institution had once doodled the schedule while sitting at his kitchen table and talking on the phone with the owners. But that had been the NFL when Bert Bell was in charge.
BEFORE THEIR TEAMS PLAYED IN WASHINGTON ON AN OCTOBER afternoon in 1964, George Halas and George Preston Marshall found themselves having an impromptu conversation. Marshall's limousine happened to pull up to the stadium just as the Bears' team bus arrived. Halas leapt from the bus and rushed over to greet Marshall. "George!" Halas exclaimed with his hand extended. "So good to see you, Chief. So really good to see you." According to a _Washington Star_ reporter who witnessed the scene, Marshall began to cry. "It's like old times," Halas said cheerfully. After a brief silence, Halas added, "If there's anything you need, George just let me know. I'll be glad to help."
Marshall nodded. Two years earlier, he had undergone a hernia operation. It was successful, but complications kept him in the hospital. Then he suffered a stroke. For decades, the Redskins' owner had been the loudest voice in the NFL. But now he was seldom able to speak at all. Marshall no longer attended the league meetings he had once dominated, and he had been too ill to attend the dedication of the Hall of Fame in Canton, Ohio, on September 7, 1963, when seventeen men became the Hall's charter class of inductees. Marshall was one of the seventeen, enshrined with playing legends including Sammy Baugh, Don Hutson, Red Grange, and Bronko Nagurski, and also Halas, Tim Mara, and Bert Bell. (Art Rooney was enshrined a year later.)
Few men had done more than Marshall to popularize pro football. He had pushed for rules that opened up the passing game. He had invented the postseason with his idea of separating the teams into two divisions and having the winners meet in a championship game. He had enlivened a dour sport with halftime pageants and marching bands.
More recently, though, Marshall had drawn only criticism for his refusal to sign African Americans players, earning himself a reputation as the NFL's fiercest racist. He was forced to relent when no less an authority than the US government began pressuring him. A new sports venue, D.C. Stadium, was opening in Washington in 1961. It seated more fans than Griffith Stadium, where the Redskins had always played, and thus offered the possibility of higher gate receipts. But the new stadium was located on federal land and overseen by the National Park Service. Stewart Udall, secretary of the interior under President John F. Kennedy, informed Marshall that the Redskins could play in the stadium only if they followed federal hiring laws. That meant no discrimination.
Marshall was furious. But support for him had eroded within the league. Mara and Bell were dead. Halas and Rooney recognized that their longtime colleague's position was untenable. They encouraged Pete Rozelle to talk to Marshall. To that point, the new commissioner had avoided confronting a league elder over an embarrassing situation, but the NFL had signed a large network television contract and could no longer afford to broadcast the games of a segregated franchise. In the calculus of what finally turned the league against Marshall, it seemed, sadly, that profits and public perception were a larger factor than principle—a prioritization some believe is still in effect today as the league grapples with player protests over civil issues and a questionable record of minority hiring among coaches.
After Rozelle spoke to him, Marshall claimed he was interested in drafting a black player with his top pick later that year. Udall grudgingly allowed the Redskins to play in D.C. Stadium as an all-white team in 1961, provided they agreed to desegregate after the season. They won just one of fourteen games that fall while protestors picketed outside D.C. Stadium on Sundays. Critics in the press and civil rights activists wondered whether Marshall would break his promise, but the Redskins selected Ernie Davis, a black All-American halfback from Syracuse, with the first pick in the 1962 draft. When Davis said he did not want to play for Marshall, the Redskins traded his rights to the Cleveland Browns for Bobby Mitchell, another black halfback. Mitchell and two other black players suited up for the Redskins in 1962.
Long before he lost that battle, Marshall's life had begun to disintegrate. His marriage to Corinne Griffith fell apart. He saw little of his children. He sold a minority interest in the Redskins to Edward Bennett Williams, a powerful Washington lawyer. His friends wondered whether the years of turmoil caused by his stance against integration contributed to his declining health.
Decades later, his name is still invoked for a different, though broadly related, reason. The team name he had selected in 1933—Redskins—has been deemed by many to be racist and offensive to Native Americans. Among the critics are Native American groups. There are calls for the franchise to change its name, as well as many fans who want to keep it in place. The team's current owner, Dan Snyder, sides with the latter group. But as a result of the current controversy, Marshall has received new scrutiny, and his record on race is as embarrassing as ever to the NFL.
In the late 1960s, as Marshall relinquished control of the Redskins, it became clear he would not live much longer. Halas and Rooney traveled to Washington for a final visit. Marshall was now partially paralyzed. "He couldn't take part in the conversation, so we had to talk in front of him. It was very hard," Rooney recalled. "Finally, Halas asked the nurse for a drink and she brought a quart of whiskey."
Rooney, who had given up alcohol several decades earlier, demurred. But Halas, who seldom drank, poured a large glass and guzzled it. "Now he got loose, real loose, talking to Marshall about things that happened in the past," Rooney recalled. "Pretty soon Marshall was laughing and crying. I told Marshall I'd need his wheelchair to get Halas home. Marshall laughed some more. I was real proud of Halas that day."
Despite all the trouble he had caused the league in prior years, and despite his repellent racial views, the NFL gave Marshall a hero's treatment after he died on August 9, 1969. Rozelle, speaking at his funeral, said, "Mr. Marshall was an outspoken foe of the status quo when most were content with it. We are all beneficiaries of what his dynamic personality helped shape over three decades."
It would have been hard for the league to criticize him in death, but not impossible. Yet it chose not to bring up race, the issue that now dominates, and tarnishes, Marshall's legacy. For his part, Marshall had put in his will a proviso for the creation of a charitable foundation in his name, but it came with a caveat: the foundation's funds would not support "the principle of racial integration in any form."
GEORGE HALAS WORE A DARK SUIT WHEN HE ENTERED A CONGRESSIONAL subcommittee room on Capitol Hill in Washington, DC, on December 10, 1981. After taking a seat in front of a panel of politicians, he cleared his throat and began to speak, occasionally looking up through thick glasses. "I am George Halas of the Chicago Bears Football Club," he said. "I was born February 2, 1895, in Chicago. Chicago has been my home for 86 years."
The panel was studying potential antitrust violations in professional sports, specifically whether franchise relocations, which always agitated fans, might rise to that level. Pete Rozelle was scheduled to address the committee and had brought along Halas for support. Halas was more than just a central figure in pro football history. Halas _was_ pro football.
"On September 17, 1920, 12 independent teams met in Canton, Ohio, in Ralph Hay's automobile showroom. Chairs were few. I sat on the running board of a Hupmobile," Halas told the committee. "All agreed we needed a league. In two hours, our league, the American Professional Football Association, was born." In a strong voice belying his age, he proceeded to detail how the league survived. "Our league was then, and still is, best exemplified as a wheel. In 1920, we were 12 independent spokes. But spokes, if they are to serve a useful purpose and make a contribution, must have a rim. A spoke may weaken, even break, but the rim prevents collapse. Our league was and is our rim. The credo of sharing became the foundation of our league. On this foundation, professional football was built. This sharing concept was unprecedented in sport."
He detailed examples of how the NFL's owners had worked together, citing the draft, scheduling, and national television deals. It was a history lesson. Halas had owned and operated the Bears for more than six decades, since the start of the 1920s. He had coached them for forty of those years, winning six championships, most recently in 1963, and had not retired from coaching until he was seventy-two.
"When I started going to Bears games at age five, my brothers and I sat on an army blanket by the bench while our grandfather coached," recalled Patrick McCaskey, one of Halas's grandsons. "We heard a lot of things. One time, he told an official, 'No man is completely worthless. You can always serve as a horrible example.' It's hard to forget that. After the games, we would wait for him outside the locker room, and regardless of how the Bears did, he always reached out to each of us and said, 'Hi, pal, how about a kiss for Grandpa?'"
By the 1970s, Halas had relinquished the job of coaching the Bears and had given up most of his front office responsibilities. Younger men, including his son, directed the affairs of his team and the league. But he continued to have a role. "The business of the league still very much occupied him," Patrick McCaskey explained. "He was on the board of NFL Charities. He was chairman of the Bears. He went to league meetings." McCaskey added, "He didn't talk much about the past. When a Bears fan asked for an autograph, he always complied. He lived the Bears and appreciated any sign that a fan did, too."
Halas had groomed his son, George Jr., to run the Bears. Known to all as Mugs, the younger Halas had many of his father's qualities, according to another of Halas's grandsons. "Mugs was so sharp, so quick, fast on his feet. Both guys were quick thinkers, not just about sports, but about politics, current events, anything," George McCaskey said. Mugs joined the Bears' front office at age twenty-five in 1950 and became the team president in 1963, the same year his father coached the Bears to a title for the last time. Mugs was a fixture in league circles when he suffered a fatal heart attack at age fifty-four on the last day of the 1979 regular season, a traumatic blow for Halas, whose wife, Min, had died thirteen years earlier.
When Halas spoke on Capitol Hill in 1981, he was still shaken about Mugs but, as always, determined to carry on. More than two decades earlier, when Lamar Hunt, the scion of a Texas oil fortune, had sought to buy the Chicago Cardinals, the team's owner, Walter Wolfner, who despised Halas, predicted the demise of his crosstown rival. "Halas is way up there in years. He's liable to pass away anytime soon," Wolfner told Hunt. Wolfner died in 1963. Halas was eighty-six and still in good health when he spoke on Capitol Hill in 1981. He told the committee,
"I have devoted all my energies to professional football. No other business enterprises command my attention. No other professions demand my time. When I returned to civilian life after World War II, I was asked to run for Congress with the guaranteed backing of the _Chicago Tribune._ I declined. I would not and could not walk out on my responsibilities to my profession, my Bears, and our NFL.
"In 60 years, I have watched our ugly duckling of a league grow into a majestic eagle.... The National Football League was not and is not an accident. Our league did and does demand hard work, planning, experimentation, and solid management. It will continue to grow and bring professional football to new communities only if the foundation and principles on which it was built are permitted to survive."
Within a year, Halas would learn he had pancreatic cancer. He died on October 31, 1983. "When he was dying, he had every intention of beating his cancer and getting back to work," Patrick McCaskey recalled. "He was an optimist. America needed optimists during the last century because of the depression and two world wars. His era shaped him. He maintained a great enthusiasm for work. There weren't any problems, only opportunities."
WHEN ART ROONEY WAS HONORED WITH INDUCTION INTO THE Hall of Fame in 1964, it was strictly for his influential role in the NFL's decision-making apparatus for more than three decades. His credentials as a team owner did not merit consideration. The Steelers had played twenty-nine seasons by then, not counting the two years during the war when they merged with other teams. In those twenty-nine years, they had posted just seven winning records. They had never won a division title outright, never played in the league championship game, and stood at fifty-three games under .500 since kicking off in 1933. The lament Rooney had inadvertently invented years earlier—"same old Steelers"—was as apt in the 1960s as it had been in the 1930s.
Still, most people in the game understood that Rooney was fully deserving of his Hall induction. He had provided wise counsel at the owners' table and served as a peacemaker in many disputes, helping the league grow and mature. He was arguably the best example of an owner more concerned about the league than his own team's success. Asked what Rooney contributed to the inner circle that ran the league, Virginia McCaskey, Halas's daughter, replied, "Integrity, certainly. But mostly, he was a wonderful man. My father's relationship with him was very warm. And his warmth benefited the league. Helping people get along. He just wanted to be a good friend to everyone." Upton Bell could also attest to Rooney's generosity, recalling that, "at one point, he was sending cash in an envelope to my father to keep the Eagles afloat."
That was typical, said one of Rooney's five sons, Art Jr. "My dad was the guy who would pay his toll on the highway and also pay the toll of the guy waiting behind him in line. He really liked people," Art Jr. said. "During the season, he would go down to the trainers' room and play cards with the injured players. One time we had a guy who had been out for two years, and when he came back, we cut him. Well, my dad came around to talk to him as he was leaving, asked how he was doing, how his wife and kids were. My dad left and the guy told the trainer, 'I've never seen anything like that. I'm bumming a free ride off him and he remembers my name and my wife's name and my kids' names?'"
When he went into the Hall in 1964, Rooney was portrayed in newspaper coverage of the event as a man who possessed more character than football acumen. The _Pittsburgh Post-Gazette_ said he was "simply a great guy" but also labeled him "a philosopher," defining the term, in a football context, as "an owner who has never won a league pennant." The contrast bothered Rooney, despite how he presented himself to the world. "There is the image of me as the benevolent loser, that even though my teams have never won anything, it doesn't bother me. Well, that's foolishness," he would say later. "I keep a lot to myself, but you'd better believe that I hurt inside every time we lose."
He only spoke from the podium briefly on the day he was inducted, but he sounded an optimistic note, predicting the Steelers' time still might come. Most observers scoffed. The team went 5-9 in 1964 and embarked on a new run of abject failure—eight straight losing seasons, including back-to-back records of 1-13 in 1969 and 2-11-1 in 1970. Rooney's squad had never looked worse. "All those years, he never had a good team. He was always hiring his friends as coaches, and I think his personal liking for players influenced his decisions," Virginia McCaskey said.
But quietly—so quietly no one noticed at first—things began to change in Pittsburgh. Rooney's son Dan was running the team by 1969. Art told him to hire a new coach without taking congeniality into consideration. Dan tapped Chuck Noll, a clever Paul Brown disciple who had been the Baltimore Colts' defensive coordinator. Meanwhile, Art Jr. led a scouting department that produced talented draft picks, including defensive tackle Joe Greene, quarterback Terry Bradshaw, cornerback Mel Blount, linebacker Jack Ham, and running back Franco Harris.
The pieces started coming together in 1972 when the Steelers won a division title, their first ever. Two years later, they won a Super Bowl. Then they won another. Before the 1970s ended, they had won four under Noll.
"After we'd won one or two Super Bowls, George Halas came to me at a league meeting and said he wanted to take me to dinner," Art Jr. recalled. "I said, 'Oh, I'll tell Dad,' and he said, 'No, I don't want your dad, I want to go just with you and [your wife] Kathleen.' We had dinner with him and his family, and when it was over, he said, 'OK, get your chair over here next to me, and Kathleen, get your chair over here, too.' He says, 'You know, you did the greatest personnel job in the history of the National Football League.' Coming from old man Halas, that was big."
When Halas died in 1983, Rooney became the last surviving member of the NFL's old guard, a kindly presence known for his ever-present cigar.
"We'd go to training camp and he'd say, 'I'd like to talk to these kids and I want to use their names,'" Art Jr. recalled. "He was very, very elderly. I would stand with him. A player would be coming off the field. He'd say, 'Who's that?' I'd say, 'John Miller.' He was a redhead and my dad would say, 'Hey Red, come over here. I'm Art Rooney. I own this team. How ya doing? Where ya from?' They'd give an answer and he'd say, 'Oh, yeah, I know that place. You know so and so?' Sometimes they did. He would do that with all of the players."
When Rooney died on August 25, 1988, it was widely reported as "the end of an era." Pro football had become a billion-dollar enterprise whose owners looked to maximize revenue streams, not play cards with the players. It was the fate of any industry that had grown so large and profitable.
Today, the NFL is one of the nation's premier sources of entertainment, having overtaken the other sports, even baseball. The game itself has changed, with players much larger, faster, and stronger than ever before, and with offenses and defenses more inventive every year. The dangers the game entails are newly apparent, too, leading some to question how long football can survive. Mara, Bell, Marshall, Rooney, and Halas would have felt at home debating the ominous subject. For them, survival was always the preeminent question, and they always seemed to find their way, together, to an answer.
# Acknowledgments
THIS BOOK GREW OUT OF A CONVERSATION BETWEEN SCOTT Waxman, my literary agent, and Dan Gerstle, a senior editor at Basic Books. Dan wanted to publish a book about the men who built the NFL. When he asked Scott to recommend an author, my name came up. Having written several books about pro football, I had long regarded the sport's first decades as promising storytelling terrain. A deal was struck. Dan and Scott, many thanks for making it possible for me to dive headlong into such a fascinating subject.
I still work full time as a "daily" sportswriter, as has been the case for nearly four decades. These days, I'm writing columns on the digital channels operated by the Baltimore Ravens of the National Football League. I really appreciate that Michelle Andres, the team's senior vice president for digital media and broadcasting, allows me to juggle my job responsibilities with writing books.
Kevin Byrne, the Ravens' senior vice president for public and community relations, introduced me to his colleagues from several other NFL teams, helping me include important voices in the narrative. The New York Giants' Pat Hanlon set up my interview with John Mara in East Rutherford, New Jersey. The Chicago Bears' Scott Hagel set up my interviews with Virginia McCaskey, George McCaskey, and Patrick McCaskey in Lake Forest, Illinois. The Pittsburgh Steelers' Burt Lauten set up my interview with Dan Rooney in Hershey, Pennsylvania, and told me how to contact Art Rooney Jr. in Pittsburgh. Upton Bell was enthusiastic about the project from the outset and helpful throughout. Dan Gray put me in touch with his father, Mike McGee. I thank them all for their time and effort.
I traveled twice to the Pro Football Hall of Fame in Canton, Ohio, to spend time at the Ralph Wilson Jr. Pro Football Research and Preservation Center. Jon Kendle, the center's archivist, oversaw my visits and directed me to the right research materials, which included newspaper coverage of many of the events depicted in the book. The online archives of the _New York Times, Chicago Tribune,_ and _Washington Post_ were also helpful. My go-to resource for checking any score or statistic was pro-football-reference.com.
As always, I'm most grateful to Mary Wynne Eisenberg, my wife of thirty-four years who, by now, is an expert in her own right at what it takes to write a book. Once again, I love you, MW, and I can't thank you enough for everything.
_—John Eisenberg_
#
**J** **OHN** **E** **ISENBERG** was an award-winning sports columnist for the _Baltimore Sun_ for two decades and is the author of nine previous books. A native Texan and University of Pennsylvania graduate, he also has written for _Sports Illustrated_ and _Smithsonian Magazine._ His columns now appear on the digital channels operated by the Baltimore Ravens of the National Football League.
# Also by John Eisenberg
_The Streak: Lou Gehrig, Cal Ripken Jr., and Baseball's Most Historic Record_
_Ten-Gallon War: The NFL's Cowboys, the AFL's Texans, and the Feud for Dallas's Pro Football Future_
_That First Season: How Vince Lombardi Took the Worst Team in the NFL and Set It on the Path to Glory_
_My Guy Barbaro: A Jockey's Journey Through Love, Triumph, and Heartbreak with America's Favorite Horse_ (written with jockey Edgar Prado)
_The Great Match Race: When North Met South in America's First Sports Spectacle_
_Native Dancer: The Grey Ghost: Hero of a Golden Age_
_From 33rd Street to the Camden Yards: An Oral History of the Baltimore Orioles_
_Cotton Bowl Days: Growing Up with Dallas and the Cowboys in the 1960s_
_The Longest Shot: Lil E. Tee and the Kentucky Derby_
# Praise for _The League_
"Talk about a team of rivals ready to claw each other to death on Sundays and join forces to sell their game from Monday to Saturday, this is it! Halas, Mara, Marshall, Bell, and Rooney—this is their story. It is also the NFL's story. How the men and the league came though the ballyhoo of the 1920s, survived the Great Depression and World War II, and set the stage for football's ascendency as the national game is told by John Eisenberg with humor, heartbreak, and insight. Before the owners were billionaires, they were just a collection of scoundrels who believed in football and money."
—RANDY ROBERTS, coauthor of _A Season in the Sun_
# Note on Sources
THIS BOOK RELIES ON ORIGINAL INTERVIEWS, NEWSPAPER AND magazine articles, web research, primary sources, and previous books on the central figures and the early days of pro football and the NFL. An important primary source, located at the Pro Football Hall of Fame, is a volume containing the official minutes of every league meeting dating back to 1920.
I have not invented conversations; everything that appears within quotation marks is cited, as are numbers that are not commonly in the public record, such as financial profit and loss figures. Football scores, statistics, and attendance figures are not cited, as they are widely available. The central characters in the book are well-known, even legendary, figures, and I have sought to stick to a factual accounting of their lives and actions, as opposed to interpreting their thoughts.
Interviews with Upton Bell, John Mara, George McCaskey, Patrick McCaskey, Virginia McCaskey, Mike McGee, Art Rooney Jr., and Dan Rooney provided invaluable insight. Robert Lyons's Bert Bell biography, _On Any Given Sunday,_ was extremely helpful, as was George Halas's autobiography, _Halas by Halas,_ and _Rooney: A Sporting Life,_ by Rob Ruck, Maggie Jones Patterson, and Michael P. Weber. It would have been impossible for me to accurately depict the NFL's early years without _Joe Carr: The Man Who Built the National Football League,_ by Chris Willis, and the splendid work of Dan Daly, author of _The National Forgotten League_ and coauthor of _The Pro Football Chronicle._
# BIBLIOGRAPHY
Ashby, Steven K., and C. J. Hawkins. _Staley: The Fight for a New American Labor Movement._ Urbana: University of Illinois Press, 2009.
Bell, Upton, with Ron Borges. _Present at the Creation: My Life in the NFL and the Rise of America's Game._ Lincoln: University of Nebraska Press, 2017.
Boswell, Thomas, Richard Justice, Tony Kornheiser, et al. _Redskins: A History of Washington's Team._ Washington, DC: Washington Post Books, 1997.
Coenen, Craig R. _From Sandlots to the Super Bowl: The National Football League._ Knoxville: University of Tennessee Press, 2005.
Cowen, Tyler. _What Price Fame?_ Boston: Harvard University Press, 2000.
Daly, Dan. _The National Forgotten League: Entertaining Stories and Observations from Pro Football's First Fifty Years._ Lincoln: University of Nebraska Press, 2012.
Daly, Dan, and Bob O'Donnell. _The Pro Football Chronicle: The Complete (Well, Almost) Record of the Best Players, the Greatest Photos, the Hardest Hits, the Biggest Scandals and the Funniest Stories in Pro Football._ New York: Collier Books, 1990.
Davis, Jeff. _Papa Bear: The Life and Legacy of George Halas._ New York: McGraw Hill, 2005.
DeVito, Carlo. _Wellington: The Maras, the Giants and the City of New York._ Chicago: Triumph Books, 2006.
Didinger, Ray, and Robert S. Lyons. _The New Eagles Encyclopedia._ Philadelphia: Temple University Press, 2014.
Doxsie, Don. _Iron Man McGinnity: A Baseball Biography._ Jefferson, NC: McFarland, 2009.
Elfin, David. _Washington Redskins: The Complete Illustrated History._ Minneapolis, MN: MVP Books, 2011.
Erghott, Robert. _Mr. Wrigley's Ball Club: Chicago and the Cubs During the Jazz Age._ Lincoln: University of Nebraska Press, 2013.
Freedman, Lew. _The Chicago Bears: The Complete Illustrated History._ Minneapolis, MN: MVP Books, 2008.
Gotterher, Barry. _The Giants of New York: The History of Professional Football's Most Fabulous Dynasty._ New York: G. P. Putnam's Sons, 1963.
Griffith, Corinne. _My Life with the Redskins._ New York: A. S. Barnes, 1947.
Halas, George, with Gwen Morgan and Arthur Veysey. _Halas by Halas: The Autobiography of George Halas._ New York: McGraw-Hill, 1979.
Helyar, John. _Lords of the Realm: The Real History of Baseball._ New York: Villard Books, 1994.
Holley, Joe. _Slingin' Sam: The Life and Times of the Greatest Quarterback Ever to Play the Game._ Austin: University of Texas Press, 2012.
Hudson, Sam. _Philadelphia and Its Public Men._ Philadelphia: Hudson and Joseph, 1909.
Loverro, Thom. _Hail Victory: An Oral History of the Washington Redskins._ Hoboken, NJ: Wiley, 2007.
Lowenfish, Leo. _Branch Rickey: Baseball's Ferocious Gentleman._ Lincoln: University of Nebraska Press, 2007.
Lyons, Robert S. _On Any Given Sunday: A Life of Bert Bell._ Philadelphia: Temple University, 2010.
MacCambridge, Michael. _America's Game: The Epic Story of How Pro Football Captured a Nation._ New York: Random House, 2004.
. _Lamar Hunt: A Life in Sports._ Kansas City, MO: Andrews McMeel, 2012.
Nelson, David M. _The Anatomy of a Game: Football, the Rules, and the Men Who Made the Game._ Newark: University of Delaware Press, 1994.
Oberholtzer, Ellis Paxson. _Philadelphia: A History of the City and Its People; A Record of 225 Years._ Vol. 4. Philadelphia: S. H. Clark, 1912.
O'Toole, Andrew. _Fight for Old DC: George Preston Marshall, the Integration of the Redskins and the Rise of a New NFL._ Lincoln: University of Nebraska Press, 2016.
Page, Joseph S. _Pro Football Championships Before the Super Bowl: A Year-by-Year History._ Jefferson, NC: McFarland, 2010.
Peterson, Robert W. _Pigskin: The Early Years of Pro Football._ New York: Oxford University Press, 1994.
Poole, Gary Andrew. _The Galloping Ghost: Red Grange, an American Football Legend._ Boston: Houghton Mifflin Harcourt, 2008.
Roberts, Randy. _A Team for America: The Army-Navy Game That Rallied a Nation at War._ Boston: Houghton Mifflin Harcourt, 2011.
Rooney, Art, Jr., with Roy McHugh. _Ruanaidh: The Story of Art Rooney and His Clan._ Pittsburgh: Self-published, 2008.
Ross, Charles K. _Outside the Lines: African Americans and the Integration of the National Football League._ New York: New York University Press, 1999.
Ruck, Robert, Maggie Jones Patterson, and Michael P. Weber. _Rooney: A Sporting Life._ Lincoln: University of Nebraska Press, 2010.
Skaler, Robert Morris, and Thomas H. Keels. _Philadelphia's Rittenhouse Square._ Charleston, SC: Arcadia, 2008.
Smith, Thomas G. _Showdown: JFK and the Integration of the National Football League._ Boston: Beacon Press, 2011.
Snider, Rick. _100 Things Redskins Fans Should Know and Do Before They Die._ Chicago: Triumph Books, 2014.
Tindall, George Brown, and David E. Shi. _America: A Narrative History._ Vol. 2. New York: W. W. Norton, 2012.
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Willis, Chris. _Joe F. Carr: The Man Who Built the National Football League._ Lanham, MD: Scarecrow Press, 2010.
# NOTES
**PROLOGUE**
**"words of congratulation":** Chris Willis, _Joe F. Carr: The Man Who Built the National Football League_ (Lanham, MD: Scarecrow Press, 2010), 335.
**it marked the first time Marshall, Halas, Bell, Rooney, and Tim Mara were together in the same room:** Official minutes, Pro Football Hall of Fame, Canton, Ohio.
**"They fought with each other":** Author interview with Upton Bell.
**"The credo of sharing":** George Halas speech to Congress on December 10, 1981, transcript at NFL.com ( _Commissioner Paul Tagliabue NFL Report,_ Winter 1999), www.nfl.info/nflmedia/news/PT_NFLReport Articles/Winter%201999.htm.
**"They were on their own":** Author interview with Upton Bell.
**CHAPTER 1: HALAS: THE FOUNDER**
**"stresses and strains":** George Halas, with Gwen Morgan and Arthur Veysey, _Halas by Halas: The Autobiography of George Halas_ (New York: McGraw-Hill, 1979), 50.
**"a very determined man":** Halas, _Halas by Halas,_ 53.
**competed in an industrial league:** Don Doxsie, _Iron Man McGinnity: A Baseball Biography_ (Jefferson, NC: McFarland, 2009), 153–155.
**"You're the expert":** Halas, _Halas by Halas,_ 54–55.
**"tired of constant wars":** Josefa Humpal Zeman, _The Bohemian People of Chicago,_ http://media.pfeiffer.edu/lridener/DSS/Addams/hh6.html.
**"One would find men of education":** Zeman, _Bohemian People of Chicago._
**"quite suddenly":** Halas, _Halas by Halas,_ 24.
**"Just when I teach you fellows how to play football":** Ibid., 35.
**"govern the rest of my life":** Ibid.
**"I ached for the excitement of a good game":** Ibid., 50.
**"The season deepened my love for football":** Ibid., 52.
**scale-house clerk:** Steven K. Ashby and C. J. Hawkins, _Staley: The Fight for a New American Labor Movement_ (Urbana: University of Illinois Press, 2009), 8.
**"I assured the men":** Ashby and Hawkins, _Staley,_ 8
**"I believe in rough games":** Christopher Klein, "How Teddy Roosevelt Saved Football," September 6, 2012, www.history.com/news/how-teddy-roosevelt-saved-football.
**"indifferent and vague":** Halas, _Halas by Halas,_ 60.
**"Chairs were few":** Ibid.
**"I sat on a runningboard":** Ibid.
**"meanest, toughest player alive":** George Trafton biography, www.profootballhof.com/players/george-trafton/biography/.
**Halas wanted to win so badly that he signed Paddy Driscoll:** Jeff Davis, _Papa Bear: The Life and Legacy of George Halas_ (New York: McGraw Hill, 2005), 61.
**"confirmed my belief":** Halas, _Halas by Halas,_ 66.
**"There were a lot of pioneers, but Joe Carr was the one":** __Author interview with Dan Rooney.
**"seethed about that 'lost title'":** Davis, _Papa Bear,_ 62.
**suspended by the league when Carr discovered they were also playing for a nonleague team in Philadelphia:** Dan Daly and Bob O'Donnell, _The Pro Football Chronicle: The Complete (Well, Almost) Record of the Best Players, the Greatest Photos, the Hardest Hits, the Biggest Scandals and the Funniest Stories in Pro Football_ (New York: Collier Books, 1990), 10–11.
**"robs the great American game":** Yost speech transcript, _Michigan Alumnus_ 28 (1922): 471.
**"College athletes have something to fight for":** "The Inquiring Reporter," _Chicago Tribune_ , October 29, 1922.
**Stagg... advocated taking away the varsity letters of college players who eventually turned pro:** Daly and O'Donnell, _Pro Football Chronicle,_ 15.
**"Under the guise of fair play":** Ibid.
**"Professional football will never replace college football":** Ibid., 40.
**he sold enough tickets to turn a $21,600 profit:** Ibid., 14.
**"I lacked enthusiasm":** Halas, _Halas by Halas,_ 91.
**"Football players are bigger than baseball players":** Ibid., 76.
**"In truth,... the Bears lived hand-to-mouth":** Ibid., 89.
**CHAPTER 2: MARA: THE PROMOTER**
**"He was one of those people":** Author interview with John Mara.
**"live best and work the least":** Carlo DeVito, _Wellington: The Maras, the Giants and the City of New York_ (Chicago: Triumph Books, 2006), 6.
**"He didn't have a lot of education":** Author interview with John Mara.
**"Little can be said":** "The New York Giants Before They Were Giants," January 10, 2012, http://www.boweryboyshistory.com/?s=The+Giants +Before+They+Were+Giants.
**"Doc March was looking for an angel":** Dan Daly, _National Forgotten League: Entertaining Stories and Observations from Pro Football's First Fifty Years_ (Lincoln: University of Nebraska Press, 2012), 56.
**"I never passed up the chance to promote anything":** Willis, _Joe F. Carr,_ 185.
**"I'm not sure you can still live the kind of life he did":** Author interview with John Mara.
**"He knew about boxing and horse racing":** Ibid.
**"Say, maybe you'd be interested in this, Tim":** Barry Gotterher, _The Giants of New York: The History of Professional Football's Most Fabulous Dynasty_ (New York: G. P. Putnam's Sons, 1963), 25–26.
**"Now what do I do?":** Gotterher, _Giants of New York,_ 26.
**"He just thought, 'I'm a promoter'":** Author interview with John Mara.
**"The Giants were born out of a combination of brute strength and ignorance":** Willis, _Joe F. Carr,_ 186.
**"Well, I'm going to see if I can put pro football over in New York":** DeVito, _Wellington_ , 19–20.
**"Isn't that the greatest run you've ever seen?":** Gotterher, _Giants of New York,_ 29.
**"He made that switch":** Author interview with John Mara.
**"Pro Elevens Clash Before 27,000 Here":** Alison Danzig, _New York Times_ , October 19, 1925.
**"a far cry":** Danzig, "Pro Elevens Clash Before 27,000 Here."
**"New York evidently is ready":** Ibid.
**"Pro football will never amount to anything":** Willis, _Joe F. Carr,_ 200.
**"run me right out of the house":** Ibid.
**Partially successful STOP:** DeVito, _Wellington,_ 22.
**"Grange will play in the Giants-Bears game":** __Gotterher, _Giants of New York,_ 34.
**"there was almost a riot":** Gotterher, _Giants of New York,_ 34.
**added up to $143,000:** Ibid., 37.
**"I was about ready to toss in my hand until Grange turned pro":** Ibid., 38.
**played seventeen games before slightly fewer than 300,000 spectators:** Daly and O'Donnell, _Pro Football Chronicle,_ 24.
**He and Grange netted some $250,000:** Willis, _Joe F. Carr,_ 209.
**"I have the biggest star in football":** Ibid., 215.
**"No blasted Irishman":** Ibid., 213.
**"I didn't make enough money last year to stuff a hat brim":** Ibid., 215.
**"Oh, it's a great game":** Ibid.
**"There's no one over there, either!":** Ibid., 225.
**Pyle and the Yankees lost $100,000.... Mara lost $40,000:** DeVito, _Wellington_ , 34.
**"It was a challenge just to stay afloat":** Author interview with John Mara.
**CHAPTER 3: MARSHALL: THE SHOWMAN**
**blue and gold:** Thomas G. Smith, _Showdown: JFK and the Integration of the National Football League_ (Boston: Beacon Press, 2011), 3.
**the first man able to palm a basketball:** Betty Hoover DiRisio, "Horse Gillum: Giant of a Man," by Lawrence County (Pennsylvania) Historical Society website, May 16, 2014, www.lawrencechs.com/horse-gillium-giant-of-a-man/.
**Meyer Davis Palace Five Orchestra:** "Champion Celtic Basketball Teams Are Strengthened," _Washington Post,_ November 29, 1925.
**"a big business requiring more of my personal attention":** "Capital Team Quits Basketball," _Washington Post,_ January 3, 1928.
**"I went to a few games":** Author interview with Virginia McCaskey.
**"fine Jacksonville hare":** George Preston Marshall, "Pro Football Is Better Football," _Saturday Evening Post,_ November 19, 1938.
**"I've been guilty of promotional ideas":** Marshall, "Pro Football Is Better Football."
**descended from Confederate officers:** Joe Holley, _Slingin' Sam: The Life and Times of the Greatest Quarterback Ever to Play the Game_ (Austin: University of Texas Press, 2012), 60.
**"making as much as twenty-five dollars per contest:** Marshall, "Pro Football Is Better Football."
**He liked to call himself the Magnificent Marshall:** Holley, _Slingin' Sam,_ 61.
**"I persisted in the conviction that I was a budding Barrymore":** Marshall, "Pro Football Is Better Football."
**"My playing days were over":** Ibid.
**"considered it a lost opportunity were he not the center of attention":** Smith, _Showdown,_ 3.
**"is not always offensive":** Ibid., 3.
**"more time for baseball, football, and basketball":** Marshall, "Pro Football Is Better Football."
**"thrilling" contest:** Ibid.
**"Why can't we have a football team":** Ibid.
**"My worst nature got the best of me":** Ibid.
**CHAPTER 4: BELL: THE PROFLIGATE SON**
**richest 10 percent... owned 75 percent:** George Brown Tindall and David E. Shi, _America: A Narrative History,_ vol. 2 (New York: W. W. Norton, 2012), 589.
**"home to more millionaires per square foot":** Robert Morris Skaler and Thomas H. Keels, _Philadelphia's Rittenhouse Square_ (Charleston, SC: Arcadia, 2008), 7.
**he married Fleurette at her family's mansion:** Robert S. Lyons, _On Any Given Sunday: A Life of Bert Bell_ (Philadelphia: Temple University, 2010), 2.
**a lawyer and Civil War veteran who had been a Republican Congressman and close confidant of two presidents:** Lyons, _On Any Given Sunday,_ 2.
**De Benneville eventually renounced the privileged life of an aristocrat:** Nelson Simonson and John Morgan, _George De Benneville, Universalist mystic,_ http://archive.uuworld.org/2003/03/lookingback.html.
**"one of the interesting weddings of the week":** _Times of Philadelphia,_ December 14, 1890.
**"yielded to the persistent demand":** Ellis Paxson Oberholzer, _Philadelphia: A History of the City and Its People; A Record of 225 Years,_ vol. 4 (Philadelphia: S. H. Clark, 1912), 376.
**"brilliant" and "leading chemists of the world":** Oberholzer, _Philadelphia,_ 376.
**"by a very nattering majority":** Ibid.
**"followed faithfully the traditions of the office":** Ibid.
**"position is evident to all":** Ibid.
**"amid such turn of the century wealth":** Lyons, _On Any Given Sunday,_ 1.
**"had a nanny when he was 2":** Ibid.
**"For a fellow like me":** Ibid., 4.
**"wanted to follow in his father's footsteps":** John Cromwell Bell Jr. biography, Pennsylvania Historical and Museum Commission, www.phmc.state.pa.us/portal/communities/governors/1876-1951/john-bell.html.
**"If you don't think I had to fight many times":** Lyons, _On Any Given Sunday,_ 1.
**"hero of countless football, baseball, and basketball battles":** Ibid., 4.
**"one of the best athletes in the history of the school":** Ibid., 4.
**"most sarcastic" and "best kidder":** Ibid., 52.
**"Although he came from a proper conservative Republican family":** Ibid., 1.
**"He'll go to Penn or he'll go to hell!":** Ibid., 3.
**"never came to class if the weather was bad outside":** Ibid., 20–21.
**"peppery little guy":** Ibid., 8.
**"great field general":** Ibid., 10.
62 " **piloted the team in masterful fashion":** Ibid., 6.
**"faultless":** Ibid., 9.
**"used such a varied selection of plays":** Ibid., 11.
**The unit received commendations:** Ibid., 12–14.
**"almost never talked about his war experience":** Author interview with Upton Bell.
**"'Penn seems destined to take the leading position":** Lyons, _On Any Given Sunday,_ 16.
**"squarely":** Ibid., 18–19.
**"My father and mother gave me everything I ever asked for":** W. C. Heinz, "Boss of the Behemoths," _Saturday Evening Post,_ December 3, 1955.
**wagered his Marmon roadster:** Lyons, _On Any Given Sunday,_ 19.
**"all the money I had and could borrow":** Ibid.
**"despite their philosophical differences, Bert was my grandfather's favorite child":** Ibid., 31.
**"reportedly dropped $50,000":** Ibid., 30.
**"Dammit, you're thirty-something":** Ibid.
**"reluctantly":** Ibid.
**"And I ain't marrying that broad":** Ibid.
**"Well, Bert":** Ibid., 30–31.
**even suited up for one AFL game:** Ibid., 45.
**turned Marshall down after consulting with Bell:** Willis, _Joe F. Carr,_ 284.
**The group paid a $2,500 guarantee to the NFL and assumed $11,000 in debts:** Lyons, _On Any Given Sunday,_ 47.
**CHAPTER 5: ROONEY: THE GAMBLER**
**"clanging, smoke-belching metropolis":** Robert Ruck, Maggie Jones Patterson, and Michael Weber, _Rooney: A Sporting Life_ (Lincoln: University of Nebraska Press, 2010), 6.
**snow on their blankets:** Art Rooney Jr., with Roy McHugh, _Ruanaidh: The Story of Art Rooney and His Clan_ (Pittsburgh: Self-published, 2008), 5.
**had no idea he was breaking the law:** Rooney Jr., _Ruanaidh,_ 9.
**spent an entire day at church praying for her:** Ibid., 6.
**"Boy, could they punch":** Ibid., 5.
**he defeated a lightweight who later won the gold medal:** __Ibid., 7.
**"wiggling, squirming, and serpentine runs":** Ibid., 12.
**"head and shoulders above his companions":** Ibid.
**Penn State offered him a cut of the proceeds:** Ibid., 13.
**played simultaneously for Indiana Normal... and Duquesne:** Ibid., 13–14.
**"the Red Grange of the independents":** Ibid., 32.
**"How much money do you make?":** Ibid., 12–13.
**"born to play the horses":** Ibid., 37.
**"I can make more money at the racetrack":** Ibid., 25.
**His co-owner was a notorious card shark:** Ibid., 22.
**bootleggers and ward heelers:** Ruck, Patterson, and Weber, _Rooney,_ xiii.
**"was no angel," "uncorroborated hearsay," and "scant evidence indicating that he was more than peripherally engaged":** Ibid.
**"every racetrack from here to Tijuana":** Ibid., 83.
**"He answers the phone":** Author interview with Art Rooney Jr.
**CHAPTER 6: ALMOST BROKE**
**"We couldn't pay our guarantee":** Halas, _Halas by Halas,_ 132.
**"The split hurt the team":** Ibid.
**"I think Pete Rozelle was the first commissioner he didn't control":** Author interview with George McCaskey.
**his modest proceeds from program sales were all that had kept the team in the black:** Halas, _Halas by Halas,_ 132.
**"He would try anything, whatever came along":** Author interview with Virginia McCaskey.
**"who never let him forget it":** Ibid.
**"I was probably ten or eleven":** Ibid.
**"The time had come for Dutch and me to stop coaching":** Halas, _Halas by Halas,_ 136.
**"astonished":** Ibid.
**"I believed him":** Ibid.
**"We had a drawer full of bills and we were overdrawn at the bank":** Ibid., 147.
**"a colorful crowd of nearly 60,000":** "Twenty Grand and the Kentucky Derby, 1931," April 20, 2010, http://colinsghost.org/2010/04/twenty-grand-and-the-kentucky-derby-1931.html.
**"raised $5,000 from a bank that was already closed":** Halas, _Halas by Halas,_ 147.
**"I called everyone I knew":** Ibid., 148.
**"He had a good partner":** Author interview with Virginia McCaskey.
**"If I get my price":** Halas, _Halas by Halas,_ 150.
**"one of the old-fashioned brawls":** Wilfrid Smith, "Packers Whip Bears, 2–0," _Chicago Tribune_ , October 17, 1932.
**"the elephants had been there":** Author interview with Virginia McCaskey.
**"It was all a bit puzzling at times":** Ibid.
**"some of the greatest players in history":** Author interview with George McCaskey.
**CHAPTER 7: NEW IDEAS**
**Buffalo, Milwaukee, Pittsburgh, St. Louis, San Francisco, and Baltimore all were larger:** From https://www.biggestuscities.com/1930.
**Tim Mara presented a motion. Halas seconded it:** Official minutes, Hall of Fame.
**"lost by a roll call vote":** Ibid.
**"I realize you men know your football inside and out":** Ibid.
**"Gentlemen, it's about time we realized we're not only in the football business":** Willis, _Joe F. Carr,_ 302.
**"Nagurski will pass from anywhere so why not make it legal?":** Joseph S. Page, _Pro Football Championships Before the Super Bowl: A Year-by-Year History_ (Jefferson, NC: McFarland, 2010), 21.
**"In every sport but football":** Daly and O'Donnell, _Pro Football Chronicle,_ 9.
**"We think we have overcome the balance previously held by the defense":** Ibid., 8–9.
**"Marshall was way ahead of everybody":** David Elfin, _Washington Redskins: The Complete Illustrated History_ (Minneapolis, MN: MVP Books, 2011), 14.
**the operation was $46,000 in the red:** Willis, _Joe F. Carr,_ 299.
**"The fact that we have in our head coach, Lone Star Dietz, an Indian":** Travis Waldron, "The 81-Year-Old Newspaper Article That Destroys the Redskins' Justification for Their Name," May 30, 2014, https://think progress.org/the-81-year-old-newspaper-article-that-destroys-the-redskins-justification-for-their-name-e76bf65b3985/.
**He just wanted to avoid any confusion with baseball's Braves:** Waldron, "The 81-Year-Old Newspaper Article That Destroys the Redskins' Justification for Their Name."
**Lillard joined the Cardinals in 1932:** Charles K. Ross, _Outside the Lines: African Americans and the Integration of the National Football League_ (New York: New York University Press, 1999), 39–45.
**"Negro Star of the Chicago Eleven Thrills 18,000 by Dazzling Runs as Cardinals Down Boston"** Ross, _Outside the Lines,_ 40.
**"Great player, elusive as all outdoors":** Daly, _National Forgotten League,_ 100.
**"We've got to get that damn nigger the hell out of there:"** Ibid.
**"I was mad, naturally":** Ibid., 100–101.
**"He said, 'There's no reason this should be happening'":** Ibid., 101.
**"It was my understanding that there was a gentleman's agreement":** Smith, _Showdown,_ 28.
**"For myself and most of the owners":** Ross, _Outside the Lines,_ 40.
**"in no way, shape, or form":** Ibid.
**many historians trace to the influence of Marshall:** Ibid., 50.
**CHAPTER 8: BENNY AND THE GIANTS**
**$40,000 debt:** Gotterher, _Giants of New York,_ 64.
**"We need Friedman":** DeVito, _Wellington,_ 49.
**"the time to pass is on first or second down":** Gotterher, _Giants of New York,_ 65.
**"Polo Grounds Crowd Watches Brilliant Aerial Display":** _New York Times,_ October 21, 1929.
**"most enthusiastic professional crowd of the year":** Arthur Daley, "Green Bay Blasts Giants Title Hopes," _New York Times,_ November 25, 1929.
**more than $20,000 ahead:** Gotterher, _Giants of New York,_ 78.
**"See the Four Horseman Ride Together Again":** Ibid., 79.
**"Take it easy on us":** Ibid., 81.
**Friedman left his apartment in Brooklyn early in the morning:** Ibid., 72.
**"I've got to build for the future":** Harold F. Parrott, "Benny Friedman Plans to Quit Pro Football for Chance to Coach," _Brooklyn Daily Eagle,_ February 13, 1931.
**$35,000 profit:** Gotterher, _Giants of New York,_ 91.
**"I'm sorry, Benny, but this is a family business":** Ibid., 92.
**"My timing was off":** Daly and O'Donnell, _Pro Football Chronicle,_ 40.
**"probably the most spectacular game of the year" and "brilliant display of offensive firepower":** "Bears Cop Pro Gridiron Title by 23–21 score," Associated Press, December 18, 1933.
**"It was a game worthy of its surroundings":** Arthur Daley, "55,000 See Chicago Bears Down Giants on Last-Minute Field Goal," _New York Times,_ November 19, 1934.
**"I know it doesn't look good":** Gotterher, _Giants of New York,_ 115.
**"It was a freakish way to lose":** Halas, _Halas by Halas,_ 180.
**"Enthusiasm turned to delirium":** Wilfrid Smith, "Giants Whip Bears for Pro Title, 30–13," _Chicago Tribune,_ December 10, 1934.
**CHAPTER 9: INSTITUTING A DRAFT**
**"They had maids and butlers":** Upton Bell, with Ron Borges, _Present at the Creation: My Life in the NFL and the Rise of America's Game_ (Lincoln: University of Nebraska Press, 2017), 23.
**"he was a man about town":** Bell, _Present at the Creation,_ 21.
**"She was the only person who could ever say no":** Ibid.
**demanded that Bell give up drinking:** Lyons, _On Any Given Sunday,_ 37.
**his future wife loaned him the necessary money:** Ibid., 47.
**a free car wash:** Ray Didinger and Robert S. Lyons, _The New Eagles Encyclopedia_ (Philadelphia: Temple University Press, 2014), 200.
**"I asked him point blank if he would sign with the Eagles":** "Back's Refusal to Sign Led to Grid Draft," Associated Press, January 30, 1957.
**"I knew what was in his mind":** "Back's Refusal to Sign Led to Grid Draft."
**"Finally, Curly sent me a contract and I just went ahead and signed it":** Richard Whittingham, _What a Game They Played: An Inside Look at the Golden Era of Pro Football_ (Lincoln, NE: Bison Books, 2002), 121–122.
**"I told Kelly I couldn't do that because I had already signed with Curly":** Whittingham, _What a Game They Played,_ 122.
**Lambeau's had been posted seventeen minutes earlier:** Willis, _Joe F. Carr,_ 339.
**"Something has to be done":** Ibid., 338.
**"I thought the proposal sound":** Ibid., 343.
**"was a hazard we had to accept for the benefit of the league":** DeVito, _Wellington,_ 84.
**"Gentlemen, I've always had the theory that pro football is like a chain":** Lyons, _On Any Given Sunday,_ 57.
**"Bert was a very persuasive man":** Art Rooney, "I Remember Bert Bell," game program, Kansas City Chiefs vs. New York Jets, September 29, 1975, Pro Football Hall of Fame.
**clergymen of varying faiths:** Lyons, _On Any Given Sunday,_ 55.
**Edwin "Alabama" Pitts:** Ibid., 53–54.
**"Bert, the only thing you haven't done is hire a good football team":** Ibid., 55.
**On February 8, 1936, the owners gathered:** Official minutes, Hall of Fame.
**"There were plenty of cigars, and the liquor flowed":** Frank Fitzpatrick, "First NFL Draft, Held at Philly's Ritz-Carlton, Went Unnoticed," _Philadelphia Inquirer,_ April 8, 2017.
**"new ruling":** "Chicago Bears Get First Call on Berwanger," _Chicago Tribune,_ February 10, 1936.
**Only twenty-four of the eighty-one players selected in 1936 suited up for a game that season:** Willis, _Joe F. Carr,_ 351.
**"I haven't decided what I will do":** Ken Crippen, "The First NFL Draft," _National Football Post,_ April 20, 2014.
**"He asked me what I wanted":** Frank Litsky, "Jay Berwanger, 88, Winner of the First Heisman Trophy," _New York Times,_ June 28, 2002.
**he founded a company that made plastic and sponge-rubber strips:** "Jay Berwanger, 88, Winner of the First Heisman Trophy."
**John McCauley, the second pick, took a job with a tool company:** Rice Athletic Hall of Fame program, presentation of awards, November 21, 1970, http://grfx.cstv.com/photos/schools/rice/genrel/auto_pdf/2011-12 /misc_non_event/FirstHOF.pdf.
**Bill Wallace... also went into business:** Ibid.
**Harry Shuford... went to law school:** Obituary, _Dallas Morning News,_ May 17, 2007.
**Al Barabas... chose minor league baseball:** Hall of Fame series, go columbialions.com, July 22, 2014, www.gocolumbialions.com/ViewArticle.dbml?ATCLID=209600296.
**John "Jac" Weller... opened a real estate and insurance business:** Biography, National Football Foundation website, www.footballfoundation.org/Programs/CollegeFootballHallofFame/SearchDetail.aspx?id=30066.
**Pepper Constable... went to Harvard Medical School:** "Dr. W. Pepper Constable, 72, Ex-official of Jersey Hospital," _New York Times,_ August 17, 1986.
**Shakespeare, the third overall pick, opted to work for the Thor Power Tool Company in Aurora, Illinois:** "Bill Shakespeare, Star Halfback at Notre Dame in 1930s, Dies," _New York Times,_ January 19, 1974.
**CHAPTER 10: BETTING BONANZA**
**Harp Vaughan and Warren Heller were two of Rooney's old friends from the Northside. Cap Oehler had worked in the coal mines. Dave Ribble carried a Teamsters card:** Ruck, Patterson, and Weber, _Rooney,_ 104.
**The quintessential early Pirate was Mose Kelsch:** Ibid., 111.
**The argument escalated until Rooney suggested they settle it with their fists:** Ibid., 106.
**drew an average of 12,489 fans per game:** Ibid., 113.
**"In those days, nobody got wealthy in sports":** Ibid.
**Bach was so incensed that he and Rooney came to blows:** Ibid., 116.
**"Halas, mistrustful by nature, may have been testing this younger man":** Ibid., 114.
**"George, you were no sure thing to win that fight":** Ibid.
**"Aside from Halas, Marshall, Curly Lambeau and Mara, I guess I, like most of the other owners, didn't pay enough attention to football":** Pat Livingston, "Long Wait Sweetens Rooney Victory," _Sporting News,_ January 6, 1973.
**"three or four":** Red Smith, "Rooney Recalls Day at the Races," _New York Times,_ April 13, 1972.
**between $19,000 and $25,000:** Ruck, Patterson, and Weber, _Rooney,_ 119.
**"Stick that dough in your kick":** Ibid.
**"What's your next move, Artie?":** Ibid.
**close to $100,000:** Ibid., 123.
**"It's Art but They Don't Like It":** Ibid.
**Mara estimated it was between $250,000 and $380,000:** DeVito, _Wellington,_ 88.
**"When George gives up the broads, I'll give up gambling":** Ruck, Patterson, and Weber, _Rooney,_ 124.
**CHAPTER 11: MOVE TO DC**
**singing about slaves in the Old South and serving mint juleps:** Smith, _Showdown,_ 19.
**a Confederate flag that had been in his family since the Civil War:** Dan Daly, "The Man Who Gave the Redskins Their Name," _Washington Times,_ September 6, 2001.
**"There were times on game day when the papers played the Radcliffe girls' field hockey team above our game":** Thomas Boswell, Richard Justice, Tony Kornheiser, et al., _Redskins: A History of Washington's Team_ (Washington: Washington Post Books, 1997), 20.
**"The nice thing about owning a pro football team is that all you have to do to move is pack your trunks":** Daly and O'Donnell, _Pro Football Chronicle,_ 70.
**"Bothered? I hope George Preston Marshall is in good voice":** Gotterher, _Giants of New York,_ 145.
**"george, stop / guess what, stop":** Holley, _Slingin' Sam,_ 77.
**"We'll get a much bigger gate in New York":** Thom Loverro, _Hail Victory: An Oral History of the Washington Redskins_ (Hoboken, NJ: Wiley, 2007) 14.
**"Marshall Moves Boston Redskins to District":** _Washington Post,_ December 17, 1936.
**Washington would grow from 486,000 residents in 1930 to 663,000 by the end of the decade:** Smith, _Showdown,_ 43.
**"What size do you wear?":** Holley, _Slingin' Sam,_ 98.
**"They're not for me, son":** Ibid.
**"My feet hurt":** Ibid., 99.
**"Which eye?":** Ibid., 111.
**Barnee Breeskin, leader of the hotel's orchestra, was on the line:** Corinne Griffith, _My Life with the Redskins_ (New York: A. S. Barnes, 1947), 37.
**Marshall was initially unenthusiastic:** Griffith, _My Life with the Redskins,_ 37.
**Griffith had the opposite reaction and quickly penned lyrics:** Ibid., 39.
146 " **Braves on the warpath":** Ibid.
**a brass ensemble composed of milk deliverymen from the Chestnut Farms Dairy:** 1948 Redskins media guide.
**"Mark me, there will be a new record for football crowds in Washington":** Shirley Povich, "Marshall Sees Team as Civic Unifier," _Washington Post,_ November 19 1937.
**"envisions the Green Bay crowd as the last convincing argument to fling into the teeth of the doubters":** Povich, "Marshall Sees Team as Civic Unifier."
**"sweep the Giants aside like rubbish":** Smith, _Showdown,_ 51.
**"The invading Washington rooters were much in evidence on the Eighth Avenue subway":** John Kieran, "The Massacre at Coogan's Bluff," _New York Times,_ December 6, 1937.
**"new costumes of burgundy and gold, with white feather head-dresses, imported straight from Hollywood":** Griffith, _My Life with the Redskins,_ 60.
**"They were simply full of loyalty and red feathers and other things":** Ibid., 61.
**"George Preston Marshall slipped unobtrusively into town today at the head of a 150-piece band and 10,000 fans":** Ibid.
**"paraded in a wild demonstration":** Shirley Povich, "DC Redskins Smear Giants, 49–14, to Win Eastern Title," _Washington Post,_ December 6, 1937.
**"in a frenzy":** Arthur Daley, "58,285 See Redskins Keep Eastern Title by Routing Giants at Polo Grounds," _New York Times,_ December 6, 1937.
**"hauled out their tomahawks":** Daley, "58,285 See Redskins Keep Eastern Title by Routing Giants at Polo Grounds."
**"gargantuan form" and "in a flash":** Ibid.
**"There is not a superlative":** Ibid.
**"joyously stampeded onto the field":** Povich, "DC Redskins Smear Giants, 49–14, to Win Eastern Title."
**The Redskins' season ticket total would soar from 958 in 1937 to 10,951 in 1940 and 31,444 by 1947:** Jack Walsh, "Marshall Made Redskins a Way of Life," _Washington Post,_ August 10, 1969.
**CHAPTER 12: BROTHERHOOD OF RIVALS**
**"That man Halas is positively revolting!":** Griffith, _My Life with the Redskins,_ 74.
**"Don't you dare say anything against Halas!":** Ibid.
**"They were the most unique set of men in American sports history":** Author interview with Upton Bell.
**"drawn together" and "love at first sight":** Griffith, _My Life with the Redskins,_ 71.
**"The owners with the staying power were the ones who came away with the decent schedules":** Michael MacCambridge, _America's Game: The Epic Story of How Pro Football Captured a Nation_ (New York: Random House, 2004), 39.
**two in the morning:** Official minutes, Hall of Fame.
**"It is absolutely vital to us":** Ibid.
**"I don't think there is a member here who would think it unreasonable":** Ibid.
**"I don't think that is a legal form of procedure":** Ibid.
**"get redder and redder":** DeVito, _Wellington,_ 93.
**"There is no use putting to a vote something that is not right":** Official minutes, Hall of Fame.
**"I didn't say I think there should be a vote on it":** Ibid.
**"I don't see any reason why he should have six games at home and the Chicago Bears only have four":** Ibid.
**"The motion is lost":** Ibid.
**a guaranteed $40,000 payout every year:** Ibid.
**"I move that the president be directed to thank Mr. Runyon for his kind offer":** Ibid.
**an average of 35,717 fans:** Willis, _Joe F. Carr,_ 363.
**"You gentlemen will destroy me":** Halas, _Halas by Halas,_ 156.
**"was bitterly opposed":** DeVito, _Wellington,_ 83–84.
**"An official went to retrieve a punt that had gone out of bounds":** Ibid., 172.
**Like Halas, Ray had played football for the Illini:** Seymour Smith, "Pro Football to Honor Ray," _Baltimore Sun,_ September 14, 1966.
**The other owners agreed to the proposal:** Jimmy Jordan, "Hugh Ray and His Stopwatch Have Done Much for Football," Associated Press, September 9, 1945.
**"He pounded the rules into his officials":** Seymour Smith, "Pro Football to Honor Ray," _Baltimore Sun,_ September 14, 1966.
**"my great contribution to the National Football League":** "Officials, Not Rams, Beat Us Sunday," _Chicago Tribune,_ November 3, 1949.
**CHAPTER 13: A STEP FORWARD**
**"When I got there, he thought I was a kid who wanted his autograph":** DeVito, _Wellington,_ 85.
**"but I was able to convince him that I was in fact a legitimate emissary":** Ibid.
**"The thinking was":** Author interview with Upton Bell.
**"It was a pretty remarkable thing":** Author interview with Virginia McCaskey.
**"I didn't think I had to put every name on that list":** DeVito, _Wellington,_ 95–96.
**"They would gather for league meetings":** Author interview with Virginia McCaskey.
**"The band had seen enough":** John Kieran, "The Rout of the Redskins," _New York Times,_ December 5, 1938.
**"A great game":** Gotterher, _Giants of New York,_ 163.
**"Eddie, we don't need a band":** Ibid.
**"absolutely ferocious" and "No such blocking and tackling":** Arthur Daley, "Record Play-Off Throng Sees Giants Halt Packers at Polo Grounds," _New York Times,_ December 12, 1938.
**"a contusion of the brain":** Daley, "Record Play-Off Throng Sees Giants Halt Packers at Polo Grounds."
**"This was the gridiron sport at its primitive best":** Arthur Daley, "The Good Old Days" _New York Times,_ December 12, 1937.
**$200,000 profit:** Gotterher, _Giants of New York,_ 166.
**CHAPTER 14: THE GREATEST ROUT**
**"I was about the same age as their daughter":** Author interview with Virginia McCaskey.
**"No one asked for his autograph":** Ibid.
**The number of radios in use in America rose from 60,000 in 1922 to 3 million in 1924 to 16.6 million by 1932:** George Will, _A Nice Little Place on the North Side: Wrigley Field at 100_ (New York: Crown, 2014), 47.
**The number of radio stations also rapidly grew, from 382 in 1922 to 681 in 1927:** Will, _Nice Little Place on the North Side,_ 47.
**Eleven of the sixteen major league owners were skeptical enough to consider banning all radio game broadcasts:** Paul Dickson, "How Radio Gave Baseball Its Voice," February 26, 2016, thenationalpastimemuseum.com.
**he allowed WMAQ, a major Chicago station, to broadcast the Cubs' home games:** Dickson, "How Radio Gave Baseball Its Voice."
**The Cubs' gate rose 140 percent between 1925 and 1929:** Will, _Nice Little Place on the North Side,_ 49.
**"Don't stop it":** Ibid., 48.
**"He loved them":** Author interview with Virginia McCaskey.
**"It wasn't a big deal to them":** Ibid.
**WGN agreed to broadcast the home games of the Bears:** Phil Rosenthal, "Are the Bears Poised to Change Radio Stations?," _Chicago Tribune,_ August 25, 2017.
**Halas made sure the broadcasts were promoted:** "Green Bay–Bears Game on WGN at 1:58 Today," _Chicago Tribune,_ December 10, 1933.
**"I remember him having dinners with us":** Author interview with Virginia McCaskey.
**"roamed the ball field, pulling down impossible passes":** Halas, _Halas by Halas,_ 183.
**"When the 1940 season began, I felt we were fit for anything or anybody":** Ibid., 186.
**"I was ready to tear the referee limb from limb":** Ibid., 187.
**"The Bears are a bunch of crybabies":** Ibid., 188.
**"I did not let the players forget":** Ibid.
**"Congratulations":** Ibid.
**The Mutual Broadcasting System paid $2,500 for the right to broadcast the game nationally on the radio:** Ibid.
**"When we were ready to go out, he pointed to the clippings":** Ibid., 190.
**"They will show you whether the Redskins are staying with the defense they used":** Ibid.
**"I could see this was going to be a great day":** Ibid., 191.
**"Our adjusted plays had them confused":** Ibid., 192.
**"We wanted revenge and we got it":** Halas, _Halas by Halas,_ 197.
**"If Charley had caught it, the score would have turned out 73–7":** Ibid., 196.
**"The weather was perfect. So were the Bears":** Arthur Daley, "Bears Overwhelm Redskins by Record Score," _New York Times,_ December 9, 1940.
**The head linesman that day had been Irv Kupcinet:** Davis, _Papa Bear,_ 159, 161.
**"the greatest team professional football has ever produced":** Ibid., 161.
**"The Bears were wonderful, weren't they?":** Holley, _Slingin' Sam,_ 170.
**CHAPTER 15: SAME OLD PIRATES**
**cost just $5,000:** Ruck, Patterson, and Weber, _Rooney,_ 164.
**finished $35,000 in the red, pushing Rooney's deficit since he joined the NFL to more than $100,000:** Ibid., 154.
**"We're not playing this week":** Ibid.,150.
**"On most teams, the coach worries about where the players are on the night before a game":** Ira Berkow, "When Johnny Blood Rode," _New York Times,_ July 11, 1982.
**"felt for a long time that Sutherland was the best coach in the profession":** Ruck, Patterson, and Weber, _Rooney,_ 164.
**"In that sense, they were opposites":** Author interview with Upton Bell.
**made the only, and thus winning, bid:** MacCambridge, _America's Game,_ 43.
**Bell brought the fifty or so diehards who attended the game into the press box:** Didinger and Lyons, _New Eagles Encyclopedia,_ 7.
**"It's days like that when it takes a very good sense of humor":** Ibid.
**Bell accepted the loan, which he repaid the following year:** Lyons, _On Any Given Sunday,_ 72–73.
**"Everyone out, time for practice!":** Ibid., 76.
**The Pirates had lost $8,000 during the season:** Ruck, Patterson, and Weber, _Rooney,_ 170.
**George Preston Marshall found a wealthy Washingtonian:** Ibid.
**"They tell me around here that I'm fighting a losing battle":** Ibid., 170–171.
**"I'm definitely going to keep the team in Pittsburgh for another season":** Ibid., 174.
**"No matter what you call a grapefruit, it still squirts in your eye":** Ibid., 175.
**he offered Sutherland only a $7,500 annual salary, which Dan Topping easily doubled:** Ibid., 173.
**"I wish Art Rooney all the luck in the world":** Ibid.
**"Say, George":** Ibid., 179.
**"broke the Halas spell":** Ibid.
**"woeful gang" that "made a mockery of themselves and the league":** Ibid., 182.
**Povich estimated that Rooney had saved $2,000 but damaged the NFL's credibility:** Ibid.
**losing an exhibition game to a minor-league team:** Daly, _National Forgotten League,_ 166.
**"After I turned him down three times in a row":** Ruck, Patterson, and Weber, _Rooney,_ 182.
**"more effective resolving NFL matters than he was in addressing the Steelers' woes":** Ibid., 176.
**"You can't blame the guy":** Ibid., 183.
**Thompson announced in February 1941 that his team would stay in Pittsburgh with a new name:** Ibid., 186.
**Rooney took him out for an evening at a popular Pittsburgh saloon:** Ibid.
**Neale, Thompson, Bell, and Rooney met at the Racquet Club in Philadelphia to divide up the players:** Lyons, _On Any Given Sunday,_ 89.
**"This is the finest squad I've ever worked with in the National Football League":** Ibid., 90.
**"Those new uniforms they're wearing threw me off a bit":** Ibid.
**"We have to do something":** Ibid.
**"You have to quit!":** Ibid.
**"He could have helped us and helped the league, too":** Daly and O'Donnell, _Pro Football Chronicle,_ 95.
**CHAPTER 16: POLITICAL WINDS**
**had a conversation about the job with J. Edgar Hoover:** Willis, _Joe F. Carr,_ 395.
**"could not overlook the splendid opportunities":** Ibid., 394.
**"I think Storck is a fine executive":** Ibid., 394–395.
**Ward himself suggested another candidate, Layden:** Ibid., 395.
**When he opened his morning newspaper, he read that Layden had been hired:** Lyons, _On Any Given Sunday,_ 86.
**"came from Chicago":** Ibid.
**"Well, that's one thing Bell got right":** Ibid.
**"Bell knew all about the progress of negotiations":** Ibid.
**"also were given authority to make an offer to one of the three":** Ibid.
**"the most constructive and finest move ever made":** Ibid.
**"I am convinced Layden is not qualified":** Willis, _Joe F. Carr,_ 396.
**But Halas asked Bidwill to keep the idea between them:** Davis, _Papa Bear,_ 196.
**"Tim, just tell me one thing, what church do you go to?":** Gotterher, _Giants of New York,_ 173.
**Marshall saw to it that Storck was relieved of an important duty:** Daly and O'Donnell, _Pro Football Chronicle,_ 84.
**"The two moguls were squaring off":** Ruck, Patterson, and Weber, _Rooney,_ 176.
**"were so often on opposite sides that I grew up looking upon Halas as an enemy":** Halas, _Halas by Halas,_ 156.
**"Their relationship was one of great warmth":** Author interview with Virginia McCaskey.
**"Would you please check up on him":** Ibid.
**"Ed sat down with them":** Ibid.
**"He and Art Rooney both loved horse racing":** Ibid.
**CHAPTER 17: DOG MEAT**
**"Attention, please":** Gotterher, _Giants of New York,_ 178.
**"Oh, my God":** Ibid.
**"I didn't even know where Pearl Harbor was":** Mike Lupica, "Mara Facing Another Tough Sunday," New York _Daily News,_ September 14, 2001.
**"He gave us such a bad account":** Dave Anderson, "The Day Colonel Donovan Was Paged," _New York Times,_ December 1, 1991.
**"What do we do now?":** Gotterher, _Giants of New York,_ 179.
**"Attention, all officers and men of the Army and Navy are to report to their stations immediately":** DeVito, _Wellington,_ 100.
**"They announced it over the loudspeakers":** Davis, _Papa Bear,_ 169.
**"the teams just didn't have the same emotions":** Ibid.
**"I didn't know what to do":** Halas, _Halas by Halas,_ 202.
**"I'll send your name to Washington":** Ibid., 203.
**When training camps opened in 1942:** Ruck, Patterson, and Weber, _Rooney,_ 203.
**Twenty rookies made New York's roster in 1942:** Gotterher, _Giants of New York,_ 184.
**"I took one look at the squad and I felt like crying":** Ibid.
**they dressed just sixteen for their first preseason game:** Ruck, Patterson, and Weber, _Rooney,_ 203.
**"keep baseball going":** From text of Roosevelt letter, www.baseball-almanac.com/prz_lfr.shtml.
**"many duties" and "I would not have chosen it":** Halas, _Halas by Halas,_ 204.
**"We were beginning to think of ourselves as unbeatable":** Ibid., 205.
**"The once mighty football empire of the Chicago Bears":** Lew Freedman, _The Chicago Bears: The Complete Illustrated History_ (Minneapolis, MN: MVP Books, 2008), 50–51.
**"George, you're too old to fight a war":** Halas, _Halas by Halas,_ 206.
**"I thought Halas would kill Marshall":** Ibid.
**"You're no big shot now!":** Ruck, Patterson, and Weber, _Rooney,_ 198.
**Rooney tore up the duty application papers and walked away:** Ibid.
**"He found people waiting for him every morning":** Ibid.
**"This team is going to win some games":** Ibid., 205.
**After the season, Rooney again suggested to his fellow owners that the NFL suspend operations:** Ibid., 208.
**"go through the motions":** Ibid., 212.
**Bert Bell had sent recruiting letters to 250 prospects:** Ibid.
**A tackle had bleeding ulcers. Another lineman was deaf in one ear:** Chris Strauss, "70 years ago, the Steelers and Eagles were One Team," _USA Today,_ December 5, 2013.
**"Please help me, Steve":** Arthur Daley, "A Mighty Stout Fella," _New York Times,_ May 18, 1964.
**"Sorry, Bert":** Daley, "A Mighty Stout Fella."
**"I believe I got my sense of the rage of conflict on the football field":** Rick Burton, "The Author of Red Badge Loved the Game More Than His Studies," _New York Times,_ March 13, 2010.
**"the nearest thing to actual war":** Randy Roberts, _A Team for America: The Army-Navy Game That Rallied a Nation at War_ (Boston: Houghton Mifflin Harcourt, 2011), 60.
**"If we don't watch it, we could get arrested for polygamy":** Ruck, Patterson, and Weber, _Rooney,_ 215.
**"together, we are sure to be strong":** Ibid.
**"We just didn't have it":** Ibid.
**CHAPTER 18: TWO WARS**
**"I would have preferred a place on a warship":** Halas, _Halas by Halas,_ 206–207.
**"contributing to high morale"** Ibid., 207.
**"I think sometimes he put the letter in a bottle and dropped it in Lake Michigan":** Ibid., 211.
**"I had promised Charley [Bidwill] I would back him":** Ibid., 206.
**"Buffalo is not ready for the league":** Craig R. Coenen, _From Sandlots to the Super Bowl: The National Football League_ (Knoxville: University of Tennessee Press, 2005), 112.
**"We've got 10 clubs operating now. Only four have ever shown a profit":** Coenen, _From Sandlots to the Super Bowl,_ 114.
**"a spirit of cooperation and friendliness":** Ibid., 119.
**"All I know of a new league is what I read in the newspapers":** Ibid.
**"The rival league spoiled their friendship"** Author interview with Virginia McCaskey.
**Dan Topping... served in the Marines for forty-two months:** Topping bio, Society for American Baseball Research, https://sabr.org/bioproj /person/f12c897a.
**Wellington Mara enlisted in the navy as a lieutenant in early 1942:** DeVito, _Wellington,_ 101.
**"He would drive his limousine right out on the practice field":** Daly, "Man Who Gave the Redskins Their Name."
**"I wouldn't go near that thing on a bet, let alone fly in it":** Ibid.
**"Our club owners are all good businessmen, not millionaires":** _New York Times,_ November 28, 1944.
**Crowley told reporters that the league already had 150 players under contract:** AAFC chronology, AAFC-NFL folder, Pro Football Hall of Fame, Canton, Ohio.
**"It had been the contention of observers ever since the AAFC was first conceived":** John Drebinger, "Topping's Eleven Joins New Circuit," _New York Times,_ December 6, 1945.
**"We've spent years of time and heaps of money building up the Giants":** "Football Owners Head Is Surprised by Topping's Withdrawal," _New York Times,_ December 6, 1945.
**"All it has done has been to balance our league better":** "Football Owners Head Is Surprised by Topping's Withdrawal."
**"will help our league by clearing things up all around":** Ibid.
**"I hope that Topping does better in the new league than he did in the old one":** Ibid.
**CHAPTER 19: THE RIGHT GUY IN CHARGE**
**"I didn't think I could take it":** Griffith, _My Life with the Redskins,_ 170.
**Within months, he would sell his controlling interest in the Palace Laundry:** Jack Chevalier obituary, _Washington Post,_ June 16, 1976.
**"over my dead body":** Lyons, _Any Given Sunday,_ 113.
**"Bell's mission in life was football":** MacCambridge, _America's Game,_ 38.
**"There were other guys in the room":** Author interview with Dan Rooney.
**"Now we have a pro running our league":** Lyons, _On Any Given Sunday,_ 116.
**"speaks the pro football language":** Ibid.
**"Gentlemen," he said, "you who know me know that I never bluff":** Ibid., 118.
**Crowley and Bell had met in Philadelphia:** Ibid., 121.
**"it is pretty plain":** Ibid., 122.
**"Bert at no time represented us":** Ibid., 123.
**"We knew Bert was talking to Crowley":** Ibid., 123–124.
**"There was a phone in the bedroom":** Bell, _Present at the Creation,_ 11.
**"All of the clubs were very jealous of the schedules":** MacCambridge, _America's Game,_ 40.
**"Only once did anyone raise his voice":** Lyons, _On Any Given Sunday,_ 128.
**CHAPTER 20: BACK ACROSS THE COLOR LINE**
**drew more than 100,000 spectators for the first time:** Alex Bower, "Derby Wins of Triple Crown Victors: Assault," _Blood-Horse,_ April 25, 2017.
**"Fuck Babe Ruth!":** Tyler Cowen, _What Price Fame?_ (Boston: Harvard University Press, 2000), 69.
**Dan Topping's Yankees drew 2.265 million fans:** From www.baseball-reference.com/teams/NYY/.
**The radio rights to the World Series sold for $150,000, a record fee:** "Through the Years: World Series Broadcast Rights Fees," _Sports Business Daily,_ October 13, 2003.
**Haley Harding, a sports reporter for the _Los Angeles Tribune,_ a black weekly newspaper, took the floor at the meeting:** Gretchen Atwood, "Unsung Heroes of Rams Football Integration," _LA Weekly,_ June 10, 2009.
**"I have heard many fine things about Washington, both as a player and as a man":** Ross, _Outside the Lines,_ 82.
**"I doubt we would have been interested in Washington if we had stayed in Cleveland":** Thomas G. Smith, "Outside the Pale," _Coffin Corner_ 9, no. 4 (1989): 13.
**"All hell broke loose":** Coenen, _From Sandlots to the Super Bowl,_ 123.
**"In ordinary conversation, Marshall refers to Negroes":** Smith, _Showdown,_ 32.
**it was a bad idea to mix black and white players on a team:** Ibid., 32–33.
**"He played on the same field with boys who are going to be scattered throughout the league":** Smith, "Outside the Pale," 9.
**"practiced civil rights before it became fashionable":** Ruck, Patterson, and Weber, _Rooney,_ 236.
**Rooney lent Posey money that kept the Grays afloat:** Ibid., 235.
**"deference to the league and his coaches":** Ibid., 236.
**"What about the Steelers, Mr. Rooney?":** Ibid., 236.
**Rooney's slow response to the Rams' reintegration was typical:** "Permanent Reintegration of Pro Football," February 19, 2010, www.profootballhof.com/permanent-reintegration-of-pro-football/.
**"Strode did not relish being a racial pioneer":** Smith, _Showdown,_ 74.
**"There will only be two kinds of men on the Pittsburgh Steeler roster this year"** Daly and O'Donnell, _Pro Football Chronicle,_ 102.
**"First time anything like that has happened out there":** Lyons, _On Any Given Sunday,_ 129.
**"I've never seen anything like it":** Ruck, Patterson, and Weber, _Rooney,_ 237.
**They would buy more than 21,000 season tickets in 1947, doubling the total from the year before** : Ibid.
**The only NFL teams that made money in 1946 were the Giants and Bears, who won the division titles, and the Redskins:** Coenen, _From Sandlots to the Super Bowl,_ 126.
**payroll had been under $100,000 in 1945 and now it was close to $300,000:** Gotterher, _Giants of New York,_ 209.
**Most teams had lost at least $100,000:** Coenen, _From Sandlots to the Super Bowl,_ 126.
**CHAPTER 21: SCANDAL**
**"He's going to be a Giants star for a long, long time":** Gotterher, _Giants of New York,_ 207.
**"both were in tears":** Lyons, _On Any Given Sunday,_ 131.
**"absolutely in the clear":** Ibid.
**"without appeal" and "undesirable":** Ibid., 132.
**"city slicker" and "country boy":** Ibid.
**"Professional football cannot continue to exist unless it is based on absolute honesty":** Ibid., 134.
**were hemorrhaging money, losing an estimated $1.5 million between them in 1947 alone:** Coenen, _From Sandlots to the Super Bowl,_ 128–129.
**"It seems un-American to me":** DeVito, _Wellington,_ 113.
**"Maybe the kid figures he'll have greater security with the Giants":** Ibid.
**O'Malley gave up the franchise after the season, having lost $300,000:** Leo Lowenfish, _Branch Rickey: Baseball's Ferocious Gentleman_ (Lincoln: University of Nebraska Press, 2007), 458.
**"I'm looking for a job":** Gotterher, _Giants of New York,_ 211.
**CHAPTER 22: EVERYONE LOSES**
**"We'll either get smart and make peace, or we'll all go bust":** Coenen, _From Sandlots to the Super Bowl,_ 132.
**Rooney still sold enough tickets to gross $900,000 in revenues, but he ended the season $40,000 in the red:** Ruck, Patterson, and Weber, _Rooney,_ 276.
**"The time is ripe for peace":** Coenen, _From Sandlots to the Super Bowl,_ 132.
**"We would talk about things":** Author interview with Mike McGee.
**eventually paid Marshall just $50,000:** Daly and O'Donnell, _Pro Football Chronicle,_ 106.
**"Bertie sat back there in his Philadelphia apartment":** Lyons, _On Any Given Sunday,_ 156.
**"We owners were a tight little group":** Halas, _Halas by Halas,_ 233.
**Marshall haughtily responded:** Daly and O'Donnell, _Pro Football Chronicle,_ 105.
**"obnoxious":** Daly, "Man Who Gave the Redskins Their Name."
**"habit of sleeping most of the day":** Ibid.
**"As with most organizations, we were perhaps too unresponsive":** Halas, _Halas by Halas,_ 233.
**"Plans here are the proverbial dime-a-dozen":** Louis Effrat, "Buffalo Franchise Bid Gains Favor at Football Meeting," _New York Times,_ January 20, 1950.
**"I banged down the gavel and started for the doors":** Lyons, _On Any Given Sunday,_ 161.
**"left the meeting in a huff":** Ibid.
**"the most important decision in the new league":** Ibid., 161–162.
**"never kicked" and "the worst of it":** Ibid., 162–163.
**"shirt-sleeved and dead tired" and "portly":** Effrat, "Buffalo Franchise Bid Gains Favor at Football Meeting."
**"chickenshit football":** David M. Nelson, _The Anatomy of a Game: Football, the Rules, and the Men Who Made the Game_ (Newark: University of Delaware Press, 1994), 298.
**In 1953, the NCAA would reinstitute limits on substitutions:** Robert W. Peterson, _Pigskin: The Early Years of Pro Football_ (New York: Oxford University Press, 1994), 193.
**CHAPTER 23: THE LITTLE BLACK BOX**
**"a little black box, about two feet square":** Halas, _Halas by Halas,_ 239.
**"There it is George, television":** Ibid.
**"The picture is so small":** Ibid.
**"George, that little box with the fuzzy picture is going to change the American way of life":** Ibid., 240.
**"Television is coming, George":** Ibid., 241.
**"asking questions":** Ibid.
**"for the first time":** Lyons, _On Any Given Sunday,_ 132–133.
**teams now received between $15,000 and $35,000 per year:** Coenen, _From Sandlots to the Super Bowl,_ 154.
**just 44,000 sets were in use in America in 1947, compared to 40 million radios:** From www.tvhistory.tv/1947%20QF.htm.
**"I could not believe it":** Halas, _Halas by Halas,_ 244.
**"So many sets were coming into Chicago homes that I lacked enthusiasm for having our games televised":** Ibid., 245.
**Within four years, it was 11,831:** Coenen, _From Sandlots to the Super Bowl,_ 161.
**In 1946, the New York Yankees became the first club to sell their local television rights, receiving $75,000:** Michael J. Haupert, "The Economic History of Major League Baseball," https://eh.net/encyclopedia /the-economic-history-of-major-league-baseball/.
**Within a decade, the Brooklyn Dodgers received $800,000 for the rights:** John Helyar, _Lords of the Realm: The Real History of Baseball_ (New York: Villard Books, 1994), 52.
**Attendance dropped 65 percent:** Coenen, _From Sandlots to the Super Bowl,_ 161.
**seven per season in each region of the country:** Ibid., 160–161.
**"I, a most cautious man":** Halas, _Halas by Halas,_ 246.
**"I determined to increase our effort to make it work for the Bears":** Ibid.
**"The worst team in our league could beat the best team in theirs":** MacCambridge, _America's Game,_ 64.
**"I would say that there was never another team in the history of sports":** Lyons, _On Any Given Sunday,_ 171.
**"We whetted our appetite for that game for about three years":** Ibid.
**teams earned just $8,000 apiece from the ABC and DuMont deals:** Coenen, _From Sandlots to the Super Bowl,_ 156.
**The next year, DuMont released data:** Ibid., 161.
**"It was quite an operation":** Halas, _Halas by Halas,_ 247.
**"But more people have seen the Bears play this year than the first 30 years of our existence put together":** Coenen, _From Sandlots to the Super Bowl,_ 155.
**Standard Oil paid $30,000 for 50 percent of the commercial time:** Halas, _Halas by Halas,_ 248.
**By the end of the decade, the Bears' network would consist:** Coenen, _From Sandlots to the Super Bowl,_ 156.
**The Steelers and Lions had six stations:** Ibid.
**NBC paid $100,000 to broadcast the league championship game from "coast to coast":** Halas, _Halas by Halas,_ 249.
**there would always be an NFL team in the city:** Lyons, _On Any Given Sunday,_ 240.
**CHAPTER 24: ALL-WHITE REDSKINS**
**were not equipped to play in the pros:** Ross, _Outside the Lines,_ 114.
**"I have nothing against Negroes but I want an all-white team":** Andrew O'Toole, _Fight for Old DC: George Preston Marshall, the Integration of the Redskins and the Rise of a New NFL_ (Lincoln: University of Nebraska Press, 2016), 1.
**"He really tried to get us up that week":** Stan Grosshandler, "The Day Dub Jones Ran Wild," _Coffin Corner_ 18, no. 4 (1996): 1.
**"We're wasting our time with him":** Ruck, Patterson, and Weber, _Rooney,_ 280.
**"All I'm asking is that you put him on the kickoff":** Ibid.
**"Would you see that your guy kicks the ball to him?":** Ibid.
**"Do you want him to go all the way?":** Ibid.
**"I told you he couldn't play!":** Ibid., 281.
**"Jack, the guy who threw that football at you is a good kid":** Rooney Jr., _Ruanaidh,_ 113.
**"I doubt it was written":** Ross, _Outside the Lines,_ 135.
**"I went to a game in Washington":** Author interview with Mike McGee.
**"We had those big capes for cold weather":** Boswell et al., _Redskins,_ 45.
**"would like very much to sign a colored player":** Ross, _Outside the Lines,_ 132.
**"the greatest reconstruction job since the Civil War":** Boswell et al., _Redskins,_ 50.
**"George Marshall, having completed 25 years in professional football, is the greatest asset sports has ever known":** Dave McKenna, "Fight for New Dixie," _Washington City Paper,_ September 2, 2011.
**"There are those who will contend":** McKenna, "Fight for New Dixie."
**"born ineligible to play for the Redskins":** Leonard Shapiro, "Post Sports Columnist Shirley Povich Dies," _Washington Post,_ June 5, 1998.
**"burgundy, gold and Caucasian":** Shapiro, "Post Sports Columnist Shirley Povich Dies."
**"There were only so many good players":** Boswell et al., _Redskins,_ 53.
**"We'll start signing Negroes when the Harlem Globetrotters start signing whites":** Rick Snider, _100 Things Redskins Fans Should Know and Do Before They Die_ (Chicago: Triumph Books, 2014), 5.
**"In modern pro football, Marshall is an anachronism, as out of date as the drop-kick":** Ryan Basen, "Fifty Years Ago, Last Bastion of N.F.L. Segregation Fell," _New York Times,_ October 6, 2012.
**CHAPTER 25: FORTY MILLION VIEWERS**
**"as much as the Maras hated to admit it, they had to agree":** DeVito, _Wellington,_ 124.
**"What's up?":** Ibid.
**"the toughest thing I ever had to do":** Ibid.
**"But... the Giants aren't for sale":** Arthur Daley, "Westward Course of Empire," _New York Times,_ December 3, 1972.
**"They'd pay $1 million":** Daley, "Westward Course of Empire."
**"maybe we ought to think about moving to Yankee Stadium":** DeVito, _Wellington,_ 133.
**"Boys, we played the Bears for the title back in '34 in weather this bad, and we nearly lost":** Ibid., 137.
**"We're going to do the same thing this year":** Ibid.
**"You betcha, Mr. Mara":** Ibid., 138.
**"We all go with sneakers!":** Ibid.
**"Unless something is done within six months, I will have to make other arrangements":** Helyar, _Lords of the Realm,_ 55.
**"the world's largest outdoor insane asylum":** Sportswriter Cooper Rollow's obituary, _Chicago Tribune,_ April 1, 2013.
**By 1958, it was 43,167:** Coenen, _From Sandlots to the Super Bowl,_ 163.
**"Up in the grandstand, a man was crying tears of joy":** Lyons, _On Any Given Sunday,_ 291.
**EPILOGUE**
**"You're going to get fired":** Lyons, _On Any Given Sunday,_ 264.
**"If I get fired, I get fired":** Ibid.
**"try to get Bert Bell's job" and "a dictator":** Ibid., 242.
**"There's no doubt Bell has the right to negotiate any differences":** Ibid., 265.
**"You have to vote so the players can have a union":** Ibid., 266.
**suffered a heart attack and died:** "Tim Mara, Pro Football Pioneer, Dies," _Chicago Tribune,_ February 17, 1959.
**his family, the Giants' team doctor, and a priest were by his side:** "Tim Mara, Pro Football Pioneer, Dies."
**"We're going to sell out next year!":** DeVito, _Wellington,_ 147.
**"finding solace in his faith":** Ruck, Patterson, and Weber, _Rooney,_ 311.
**"I'd rather die watching football than in my bed with my boots off":** "Former FBI Agent Temporarily Acting as Commissioner of Pro Grid League," Associated Press, _York (Pennsylvania) Gazette and Daily,_ October 13, 1959.
**"There was a commissioner's box, which he never sat in":** Author interview with Upton Bell.
**"What better way was there for him to go out?":** Ibid.
**"like Caruso dying in the third act of Pagliacci":** Lyons, _On Any Given Sunday,_ 306.
**"I don't know how we'll replace him":** Ibid., 310.
**"That move alone probably saved the league":** Author interview with Upton Bell.
**"There is no such thing as an indispensable man":** Lyons, _On Any Given Sunday,_ 310.
**"has done more for professional football than any other man":** Ibid.
**"He's certainly the only commissioner in sports history":** Author interview with Upton Bell.
**"He was going to buy the Eagles back":** Ibid.
**"So good to see you, Chief":** Morris Siegel, "Tears Flow as Marshall and Halas Hold Reunion," _Washington Star,_ October 26, 1964.
**"He couldn't take part in the conversation":** Ruck, Patterson, and Weber, _Rooney,_ 375.
**"Now he got loose, real loose":** Ibid.
**"Mr. Marshall was an outspoken foe of the status quo":** Marshall biography, www.profootballhof.com/players/george-preston-marshall/biography/.
**"the principle of racial integration in any form":** Michael Tomasky, "The Racist Redskins," _Daily Beast,_ June 1, 2013.
**"I am George Halas of the Chicago Bears Football Club":** George Halas speech to Congress on December 10, 1981.
**"When I started going to Bears games at age five":** Author interview with Patrick McCaskey.
**"Mugs was so sharp":** Author interview with George McCaskey.
**"Halas is way up there in years":** Michael MacCambridge, _Lamar Hunt: A Life in Sports_ (Kansas City: Andrews McMeel, 2012), 83.
**"When he was dying":** Author interview with Patrick McCaskey.
**"Integrity, certainly":** Author interview with Virginia McCaskey.
**"at one point, he was sending cash in an envelope to my father":** Author interview with Upton Bell.
**"My dad was the guy who would pay his toll":** Author interview with Art Rooney Jr.
**"simply a great guy" and "a philosopher" and "an owner who has never won a league pennant":** Vince Johnson, "Rooney Unique in Pro Football Hall of Fame," _Pittsburgh Post-Gazette,_ September 7, 1964.
**"There is the image of me as the benevolent loser":** From unlabeled 1972 magazine profile, page 8c, Rooney folder, Pro Football Hall of Fame, Canton, Ohio.
**"All those years, he never had a good team":** Author interview with Virginia McCaskey.
**"After we'd won one or two Super Bowls":** Author interview with Art Rooney Jr.
**"We'd go to training camp and he'd say, 'I'd like to talk to these kids'":** Ibid.
# Index
Adderly, Herb,
Aguirre, Joe,
Akron Pros, 21–22
All-America Football Conference (AAFC), 229–230,
financial issues, 261–262, 269–270
formation of, 223–225
merger with NFL, 277–281
vs. NFL, 223–225, , , 233–234, , , , , 261–262, 263–264
NFL's banning of players signed with,
racism/racial integration and,
rumor of Bell's jump to, 243–245
teams disbanding, 279–281, 285–286
television broadcasting,
Ameche, Alan, 325–326
Ameche, Don, ,
American Basketball League, 49–51
American Bowling Congress,
American Football League (Grange League), 46–48, ,
American Football League (1936–1937), 170–171, ,
American Professional Football Association (APFA), 27–28,
constitution and bylaws,
formation of, , ,
name change to National Football League,
sharing as foundation of, 335–336
Anderson, Billy,
Anderson, Edwin,
Anderson, Rochester,
Andrews, Leroy,
Angsman, Elmer,
Antwine, Houston,
Artoe, Lee,
Associated Press, , , , , , , , , ,
Bach, Joe, , , , 304–305
Bachman, Charlie,
_Baltimore Afro-American,_
Baltimore Colts, ,
1947 season,
1948 season,
1957 season, 311–312
1958 season, 323–326
1958 season (championship game), 325–326
Barabas, Al,
baseball, , , , , 249–250, 320–322
Black Sox gambling scandal and,
company teams,
during depression era,
racism/racial integration and, , , ,
television broadcasting, 291–292, ,
World Series, , , , , , , , , , , , ,
Battles, Cliff, , , , ,
Baugh, Sammy, 144–146, , , , , , , , 227–228, 227 (photo), 236–237, , , ,
as Hall of Fame inductee,
Bell, De Benneville "Bert," 56–69, 63 (photo), , , , 117–122, , , 195–199, , 241 (photo), , , 317–318
AAFC and,
AAFC jump rumor and, 243–245
Baltimore Colts-New York Giants 1958 championship game and, 325–326
Bell–Rooney partnership and, 196–199
as captain and quarterback of Penn Quakers, 62–65
as central figure in league circles, 330–331
Cleveland Rams move to Los Angeles and, 242–243
as coach at Penn, 65–66,
as coach at Temple,
as coach of Pittsburgh Steelers, 197–198
as coaching advisor for Philadelphia Quakers, 67–68
cut off from family wealth and,
death of, 329–332
during depression era,
draft and, , 125–126,
early years and, 60–61
education of, 61–62
family wealth and history and, , 55–60
financial issues and, , 277–278
gambling and, , 66–67
Green Bay Packers and, ,
Halas's respect for, 207–208
as Hall of Fame inductee,
health issues of,
Hutson and, 120–121
Kostka and, 119–120,
marriage of, 117–118
Marshall and, 245–246
in military, 63–64
at National-American Football League first meeting in 1950, 282–286
New York Giants gambling scandal and, 263–268, 267 (photo)
NFL-AAFC merger and, 278–281
as NFL commissioner, , 239–243, 243–246, ,
as NFL commissioner, and 10-year contract,
NFL commissioner search and, 200–203
on NFL executive committee, 195–196
NFL Frankford Yellow Jackets purchase and,
at NFL meeting, Victoria Hotel, NY, Dec. 1934, 2–7
Philadelphia Eagles 1949 championship controversy and,
Philadelphia Eagles 1950 game with Cleveland Browns and, 293–296
as Philadelphia Eagles owner, , 118–122, 122–126, , 191–192
Philadelphia Eagles-Pittsburgh Steelers franchise swap and, 196–197, ,
Pittsburgh Steelers sale and,
as playboy/bon vivant, ,
players' union and, 327–329
racism/racial integration and,
resignation as NFL coach,
Rooney and, , 190–191
scheduling and, , , 245–246,
television broadcasting and, 293–296, ,
_See also_ Philadelphia Eagles; Philadelphia Eagles Football Club, Inc.
Bell, Fleurette de Benneville (née Myers; mother), 57–58, 59–60,
Bell, Frances (née Upton; wife), 117–118
Bell, John Cromwell, Sr. (father), 57–59, , 66–67,
Bell, John "Jack" Cromwell, Jr. (brother), , 60–61,
Bell, Upton (son), , , , , , , , , , , ,
father's death and, ,
Bendix, Vincent,
Benningsen, Roy, 241 (photo)
Bergman, Arthur "Dutch,"
Berle, Milton,
Berry, Raymond, 325–326
Bertolet, Esther,
Berwanger, Jay, , 125–126
Bidwill, Charles, 82–83, , , , 202–203, ,
Chicago Bears and, 89–90
Chicago Cardinals and, 89–90
Chicago Cardinals proposed move to Los Angeles and, 204–205,
Chicago Cardinals-Pittsburgh Steelers merger during World War II,
Cleveland Rams move to Los Angeles and, 242–243
death of, ,
Portsmouth Spartans and,
Black Sox gambling scandal,
Blount, Mel,
Bosseler, Don,
Boston Braves, 54–55, 94–97, , , , . _See also_ Marshall, George Preston
Boston Bulldogs,
Boston Celtics,
_Boston Globe,_ , 143–144
Boston Red Sox, 10, , , 249–250
Boston Redskins,
1933 season, 99–101
1935 season,
1936 season, 128–129, 132–133, 139–140, , 142–143
_See also_ Marshall, George Preston
Boston Yanks, 220–221, ,
boxing, , , , ,
Bradley, Harold,
Bradshaw, Terry,
Branca, Ralph,
Breeskin, Barnee, ,
Brickley, Charlie,
Brickley's Giants, , ,
Brizzolara, Ralph, 241 (photo)
Brooklyn College's basketball varsity scandal,
_Brooklyn Daily Eagle,_
Brooklyn Dodgers (NFL/AAFC), , 84–85, , 120–121, , , 230–231
1939 season,
1940 season,
1941 season, 209–211
1941 season (prewar),
1943 season,
1947 season, ,
1948 season, ,
game attendance and,
radio broadcasting,
_See also_ Topping, Dan
Brooks, Louise,
Brown, Jim, , 311–312
Brown, Paul, 229–230, , , , 283–284, 287–288, , , ,
Brown, Rosey, 307–308,
Brueil, James,
Bryant, Paul "Bear,"
Buffalo Bills, ,
Buss, Art,
Cagle, Chris "Red," 108–109
Canadian Football League,
Canton Bulldogs, , , ,
Capone, Al,
Caroline, J. C.,
Carr, Joe, 26–27, , , , , , 162–163, 174–175, , ,
as APFA president, 23–24
basketball and,
Boston Braves and,
championship trophy and, , 3 (photo)
as Columbus Panhandlers manager,
contribution to NFL by,
death of,
disguised college players and,
draft and,
Hutson and,
Marshall's Boston Braves and, 54–55
New York Giants franchise and, 33–34,
at NFL meeting, Victoria Hotel, NY, Dec. 1934, 2–5
as NFL president, 33–34
owners as partners ethos and, 167–168
players jumping from team to team and,
racism/integration and, ,
rule changes and, 98–99
Casey, Bernie,
Cassatt, Alexander,
Central Basketball League,
Chamberlain, George, 12–13
Champaign Legion,
Charles, Ezzard,
Chevalier, John,
Chicago Athletic Association,
Chicago Bears, 3–4, 29–30, , 180–187,
1925 season, 41–43
1932 season, 90–91,
1932 season (championship game), 91–93, 92 (photo)
1933 season, 113–115
1933 season (championship game), 114 (photo), 115–116
1934 season (championship game), 1–2, , 3 (photo),
1935 season,
1936 season,
1937 season, , 155–156,
1937 season (championship game), 155–156,
1939 season, 181–182,
1940 season, 182–183,
1940 season (championship game), 183–187, 185 (photo),
1941 season, , 211–212, 212–213, 213–214
1941 season (championship game),
1942 season, 223–224
1942 season (championship game), 214–215, 215 (photo),
1943 season, 217–218,
1943 season (championship game), , 227 (photo)
1944 season,
1945 season (postwar),
1946 season, ,
1946 season (championship game), 263–268
1947 season, , ,
1951 season, , , 302–304
1956 season,
1956 season (championship game), 319–320
1963 season (championship game),
during depression era, 81–93
financial issues,
game attendance and, ,
Grange and,
Luckman and, 181–182
McAfee and,
players' union and,
as popular and profitable, 223–224
racism/racial integration and, , , 302–304,
radio broadcasting, 178–179
television broadcasting, , , , ,
updated T formation and, 180–181, ,
_See also_ Halas, George Stanley
Chicago Bruins, ,
Chicago Cardinals, , , 89–90
1933 season, 101–103
1936-1947 season, 270–271
1937 season,
1940 season,
1941 season, , 211–212,
1943 season, 217–218
1946 season,
1947 season,
1947 season (championship game),
1948 season,
1952 season,
1954 season,
1955 season,
1957 season, 322–323
draft, 270–271
game attendance and,
proposed move to Los Angeles, 204–205,
racism/racial integration and, ,
radio broadcasting, 177–179
television broadcasting,
Chicago Cardinals-Pittsburgh Steelers merger during World War II, 220–221
Chicago Cubs, 177–179
_Chicago Daily Times,_
Chicago Rockets (1947),
Chicago Staleys (later Chicago Bears), 27–30
_Chicago Tribune,_ , 27–28, , , , , , , , , , , ,
Christman, Paul,
Cincinnati Reds (NFL), 3–4
Clark, Dutch, 91–92
Clark, Potsy,
Cleveland Browns, 261–262,
1946 season,
1947 season, 268–269,
1948 season,
1948 season (championship game),
1949 season, ,
1950 season-opening game vs. Eagles, 293–296, 295 (photo)
1951 season, 302–304,
1953 season,
1955 season,
1957 season, ,
1958 season, ,
racism/racial integration and, , , , ,
television broadcasting,
Cleveland Bulldogs,
Cleveland Indians (NFL), ,
Cleveland Rams, ,
1937 season, 191–192
1941 season,
1941 season,
1942 season,
1943 season, ,
1944 season,
1945 season (championship game), 235–238
game attendance and,
move to Los Angeles and, , 241–243
_See also_ Reeves, Dan
Cohen, Abe,
College All-Star Game, , , ,
college football, , , 29–30,
during depression era,
fanatical following,
"Million Dollar Backfield" draft and, 270–271
as national pastime,
players turning pro, ,
vs. pro football, 28–29
racism/racial integration and,
substitution rule and, 286–288
television broadcasting,
violent collisions and deaths in,
during World War II,
Collins, Ted, , , ,
Columbus Panhandlers,
company baseball teams,
company football teams,
Concannon, Mike,
Conerly, Charlie, 272–273, , , , , , ,
Conn, Billy, ,
Constable, Pepper,
Cooper, Chuck,
Corum, Bill, 136–137,
Crane, Stephen, 219–220
Crosby, Bing,
Crouse, Buck,
Crowley, Jim, , , , , 243–245,
Cuff, Ward,
_Daily Racing Form,_
Daley, Arthur, , , , , ,
Daly, Dan,
Danowski, Ed, ,
Danzig, Alison, 38–39
Davis, Ernie, 333–334
Dayton Triangles,
De Benneville, George, 57–58
defense industry, 253–254
DeGroot, Dudley, 226–228
Dempsey, Jack, ,
Detroit Lions, , , , , , ,
financial issues,
game attendance and,
racism/racial integration and, 301–302
sale of,
television broadcasting,
Detroit Wolverines,
Dietz, William "Lone Star," 100–101
DiMeolo, Luby,
Ditka, Mike,
Donelli, Aldo "Buff," 198–199
Donovan, Walter,
Donovan, William J.,
Doolan, Jack,
Douds, Forrest "Jap," ,
Doyle, Larry,
Dressen, Charlie,
Driscoll, Paddy, , , , , ,
Dudley, Bill, 216–217, ,
Duluth Kelleys,
Duncan, Mark,
Edwards, Turk,
Eisenhower, Dwight,
Ennis, Al, 241 (photo)
Feathers, Beattie,
Filchock, Frank, , 227–228,
New York Giants gambling scandal and, 264–268, 267 (photo), ,
Flaherty, Ray, , , , , , , , , , ,
Folwell, Bob, ,
football/professional football
appeal of, 274–275
vs. college football, 28–29
college football players turning to, ,
company teams,
as high drama, ,
noncelebrity status of, 176–177
Fortmann, Dan,
Frankford Yellow Jackets, , 37–38, , , ,
Frick, Ford,
Friedlund, J. Arthur,
Friedman, Benny, 105–107, , 110–113
Fuchs, Emil,
Galimore, Willie,
gambling scandals
Black Sox,
Brooklyn College's basketball varsity,
New York Giants, 264–268, ,
Garfield, James,
Garner, John,
Gehrig, Lou,
Gibson, Althea,
Gibson, Billy, 33–34, , ,
Gifford, Frank, , , , ,
Goldberg, Marshall, 259–260,
Golden Gophers,
Graham, Frank,
Graham, Otto, , , ,
Grange, Harold "Red," , 40–49, , , , , , , , , 105–106, , ,
Grange League, , , . _See also_ American Football League
Great Depression era, , 81–200, , , , , , ,
Great Lakes Naval Training Base, ,
Greater Texas and Pan-American Exposition,
Green Bay Packers, ,
1929 season,
1932 season, 90–91
1936-1939 season,
1937 season, 147–148
1938 season (championship game), 172–175, 173 (photo)
1939 season,
1940 season, , ,
1941 season, 212–213
1945 season,
1947 season, 268–269,
1948 season,
1950s seasons, 298–300
1958 season, 299–300
City Stadium and,
during depression era, 86–87
draft and,
game attendance and, 161–162
Hutson and, 120–121
racism/racial integration and,
using college players,
_Green Bay Press-Gazette,_
Greene, Joe,
Grier, Rosey, ,
Griffith, Clark,
Griffith, Corinne, 140–141, , , , , 155–156, , , ,
marriage to Marshall and, 139–140
Grigas, Johnny,
Groomes, Melvin,
Haines, Henry "Hinky," , ,
Halas, Barbara (mother), 13–16,
Halas, Frank (father), 14–16
Halas, George "Mugs," Jr. (son), ,
as Chicago Bears' president, 336–337
death of,
in military, 213–214
Halas, George Stanley, 11–30, 26 (photo), , 43–44, , , , , , 215 (photo), , , 335–337
AAFC and, 223–224, ,
address to congressional subcommittee on antitrust violations in pro sports, 335–336,
baseball and,
Bell's jump to AAFC rumor and,
Bidwill and, 89–90, 204–205
brotherhood of NFL men and, 155–156
championship game sites and,
championship trophy and, 3 (photo)
checking up on daughter's potential son-in-law by, 207–208
Chicago Bears 1932 championship game and, 90–93
as Chicago Bears owner, coach, player, and promoter, 28–30, , 81–93, 180–187, 185 (photo),
Chicago Bruins basketball and, ,
Chicago Cardinals proposed move to Los Angeles and,
as Chicago Staleys owner, coach, and player, 25–28
clash between Lambeau and,
clash between Mara and,
clash between Marshall and, ,
clash between Ward and,
Cleveland Rams move to Los Angeles and, 242–243
on college football team,
"credo of sharing" and,
death of, ,
death of son and,
draft and, 121–122, ,
early years and, 11–16
education of, 15–16
financial issues and, 81–93, 277–278
football injuries and, ,
Friedman and, ,
game attendance and, 161–162
grandsons of,
Grange and,
Green Bay Packers and,
as Hall of Fame inductee,
IOUs to pay salaries and, ,
Lambeau and, 86–87
laundry business and, 88–89,
Luckman and, 181–182
marriage of,
Marshall's death and,
Marshall's racism and,
McAfee and,
in military, 213–215, , , ,
modest family beginnings of,
National-American Football League first meeting (1950), 283–286
in navy sports program, 16–17
as New York Yankee,
NFL-AAFC merger and, 277–281
NFL commissioner search and, 201–204, 238–240
at NFL meeting, Victoria Hotel, NY, Dec. 1934, 2–7
owners as partners ethos and, 167–168
Packers using college players and,
players' union and, 327–329
on pro vs. college football, 28–29
racism/racial integration and, , , 302–304, , ,
radio broadcasting and, 178–179
Ray and, 163–164,
Rooney and, , 133–134, , ,
Rooney Jr. and, 339–340
rule changes and, ,
scheduling and, 157–160,
semipro team and, 17–18
Shaughnessy and, 180–181
slow pace of games and, 162–163,
St. Paul minor league team and,
as Decatur Staleys' coach and player, 12–13, 18–24, 24–25
Sternaman as pro football business partner of,
T formation and, , 180–181, ,
television broadcasting and, 289–293, 296–297, , ,
during World War II,
_See also_ Chicago Bears
Halas, Virginia (daughter). _See_ McCaskey, Virginia
Halas, Walter (brother), , , , 241 (photo)
Halas, Wilhelmina "Min" (née Bushing; wife), , , , ,
Hall of Fame inductees, , , , , , , , , , , , 337–338,
Halloran, Bill, ,
Ham, Jack,
Hamilton, Thomas J.,
Hammond (Indiana) Pros,
Hapes, Merle, 264–268
Harder, Pat,
Harding, Haley,
Harley, Bill, ,
Harley, Chic,
Harris, Franco,
Hauk, William,
Hay, Ralph, ,
Hearst, John "Jack,"
Hearst, William Randolph,
Hein, Mel, , , ,
Heinrich, Don,
Heinz, W. C., ,
Heisman, John, ,
Heisman Trophy, ,
Heller, Warren,
Henderson, "Gloomy Gus,"
Hennie, Sonja,
Herber, Arnie, ,
Hinkle, Clarke, , 173 (photo)
Homestead Grays,
Hoover, J. Edgar,
Hope, Bob,
Hope-Harveys, 73–74
horse racing, , , ,
during depression era,
television broadcasting, ,
Howell, Jim Lee, 316–317,
Hubbard, Cal,
Huff, Sam, ,
Huggins, Miller, ,
Hughes, Honolulu,
Hunt, Lamar,
Hutson, Don, 120–121, , , ,
Ingram, Jonas, 283–284
Interstate Basket Ball League,
Isbell, Cecil,
J. P. Rooneys, 74–75
Jackson, Bob,
Johnsos, Luke, 222–223
Jones, David, 89–90
Jones, Dub, , 303–304
Jones, Jesse,
Jones, Ralph, 83–84, ,
Justice, Ed,
Kakasic, George,
Karamatic, George,
Keck, Harry,
Keeshin, John, ,
Kelly, Grace,
Kelly, Jack, 63–64, 201–202
Kelly, John "Shipwreck," 120–121
Kelsch, Mose, ,
Kemp, Ray, , 102–103,
Kennedy, John F.,
Kenosha Maroons,
Kessing, O. O. "Scrappy,"
Kewanee Walworths,
Kieran, John, ,
Kiesling, Walt, , , , ,
Kinard, Frank "Bruiser,"
Kindt, Don,
Kostka, Stan, 119–121
Kupcinet, Irv, 186–187
Lacy, Sam,
Ladd, Ernie,
Lambeau, Curly, , , 86–87, , , , , , , 241 (photo), ,
Landis, Kennesaw Mountain, ,
Landry, Tom, 316–317, ,
Lane, Dick "Night Train,"
Latrobe (Pennsylvania) YMCA,
Layden, Elmer, 198–199, 200–204, , , , , 238–239, ,
Layne, Bobby,
Leemans, Tuffy, , ,
Lenox, Bill,
Levy, Fred,
Lewellen, Verne,
Lewis, Art "Pappy,"
Lillard, Joe, 101–102,
Lincoln, Abraham,
Lindheimer, Ben, , ,
Little, Lou, ,
Lombardi, Vince, , , 316–317, ,
Lombardo, Guy,
Los Angeles Bulldogs, ,
Los Angeles Dons, ,
Los Angeles Rams
1945 season,
1946 season, , , , , 255–257, 256 (photo), , ,
1948 season, ,
1949 season, 281–282,
1949 season (championship game), ,
1950 season,
financial issues,
racism/racial integration and, , , 255–257, 256 (photo), , ,
television broadcasting, , 297–298
_Los Angeles Times,_
_Los Angeles Tribune,_
Louis, Joe,
Luckman, Sid, 181–182, 184–185, , , , ,
MacArthur, Douglas,
Macon, Eddie, ,
Majestic Radios, 74–75
Malone, Charley, ,
Mandel, Fred, 202–203, 241 (photo),
Maniaci, Joe, 184–185
Mann, Bob, 301–302
Mantle, Mickey,
Mara, Jack (son), , , , , , , 77–78, , , 241 (photo),
championship trophy and, , , 3 (photo)
Giants' daily operations and,
Giants franchise transfer to,
as Giants' president, , 129–130
New York Giants gambling scandal and,
Owen's firing and, 315–316
players' union and,
Mara, John (grandson), , , ,
Mara, Lizette (wife), ,
Mara, Timothy James, 31–48, 39 (photo), , , , 77–78, , , , , 241 (photo)
AFL as attack on,
Baltimore Colts–New York Giants 1958 championship game,
boxing and, ,
Cagle and, 108–109
championship game sites and,
championship trophy and, , , 3 (photo)
clash between Halas and,
clash between Marshall and, , , , 206–207
coal, liquor, and lawbook bindery businesses of, 34–35,
Conerly and, 272–273,
death of,
during depression era,
Detroit Wolverines and,
draft and, 121–122, 123–124, , 166–168
early years and, 31–33
financial issues and, , 47–48, , , 277–278
Friedman and, 105–107, , 110–111, 111–112
Granges and, 40–43
as Hall of Fame inductee,
horse racing, booking making, gambling and, 31–33, , , 134–137, 135 (photo), ,
Howell and, 316–317
Landry and, 316–317
lawsuits and,
Lombardi and, 316–317
modest family beginnings of,
at National-American Football League first meeting in 1950, ,
New York Giants, and changes in 1950s and, 314–320
New York Giants, and franchise transfer to sons and,
New York Giants, and offer to buy, 317–318
New York Giants, and Yankee Stadium and, 321–322
New York Giants during depression era and, 104–116
New York Giants franchise and, 34–35
New York Giants gambling scandal and, 264–266
as New York Giants owner, , , , 41–43, 171–172, 174–175
NFL-AAFC merger and, ,
NFL commissioner search and,
at NFL meeting, Victoria Hotel, NY, Dec. 1934, 2–7
NFL territorial rights to New York and,
Notre Dame and, 109–110
Owen and, ,
Owen's firing and, 315–316
Pittsburgh Steelers/Philadelphia Eagles merger during World War II and,
players' union and, 328–329
racism/racial integration and, , 301–302,
Rooney and, , , ,
rule changes and,
scheduling and, 157–160
television broadcasting and, ,
Topping's defection to AAFC and, 231–233
during World War II, 210–211
_See also_ New York Giants
Mara, Wellington (son), , , , , , , , , , , , ,
Conerly and,
draft and, 166–169
Leemans and,
in military,
New York Giants' daily operations and, ,
New York Giants franchise transfer to,
as New York Giants' secretary, 166–167
Owen's firing and, 315–316
racism/racial integration and,
during World War II,
March, Harry A. "Doc," , 104–105, , 223–224
AFL and, 170–171
Friedman and,
Marshall and,
New York Giants and, , , 36–37, , ,
Mare Island Marines,
Marshall, George Preston, 49–55, 54 (photo), , , , , , , , 241 (photo), , , , 332–335
as American Basketball League owner, 49–51
Baugh and, 144–146, 147–151
Bell and, 245–246
Bell as commissioner and, 240–241
as Boston Braves owner, 54–55, 94–97, ,
Boston franchise and, ,
as Boston Redskins owner, 99–101, 128–129, 132–133, 139–140, , , 142–143
brotherhood of NFL men and, 155–156
business ventures of, 50–54, , , ,
children of,
clash between Halas and, ,
clash between Mara and, , , , 206–207
Cleveland Rams move to Los Angeles and, 242–243
contribution to NFL by,
death of, 334–335
death of father and,
during depression era,
Dietz and, 100–101
draft and, , ,
early years and, 50–54
financial issues and, 277–278
as Hall of Fame inductee,
health issues of,
March and,
marriage and divorce of, 53–54
family beginnings of,
Morabito and,
at National-American Football League first meeting in 1950, 283–286
newspaper coverage and,
NFL-AAFC merger and, 277–281
NFL commissioner search and, , , ,
at NFL meeting, Victoria Hotel, NY, Dec. 1934, 2–7
Pittsburgh Steelers-Philadelphia Eagles merger during World War II and,
players' union and, 327–329
as producer of Greater Texas and Pan-American Exposition,
racism/racial integration and, , , 252–253, , , 302–303, , 308–313, 333–335
respect for Rooney by,
rule changes and, 97–99, ,
scheduling and, 157–160,
team halftime shows, band, fight song and, , , ,
television broadcasting and, , , ,
title game and,
Topping's defection to AAFC and,
as Washington Redskins owner, 141–142, 143–151, 144–151, 155–156, 171–172, 183–187, ,
Washington Redskins sale and,
wife of, 139–140 ( _see also_ Griffith, Corinne)
during World War II, 226–228
_See also_ Boston Braves; Boston Redskins; Washington Redskins
Marshall, Robert "Rube,"
Martin, Pepper,
Mason, Tommy,
Massilon Tigers, ,
Matson, Ollie, ,
Maxim, Joey,
Maxwell, Don, , , 289–291
Mays, Willie,
McAfee, George, , , ,
McBride, Arthur, , 229–230
McBride, Mickey,
McCann, Dick,
McCaskey, Ed, 207–208
McCaskey, George, ,
McCaskey, Patrick, ,
McCaskey, Virginia (née Halas), , , , 88–89, , , , , , , 207–208, , ,
McCauley, John, ,
McClairen, Jack "Cy,"
McCormick, Frank, 201–202
McDonald, Tommy,
McGee, Mike, 279–280,
McGinnity, Joe "Ironman,"
McLean, Raymond "Scooter,"
McMillen, Jim,
McNally, Johnny "Blood," , , , , ,
Michalske, Mike, ,
Mid-Atlantic League,
military forces, racism/racial integration and,
"Million Dollar Backfield" draft, 270–271
Millner, Wayne,
Milstead, Century,
Milwaukee Badgers,
Milwaukee Braves,
Minnesota Vikings,
Mitchell, Bobby,
Modzelewski, Ed,
Moline Tractors,
Moore, Lenny,
Moore, Wilbur, 214–215
Morabito, Anthony, 224–225, 229–230, ,
Motley, Marion, , , , 295 (photo),
Muller, Wes,
Musick, Phil,
Musso, George,
Myers, Dave,
Myers, Leonard,
Myhra, Steve,
Nagurski, Bronko, , , 92–93, , , ,
National-American Football League, , 282–286
National Association for the Advancement of Colored People, ,
National Collegiate Athletic Association (NCAA), , , , , 286–287,
National Football League (NFL), ,
vs. AAFC, 223–225, , , 233–234, , , , , 261–262, 263–264
AAFC's merger with, 277–281
banning of players signed with AAFC,
as brotherhood of men, 155–156
commissioner search, 200–204, 238–240
credo of sharing as foundation of, 5–6
during depression era, 81–200,
distributions of players from disbanding AAFC teams, 285–286
divisions, 1–2, , 284–285
draft, 121–127, 166–169, , , 270–271, ,
establishment of finance committee,
financial issues, 261–262,
formal organization,
game attendance and, 162–163
"individualistic, capitalistic ethos,"
meeting, Victoria Hotel, NY, Dec. 1934, 1–7
mergers, 217–221, 277–281
military duty of owners and players in, 213–215, 217–218, , 225–228, , ,
as multi-billion-dollar enterprise, ,
officials' signaling of rulings and,
owners' contributions to,
owners ( _see_ Bell; Halas; Mara; Marshall; Rooney)
players' union, 327–329
position against gambling,
as premier source of entertainment,
racism and ( _see_ racism/racial integration)
radio broadcasting, 177–179, ,
renamed National-American Football League,
return to original name,
rival leagues and, 46–48
rule re: passing, ,
rule re: player injuries,
rule re: 60-40 gate split, 298–299
rule re: substitutions, 286–288,
rule re: televised games,
rule re: waiver,
rules, 97–99, , 163–165, 236–237
scheduling, , 157–160
slow pace of games and, 162–163,
as sports superpower,
as struggling organization, 44–48
television broadcasting, 289–298, , , ,
during World War II, 209–230
National League,
National Recovery Act,
Neale, Greasy, , ,
_New York Daily News,_ ,
New York Giants, 3–4, 33–43, 43–48, 84–85
1925 season, 41–43
1929 season, ,
1930 season, 108–111
1931 season,
1932 season, ,
1933 season, 113–115
1933 season (championship game), 114 (photo), 115–116
1934 season (championship game), ,
1936 season, 129–130
1937 season, 146–147, 148–151, 171–172
1938 season, 171–172
1938 season (championship game), 172–175, 173 (photo)
1939 season, , 205–206
1940 season,
1940s seasons,
1941 season, 209–211,
1941 season (championship game),
1942 season, , 223–224
1943 season,
1944 season,
1945 season, ,
1946 season, , , , 263–264
1946 season (championship game), 263–268, 264–268, ,
1947 season, 268–269,
1948 season, , ,
1949 season, ,
1951 season,
1952 season,
1953 season,
1954 season,
1955 season,
1956 season, 318–319,
1956 season (championship game), 319–320
1957 season, 321–323, 322–323
1958 season, 323–326
1958 season (championship game), 325–326
1959 season (championship game),
AFL's New York Yankees (football team) declaration of war on,
Cagle and, 108–109
changes in 1950s, 314–320
debt during depression era, 104–116
draft and, ,
financial issues, , 104–116,
financial profits,
franchise, 33–35
Friedman and, 105–107, , 110–111, 111–112
gambling scandal, 264–268,
Leemans and,
Lombardi and,
offer to buy, 317–318
Owen and, , ,
as popular and profitable, 223–224
racism/racial integration and, , 301–302, 305–306, 307–308
radio broadcasting,
television broadcasting, ,
during World War II,
Yankee Stadium and, , 321–322
_See also_ Mara, Timothy James
New York Giants (baseball),
_New York Journal–American,_ , ,
_New York Times,_ , , , 38–39, , , , , , , , , 149–150, , , , , , , , , ,
New York Yankees (baseball), , 12–13, , , , , 249–250, 280–281, ,
World Series,
_See also_ Topping, Dan
New York Yankees (football), 170–171,
1946 season, 263–264,
1947 season, 268–169
1948 season, , ,
1949 season, 280–281
as declaration of war on New York Giants,
radio broadcasting,
as struggling team, 46–48
television broadcasting,
Newman, Harry, ,
Neyland, Robert,
Nimitz, Chester,
Nixon, Richard,
Noll, Chuck,
Notre Dame, , , , 109–110
O'Brien, Chris, ,
O'Brien, Davey, ,
O'Brien, Jay,
O'Brien, Morgan, ,
O'Dwyer, William, 264–265
Oehler, Cap,
Office of the Coordination of Information,
O'Hara, John,
_Ohio State Journal,_
O'Malley, Walter, , ,
Osmanski, Bill, , , 185 (photo)
Owen, Steve, , , , , , , , , ,
A formation attack and,
Mara's firing of, 315–316,
New York Giants gambling scandal and, 264–265
racism/racial integration and,
"umbrella defense" and,
during World War II,
Paris, Alvin, 264–266
Parker, Ace,
Parker, Buddy,
Parker, Jim,
Paula, Carlos,
Pegler, Westbrook,
Penn, William,
Penn Quakers, 62–65
_Philadelphia Bulletin,_
Philadelphia Eagles, , , , , 118–122
1933 season,
1934 season,
1935 season, , 122–123
1936 season,
1937 season, , 191–192
1938 season, ,
1939 season, , ,
1940 season, 194–195
1941 season,
1941 season, ,
1944 season, ,
1945 season,
1945 season,
1946 season, , ,
1947 season,
1947 season (championship game),
1948 season,
1949 season,
1949 season (championship game), ,
1950 season, 293–296, 295 (photo)
1959 season,
financial issues, ,
game attendance and,
Kostka and, 119–120,
Pitts and,
television broadcasting, ,
during World War II,
_See also_ Bell, DeBenniville "Bert"
Philadelphia Eagles Football Club, Inc.,
Philadelphia Eagles-Pittsburgh Steelers
franchise swap, 196–197, ,
merger during World War II, 217–221
_Philadelphia Inquirer,_
Philadelphia Quakers, 67–68
Philadelphia Yellow Jackets,
Pitts, Edwin "Alabama,"
Pittsburgh Athletic Club,
_Pittsburgh Courier,_ 254–255, ,
_Pittsburgh Daily Post,_
Pittsburgh Iron Men,
Pittsburgh Panthers, , ,
Pittsburgh Pirates (NFL), , 128–134
1933 season, 101–103, 130–133
1934 season, 131–132
1936 season, 128–130, 129–130, 132–133, 133–134
1938 season, 188–190
1939 season, ,
1940 season, 193–194
financial issues, 188–190
game attendance and,
injured players and,
_See also_ Rooney, Arthur "Art"
_Pittsburgh Post-Gazette,_
_Pittsburgh Press,_ ,
Pittsburgh Steelers, , ,
1940 season, 193–199
1941 season, 197–199
1942 season, 216–217
1943 season,
1945 season,
1946 season, 257–261
1947 season, , , 276–277
1948 season, , ,
1950 season,
1951 season, , 302–303,
1952 season, 254–255, 304–306
1956 season,
1959 season,
1964 season,
1969 season,
1970 season,
1970s seasons (Super Bowl championships), 339–340
1972 season,
racism/racial integration and, 254–255, 302–303, 304–306
sale of,
television broadcasting,
during World War II,
_See also_ Rooney, Arthur "Art"
Pittsburgh Steelers-Chicago Cardinals
merger during World War II, 220–221
Pittsburgh Steelers-Philadelphia Eagles
franchise swap, 196–197, ,
merger during World War II, 217–221
_Pittsburgh Sun-Telegraph,_
Plasman, Dick,
Podoley, Jim, ,
Pollard, Fritz, ,
Pool, Hamp,
Poole, Jim,
Portsmouth Spartans, , , 91–93, 92 (photo)
Posey, Cum,
Potteiger, Potty,
Pottsville Maroons, , ,
Povich, Shirley, 145–146, , , , , ,
Powers, Jimmy,
Providence Steam Roller, ,
Pyle, C. C., , 43–48, ,
Racine Cardinals, , , ,
racism/racial integration, , 22–23, , 101–103, 251–257, 273–274, 301–313, 333–335
radio broadcasting. _See under_ National Football League
Ray, Hugh "Shorty," 163–165
Reeves, Dan, , , 235–236, , 241–243, 241 (photo), , , . _See also_ Cleveland Rams; Los Angeles Rams
Reeves, Eddie,
Reid, Daniel,
Ribble, Dave,
Rice, Grantland,
Richards, George "Dick,"
Rickey, Branch, 272–273,
Robeson, Paul,
Robinson, Bill, 305–306
Robinson, Jackie, , , , , , , ,
Robustelli, Andy, ,
Rock Island Independents,
Rockford Athletic Club,
Rockne, Knute, , 109–110,
Rooney, Art, Jr. (son), , , 339–340
Rooney, Art (grandfather), 70–71
Rooney, Arthur "Art" Joseph, , , 76 (photo), , , , 193–199, , , 241 (photo), , , 337–340
as amateur boxer,
Baltimore Colts-New York Giants 1958 championship game, ,
baseball and, ,
Bell and, as best friends, 190–191
Bell–Rooney partnership and, 196–199
Bell's death and,
black athletes and, ,
boxing cards and,
championship game sites and,
children of, ,
as college football player,
death of,
during depression era,
draft and, 124–125, 168–169
early years and, 70–73
education of, 72–73
fight cards and, ,
financial issues and, , 277–278
generosity of,
Halas and, , 133–134, , ,
as Hall of Fame inductee, , 337–338,
as Hope-Harveys (later Majestic Radios; later J. P. Rooneys) owner, coach, and player, 73–75
horse farm and,
horse racing, boxing, gambling and, 75–77, 134–138, 135 (photo), , ,
Mara's death and,
marriage of, 76–77
Marshall and Mara clash and,
Marshall's death and,
Marshall's racism and,
modest family beginnings of,
at National-American Football League first meeting in 1950, 283–286
NFL-AAFC merger and, 277–281
NFL commissioner search and, , 202–204, ,
NFL franchise and, 77–78
at NFL meeting, Victoria Hotel, NY, Dec. 1934, 2–7
as Pittsburgh Pirates owner, , 128–134, 188–190, 191–192
Pittsburgh Steelers-Chicago Cardinals merger during World War II,
as Pittsburgh Steelers owner,
Pittsburgh Steelers-Philadelphia Eagles franchise swap and, 196–197, ,
Pittsburgh Steelers sale and,
Pittsburgh Steelers/Philadelphia Eagles merger during World War II and, 217–221
players' union and, 327–329
Polish Refugee Relief Fund and,
politics and, 188–189
as prep academy halfback, 72–73
racism/racial integration and, 254–255, 302–303, 304–306, ,
respect of owners for,
scheduling and, 157–160
as semipro baseball player,
60-40 gate split and, 298–299
Super Bowl championships and, 339–340
Sutherland as Pittsburgh Steelers head coach and, 257–261
Sutherland's death and, 276–277
television broadcasting and,
during World War II, , 216–218, 220–222
_See also_ Philadelphia Eagles Football Club, Inc.; Pittsburgh Pirates; Pittsburgh Steelers
Rooney, Dan (brother),
Rooney, Dan (son), , , ,
as Pittsburgh Steelers owner, 23–24
players' union and,
Rooney, Daniel (father), 71–72,
Rooney, Jim (brother), 74–75
Rooney, John (brother),
Rooney, Kathleen "Kass" (née McNulty; wife), 76–77, , ,
Rooney, Margaret (née Murray; mother), 71–72,
Rooney, Timothy James (son),
Roosevelt, Franklin, , , , , , , 253–254
Roosevelt, Theodore, , , ,
Rose Bowl, 16–17, , , , , ,
Rosenbloom, Carroll,
Rosenblum, Max,
Rote, Kyle, ,
Rozelle, Pete, , , , , 334–335
Runyon, Damon, , 160–161
Russell, Bo,
Russell, Jane,
Rutgens, Joe,
Ruth, Babe, , , , , , , ,
San Francisco 49ers, , , ,
Sanders, Orban Eugene "Spec,"
Schnelker, Bob,
Shakespeare, Bill, ,
Shaughnessy, Clark, 180–181, ,
Shuford, Harry,
Slater, Duke,
Smith, Al, , ,
Smith, Chet,
Smith, Don,
Smith, Riley, , , , ,
Smith, Thomas, 255–256
Smith, Wilfrid, 90–91
Snead, Norm,
Snyder, Bob,
Snyder, Dan,
Soar, Hank,
Spinks, Jack, ,
St. Louis Gunners, ,
Stagg, Amos Alonzo, , ,
Staley, Eugene, , , ,
Staley Chicago team. _See_ Chicago Staleys
Staley Decatur team, 12–13, 18–24, 24–25
Staten Island Stapletons,
Sternaman, Dutch, , , , 87–88
stock market crash of 1929, , , , , 106–107
Stoneham, Horace, ,
Storck, Carl, 159–160, , , , 203–204, 206–207
Strode, Woody, , 255–257, 256 (photo)
Strong, Ken,
Stydahar, Joe,
Super Bowl, , 339–340
Sutherland, Jock, , , , , 257–261, 276–277
Taliaferro, George,
tennis,
_Texaco Star Theater,_
Thompson, Alexis, 196–198, , ,
financial issues and,
Philadelphia Eagles/Pittsburgh Steelers franchise swap and, 196–197, ,
Thompson, Tommy,
Thorpe, Jim, , , , , , 36–37, , ,
Tilden, Bill,
_Time_ magazine, , ,
Topping, Dan, , , , 230–231, 238–239, , , , , , ,
Brooklyn Dodgers and,
defection to AAFC and, 230–233
Mara's territorial rights to New York and,
in military, 225–227,
New York Yankees franchise and, ,
Yankee Stadium purchase and, ,
_See also_ Brooklyn Dodgers; New York Yankees (baseball)
Trafton, George,
Trans-America Football League (TAFL),
Trippi, Charlie,
Truman, Harry, ,
Trumbauer, Horace,
Tunnell, Emlen, 273–274, 301–302, ,
Tunney, Gene, , , , , , ,
Udall, Stewart,
Unitas, Johnny, , 324–325,
United Press International,
United States Football League (USFL),
Van Buren, Steve, 294–295
Vanzo, Fred,
Vaughan, Harp,
Veeck, Bill,
Walker, Jimmy,
Wallace, Bill,
Walsh, Chile, , 251–252
Wanamaker, John,
Ward, Arch, , , 179–180, , ,
class between Halas and,
Cleveland Rams move to Los Angeles and,
formation of AAFC and, 223–225
Ward, Ruth,
Ward, Tom,
Washington, Kenny, 251–252, , 255–257, 256 (photo),
_Washington Post,_ , , 145–146, , , , , , ,
Washington Redskins, 141–151,
1937 season, 144–151, 146–147, 147–148, 148–151, 155–156, 171–172, ,
1937 season (championship game), 155–156,
1938 season, 171–172
1939 season, 205–206
1940 season, , 182–183, 194–195
1940 season (championship game), 183–187, 185 (photo),
1941 season,
1942 season, , 223–224
1942 season (championship game), 214–215, 215 (photo),
1943 season,
1943 season (championship game), , 227 (photo)
1944 season, , 227–228
1945 season (championship game), 235–238
1945 season,
1946 season, , ,
1947 season, , , ,
1948 season,
1949 season, 281–282
1950s seasons, 308–313
1951 season, , 302–303,
1954 season,
1955 season,
1958 season,
1961 season, 312–313,
1962 season,
band, , 171–172,
Baugh and, 144–146, 147–151
financial issues,
game attendance and, ,
as popular and profitable, 223–224
racism/racial integration and, , , 302–303, 308–313
sale of,
team halftime shows, band, and fight song, , , ,
television broadcasting, ,
_See also_ Marshall, George Preston
Washington Senators, , ,
_Washington Star,_
_Washington Times,_
Waterfield, Bob, , , , , , ,
Watkins, Bobby,
Watner, Abraham, ,
Webster, Alex, , ,
Weightman, William,
Weis, George, 280–281
Weller, John "Jac,"
Wheeling (West Virginia) Stingers,
White, Byron "Whizzer," ,
White, Walter,
Widener, Peter,
Williams, Edward Bennett,
Willis, Bill, , ,
Wojciechowicz, Alex,
Wolfner, Walter,
World War II era, 209–230
1941 season, 209–214
1942 season, 214–215, 216–217, 223–224
1943 season, 217–220, , , 227 (photo)
1944 season, 220–221, 224–225, 227–228
1945 season, 229–230
1945 season, 230–234
college football during,
NFL players and owners in military during ( _see under_ National Football League)
Wray, Lud, 2–3, 65–66, , , , , ,
wrestling,
Wrigley, William, 177–178
Wrigley Field,
Yankee Stadium, , , 318–319, 321–322
Yost, Fielding, ,
Young, Andrew "Doc,"
Young, Lou, 65–66
Younger, Paul "Tank," ,
Zeman, Josefa Humpal,
Zuppke, Robert, , ,
# Contents
1. Cover
2. Title Page
3. Copyright
4. Table of Contents
5. Dedication
6. Prologue
7. PART ONE
1. 1 Halas: The Founder
2. 2 Mara: The Promoter
3. 3 Marshall: The Showman
4. 4 Bell: The Profligate Son
5. 5 Rooney: The Gambler
8. PART TWO
1. 6 Almost Broke
2. 7 New Ideas
3. 8 Benny and the Giants
4. 9 Instituting a Draft
5. 10 Betting Bonanza
6. 11 Move to DC
9. PART THREE
1. 12 Brotherhood of Rivals
2. 13 A Step Forward
3. 14 The Greatest Rout
4. 15 Same Old Pirates
5. 16 Political Winds
6. 17 Dog Meat
7. 18 Two Wars
8. 19 The Right Guy in Charge
10. PART FOUR
1. 20 Back Across the Color Line
2. 21 Scandal
3. 22 Everyone Loses
4. 23 The Little Black Box
5. 24 All-White Redskins
6. 25 Forty Million Viewers
11. Epilogue
12. Acknowledgments
13. About the Author
14. Also by John Eisenberg
15. Praise for _The League_
16. Note on Sources
17. Bibliography
18. Notes
19. Index
# Navigation
1. Begin Reading
2. Table of Contents
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Euchlaena ochrearia är en fjärilsart som beskrevs av Mcdunnough 1940. Euchlaena ochrearia ingår i släktet Euchlaena och familjen mätare. Inga underarter finns listade i Catalogue of Life.
Källor
Mätare
ochrearia | {
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Razor-qt — свободная среда рабочего стола для X Window System. Разработчики описывают Razor-qt как «современное, удобное в использовании и быстрое окружение рабочего стола, основанное на Qt. В отличие от множества других сред рабочего стола, Razor-qt работает на слабых ПК также хорошо».
На февраль 2012 года окружение составляют: панель, рабочий стол, апплет запуска приложений, центр управления настройками и управление сессиями. Каждый из этих компонентов может быть включён или отключён пользователем.
Razor-qt работает с большинством современных менеджеров окон для X Window System, такими как Openbox, KWin, fvwm.
21 июля 2013 года разработчики Razor-qt заявили о слиянии с проектом LXDE-Qt под новым названием LXQt.
См. также
LXDE
Ссылки
Проект Razor-qt на сайте GitHub
Примечания
Среды рабочего стола
Программное обеспечение с лицензией GNU GPL
Приложения, использующие Qt
Свободное программное обеспечение, написанное на C++ | {
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{"url":"https:\/\/www.gradesaver.com\/textbooks\/math\/calculus\/calculus-3rd-edition\/chapter-12-parametric-equations-polar-coordinates-and-conic-sections-12-5-conic-sections-exercises-page-636\/30","text":"## Calculus (3rd Edition)\n\n- the vertices are $(\\pm 4,0)$ and $(0, \\pm 2)$ - the foci are $(0, \\pm \\sqrt{12})$ - the center is $(0,0)$\nThe equation $4x^2+ y^2=16$ can be written in the form $$\\left(\\frac{x}{2}\\right)^{2}+\\left(\\frac{y}{4}\\right)^{2}=1$$ which is an ellipse with $a=2, b=4$ so $b\\gt a$ and hence $c=\\sqrt{b^2-a^2}=\\sqrt{16-4}=\\sqrt{12}$. So, we have: the vertices are $(0,\\pm 4)$ and $(\\pm 2,0)$ the foci are $(0, \\pm \\sqrt{12})$ the center is $(0,0)$","date":"2020-01-22 14:02:03","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9665433764457703, \"perplexity\": 81.38320237403441}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-05\/segments\/1579250607118.51\/warc\/CC-MAIN-20200122131612-20200122160612-00522.warc.gz\"}"} | null | null |
» Prince Edward Island
Media Education in Prince Edward Island
This section comprises a curricular overview (below), as well as information about professional development for media education, and about media education associations in Prince Edward Island in the left menu.
Also included in the left menu are curriculum outcome charts from Prince Edward Island's English Language Arts, Social Studies and Communication and Information Technology curricula. These charts include links to supporting MediaSmarts resources and lessons.
Last reviewed in August 2021
Curricular Overview
Media literacy in Prince Edward Island is integrated throughout the curricula at the elementary and secondary levels - especially in the English Language Arts curriculum.
The Prince Edward Island Department of Education follows the English Language Arts framework developed under the auspices of the Atlantic Provinces Education Foundation (APEF), a curriculum consortium formed in 1995.
Media literacy figures prominently in the APEF English Language Arts curriculum. The curriculum builds on the concept that literacy means moving beyond competency in the written word, to the ability to use and understand visual and technological means of communication. Its goal is to create critical media consumers who can, and will, bring critical analysis to their use of the media.
In the APEF English Language Arts Curriculum Guides, the "Role of Media Literacy" is described separately from the roles of Drama, Literature, Critical Literacy, Visual Literacy and Information Literacy.
According to the guide for Grades 7-9:
Media literacy deals with the culture and lifestyle of students. They enjoy thinking and talking about what is going on in the media. For teachers, it is an opportunity to have students examine how they are influencing and being influenced by popular culture.
The guide also states:
How teachers choose to integrate media literacy into the English language arts program will be determined by what the students are reading and writing. On some occasions students might be involved in comparing (the print version of a story to the film version; ad images to the product being sold), examining (the use of images in music videos and newspapers, sexism in advertising), writing (an article in a magazine, a letter to an editor), producing (a pamphlet on an issue, a radio ad), and creating (a video, a school radio show, announcements for the school PA). Media literacy is a form of critical thinking that is cross-curricular. It is more about good questions than correct answers.
The guide for Grades 10-12 builds on those ideas and includes statements such as:
For teachers media literacy is an opportunity to examine the reliability, accuracy and motives of these sources;
Media study allows students to investigate issues of power and control. Mass media information is being consolidated into the hands of a few people. There are relatively few decision makers or gatekeepers to decide what and who gets heard.
In addition to the media outcomes in the English Language Arts curriculum, most secondary schools in Prince Edward Island offer an elective media course at the Grade 11 level. Individual junior high schools are also free to create a media course if they wish.
Media literacy also figures prominently in the APEF Social Studies framework.
Business Education 10-12
Communication and Information Technology Literacy K-12
English Language Arts 10-12
Social Studies K-12
Technology Education K-12
Young Canadians In A Wired World | {
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{"url":"https:\/\/math.stackexchange.com\/questions\/1618068\/least-and-greatest-value-of-z-given-that-z-4-z-2","text":"# Least and greatest value of $|z|$ given that $|z- 4\/z| = 2$?\n\nIf the complex number $z$ satisfies the equation $\\left\\lvert z- {4\\over z}\\right\\rvert = 2$ then the least and the greatest values of $|z|$ are ?\n\nMy try $\\left\\lvert z- {4\\over z}\\right\\rvert = 2$\n\n$\\left| |z| - \\left\\lvert z- {4\\over z}\\right\\rvert \\right| \\le 2$.\n\n\u2022 Jan 19, 2016 at 11:39\n\u2022 How do you define $\\mathrm{mod}(z)?$ Jan 19, 2016 at 11:40\n\u2022 mod(z) is defined as $\\sqrt( x^2+y^2)$ if Z= x+iy Jan 19, 2016 at 11:41\n\u2022 @ labbhattacharjee i have seen it and know the inequalities but cannot understand how to proceed further Jan 19, 2016 at 11:44\n\u2022 Divide by $2$ and let $w = \\frac{z}{2}$. The equation becomes $\\lvert w - 1\/w\\rvert = 1$. Square it, you get (after a little rearranging) a quadratic equation in $x = \\lvert w\\rvert^2$. Jan 19, 2016 at 13:50\n\nGiven $$\\left|z-\\frac{4}{z}\\right| = 2$$ and here we have to find $\\max$ and $\\min$ of $|z|$\n\nSo $$|z| = \\left|\\left(z-\\frac{4}{z}\\right)+\\frac{4}{z}\\right|\\leq \\left|z-\\frac{4}{z}\\right|+\\frac{4}{|z|}$$\n\nAbove we have used $\\bf{\\triangle \\; Inequality}$\n\nSo $$|z|\\leq 2+\\frac{4}{|z|}\\Rightarrow |z|^2-2|z|\\leq 4$$\n\nSo $$\\left(|z|-1\\right)^2 \\leq 5$$\n\nNow after that You can solve it.\n\n\u2022 Hey. (excuse me for no mathjax. I will update this). If you consider the identity |z1(+-)z2| <= |z1| + |z2|, where z1=z and z2=4\/z, then wont the inequality become 2<= |z|+|4\/z|, which is totally the different thing? Dec 5, 2016 at 13:07\n\nIf you know $\\left|\\frac zw\\right|=\\frac{|z|}{|w|}$, then you can solve your inequality for real $|z|$. Then see if real $z$ attains those max and min.\n$$|r-4\/r|\\leq2\\\\-2r\\leq r^2-4\\leq2r\\\\5\\leq(r+1)^2,(r-1)^2\\leq5\\\\-1+\\sqrt{5}\\leq r\\leq1+\\sqrt{5}$$\n\n\u2022 But how is this helpful?? Jan 19, 2016 at 13:39","date":"2022-05-21 02:28:01","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\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8351997137069702, \"perplexity\": 654.0545432204744}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662534773.36\/warc\/CC-MAIN-20220521014358-20220521044358-00162.warc.gz\"}"} | null | null |
class EmailAttachment < ActiveRecord::Base
mount_uploader :attachment, AttachmentUploader
before_save :update_attachment_attributes
before_create :save_original_filename
belongs_to :email_message
validates :attachment, presence: true
# :file_size => {
# :maximum => 1.0.megabytes.to_i
# }
validate :image_size_validation, if: 'attachment?'
def image_size_validation
errors.add(:attachment, 'should be less than 1M') if attachment.size > 1.0.megabytes.to_i
end
private
def save_original_filename
# logger.info "ATTACHMENT: #{attachment.file.original_filename}"
self.original_file_name = attachment.file.original_filename
end
def update_attachment_attributes
return unless attachment.present? && attachment_changed?
self.content_type = attachment.file.content_type
self.file_size = attachment.file.size
end
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\section*{INTRODUCTION}
\noindent
The classical \emph{Wiener--Hopf algebra} $A_{\reals_+}\,$, also known as the \emph{reduced Toeplitz algebra}, is an object of basic interest in Operator Theory. It may be defined as the C$^*$-algebra of bounded operators on $\Lp[^2]0{\reals_+}$ generated by all \emph{Wiener--Hopf operators}
\[
(W_fg)(x)=\int_0^\infty f(x-y)g(y)\,dy\mathfa g\in\Lp[^2]0{\reals_+}\,,\,f\in\Lp[^1]0{\reals}\,,\,x\in\reals_+\ .
\]
The \emph{symbol map} $\sigma:A_{\reals_+}\to\Ct[_0]0\reals$ is the surjective $*$-morphism defined on generators by $\sigma(W_f)=\Hat f\,$, where the latter denotes the Fourier transform of $f\in\Lp[^1]0\reals\,$. It gives rise to a short exact sequence
\[
\xymatrix{0\ar[r]&\knums\ar[r]&A_{\reals_+}\ar[r]^-{\sigma}&S=\Ct[_0]0\reals\ar[r]&0}\ .\tag{$*$}
\]
Let $\partial:K_1(S)\to K_0(\knums)=\ints$ be the connecting map in $K$-theory induced by this exact sequence. The following theorem is well-known.
\begin{Th*}
If $T$ is a Fredholm operator contained in the unitisation of $A_{\reals_+}\,$, then
\[
\partial[\sigma(T)]=\Index T\in\ints=K_0(\knums)\ .
\]
Moreover, $\partial$ is a group isomorphism, and for any $n\in\ints\,$, there exists a Fredholm element $T$ as above such that $\Index T=n\,$.
\end{Th*}
\noindent
The six-term exact sequence immediately gives the following corollary.
\begin{Cor*}
We have $K_i(A_{\reals_+})=0$ for $i=0,1\,$.
\end{Cor*}
\noindent
In fact, the Theorem might also be deduced from the statement of the Corollary, by using the six term exact sequence.
Moreover, the Theorem can be used to prove Bott periodicity and thus the existence of the six-term exact sequence. This is the approach taken by Cuntz \cite{cuntz-bott}. (Cuntz defines $A_{\reals_+}$ algebraically, and his elegant deduction of the $K$-triviality of this C$^*$-algebra is quite different from the one we shall propose below.)
\medskip\noindent
From the point of view of analysis and index theory, it seems natural to consider the multivariate generalisation of the Wiener--Hopf algebra and to study its $K$-theory.
Thus, let $\Omega\subset\reals^n$ be a closed convex cone, which we assume to be \emph{pointed}, i.e.~$\Omega$ contains no affine line, and \emph{solid}, i.e.~$\Omega$ generates $\reals^n$ as a vector space. Then \emph{Wiener--Hopf operators} shall be the bounded operators on $\Lp[^2]0\Omega$ given by
\[
(W_fg)(x)=\int_\Omega f(x-y)g(y)\,dy\mathfa g\in\Lp[^2]0\Omega\,,\,f\in\Lp[^1]0{\reals^n}\,,\,x\in\Omega\ .
\]
The C$^*$-algebra $A_\Omega$ of bounded operators generated by the $W_f$ will be called the \emph{Wiener--Hopf algebra}. This C$^*$-algebra and its relatives are the object of study of quite an extensive literature, and we refer the interested reader to the introduction of our joint paper with Troels Johansen \cite{alldridge-johansen1}, for a partial overview.
Just as in the $n=1$ case, there is an obvious symbol map $\sigma:A_\Omega\to\Ct[_0]0{\reals^n}\,$, which continues to be a surjective $*$-morphism for $n>1\,$. However, it is not to be expected that the kernel of $\sigma$ (the commutator ideal) equals the ideal of compact operators in this case. Rather, $A_\Omega$ has a composition series whose length is at most $n\,$. For the remainder of the paper, let us assume that $\Omega$ is \emph{polyhedral}, i.e.~finitely generated as a convex cone. Then the length of the composition series is exactly $n\,$, cf.~\cite{alldridge-johansen1}.
However, on the level of $K$- and even $KK$-theory, this distinction is invisible. Indeed, we shall prove in this paper the following theorem.
\begin{Th}
Let $\Omega$ be a polyhedral cone. Then $A_\Omega$ is $KK$-contractible, and $A_\Omega/\knums$ and $S$ are $KK$-equivalent.
\end{Th}
This Theorem was previously known only for a particular class of polyhedral cones called \emph{exhaustible}, and is due to Buyukliev \cite{buyukliev} in this case. He exploits the particular combinatorial structure of these cones to prove the Theorem via Mayer--Vietoris sequences and the exact six-term sequence.
Arguably, in the general polyhedral case, the proof of $KK$-contractibility must take the whole combinatorial structure of an arbitrary polyhedral cone into account. In fact, the following result comes about as spin-off of our proof the above Theorem.
\begin{Th}
Let $\Omega$ be a cone with polyhedral base $P\,$. Then the isomorphism class of $A_\Omega$ completely determines the combinatorial type of $P\,$, i.e., the lattice isomorphism class of its lattice of faces.
\end{Th}
This is turn relies on the fact that the cellular differential of $P\,$, considered as a CW complex by considering each $j$-face as a $j$-cell, may be identified with the $d^1$ differential of the $E^1$ term of the Atiyah--Hirzebruch spectral sequence induced by the composition series alluded to above, a result which may be interesting in itself. We will describe this in detail below.
\section{STRUCTURE OF THE WIENER--HOPF ALGEBRA}
\noindent
In this section, we review some results on the composition series of the Wiener--Hopf algebra $A_\Omega\,$, in particular, the construction and computation of certain `index maps'. These results are actually valid far beyond the case of polyhedral cones. However, restricting to polyhedral cones simplifies matters considerably, so we state them in this case only. The interested reader is referred to our joint papers with Troels Johansen \cite{alldridge-johansen1, alldridge-johansen2}, for the general case.
\subsection{Composition Series and Analytical Index Formula}
Let $\Omega\subset\reals^n$ be a pointed and solid polyhedral cone. $\Omega$ is spanned by its exposed rays, and one may choose a set $E$ of generators of exposed rays contained in an affine hyperplane $H\,$. There exists a linear automorphism $L$ of $\reals^n$ such that $L(H)=1\times\reals^{n-1}\,$. Let $P$ be the convex hull of all $x$ such that $(1,x)\in L(E)\,$. Then $P$ is a convex polyhedron in $\reals^{n-1}\,$, and
\[
L(\Omega)=\reals_+\cdot(1\times P)=\Set1{(\lambda,\lambda\cdot x)}{\lambda\sge0\,,\,x\in P\subset\reals^{n-1}}\ .
\]
Henceforth, we will omit reference to the linear automorphism $L\,$, and assume that $\Omega=\reals_+\cdot(1\times P)$ where the set $P\subset\reals^{n-1}$ is a convex polyhedron. This assumption is no loss of generality, since the C$^*$-algebras $A_\Omega$ and $A_{L(\Omega)}$ are isomorphic.
For $j=-1,\dotsc,n-1\,$, let $f_j$ be the number of $j$-dimensional convex faces of $P$ (where the empty set is considered as the unique face of dimension $-1$). This somewhat annoying index shift is an artefact introduced by considering $j$-faces of $P$ as $(j+1)$-faces of $\Omega\,$, and will continue to trouble us in the following.
\begin{Th*}[Muhly--Renault \cite{muhly-renault}]\label{th:whfiltration}
There exists a finite filtration of $A_\Omega$ by ideals $I_0=0\subset I_1=\knums\subset\dotsm\subset I_{n+1}=A_\Omega$ such that $I_{j+1}/I_j$ is a liminary C$^*$-algebra with spectrum $\{1,\dotsc,f_{j-1}\}\times \reals^j\,$.
\end{Th*}
Both the ideals $I_j$ and the isomorphism of the subquotients $I_{j+1}/I_j$ with the algebras $\Ct[_0]0{\{1,\dotsc,f_{j-1}\}\times\reals^j}\otimes\knums\,$, $j<n\,$, and $\Ct[_0]0{\reals^n}\,$, $j=n\,$, respectively, are given quite explicitly, but we shall not need the precise formulae.
Let $\partial_j:K^i_c(\{1,\dotsc,f_{j-1}\}\times\reals^j)\to K^{i+1}_c(\{1,\dotsc,f_{j-2}\}\times\reals^{j-1})\,$, $j=1,\dotsc,n\;$, be the $K$-theory connecting maps induced by the exact sequences
\[
\xymatrix{0\ar[r]&I_j/I_{j-1}\ar[r]&I_{j+1}/I_{j-1}\ar[r]^-{\sigma_j}&I_{j+1}/I_j\ar[r]&0}\ .
\]
Let $F_j$ be the set of $j$-dimensional faces of $P\,$, and let $\Omega_F\,$, for $F\in P\,$, be the face of $\Omega$ spanned by $F\,$. For any $A\subset\reals^n\,$, let $\Span0A$ denote the linear span. We may identify $\{1,\dotsc,f_{j-1}\}\times\reals^j$ with the trivial rank $j$ vector bundle
\[
\Sigma_j=\Set1{(F,y)\in F_{j-1}\times\reals^n}{y\in\Span0{\Omega_F}}
\]
over the finite base $F_{j-1}\,$.
For any subset $A\subset\reals^n\,$, let $A^*=\Set0{y\in\reals^n}{\Scp0yA\sge0}$ be the dual cone, and let $A^\perp=\Set0{y\in\reals^n}{\Scp0yA=0}$ be the orthogonal complement of the linear span. Then define, for any face $F$ of $P\,$,
\[
\Omega_F^\circledast=\Set1{x\in\Span0{\Omega_F^\perp\cap\Omega^*}}{\Scp0xy\sge0\smathfa y\in \Omega_F^\perp\cap\Omega^*}\ .
\]
(This notation differs from \cite{alldridge-johansen1, alldridge-johansen2}.)
The continuous field of Hilbert spaces $(\Lp[^2]0{\Omega_F^\circledast})_{(F,y)\in\Sigma_j}$ naturally defines a Hilbert $\Ct[_0]0{\Sigma_j}$-module $\mathcal E_j\,$. The $*$-morphism $\sigma_j$ extends to a representation of $A_\Omega$ by adjointable endomorphisms of this Hilbert module. By these means, the map $\partial_j$ lends itself to an analytical expression, as follows.
\begin{Th*}[A.--Johansen \cite{alldridge-johansen1}]
Let $a\in M_N(I_{j+1}^+)$ represent the $K$-theory class $[\sigma_j(a)]\in K^1_c(\Sigma_j)\,$. Then $\sigma_{j-1}(a)$ is a Fredholm operator on the Hilbert $\Ct[_0]0{\Sigma_{j-1}}$-module $\mathcal E_{j-1}^N\,$, and
\[
\partial_j[\sigma_j(a)]=\Index\sigma_{j-1}(a)\in K^0_c(\Sigma_{j-1})\ .
\]
\end{Th*}
\subsection{$KK$-Theoretical Index Formula}
The finite set
\[
\mathcal P_j=\Set1{(E,F)\in F_{j-2}\times F_{j-1}}{E\subset F}
\]
may be considered as bibundle w.r.t.~the obvious projections $\xi:\mathcal P_j\to F_{j-2}$ and $\eta:\mathcal P_j\to F_{j-1}$ ($j\sge1$). The map
\[
\eta^*\Sigma_j\to\xi^*\Sigma_{j-1}:(E,F,y)\mapsto(E,F,p_E(y))
\]
realises $\eta^*\Sigma_j$ as the trivial line bundle over the base $\xi^*\Sigma_{j-1}\,$. (Here, for $A\subset\reals^n\,$, $p_A$ denotes the orthogonal projection onto $\Span0A\,$.) Indeed, a nowhere vanishing section is given by the map
\[
s_j:\xi^*\Sigma_{j-1}\to\eta^*\Sigma_j:(E,F,u)\mapsto(E,F,u+e_F(E))
\]
where the unit vector $e_F(E)\in\Omega_E^\perp\cap\Span0{\Omega_F}$ is given as follows. If $\check \Omega_F=\Omega_F^\perp\cap\Omega^*$ denotes the dual face of $\Omega_F\,$, then $\check\Omega_F^\perp\cap\Omega_E^\circledast$ is an extreme ray of $\Omega_E^\circledast\,$, and $e_F(E)$ is the unique unit vector contained in this ray.
The trivial line bundle $\eta^*\Sigma_j\to\xi^*\Sigma_{j-1}$ induces an isomorphism of $K$-groups $K_c^i(\eta^*\Sigma_j)\to K_c^{i+1}(\xi^*\Sigma_{j-1})\,$. It is given by multiplication by an invertible $KK$-theory element $y_j\in KK^1(\eta^*\Sigma_j,\xi^*\Sigma_{j-1})$ where for locally compact Hausdorff spaces $X$ and $Y\,$, we write $KK^q(X,Y)=KK(\Ct[_0]0X,\Ct[_0]0{\reals^q\times Y})\,$. Another way to think about $y_j$ is that it is `fibre integration', i.e.~the inverse of the Thom isomorphism for the above line bundle. This depends on the choice of an orientation; we will go into detail further below.
The only other ingredients needed for our index formula (at least in the polyhedral case) are the projections $p_\xi:\xi^*\Sigma_{j-1}\to\Sigma_{j-1}$ and $p_\eta:\eta^*\Sigma_j\to\Sigma_j$ induced, respectively, by $\xi$ and $\eta\,$. Since $\xi$ and $\eta$ have finite domain, $p_\xi$ and $p_\eta$ are proper, and thus induce $*$-morphisms $\pmb\xi:\Ct[_0]0{\Sigma_{j-1}}\to\Ct[_0]0{\xi^*\Sigma_{j-1}}$ and $\pmb\eta:\Ct[_0]0{\Sigma_j}\to\Ct[_0]0{\eta^*\Sigma_j}\,$, respectively.
\begin{Th*}[A.--Johansen \cite{alldridge-johansen2}]
Let $1\sle j\sle n\,$. As elements of $KK^1(\Sigma_{j-1},\Sigma_j)\,$,
\[
\partial_j=\pmb\xi_*\pmb\eta^*y_j\ .
\]
\end{Th*}
\section{COHOMOLOGICAL INDEX AND CELLULAR DIFFERENTIAL}
\subsection{Cohomological expression of the index}
If $X$ is a locally compact space, then there is a natural ring morphism $\ch:K_c^*(X)\to \bigoplus_{k=0}^\infty H^{*+2k}(X,\rats)\,$, called the \emph{Chern character}, which is rationally an isomorphism.
Let $\pi:V\to X$ be an oriented real vector bundle. We have Thom isomorphisms
\[
\vphi_V:K_c^*(X)\to K_c^{*+\rk V}(V)\mathtxt\AND\psi_V:H_c^*(X)\to H_c^{*+\rk V}(V)\ .
\]
In the special case that $V$ is \emph{trivial}, these are related via the Chern character, i.e.~$\ch\circ\vphi_V=\psi_V\circ\ch\,$. (In general, of course, the interplay is more subtle.)
As is customary, we denote integration along the fibres of $\pi\,$, which is the inverse map $\psi_V^{-1}:H_c^{*+\rk V}(V)\to H_c^*(X)\,$, by $\pi_*\,$.
In particular, applying this to $y_j^{-1}:K_c^*(\xi^*\Sigma_{j-1})\to K_c^{*+1}(\eta^*\Sigma_j)\,$, we immediately obtain the following cohomological expression of the index map $\partial_j\,$.
\begin{Prop}
For all $u\in K_c^i(\Sigma_j)\,$, we have
\[
\ch(\partial_j(u))=p_{\eta*}\pi_*p_\xi^*\ch(u)\mathtxt{in}\bigoplus_{k=0}^\infty H_c^{2k+i+1}(\Sigma_{j-1},\rats)
\]
where $\pi$ denotes the projection of the (trivial) line bundle $\eta^*\Sigma_j\to\xi^*\Sigma_{j-1}\,$.
\end{Prop}
We remark that
\[
K_c^i(\Sigma_j)=K_c^i(F_{j-1}\times\reals^j)=\begin{cases}0&i+j\equiv1\pmod 2\ ,\\\ints^{f_{j-1}}&i+j\equiv0\pmod2\ ,\end{cases}
\]
so that $K_c^*(\Sigma_j)$ has no torsion. In particular, $\ch$ is injective on $K_c^*(\Sigma_j)\,$. It is known that its image is the integral cohomology $H^*_c(\Sigma_j,\ints)\,$, cf.~\cite[Proposition 4.3]{hatcher-vbktheory}. In particular, $\partial_j$ is completely determined by its cohomological expression, and the latter is integral.
In we take the trivialisation of $\eta^*\Sigma_j\to\xi^*\Sigma_{j-1}$ to be given by the non-vanishing section $s_j$ defined above, then the orientation of this bundle is induced by choices of orientations of $\Sigma_{j-1}$ and $\Sigma_j\,$. These will be induced by choices of trivialisations of these bundles. (The triviality of the latter bundles is particular to the polyhedral situation.) As we shall presently see, the detailed inspection of these choices leads directly to the explicit expression of $\partial_j$ as a cellular differential.
\subsection{The Wiener--Hopf Index as a Cellular Differential}
The $n$-dimen\-sion\-al convex polytope $P$ can be considered as a finite CW complex by taking the $j$-faces to be the $j$-cells. (Topologically, $P$ is of course an $n$-cell, so there are simpler ways to consider it as a CW-complex. However, our point of view captures the combinatorics of the face lattice.) The cellular complex is then $(H^0(F_j),d_j)$ where $H^0(F_j)$ is the free Abelian group generated by the $j$-faces.
The vector bundle $\Sigma_j\to P_j$ is trivial, hence orientable, and we have a Thom isomorphism $\psi_j:H^0(F_j)\to H^j_c(\Sigma_{j+1})$ given by the choice of an orientation. Let us make this choice explicit. A trivialisation of $\Sigma_j$ is given by the map
\[
F_{j-1}\times\reals^j\to\Sigma_j:(F,y)\mapsto(F,A_Fy)
\]
where for each $F\in F_{j-1}\,$, $A_F:\reals^j\to\Span0{\Omega_F}$ is a linear isomorphism. An orientation of (the fibres of) $\Sigma_j$ is given by pulling back the standard orientation $\sigma^+=\eps\circ\det$ of $\reals^j$ to $\Span0{\Omega_F}$ along $A_F^{-1}$ to an orientation $\sigma_F\,$. The Thom isomorphism $\psi_j$ is given by the cup product with the Thom class $c_j\in H^j_c(\Sigma_j)$ which is determined by the condition
\[
\int_{(\Span0{\Omega_F},\sigma_F)}c_j(F,\cdot)=1\mathfa F\in F_{j-1}\ .
\]
The line bundle $\pi:\eta^*\Sigma_j\to\xi^*\Sigma_{j-1}$ is oriented by the choice of the non-vanishing section $s_j\,$. Observe that for each $(E,F)\in\mathcal P_j\,$, there exists a unique orientation $\sigma$ on $\Span0{\Omega_F}$ such that
\[
\sigma(e_F(E),v_1,\dotsc,v_{j-1})=\sigma_E(v_1,\dotsc,v_{j-1})\mathfa v_1,\dotsc,v_{j-1}\in\Span0{\Omega_E}\ .
\]
We denote by $[E:F]=\pm1$ the unique sign such that $\sigma_F=[E:F]\cdot\sigma_E\,$. If $E\not\subset F\,$, we define $[E:F]=0\,$.
\begin{Prop}
For $0\sle j\sle d\,$, let $\tilde d_j:H^0(F_j)\to H^0(F_{j-1})$ be the map induced by the index map $\partial_{j+1}:K_c^{j+1}(\Sigma_{j+1})\to K_c^j(\Sigma_j)$ and the Thom isomorphisms $\psi_{j+1}\,$, $\psi_j\,$, via the relation
\[
\psi_j\circ\tilde d_j\circ\psi_{j+1}^{-1}\circ\ch=\ch\circ\,\partial_{j+1}\ .
\]
Then $\tilde d_j$ is given on generators by the formula
\[
\tilde d_j(F)=\sum_{E\subset F}[E:F]\cdot E\ .
\]
\end{Prop}
\begin{proof}
Consider a form $c_{j+1}\in\Gamma_c(\Sigma_{j+1},\wedge^{j+1}T^*\Sigma_{j+1})$ representing the Thom class in $H^{j+1}_c(\Sigma_{j+1})\,$. Then $p_\eta^*c_{j+1}$ is represented by
\[
\eta^*\Sigma_{j+1}\to\wedge^{j+1}T^*\eta^*\Sigma_{j+1}:(E,F,u)\mapsto c_{j+1}(F,u)\ .
\]
Because we have the decomposition $\Span0{\Omega_F}=\reals\cdot e_F(E)\oplus\Span0{\Omega_E}\,$, the Fubini theorem gives
\[
\int_{(\Span0{\Omega_E},\sigma_E)}\int_\reals p_\eta^*c_{j+1}(E,F,\cdot+te)(e,\cdot)\,dt=[E:F]\cdot\int_{(\Span0{\Omega_F},\sigma_F)}c_{j+1}(F,\cdot)=[E:F]\ ,
\]
where we write $e=e_F(E)\,$. Since this condition characterises the Thom class $c_j$ up to the factor $[E,F]\,$,
\[
\pi_*p_\eta^*c_{j+1}(E,F,\cdot)=[E:F]\cdot c_j(E,\cdot)\mathtxt{in}H_c^j(\Span0{\Omega_E})\ .
\]
We find
\[
p_{\xi*}\pi_*p_\eta^*c_{j+1}(E,u)=\sum_{F\subset E}\pi_*p_\eta^*c_{j+1}(E,F,u)=\sum_{F\subset E}[E:F]\cdot c_j(E,u)\ .
\]
Applying the cup product, the conclusion follows.
\end{proof}
In order to see that the maps $\tilde d_j$ coincide with the cellular differentials $d_j\,$, let us explicitly describe $d_j\,$. To that end, we construct attaching maps. First, for any convex set $C\subset\reals^j$ containing the origin in its interior, let $\mu_C$ be its Minkowski gauge. If, more generally, the convex set $C$ has non-void interior and $b_C$ is its barycentre, then the map
\[
\vphi_C:\reals^j\to\reals^j\ , \
\vphi_C(x)=\begin{cases}\frac{\mu_{C-b_C}(x-b_C)}{\Norm0{x-b_C}}\cdot(x-b_C)&x\neq b_C\ ,\\
0&x=b_C\ ,\end{cases}
\]
is a homeomorphism inducing homeomorphisms $C\to\ball^j$ and $\partial C\to\sph^{j-1}$ where the latter has degree $1\,$.
Next, for any $j$-face $F\in F_j\,$, let the linear isomorphism $A_F:\reals^{j+1}\to\Span0{\Omega_F}$ used above to trivialise $\Sigma_{j+1}$ be chosen such that $A_F(0\times\reals^j)$ is the linear subspace parallel to the affine span of $F\,$, and such that $\tilde F:=A_F^{-1}(F-b_F)\subset\ball^j\,$. We then define the attaching map for the $j$-cell associated with $F$ by
\[
\phi_F:\ball^j\to F\subset P:x\mapsto A_{\vphantom{\tilde F}F}^{\vphantom{-1}}\vphi_{\tilde F}^{-1}(x)+b_F
\]
If for any pair $(E,F)\in F_{j-1}\times F_j$ the number $c_{EF}\in\ints$ denotes the degree of the composite
\[
\xymatrix{%
\sph^{j-1}\ar[r]^-{\phi_F}&\partial F\ar[r]&P/(P\setminus E^\circ)=E/\partial E\ar[r]^-{\phi_E^{-1}}&\ball^{j-1}/\sph^{j-2}\ar[r]&\sph^{j-1}}
\]
where the rightmost map is the standard one ($x\mapsto(ux,2\Norm0x-1)$ where $u$ is suitably chosen), then the cellular differential $d_j:H^0(F_j)\to H^0(F_{j-1})$ is defined on generators by
\[
d_j(F)=\sum_{E\subset F}c_{EF}\cdot E\ .
\]
\begin{Prop}[degree-coeff]
We have $c_{EF}=[E,F]$ for any pair $(E,F)\in F_{j-1}\times F_j\,$. In particular, the cellular differential $d_j$ coincides with $\tilde d_j\,$.
\end{Prop}
\begin{proof}
Let $H_0:\partial F\to\sph^{j-1}$ be the composite
\[
\xymatrix{%
\partial F\ar[r]&P/(P\setminus E^\circ)=E/\partial E\ar[r]^-{\phi_E^{-1}}&\ball^{j-1}/\sph^{j-2}\ar[r]&\sph^{j-1}}\ .
\]
Next, let $1\sge t>0\,$. Let $e$ be a positive multiple of the projection of $e_F(E)$ onto the subspace $0\times\reals^n=\Span0P\,$, and define
\[
F_s=\Set1{x\in F}{\Rscp0{x-b_E}e\sle s}\mathfa s\in[0,1]\ ,
\]
the elements of `height' $\sle s$ over $E\,$. By definition of $e\,$, $F_0=E\,$. We may take $e$ to be normalised in such a way that $F_1=F\,$.
We wish to define a map $H_t:\partial F_t\to\sph^{j-1}\,$. To that end,
define an affine map
\[
A_t:\reals\times\reals^{j-1}\to\reals^n\mathtxt{by}A_t(2s-t,x)=s\cdot e+A_Ex+b_E\ .
\]
Then $\tilde F_t=A_t^{-1}(F_t)$ is a compact convex subset of $\reals^j$ containing $0$ in its interior. Define
\[
H_t:F_t\cap\partial F\to\sph^{j-1}\mathtxt{by}H_t=f_t\circ\vphi_t^{-1}\circ A_t^{-1}\ ,
\]
where $\vphi_t=\vphi_{\tilde F_t}$ and for $r\in[0,1]\,$, $f_r:\sph^{j-1}\to\sph^{j-1}$ is given by
\[
f_r(s,x)=\Parens1{ux,\min\Parens1{1,-1+2\tfrac{s+1}{r+1}}}\ ,
\]
for suitably chosen $u\,$. The map $f_r$ maps all points of the sphere of height $\sge r$ to the `north pole' $e_j=(0,\dotsc,0,1)\,$.
The set
$B=\partial F_t\cap\Set1x{\Rscp0{x-b_E}e=t}$ bounds a flat in $F_t\,$. Since $\tilde F_t\subset\ball^j\,$, the elements of $\vphi_t^{-1}(A_t^{-1}(B))$ have
$j$th coordinate $\sge t\,$. Thus, $H_t$ maps $B$ to $e_j\,$, and hence extends to all of $\partial F$ by sending $\partial F\setminus F_t$ to $e_j\,$. Moreover,
$H_t\,$, together with $H_0\,$, form a homotopy. We conclude
\[
c_{EF}=\deg H_0\circ\phi_F=\deg H_1\circ\phi_F=\mathop{\mathrm{sign}}\det((e,A_E)^{-1}A_F)=[E:F]\ ,
\]
which proves our claim.
\end{proof}
\section{PROOF THE MAIN THEOREM}
\subsection{Invariance of the Combinatorial Type of $P$}
Recall that the \emph{combinatorial type} of the convex polyhedron $P$ is the lattice isomorphism class of the lattice of convex faces of $P\,$. The \emph{$f$-vector} of $P$ is the vector $(f_0,\dotsc,f_n)$ whose component $f_j$ is the numbers of $j$-faces.
The following theorem is a somewhat surprising if simple consequence of \thmref{Prop}{degree-coeff}.
\begin{Th}
Let $\Omega$ be a convex cone with polyhedral base $P\,$. Then the isomorphism class of $A_\Omega$ determines the combinatorial type of $P\,$. I.e., if $\Omega'$ is another cone with polyhedral base $P'\,$, and $A_\Omega$ and $A_{\Omega'}$ are isomorphic, then $P$ and $P'$ have isomorphic face lattices.
\end{Th}
\begin{proof}
The ideals in the filtration $(I_j)$ of $A_\Omega$ from \thmref{Th}{whfiltration} are recursively characterised by the property that $I_{j+1}/I_j$ is the largest liminary ideal of $A_\Omega/I_j$ with Hausdorff spectrum. Thus, the $f$-vector of $P$ and the index maps, and thus the maps $d_j\,$, are uniquely determined up to a choice of orientations. In particular, the absolute values $\Abs0{[E:F]}$ are uniquely determined for any pair of faces $(E,F)$ where $E$ is of codimension one in $F\,$. But these numbers determine the lattice order. Hence the assertion.
\end{proof}
\subsection{The $KK$-contractibility of $A_\Omega$}
As C$^*$-algebras with finite ideal filtrations with subquotients stably isomorphic to multiples of $\Ct[_0]0{\reals^n}\,$, $A_\Omega$ and $A_\Omega/\knums$ belong to the bootstrap category $\mathcal N$ and therefore obey the UCT \cite[Definition 22.3.4, Theorem 23.1.1]{blackadar-ktheory}. In order to determine their $KK$ equivalence class, it suffices to compute their $K$-theory.
The C$^*$-algebra $A_\Omega$ has a filtration by ideals $(I_j)\,$, and since $I_1=\knums\,$, $A_\Omega/\knums$ has the filtration by ideals given by $(I_j/I_1)\,$. For any C$^*$-algebra $A$ filtered by ideals $(I_j)\,$, Schochet has introduced an Atiyah--Hirzebruch type homology spectral spectral sequence $(E^r_{p,q})$ which converges to the $K$-theory of $A\,$. In the case of $A=A_\Omega\,$, by \cite[Theorem 2.1]{schochet-topmeth1}, its $E^1$ term is
\[
E^1_{p,q}=K_{p+q}(I_p/I_{p-1})=
\begin{cases}
H^0(F_{p-2})&q\equiv1\pmod2\ ,\\
0&q\equiv0\pmod2\ .
\end{cases}
\]
Hence, every other column of $E^1$ is zero. Hence, $E^r$ abuts to $E^2\,$.
\begin{Prop}
The homology spectral sequence $E_{p,q}^r$ in $K$-theory induced by the filtration $(I_j)$ abuts to its $E^2$ term, which is zero. In particular, $K_*(A_\Omega)=0$ and $K_*(A_\Omega/\knums)=K_*(\cplxs)\,$.
\end{Prop}
\begin{proof}
By definition, the $d^1$ differential is the composite
\[
\xymatrix{%
E^1_{p,1}=K_{p+1}(I_p/I_{p-1})\ar[r]^-{\partial}&K_p(I_{p-1})\ar[r]&K_p(I_{p-1}/I_{p-2})=E^1_{p-1,1}}
\]
where the first map is the boundary map in the exact six-term sequence in $K$-theory, and the second is induced by the quotient map $I_{p-1}\to I_{p-1}/I_{p-2}\,$. Considering
the commutative diagram with exact rows,
\[
\xymatrix{%
0\ar[r]&I_{p-1}\ar[r]\ar[d]&I_p\ar[r]\ar[d]&I_p/I_{p-1}\ar@{=}[d]\ar[r]&0\\
0\ar[r]&I_{p-1}/I_{p-2}\ar[r]&I_p/I_{p-2}\ar[r]&I_p/I_{p-1}\ar[r]&0
}
\]
it follows from the naturality of connecting maps that $d^1$ is also given by the connecting map for the lower line. This is just the map $\partial_{p-1}\,$. We have already noted that $\partial_{p-1}$ is uniquely determined by its cohomological expression, and the latter gives the cellular differential $d_{p-2}\,$. Thus, $(E^1_{p,1},d^1_p)$
is up to a shift, just the augmented cellular chain complex of the CW complex $P\,$. Since $P$ is contractible, this complex is exact. Hence, $E^2=0\,$, and the first statement follows.
To complete the proof, observe that dividing by $I_1=\knums$ corresponds to removing the augmentation from the cellular complex. The resulting complex has cohomology concentrated in degree zero, and $H^0(F_0)=\ints\,$. (Alternatively, use the exact six-term sequence.)
\end{proof}
\begin{Cor}
The C$^*$-algebra $A_\Omega$ is $KK$-contractible, and $A_\Omega/\knums$ and $S$ are $KK$-equivalent.
\end{Cor}
\begin{Cor}
The isomorphism $K_1(A_\Omega/\knums)\to\ints$ given by computing the numerical index of Fredholm Wiener--Hopf operators, is an isomorphism.
\end{Cor}
\begin{proof}
The groups $K_1(A_\Omega/\knums)$ and $\ints$ are isomorphic, and Buyukliev \cite{buyukliev} has constructed a Fredholm Wiener--Hopf operator of index one.
\end{proof}
\medskip\emph{Acknowledgements.}
Part of this work was conducted while the author was a visitor at the Institut Henri Poincar\'e, Paris. The author wishes to thank the institute for its hospitality and the organisers of the Special Trimester on `Groupoids, Stacks in Physics and Geometry' for their support.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,610 |
Q: A minor CSS issue about footer This is my simple webpage :-
<html>
<head>
<style type="text/css">
.body{
max-width:3072px;
min-width:3072px;
margin:0px auto;
background: url('Stripes.png') no-repeat #293231;
background-attachment:fixed;
background-position:0% 25%;
}
.back{
z:index:0;
}
</style>
</head>
<body class="body">
<table cellpadding="0" cellspacing="0">
<tr>
<td>
<img src='Main.jpg' class="back"/>
</td>
<td>
<img src='Page2.jpg'/>
</td>
<td>
<img src='Page3.jpg'/>
</td>
</tr>
<tr>
<td>
<img src='MiddleLeft.png'/>
</td>
<td>
<img src='MiddleMiddle.png'/>
</td>
<td>
<img src='MiddleRight.png'/>
</td>
</tr>
<tr>
<td>
<img src='footer.jpg'/>
</td>
<td>
<img src='footer.jpg'/>
</td>
<td>
<img src='footer.jpg'/>
</td>
</tr>
</table>
</body>
</html>
Problem here is due to my large monitor the footer doesn't appear at the bottom of the monitor. It appears somewhere in the middle. How do i ensure that footer appears only at the bottom of the screen irrespective of the size of the screen?
A: Have a look at:
A Bulletproof Sticky Footer, Woohoo!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,689 |
{"url":"https:\/\/www.alignmentforum.org\/posts\/jYvm4mmjvGHcPXtGL\/a-concrete-proposal-for-adversarial-ida","text":"# 8\n\nAI\nFrontpage\n\nNote: This post came out of a conversation with Geoffrey Irving and Buck Shlegeris.\n\nEpistemic Status: I suspect Paul has already thought of most or all of the ideas presented here, though I nevertheless found the exercise of carefully specifying an IDA implementation helpful and suspect others may find reading it helpful as well.\n\nThis is a proposal for how to train a machine learning model to approximate HCH using Iterated Distillation and Amplification (IDA). This particular proposal came out of a desire to use a debate-like adversary to improve the amplification process, and the primary goal of this proposal is to show how one could do that. Though I have tried to retain a lot of the relevant detail, I have made two simplifications to make this proposal easier to specify: I am attempting to approximate something closer to weak HCH rather than strong HCH and I am only allowing the generation of two subquestions at a time. I am confident that those simplifications could easily be dropped, though I think doing so here would only make this presentation more complicated.\n\nBefore I proceed, I want to make one final note: this is not a proposal for how to build an aligned AGI. I think there are still a whole bunch of issues that would prevent this proposal from actually working.\n\n## Definitions\n\n\u2022 Let be the set of all questions in natural language.\n\u2022 Let be the set of all answers in natural language.\n\u2022 Let be the sum type of either or representing either an answer to the given question or two subquestions to help answer it.\n\u2022 Let be the answer that a human gives to the given question.\n\u2022 Let be the answer or subquestion pair generated by a human when asked what to do with the given question.\n\u2022 Let be the answer or two subquestions generated by a human to some question when given answers to two subquestions related to that question.\n\u2022 Let be a model (the training procedure for which we will describe below) from questions to a probability distribution over strings representing answers. Specifically, we will implement the probability distribution by having our model output an embedding vector which yields the probability distribution when fed into some trained language model (by repeatedly conditioning on previous characters and multiplying all the conditional probabilities).\n\u2022 Let be the function from questions to an embedding vector representing a distribution over answers or subquestions generated by asking what to do with the given question. For the two subquestion case we enforce that the distribution is symmetric wrt interchange of the subquestions.\n\u2022 Let be the function from two answers to an embedding vector representing a distribution over answers or subquestions generated by asking to integrate the given subquestion answers into an answer to the original question. We again enforce symmetry wrt interchange of the subquestions.\n\u2022 Let be an adversary model which we will train (as described below) to predict how good the given answer is to the given question.\n\u2022 Let be an adversary model for generated by calling using the same transformation as used to implement from .\n\u2022 Let be an adversary model for generated by calling using the same transformation as used to implement from .\n\u2022 Let be some Gumbel random variable such that each use of below is its own independent sample from a Gumbel distribution. We use a Gumbel random variable so that we can use the Gumbel-max trick to effectively do Boltzmann exploration.\n\n## Amplification\n\nThe goal here is to use the adversary to determine which portions of the HCH tree we actually go down to maximize our sample efficiency wrt . Specifically, the amplification procedure is as follows:\n\n1. Generate some question either from the training distribution or from the output of some adversary.\n\n2. Call . If we get an answer, let and skip to the end. Otherwise, let .\n\n3. Call to generate scores and .\n\n4. Without loss of generality, let and recurse on (by setting in the subcall) to generate (from the of the subcall) and let .\n\n5. Call . If we get an answer, let . Otherwise, let and return to step 3.\n\nThis procedure should eventually produce an answer, though we then need to compute the following losses for :\n\nNote that some of these losses are actually for the same model since are implemented internally by calling and are implemented internally by calling .\n\n## Distillation\n\nFor the distillation procedure, we want to improve by training it to approximate its own -consulting- tree. Specifically:\n\n1. Generate some as in amplification.\n\n2. Call . If we get an answer, let and skip to the end. Otherwise, let .\n\n3. Let and .\n\n4. Call . If we get an answer, let . Otherwise, let and return to step 3.\n\nThen, compute the following losses for :\n\n## Iteration\n\nFinally, we want to iterate the above procedure by replacing in the amplification procedure with some . First, let be some confidence threshold. Then, we will define the following primed s:\n\n\u2022 Let .\n\u2022 Let\n\u2022 Let\n\nThis procedure allows us to continue amplifying the model while using the adversary to require only minimal human data that is selected so as to be maximally helpful.\n\n## Conclusion\n\nThis proposal differs in a couple of ways from previous proposals made by Paul. First, Paul has recently moved away from discrete amplification\/distillation steps. This proposal, however, provides a way to recover discrete steps while still collapsing the recursion. In practice, however, you might still just want to stick with the amplification procedure described here without doing the distillation step, as it isn't strictly necessary.\n\nSecond, this proposal uses an adversary to guide the training process. This technique is similar to the concept of importance sampling. The main benefit of this approach is that it takes advantage of active learning by allowing the system to choose which questions and subquestions would be most useful for it to have answered by a human.\n\nAnother benefit of the adversary, however, is that it could make transparency much easier. One of the major benefits of IDA is that gets trained to approximate its own -consulting- tree. As a result, understanding the reasoning that went into the final answer produced by can be recovered by unfolding its tree (at least in the limit of perfect training). However, unfolding the entire tree is very expensive, as it's linear in the size of the tree. With an adversary, however, you can choose which portions of the tree to unfold first by calling the adversary, enabling you to find errors much more quickly; for a perfect adversary, this reduces the problem of finding an error to instead of .\n\nThus, the hope is that the use of such an adversary could assist both in making IDA more competitive (by increasing sample efficiency and using active learning) and in making IDA safer (due to the increased ease of transparency).\n\nIt should be noted, however, that it is also possible that the use of such an adversary might make the safety situation for IDA worse. First, it introduces the possibility of a robustness to relative scale failure if either or gets significantly stronger than the other. One possible way to resolve such an issue, however, might be to give the ability to call and vice versa, allowing them to use each other to boost their own capabilities. Second, for an and system that are themselves optimizers, with goals that don't perfectly match up with their loss functions, they could cooperate to make it arbitrarily unlikely that is ever consulted on some specific question. Third, even if and weren't cooperating, an RSA-2048-style failure could still prevent the identification of malicious cognition. Resolving failures of these second two types is still an open question (EDIT: see \"Risks from Learned Optimization in Advanced Machine Learning Systems,\" by Hubinger, van Merwijk, Mikulik, Skalse, and Garrabrant).\n\nAI2\nFrontpage\n\n# 8\n\nNew Comment\n\nSummary:\n\nThis post presents a method to use an adversary to improve the sample efficiency (with respect to human feedback) of iterated amplification. The key idea is that when a question is decomposed into subquestions, the adversary is used to predict which subquestion the agent will do poorly on, and the human is only asked to resolve that subquestion. In addition to improving sample efficiency by only asking relevant questions, the resulting adversary can also be used for interpretability: for any question-answer pair, the adversary can pick out specific subquestions in the tree that are particularly likely to contain errors, which can then be reviewed.\n\nOpinion:\n\nI like the idea, but the math in the post is quite hard to read (mainly due to the lack of exposition). The post also has separate procedures for amplification, distillation and iteration; I think they can be collapsed into a single more efficient procedure, which I wrote about in this comment.\n\nGiven that you are training the model during amplification, I don't really see why you also have a distillation step, and an iteration step. I believe the point of that separation is to allow amplification to not involve ML at all, so that you can avoid dealing with the issues around bootstrapping -- but if you train while amplifying, you are already bootstrapping. In addition, you're requiring that exactly one subquestion be sent to the human, but it seems better to allow it to be zero, one or two, depending on how confident the adversary is in the ML model's answer. Concretely, I would get rid of both distillation and iteration, and change step 4 of the amplification procedure:\n\n4. For , flip a biased coin , where is a function that computes recursion probabilities from adversary scores. If , compute by recursing on , else set .\n\nYou could compute if you want to use a confidence threshold with Boltzmann exploration.\n\nThis new procedure allows for the behavior you have with distillation, in the cases where it actually makes sense to do so: you recover distillation in the case where the adversary thinks that the answers from to both subquestions are good.\n\nThe last two adversary losses have a typo: you should be computing the difference between the adversary's prediction and the true loss, not the sum.\n\nMeta: I found this post quite hard to read, since everything was written in math with very little exposition.\n\nI considered collapsing all of it into one (as Paul has talked about previously), but as you note the amplification procedure I describe here basically already does that. The point of the distillation step, thus, is just to increase sample efficiency by letting you get additional training in without requiring additional calls to . I do agree that you could include the iteration procedure described here into the amplification procedure, which is probably a good idea, though you'd probably want to anneal in that situation, as starts out really bad, whereas in this setup you shouldn't have to do any annealing because by the time you get to that point should be performing well enough that it will automatically anneal as its predictions get better. Also, apologies for the math--I didn't really have the time to write up more explanation, so it was a choice between posting it as is or not posting it at all, and I went with posting it as is.\n\n(Also, the sum isn't a typo--I'm using the adversary to predict the negative of the loss, not the loss, which I admit is confusing and I should probably switch it.)\n\nI didn't really have the time to write up more explanation, so it was a choice between posting it as is or not posting it at all, and I went with posting it as is.\n\nMakes sense. I think I could not tell how much I should be trying to understand this until I understood it. I probably would have chosen not to read it if I had known how long it would take and how important I thought it was (ex-post, not ex-ante). For posts where that's likely to be true, I would push for not posting at all.\n\nAnother way you could see this: given my current state of knowledge about this post, I think I could spend ~15 minutes making it significantly easier to understand. The resulting post would have been one that I could have read more than 15 minutes faster, probably, for the same level of understanding.\n\nI think it's not worth making a post if you don't get at least one person reading it in as much depth as I did; so you should at the very least be willing to trade off some of your time for an equal amount of time of that reader, and the benefit scales massively the more readers you have. The fact that this was not something you wanted to do feels like a fairly strong signal that it's not worth posting since it will waste other people's time.\n\n(Of course, it might have taken you longer than 15 minutes to make the post easier to understand, or readers might usually not take a whole 15+ minutes more to understand a post without exposition, but I think the underlying point remains.)\n\nThe point of the distillation step, thus, is just to increase sample efficiency by letting you get additional training in without requiring additional calls to H\n\nNote that my proposed modification does allow for that, if the adversary predicts that both of the answers are sufficiently good that neither one needs to be recursed on. Tuning in my version should allow you to get whatever sample efficiency you want. An annealing schedule could also make sense.\n\n(Also, the sum isn't a typo--I'm using the adversary to predict the negative of the loss, not the loss, which I admit is confusing and I should probably switch it.)\n\nAh, yeah, I see it now.","date":"2021-04-22 01:37:21","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\": 0.840120792388916, \"perplexity\": 583.9476871611896}, \"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\/1618039560245.87\/warc\/CC-MAIN-20210422013104-20210422043104-00208.warc.gz\"}"} | null | null |
\section{Introduction}\label{sec:intro}
Black hole collisions are presently of great recent interest as one of
the ``grand challenges'' in high performance
computing\cite{grandchallenge}. The results of those studies, in turn,
can be important to the understanding of detectable sources of
gravitational waves\cite{ligo}.
To the present date the only case that has been extensively studied is
the head-on collision, from rest, of two holes starting with the
initial value solution given by Misner\cite{misner}. The spacetime
growing out of those initial data has been computed by the techniques
of numerical relativity\cite{anninos_etal93}, and has been studied by
analytic
means\cite{price_pullin94}\cite{all}\cite{abrahams_cook94}.
The initial value solution of Brill and Lindquist\cite{bl} (hereafter
``BL''), like the Misner solution, represents two initially stationary
nonspinning holes. Neither solution contains any initial radiation of
short wavelength compared to the characteristic size of the throats.
Outside the horizon the two initial value solutions can be thought of
as differing in the initial distortion of each throat caused by the
presence of the other throat.
There is in fact no solution of the initial value equations of general
relativity that is uniquely singled out as representing two initially
stationary holes. The Misner solution and BL solution are special
only in their mathematical convenience, and in the topological
properties of the geometry of the initial surface extended inside the
throats. Specifically, the Misner solution may be thought of
as having a two-sheeted topology. The two throats representing
the two black holes connect an upper ``physical'' sheet to
a single lower sheet isometric to the upper one.
In contrast, in the three-sheeted BL solution,
each of the throats connects from the
upper sheet to a separate lower sheet. The isometry between
the two sheets in the Misner solution results from an infinite
series of image terms in the solution to the hamiltonian
constraint. It is reasonable to expect that these terms
might lead to additional gravitational radiation, not present
in the BL solution. Other physical consequences of the image
terms have been studied in Ref. \cite{ck}.
Here we extend the analytic study of collisions of holes to the case
of BL initial data. There are two main justifications for doing this.
The first is that analytic answers are a useful aid to development of
the codes used in numerical relativity. The values reported here for
radiated energy can be tested against numerical codes for evolution of
axisymmetric initial data. For initially close black holes, it will be
interesting to see whether those codes agree with the analytic answers
as well as they do in the case of Misner initial data.
The second reason for some interest in the evolution of BL data is the
general question of the relationship of initial data to the generation
of gravitational radiation. In astrophysically realistic problems the initial
data will necessarily come from some approximation scheme, such as
post-Newtonian solutions. Such an approach is justified if the
gravitational wave signal generated depends only on certain general
features of the initial data and is insensitive to many details
(e.g., topology). The
comparison of the evolution of BL and Misner data gives us a simple
model for studying this question, and an interestingly simple (though
limited) answer.
In the next section we describe the application of close-limit
perturbation theory to the evolution of BL initial data. In Sec.~III
results are given for the radiation predicted by perturbation
theory. These results are compared with available fully numerical
results for the BL case, and are compared with analogous results
previously reported for collision from Misner initial data.
\section{Close-limit perturbation theory for BL initial data}
Like the Misner solution, the BL geometry is conformally flat and
takes the form $ds^2=\Phi^4\,ds_{\rm flt}^2$, where $ds_{\rm flt}^2$ is
the line element for flat 3-dimensional space, and where $\Phi$
satisfies the Laplace equation in the flat space. In terms of
spherical coordinates $R,\theta,\phi$, for $ds_{\rm flt}^2$, the
Misner or BL metrics can be written.
\begin{equation}\label{eq:conflat}
ds^2=\Phi^4(R, \theta;
\mu_0)\left(dR^2+R^2\left[d\theta^2
+\sin^2\theta\,d\phi^2
\right]\right)\ .
\end{equation}
For the BL geometry, the form of $\Phi$, aside from a factor of 2,
corresponds to the potential of Newtonian theory, with points of mass
$m$ at positions $z=\pm z_0$ on the $z$ axis:
\begin{equation}
\Phi_{\rm BL}=1+\frac{1}{2}
\left(\frac{m}{\sqrt{R^2\sin^2{\theta}+(R\cos{\theta}-z_0)^2}}
+\frac{m}{\sqrt{R^2\sin^2{\theta}+(R\cos{\theta}+z_0)^2}}\right)\ .
\end{equation}
For $R>z_0$ the square roots can be expanded in a power series in
$z_0/R$ and the BL 3-geometry written as
\begin{equation}\label{eq:BLinR}
ds^2_{\rm BL}=\left[1+\frac{M}{2R}\sum_{\ell=0,2,\dots}
\left(\frac{z_0}{R}\right)^{\ell}P_\ell(\cos{\theta})
\right]^4 \left(dR^2+R^2\left[d\theta^2
+\sin^2\theta\,d\phi^2
\right]\right)\ ,
\end{equation}
where the $P_\ell$ are the Legendre polynomials, and where $M\equiv2m$.
We next make a transformation of the radial coordinate $R$ to a new
coordinate $r$, as if we were transforming, in the Schwarzschild spacetime,
from isotropic coordinates to Schwarzschild coordinates:
\begin{equation}\label{eq:Rdef}
R=\left(\sqrt{r} +\sqrt{r-2M}\right)^2/4\ .
\end{equation}
It is convenient now to rewrite the line element for the 3-geometry as
\begin{equation}\label{eq:BLds}
ds^2_{\rm BL}=\left[1+\frac{M/(2R)}{1+M/(2R)}\sum_{\ell=2,4,\dots}
\left(\frac{z_0}{M}\right)^\ell\left(\frac{M}{R}\right)^{\ell}P_\ell(\cos{\theta})
\right]^4 \left(\frac{dr^2}{1-2M/r}+r^2\left[d\theta^2
+\sin^2\theta\,d\phi^2 \right]\right)\ ,
\end{equation}
where the meaning of $R$ is given by (\ref{eq:Rdef}).
The geometry in (\ref{eq:BLds}) reduces to the Schwarzschild geometry
if the summation in the leading factor on the right is ignored. That
summation, then, contains the information about the deviations from
sphericity and is the starting point for close-limit nonspherical
perturbation calculations\cite{ap1}. In particular, the parameter
$\epsilon\equiv z_0/M$ can be considered an expansion parameter for
perturbation theory. If, for each multipole index $\ell$, we keep only
the leading order in $\epsilon$, the approximation to the BL initial geometry
takes the form
\begin{equation}\label{eq:BLlin}
ds^2_{\rm BL}\approx\left[1+\frac{2M/R}{1+M/(2R)}\sum_{\ell=2,4,\dots}
\left(\frac{z_0}{M}\right)^\ell\left(\frac{M}{R}\right)^{\ell}P_\ell(\cos{\theta})
\right] \left(\frac{dr^2}{1-2M/r}+r^2\left[d\theta^2
+\sin^2\theta\,d\phi^2 \right]\right)\ .
\end{equation}
In principle, for each multipole index $\ell$, one can read off the
metric perturbations (which are purely even parity) from
(\ref{eq:BLlin}), can construct Moncrief's\cite{moncrief74} gauge
invariant perturbation wave function $\psi_{\rm pert}$, and can evolve
that wave function with the Zerilli equation\cite{zerilli}. In
practice, this need not be explicitly carried out. There is a
striking similarity between the expressions in
(\ref{eq:BLinR})-(\ref{eq:BLlin}) and the equivalent expressions for
the Misner geometry\cite{price_pullin94}\cite{all}. The single
difference is the coefficients in the series appearing in
(\ref{eq:BLinR})-(\ref{eq:BLlin}). For the Misner initial geometry
the coefficients are $\kappa_\ell(\mu_0)$. The dimensionless quantity $\mu_0$
parametrizes the initial separation of the
throats, and the $\kappa$'s are functions given in Ref.\cite{all}.
The single change
\begin{equation}
(z_0/M)^\ell\rightarrow4\kappa_\ell(\mu_0)
\end{equation}
converts (\ref{eq:BLinR})-(\ref{eq:BLlin}) to their equivalent form
for the Misner case. This means, for a given $\ell$, that $\psi_{\rm
pert}$ for the BL case has precisely the same form as for the Misner
case; the outgoing gravitational waves, according to perturbation
theory, are identical in shape. They differ only in a multiplicative
factor. Since power carried by outgoing waves is proportional to the
square of $\psi_{\rm pert}$ the results for BL infall, for each
$\ell$, can be found by multiplying the Misner results by
$[(z_0/M)^\ell/4\kappa_\ell(\mu_0)]^2$.
We note in passing that the ``forced linearization'' procedure
discussed in Ref. \cite{ap1} is, of course, also applicable to
the BL data.
This Misner-BL equivalence applies for any separation of the holes.
For large separations of the throats it is not surprising that the
gravitational waves generated by BL and by Misner initial data should
be similar. For small initial separations, however, there is a
significant difference between the 3-geometries of Misner and BL, and
it does seem strange that the gravitational waveforms should be
identical. Furthermore, it is for close initial separation that
perturbation theory is most applicable, so the prediction of identical
linearized waveforms is also a prediction about the actual waveforms.
How can such different initial conditions give rise to identical outgoing
waveforms?
It is important to realize that the linearized outgoing waves are
identical in form for each $\ell$, but the ratio of multipole
contributions differs for BL and Misner. In Fig.~1 this difference
in multipoles is shown quantitatively. For a given value of $\mu_0$
in the Misner geometry, an equivalent configuration for the BL
geometry is defined by setting the quadrupole amplitudes of $\psi_{\rm
pert}$ equal, i.e., by setting $(z_0/M)=2\sqrt{\kappa_2(\mu_0)}$. The
ratios of the BL amplitude to the Misner amplitude are then computed
for $\ell=4$ and $\ell=6$. (These amplitude ratios are in fact simply
$4\kappa_2(\mu_0)^2/\kappa_4(\mu_0)$ and
$16\kappa_2(\mu_0)^3/\kappa_4(\mu_0)$.) At large separation the
amplitude ratios approach unity; this shows that in the limit of large
separation the external fields become identical in the two initial
geometries. For small separations, however, the BL solution has a
relatively smaller contribution due to higher multipole moments; its
geometry is more quadrupole dominated. Though this is a relatively
important difference in the initial geometry near the throats, it is
of little importance for the gravitational radiation. Even for the
Misner initial conditions, the radiation is heavily quadrupole
dominated. It is possible that the lesson of this example has
a broader generality: the outgoing radiation can be insensitive to
many details of the initial data and even for strong field sources a
knowledge of the quadrupole moment may be all that is needed.
It is worth asking whether there is any deep physical meaning in the
fact that the only difference between the BL and Misner linear
perturbations is the ratio of the multipole amplitudes. This follows
from the fact that for a conformally flat 3-metric, with the form
(\ref{eq:conflat}), the factor $\Phi$ satisfies the flat space
Laplacian. If the solution is axisymmetric and asymptotically flat it
must be of the form
$\sum(\alpha_\ell/R^{\ell+1})P_\ell(\cos{\theta})$; solutions can
differ only in the values of the constants $\alpha_\ell$. So the
striking similarity of the BL and the Misner perturbations is a direct
result of the choice of the conformally flat form
(\ref{eq:conflat}). This choice is dictated by convenience, and need
not be made in principle. For more general momentarily stationary
initial geometries the linearized waveforms for each multipole will
have different appearance. For example, one could generate
valid initial data representing a Schwarzschild spacetime
with a nonconformally-flat perturbation by choosing an arbitrary
(small) metric perturbation and solving the linearized hamiltonian constraint
for the conformally-flat part of the perturbation. The gauge-invariant
function would then be computed from the full perturbation.
\section{Radiation Energy: BL vs. Misner}
The first, and most difficult, step in comparing radiation from the
two initial value sets is to decide on the basis for comparison: How
does one compare a BL problem with a particular value of $z_0/M$ with
a Misner problem of a particular $\mu_0$? At large separations it is
not difficult; one can compare BL and Misner configurations in which
the masses and separation of the holes are identical. For small
separations, however, the separation of the holes is somewhat
ambiguous. To deal with small, as well as large, separations we
choose a reasonably natural and convenient specific measure of the
separation $L$: the proper distance along the symmetry axis, between
the outermost disjoint marginally outer-trapped surfaces
around each throat. (For $z_0/M$ less than about 0.4, a single
apparent horizon encompasses both holes).
The locations of the marginally outer-trapped surfaces was
found using a standard shooting technique applicable to
axisymmetric spatial slices\cite{ah}.
We characterize both BL
and Misner configurations with $L/M$, where $M$ is the mass of the
spacetime. It is, of course, interesting not only to compare the
linearized predictions for BL against those for Misner, but also to
compare both against the results of numerical solutions of the fully
nonlinear field equations. For the Misner initial geometry the
numerical results are known from the work reported in
Ref.~\cite{anninos_etal93}. For BL initial conditions two data points
are available: cases c2 and c4 of from Ref.\cite{ast95}.
These numerically generated spacetimes have euclidean spatial topology,
with initial data consisting of spherical (in the conformal space)
collisionless matter configurations. When the initial configurations are
sufficiently compact, the matter is all inside disjoint apparent
horizons and the external 3-geometry is identical to the BL data.
For clarity, the results are presented in three separate
figures. Figure 2 shows the comparison of perturbation results and
numerical results for the Misner case. The perturbation energies
($E/M\approx0.0251\kappa_2^2(\mu_0))$ are those of
Ref.~\cite{price_pullin94}, except that energy has been plotted as a
function of $L/M$, rather than of $\mu_0$. The numerical data are
those of Refs.~\cite{anninos_etal93} and \cite{all}. Figure 3 shows
the analogous results for the BL case, for which the energy is
$E/M\approx0.0251[(z_0/M)^2/4]^2$. The two ``numerical'' data points
here are those of Ref.~\cite{ast95}.
Figure 2 shows that for the Misner case, linearized predictions begin
to diverge from the fully numerical results at around $L/M=4$. It is
fortunate that the numerical results available for the BL case are for
$L/M$ in the range 3--4. From Fig.~3 we can infer that for $L/M$ less
than around 3, the agreement between linearized and numerical results
is very good for BL collisions, and for $L/M$ above 4 there is
significant disagreement. In this sense there is little difference
between Misner and BL cases. Figure 4 shows the perturbation theory
comparison of Misner and BL cases. This figure shows that there is
little difference between the predicted radiation when $L/M$ is
greater than around 2. It is, therefore, not surprising that the
agreement between numerical and perturbation results, which breaks
down well above $L/M=2$, does not distinguish between BL and Misner
collisions. It is also not surprising that in BL collisions, as in
Misner collisions\cite{all}, the radiation is always quadrupole
dominated. (The large values of hexdecapole energy in Fig.~3 occur only
at separations large enough that linearized theory wildly
overestimates radiation.)
The results in Fig.~4 would seem to suggest that, for black holes
initially close, BL initial conditions lead to less radiation than
Misner black holes, as expected by the presence of image
terms in the Misner solution. An alternative interpretation
is that, for equal
radiation, the initial separation of the apparent horizons is greater
in the BL case than in the Misner case. Since equal radiation implies
equal quadrupole moments, this means that the different multipole
structure of the BL and Misner geometries makes the proper distance
between apparent horizons larger in the BL case when quadrupole
moments are equal. In this sense then, Fig.~4 is more of a depiction of
proper distances than of radiation.
This motivates asking whether there is a way of comparing BL and
Misner scenarios that is better, or at least different, from using
$L/M$. Another physically meaningful measure of how close the initial
throats are is the gravitational binding energy.
The gravitational binding energy is the difference between the
ADM energy of an initial data set representing two
black holes at finite separation and the energy of an
initial data set with the holes infinitely separated
(the sum of the bare masses of the holes).
For BL data this is given by\cite{bl}
\begin{equation}
{E_B \over M} = -{1 \over 8 z_0}.
\end{equation}
For Misner data one has\cite{lind63}
\begin{equation}
{E_B \over M} = - {\sum_{n=1}^{\infty} (n-1){\mathop{\rm
csch}\nolimits}{n \mu_0} \over \sum_{n=1}^{\infty}
{\mathop{\rm csch}\nolimits}{n \mu_0} }
\end{equation}
Radiated energy is plotted against
binding energy in Fig.~5, but the results give a picture very much
like that of Fig.~4. In particular, for small initial separations
(tightly bound initial configurations) there is less energy radiated
from a BL collision than from a Misner collision. For large initial
separations (small binding energies) the difference in radiated energy
is small for configurations with the same binding energy. The BL and
Misner cases become significantly different (say by a factor of 2) for
binding energy (binding energy/$M\approx-1.5$) that corresponds
roughly to the point ($L/M\approx1.3$) at which the BL and Misner
energies separate in Fig.~4.
We thank Greg Cook, Jorge Pullin, Ed Seidel, Stuart Shapiro,
Wai-Mo Suen, and Saul Teukolsky for helpful
discussions. AMA was supported by NSF grant PHY 93-18152/ASC 93-18152
(ARPA supplemented), and RHP was supported by NSF grant PHY95-07719.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,577 |
Bryan Adams Blames Coronavirus on "Bat Eating, Wet Market Animal Selling, Virus Making Greedy Bastards"
By Calum Slingerland
While Bryan Adams became a star with 1984's Reckless, a much stronger word should be ascribed to xenophobic comments about the coronavirus pandemic the Canadian songwriter let fly on Instagram this evening.
Today, Adams shared a solo acoustic rendition of "Cuts Like a Knife" on the platform, using the caption to lament a string of cancelled shows at London, UK's Royal Albert Hall before busting out some terribly racist remarks.
Adams proceeded to pin his cancelled performances on "some fucking bat eating, wet market animal selling, virus making greedy bastards" for putting "the whole world...on hold."
Adams's complete caption reads as follows:
CUTS LIKE A KNIFE. A song by me. Tonight was supposed to be the beginning of a tenancy of gigs at the @royalalberthall, but thanks to some fucking bat eating, wet market animal selling, virus making greedy bastards, the whole world is now on hold. My message to them other than "thanks a fucking lot" is go vegan. To all the people missing out on our shows, I wish I could be there more than you know. It's been great hanging out in isolation with my children and family, but I miss my other family, my band, my crew and my fans. Take care of yourselves and hope we can get the show on the road again soon. I'll be performing a snippet from each album we were supposed to perform for the next few days. X
On top of the racism, Adams's unhinged caption references a prevalent conspiracy theory in which the coronavirus is believed to have been created in a Chinese lab. The claim — which has been parroted by prominent American conservatives and politicians including president Donald Trump — has been widely rejected by scientists.
While a good portion of Adams's fans continue to gloss over his ugly comments on Instagram, he has concurrently been getting tuned up on Twitter all the while.
UPDATE (5/12, 1:45 p.m. ET): Following the massive wave of backlash, Adams has now issued an apology. "Apologies to any and all that took offence to my posting yesterday," he wrote in a follow-up Instagram post (see below). "No excuse, I just wanted to have a rant about the horrible animal cruelty in these wet-markets being the possible source of the virus, and promote veganism. I have love for all people and my thoughts are with everyone dealing with this pandemic around the world."
CUTS LIKE A KNIFE. A song by me. Tonight was supposed to be the beginning of a tenancy of gigs at the @royalalberthall, but thanks to some fucking bat eating, wet market animal selling, virus making greedy bastards, the whole world is now on hold. My message to them other than "thanks a fucking lot" is go vegan. To all the people missing out on our shows, I wish I could be there more than you know. It's been great hanging out in isolation with my children and family, but I miss my other family, my band, my crew and my fans. Take care of yourselves and hope we can get the show on the road again soon. I'll be performing a snippet from each album we were supposed to perform for the next few days. X❤️ #songsfromisolation #covid_19 #selfisolation #bryanadamscutslikeaknife
A post shared by Bryan Adams (@bryanadams) on May 11, 2020 at 8:45am PDT
INTO THE FIRE. Title track from the same album. Apologies to any and all that took offence to my posting yesterday. No excuse, I just wanted to have a rant about the horrible animal cruelty in these wet-markets being the possible source of the virus, and promote veganism. I have love for all people and my thoughts are with everyone dealing with this pandemic around the world. Here's the appropriately titled song that would have been performed tonight at the @royalalberthall . #bryanadamsintothefire #songsfromisolation #covid19 #banwetmarkets #govegan
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 856 |
María Teresa Freyre de Andrade (27 January 1896 – 20 August 1975) was a Cuban librarian and information scientist, the founder of the national public library system in Cuba (Red Nacional de Bibliotecas Públicas), and a pioneer of modern Cuban librarianship. She was the first director of the José Martí National Library in Havana, having been appointed by Fidel Castro after the Cuban Revolution in 1959. Freyre de Andrade envisioned a model of the biblioteca popular, a "popular library," which, in contrast to a public library where "the book stands still on its shelf waiting for the reader to come searching for it," would be "eminently active" in finding its readers.
Biography and education
Freyre de Andrade was born on 27 January 1896 in St. Augustine, Florida, where her father, Fernando Freyre de Andrade, had sought refuge for his family. Her family later returned to Cuba to fight in the revolution, where Fernando rose to the rank of general. Freyre de Andrade was forced to move to Paris in 1932 after the Machado regime killed three of her uncles. She studied French and library science at the Sorbonne between 1936 and 1937 and graduated in 1938 with a diploma in librarianship from the Ecole de Chartes. She returned to Cuba in 1938, where she lived most of the rest of her life until her death in Havana at age 79, in August 1975. She is buried in the Colón Cemetery in Havana.
Political activity
While living as an exile in Paris, Freyre de Andrade engaged in political activism against the Machado government. In 1933, together with Enrique Martínez and on behalf of the Committee of Young Cuban Revolutionaries (Comité de Jóvenes Revolucionarios Cubanos), she published the brochure El terror en Cuba, in which she denounced the horrors of the Machado regime.
She was appointed senator by the Cuban People's Party in 1948 and was imprisoned several times in the Guanabacoa prison. She was later forced into exile a second time in 1957 due to her opposition to the government of Fulgencio Batista.
Library career
After being appointed by Fidel Castro as the director of the Jose Martí National Library in Havana in 1959, Freyre de Andrade and her staff began to enact her vision of a "popular library," which would "mobilize the book and make it go in search of the reader." This included using buses that served as mobile libraries for rural areas where no libraries existed. Under the direction of María Teresa Freyre de Andrade, the National Library became one of the most active centers of Havana's cultural life, from preserving cultural heritage to offering literary programs and opening special collections of music and the visual arts.
In the early 1960s, Freyre de Andrade led the creation of the National Libraries Directorate (Dirección Nacional de Bibliotecas). This enabled her to put into practice her dream of integrating all the existing libraries across Cuba. Her work, which both integrated existing libraries and created new ones, resulted in the National Network of Public Libraries (Red Nacional de Bibliotecas Públicas), which provided each province with a public library to serve their information needs. As Director of the DGB, Freyre de Andrade attended each of these libraries several times a year, traveled across provinces to check the proper functioning of each and every one of the libraries that made up the network.
Freyre de Andrade founded the first professional library schools in Cuba for library training at a time when the country needed qualified personnel for professional performance.
Freyre de Andrade also inspired and developed a new model for political librarianship in Cuba, which rather than copying English models of libraries, was designed to "take an active part in what is the Revolution." Cuban librarians under Freyre de Andrade actively sought out materials that had previously been censored from library collections before the revolution, including politically critical publications from the 1950s. As part of this project of revolutionary librarianship, Freyre de Andrade and her Cuban library colleagues also became involved in the broader project of creating Cuba's own "computing industry and information infrastructure," which ultimately led to "a distinctive new field of information science, which inherited the revolutionary ideals of Cuban librarianship."
Children's librarianship
Freyre de Andrade was passionate about children's literacy and education. In 1930, she founded and edited the children's educational magazine Mañana. She was later awarded scholarships from the American Library Association to continue her education in children's literature and librarianship at Columbia University.
Cuban storyteller Mayra Navarro notes that Freyre de Andrade applied American child librarianship practices to Cuba: "At the end of the 1940s, Dr. María Teresa Freyre de Andrade brought to Cuba the experiences of libraries in the United States, which were beginning to have specialized spaces dedicated to children. When she became the director of the National Library at the beginning of the Revolution, she established a space in her youth department called "Storytime." This was aimed at the formation of a reading habit and the children's approach to literature, even before they could read."
As part of her work leading the National Library, Freyre de Andrade led collection development for children's literature. Per Eliseo Diego, who was in charge of the Department of Children's Literature and Narratives at the Martí National Library in Havana at the beginning of the Cuban Revolution: "The Revolution had the right to appoint María Teresa Freyre de Andrade as director of the National Library. She had the happy initiative of creating the first public library for children that existed in Cuba and that led our youngest readers to get in touch with books that until then they had no access."
Legacy
In 2004, the Cuban Association of Librarians(ASCUBI) formalized the creation of the María Teresa Freyre de Andrade National Prize, which is awarded to distinguished personalities for their work in public libraries. The Association of Cuban Historians also created an award in her name for librarians who support the work of historians.
The Jose Martí National Library, unusually for a national library, contains within its space a public circulating library, the María Teresa Freyre de Andrade Circulating room, in her honor.
References
1896 births
1975 deaths
People from St. Augustine, Florida
Cuban librarians
Cuban senators
Partido Ortodoxo politicians
Paris-Sorbonne University alumni | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,319 |
package com.zimbra.qa.selenium.projects.ajax.tests.zimlets.url;
import java.io.File;
import java.util.*;
import org.testng.annotations.*;
import com.zimbra.qa.selenium.framework.core.Bugs;
import com.zimbra.qa.selenium.framework.ui.*;
import com.zimbra.qa.selenium.framework.util.*;
import com.zimbra.qa.selenium.projects.ajax.core.AjaxCommonTest;
import com.zimbra.qa.selenium.projects.ajax.ui.mail.DisplayMail;
import com.zimbra.qa.selenium.projects.ajax.ui.mail.DisplayMail.Field;
public class GetMessage extends AjaxCommonTest {
@SuppressWarnings("serial")
public GetMessage() {
logger.info("New "+ GetMessage.class.getCanonicalName());
// All tests start at the login page
super.startingPage = app.zPageMail;
// Basic settings
super.startingAccountPreferences = new HashMap<String, String>() {{
put("zimbraPrefGroupMailBy", "message");
}};
}
@Test( description = "Receive a mail with a basic URL",
groups = { "smoke" })
public void GetMessage_01() throws HarnessException {
// Create the message data to be sent
String subject = "subject" + ZimbraSeleniumProperties.getUniqueString();
String url = "http://www.vmware.com";
String body = "text " + System.getProperty("line.separator") + url + System.getProperty("line.separator") + "text"+ ZimbraSeleniumProperties.getUniqueString() + System.getProperty("line.separator") ;
// Send the message from AccountA to the ZWC user
ZimbraAccount.AccountA().soapSend(
"<SendMsgRequest xmlns='urn:zimbraMail'>" +
"<m>" +
"<e t='t' a='"+ app.zGetActiveAccount().EmailAddress +"'/>" +
"<su>"+ subject +"</su>" +
"<mp ct='text/plain'>" +
"<content>"+ body +"</content>" +
"</mp>" +
"</m>" +
"</SendMsgRequest>");
// Click Get Mail button
app.zPageMail.zToolbarPressButton(Button.B_GETMAIL);
// Get all the messages in the inbox
DisplayMail display = (DisplayMail) app.zPageMail.zListItem(Action.A_LEFTCLICK, subject);
// Wait for a bit so the zimlet can take affect
SleepUtil.sleep(5000);
// Get the HTML of the body
HtmlElement bodyElement = display.zGetMailPropertyAsHtml(Field.Body);
// Verify that the phone zimlet has been applied
// <a href="http://www.vmware.com" target="_blank">http://www.vmware.com</a>
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url +"']", null, (String)null, 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url +"']", "target", "_blank", 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url +"']", null, url, 1);
}
@Test( description = "Receive a mail with two URLs in body",
groups = { "functional" })
public void GetMessage_02() throws HarnessException {
// Create the message data to be sent
String subject = "subject" + ZimbraSeleniumProperties.getUniqueString();
String url1 = "http://www.vmware.com";
String url2 = "http://www.google.com";
String body = "url1: " + url1 + " url2: "+ url2;
// Send the message from AccountA to the ZWC user
ZimbraAccount.AccountA().soapSend(
"<SendMsgRequest xmlns='urn:zimbraMail'>" +
"<m>" +
"<e t='t' a='"+ app.zGetActiveAccount().EmailAddress +"'/>" +
"<su>"+ subject +"</su>" +
"<mp ct='text/plain'>" +
"<content>"+ body +"</content>" +
"</mp>" +
"</m>" +
"</SendMsgRequest>");
// Click Get Mail button
app.zPageMail.zToolbarPressButton(Button.B_GETMAIL);
// Get all the messages in the inbox
DisplayMail display = (DisplayMail) app.zPageMail.zListItem(Action.A_LEFTCLICK, subject);
// Wait for a bit so the zimlet can take affect
SleepUtil.sleep(5000);
// Get the HTML of the body
HtmlElement bodyElement = display.zGetMailPropertyAsHtml(Field.Body);
// Verify that the phone zimlet has been applied
// <a href="callto:1-877-486-9273" onclick="window.top.Com_Zimbra_Phone.unsetOnbeforeunload()">1-877-486-9273</a>
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url1 +"']", null, (String)null, 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url1 +"']", "target", "_blank", 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url1 +"']", null, url1, 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url2 +"']", null, (String)null, 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url2 +"']", "target", "_blank", 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url2 +"']", null, url2, 1);
}
@Test( description = "Validate the url zimlet matches valid URLs",
groups = { "functional" })
public void GetMessage_03() throws HarnessException {
final String subject = "subject12955323015009";
final String mime = ZimbraSeleniumProperties.getBaseDirectory() + "/data/public/mime/url01/valid_url.txt";
final String url1 = "http://www.vmware.com";
final String url2 = "https://www.vmware.com";
// Inject the example message
LmtpInject.injectFile(app.zGetActiveAccount().EmailAddress, new File(mime));
// Click Get Mail button
app.zPageMail.zToolbarPressButton(Button.B_GETMAIL);
// Get all the messages in the inbox
DisplayMail display = (DisplayMail) app.zPageMail.zListItem(Action.A_LEFTCLICK, subject);
// Wait for a bit so the zimlet can take affect
SleepUtil.sleep(5000);
// Get the HTML of the body
HtmlElement bodyElement = display.zGetMailPropertyAsHtml(Field.Body);
// Verify that the phone zimlet has been applied
// <a href="callto:1-877-486-9273" onclick="window.top.Com_Zimbra_Phone.unsetOnbeforeunload()">1-877-486-9273</a>
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url1 +"']", null, (String)null, 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url1 +"']", "target", "_blank", 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url1 +"']", null, url1, 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url2 +"']", null, (String)null, 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url2 +"']", "target", "_blank", 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url2 +"']", null, url2, 1);
}
@Test( description = "Validate the url zimlet does not match invalid URLs",
groups = { "functional" })
public void GetMessage_04() throws HarnessException {
final String subject = "subject12976223025009";
final String mime = ZimbraSeleniumProperties.getBaseDirectory() + "/data/public/mime/url01/invalid_url.txt";
// Inject the example message
LmtpInject.injectFile(app.zGetActiveAccount().EmailAddress, new File(mime));
// Click Get Mail button
app.zPageMail.zToolbarPressButton(Button.B_GETMAIL);
// Get all the messages in the inbox
DisplayMail display = (DisplayMail) app.zPageMail.zListItem(Action.A_LEFTCLICK, subject);
// Wait for a bit so the zimlet can take affect
SleepUtil.sleep(5000);
// Get the HTML of the body
HtmlElement bodyElement = display.zGetMailPropertyAsHtml(Field.Body);
// TODO:
// Not sure which URL's to add to the mime
// Need to mine bugs for URLs that give issues
// Add URLS to the sample mime and add verification points here.
logger.info(bodyElement.prettyPrint());
}
@Test( description = "Receive a mail with a url in subject",
groups = { "functional" })
public void GetMessage_05() throws HarnessException {
// Create the message data to be sent
String url = "http://www.vmware.com";
String subject = "subject " + url;
// Send the message from AccountA to the ZWC user
ZimbraAccount.AccountA().soapSend(
"<SendMsgRequest xmlns='urn:zimbraMail'>" +
"<m>" +
"<e t='t' a='"+ app.zGetActiveAccount().EmailAddress +"'/>" +
"<su>"+ subject +"</su>" +
"<mp ct='text/plain'>" +
"<content>content"+ ZimbraSeleniumProperties.getUniqueString() +"</content>" +
"</mp>" +
"</m>" +
"</SendMsgRequest>");
// Click Get Mail button
app.zPageMail.zToolbarPressButton(Button.B_GETMAIL);
// Get all the messages in the inbox
DisplayMail display = (DisplayMail) app.zPageMail.zListItem(Action.A_LEFTCLICK, subject);
// Wait for a bit so the zimlet can take affect
SleepUtil.sleep(5000);
// Find the subject and the phone span
String locator = "css=span[id$='_com_zimbra_url']";
ZAssert.assertTrue(display.sIsElementPresent(locator), "Verify the phone zimlet applies to the subject");
ZAssert.assertEquals(display.sGetText(locator), url, "Verify the phone zimlet highlights the phone number");
}
@Bugs(ids = "29018,67927")
@Test( description = "Receive a mail with a URL in angled brackets",
groups = { "functional" })
public void GetMessage_06() throws HarnessException {
// Create the message data to be sent
String subject = "subject" + ZimbraSeleniumProperties.getUniqueString();
String url = "http://www.vmware.com";
String body = "text <" + url + "> text "+ ZimbraSeleniumProperties.getUniqueString();
// Send the message from AccountA to the ZWC user
ZimbraAccount.AccountA().soapSend(
"<SendMsgRequest xmlns='urn:zimbraMail'>" +
"<m>" +
"<e t='t' a='"+ app.zGetActiveAccount().EmailAddress +"'/>" +
"<su>"+ subject +"</su>" +
"<mp ct='text/plain'>" +
"<content>"+ body +"</content>" +
"</mp>" +
"</m>" +
"</SendMsgRequest>");
// Click Get Mail button
app.zPageMail.zToolbarPressButton(Button.B_GETMAIL);
// Get all the messages in the inbox
DisplayMail display = (DisplayMail) app.zPageMail.zListItem(Action.A_LEFTCLICK, subject);
// Wait for a bit so the zimlet can take affect
SleepUtil.sleep(5000);
// Get the HTML of the body
HtmlElement bodyElement = display.zGetMailPropertyAsHtml(Field.Body);
// Verify that the phone zimlet has been applied
// <a href="http://www.vmware.com" target="_blank">http://www.vmware.com</a>
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url +"']", null, (String)null, 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url +"']", "target", "_blank", 1);
HtmlElement.evaluate(bodyElement, "//a[@href='"+ url +"']", null, url, 1);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,574 |
O Festival Internacional de Música de Macau (FIMM; ) é um evento musical realizado anualmente pelo Instituto Cultural, através dos auspícios do governo da Região Administrativa Especial de Macau. A primeira edição ocorreu a 24 de outubro de 1987, sendo as três primeiras edições realizadas pela Direção dos Serviços de Turismo. Em 1991, passou a estar sob a organização do Instituto Cultural.
Palcos de apresentação
Centro Cultural de Macau
Igreja de São Domingos
Igreja e Seminário de São José
Teatro Dom Pedro V
Fortaleza do Monte
Torre de Macau
Casa do Mandarim
Óperas
Cavalleria rusticana, composição de Pietro Mascagni, libreto de Giovanni Targioni-Tozzetti e Guido Menasci
Pagliacci, composição e libreto de Ruggero Leoncavallo
Rigoletto, composição de Giuseppe Verdi, libreto de Francesco Maria Piave
Don Giovanni, composição de Wolfgang Amadeus Mozart, libreto de Lorenzo Da Ponte
Il trittico (Il tabarro, Suor Angelica e Gianni Schicchi) de Giacomo Puccini
Le nozze di Figaro, composição de Wolfgang Amadeus Mozart, libreto de Lorenzo Da Ponte
Dido and Aeneas de Henry Purcell, libreto de Nahum Tate
Il trovatore, composição de Giuseppe Verdi, libreto de Salvadore Cammarano e Leone Emanuele Bardare
Acis e Galatea, composição de Georg Friedrich Händel, libreto de John Gay
Der Freischütz, composição de Carl Maria von Weber, libreto de Johann Friedrich Kind
La serva padrona, composição de Giovanni Battista Pergolesi, libreto de Gennaro Antonio Federico
Tosca, composição de Giacomo Puccini, libreto de Luigi Illica e Giuseppe Giacosa
Norma, composição de Vincenzo Bellini, libreto de Felice Romani
Faust, composição de Charles Gounod, libreto de Jules Barbier e Michel Carré
Musicais da Broadway
Chicago, música de John Kander, letras de Fred Ebb
West Side Story, música de Leonard Bernstein, letras de Stephen Sondheim, libreto de Arthur Laurents
Guys and Dolls, música e letras de Frank Loesser, libreto de Jo Swerling e Abe Burrows
Grease, música e letras de Jim Jacobs, Warren Casey e John Farrar, libreto de Jim Jacobs e Warren Casey
Fame, música de Steve Margoshes, letras de Jacques Levy, libreto de José Fernandez
Peter Pan, música de Jule Styne, Mark Charlap e Trude Rittmann (arranjos de dança), letras de Betty Comden, Adolph Green e Carolyn Leigh, libreto de James Matthew Barrie
Miss Saigon, música de Claude-Michel Schönberg, letras de Alain Boublil e Richard Maltby Jr., libreto de Claude-Michel Schönberg e Alain Boublil
Hairspray, música de Marc Shaiman, letras de Scott Wittman e Marc Shaiman, libreto de Mark O'Donnell e Thomas Meehan
Ligações externas
1987 na música
Cultura de Macau
Festivais de música de Macau | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 286 |
Q: Arduino - how to concatenate byte arrays to get a final array I have the following Arduino function:
void SendCommandToDisplay(byte message[], byte size)
{
byte header[] = {0x5A, 0xA5};
byte result[] = {};
memcpy(result, header, sizeof(header));
memcpy(result+sizeof(header), message, size);
for (byte i=0; i<sizeof(result); i++)
{
Serial.print(result[i], HEX);
Serial.print(' ');
}
}
Then I call this function as follows:
byte test[]={0x82, 0x20, 0x10, 0x00, 0x03};
SendCommandToDisplay(test, sizeof(test) / sizeof(byte));
And seems is not working, I'm doing something wrong or maybe I have to do a reference or pointer. Any clue?
A: You are not allocating memory for the result variable - in your case try this:
void SendCommandToDisplay(byte message[], byte size)
{
byte header[] = {0x5A, 0xA5};
byte result[sizeof(header)+size];
memcpy(result, header, sizeof(header));
memcpy(result+sizeof(header), message, size);
for (byte i=0; i<sizeof(result); i++)
{
Serial.print(result[i], HEX);
Serial.print(' ');
}
}
Once simple approach to inserting the byte count (of message) following header is to change how the header is initialized:
byte header[] = {0x5A, 0xA5, size};
Note: a prior edit added an alternative to use the sizeof(message) but that was incorrect and removed - sizeof(message) where message is a parameter returns the sizeof of a pointer which is 2 on an arduino.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,510 |
\section{Introduction}
Assume that we are given two dynamical systems, whose underlying
dynamics might be unknown. We are interested in designing a \emph{classifier},
that is a machine which, given an observed trajectory generated by either the systems,
correctly identifies which of the candidate systems has generated such a trajectory.
We will refer to this problem as the problem of \emph{classification for dynamical systems}.
Problems of this type are ubiquitous within the community of \emph{systems and control}.
For instance, in fault detection one system may represent the
behavior in nominal conditions and another a prescribed
faulty behavior. Similarly, in networked control one system
may represent the closed-loop behavior when data are
successfully transmitted, while another system may represent the
open-loop behavior in the presence of packet dropouts.
Problems of this type naturally arise also when dealing with systems
that naturally exhibit multiple operating modes, for example switched circuits.
On the other hand, in \emph{computer science}, classification is the core of \emph{machine learning}
for pattern recognition \cite{Vapnik1995,Burges1998}, which has found several applications
in different fields of engineering, including applications that are
intensively studied in control engineering like fault detection and diagnosis \cite{Mahadevan2009}.
Yet, with regard to this problem, the interaction between these two communities has been low.
Within the {systems and control} community, classification
for dynamical systems has been studied in connection
with the analysis of switched\,/\,multi-mode systems
\cite{ViChSoSa03}\nocite{BaEg04,VuLiberzon2008,Lou2011,Ba13}-\cite{battSCL},
often under the term \emph{mode-identification},
which is defined as the problem of reconstructing the active mode of a switched
system from its output trajectories.
The common approach is a \emph{model-based} approach:
assuming a correct model of the system for each operating mode,
one can check whether or not mode-identification is feasible
via dynamic-dependent conditions, and mode-identifiers (in fact, classifiers)
can be obtained in terms of rank tests, least-square functions or dynamical systems.
While the theory also generalizes to noisy observations \cite{battSCL,TanLibCDC2011}
and to some types of nonlinear dynamics \cite{TanLibAUTOMATICA2010,battTAC},
little is known on how to approach model-based classification
if one departs from the hypothesis that the dynamics of the system are known with perfect accuracy.
Even in the simplest case where the dynamics are associated with \emph{parametric}
uncertainty, building a classifier is a non-trivial task. The difficulty is similar to the one
encountered in adaptive control based on multiple models, where a main issue
is indeed to guarantee that modelling inaccuracies do not destroy the
learning capability of the control scheme \cite{liberzon}.
In computer science, the main paradigm to classification
is instead the \emph{data-driven} paradigm.
Classifiers are designed by choosing a function with adjustable parameters
selected using a number of training data, called the \emph{examples}. The resulting function
(the classifier) is then evaluated according to its capability to \emph{generalize} from the training dataset,
that is to correctly map new examples. Popular methods are \emph{Neural Networks} (NN)
and \emph{Support Vector Machines} (SVM), whose
capability to {generalize} from a training dataset can be quantified
via suitable loss functions such as the \emph{risk} function \cite{Vapnik1995}.
{Data-driven} methods have the intrinsic potential to overcome issues related to model uncertainty,
and have already proven their effectiveness in challenging applications such as the prediction of epileptic
seizures from recording of EEG signals \cite{Chisci2010}.
However, it is not obvious how to tailor the analysis and design
of data-driven methods to the specific context where data come from dynamical systems.
It is worth pointing out that classification of data generated
from dynamical systems is not new in computer science. In fact, it can be
regarded as classification of \emph{time series} once we assume the existence
of an underlying data-generating system. Yet, approaches which take
this standpoint still try to incorporate models into the learning task, either
to extract from data informative \emph{features} \cite{Brodersen2011}
or to construct suitable \emph{kernel} functions \cite{Jebara2004,Vishwanathan2007}.
While incorporating models is a natural step to take, it
leads to the previous question of how to handle model uncertainty,
and does not help to understand the performance
achievable by model-free schemes.
Similar issues related to model-based approaches have been pointed out
also in the context of \emph{clustering} \cite{Lauwers2017}.
In this paper, we consider autonomous linear systems and approach the
classification problem from both model-based and data-driven perspectives,
pointing out relative merits and establishing connections between the two.
We first consider a model-based approach and derive a classifier assuming the
knowledge of the system dynamics. This approach has two fundamental merits:
i) to highlight necessary conditions for the existence of a correct classifier (problem feasibility);
ii) to guide the design and analysis of a data-driven solution.
In connection with ii), the model-based approach shows that
under problem feasibility one can design a correct classifier
which can be interpreted in terms of \emph{polynomial kernels} \cite{Burges1998}.
Building on this result, we consider a data-driven approach based on SVM.
By using properties stemming from the model-based solution,
we provide bounds on the margin of the classifier
and quantify its generalization performance \cite{Bartlett1999}
as a function of the systems one wishes to classify.
The rest of this paper is as follows. Sections II and III formalize
the problem of interest, and recall basic concepts regarding SVM.
In Sections IV and V, we present the main results. Section VI discusses the results and open problems.
Numerical simulations are reported in
Section VII, while Section VIII provides concluding remarks.
\section{Framework}\label{overview}
Consider two linear dynamical systems
\begin{eqnarray} \label{eq:sys}
\def1.7{1.3}
\Sigma_i \, \sim \, \left\{
\begin{array}{l}
x_{i}(t+1) = A_{i} \, x_i(t) \\
y_i(t) = C_{i} \, x_i(t)
\end{array}, \quad i =1,2
\right.
\end{eqnarray}
where $t \in \mathbb Z_+ := \{0,1,\ldots\}$ denotes time; $x_i \in {\mathop{\Bbb R}}^{n_i}$
is the state; $y_i \in {\mathop{\Bbb R}}^m$ is the output; $A_i$ and $C_i$ are state and output
transition matrices. We will assume that each $\Sigma_i$
is observable (in a control-theoretic sense).
This entails no loss of generality in that if $\Sigma_i$
is not observable, all subsequent developments apply to the
observable subsystem obtained via a Kalman observability
decomposition.
Assume now that we are given a sequence
\begin{eqnarray} \label{eq:observ_vector}
Y \, :=\, \mbox{col} (y(0),y(1),\ldots,y(N-1))
\end{eqnarray}
of $N$ measurements generated by one of the two systems, that is
$Y = \mbox{col} (y_i(0),y_i(1),\ldots,y_i(N-1))$ with $i \in \{1,2\}$,
but we have no direct information on which of the two systems has generated $Y$.
We are interested in determining which of the two systems
has generated $Y$, referring to this problem as
the problem of \emph{classification}.
To make the problem definition precise, let
\begin{eqnarray} \label{eq:obs_matrix}
\mathcal O_i \, := \,
\left[
\begin{array}{c}
\, C_i \,\\
\,C_i\,A_i \, \\
\vdots \\
\,\,C_i\,(A_i)^{N-1} \,\,
\end{array}
\right ]
\end{eqnarray}
be the observability matrix of order $N$ of the pair $(C_i,A_i)$,
and let
\begin{eqnarray} \label{eq:set_L}
\mathcal L_i \, := \,
\left\{ \mathcal O_i x, \, x \in \mathbb R^{n_i}: \,\, \mathcal O_i x \ne 0 \right\}
\end{eqnarray}
be the set of all possible nonzero trajectories
of $N$ samples that can be generated by the $i$-th system.
\vskip 0.1 true cm
\begin{definition}[Classifiers and correctness] \label{def:class}
A \emph{classifier} is any function $f: \mathcal Y \rightarrow \mathbb R$, where
$\mathcal Y$ is the space of the input data.
A {classifier} for the dynamical systems in (\ref{eq:sys}) is said to be \emph{correct} if it satisfies:
\begin{eqnarray} \label{eq:classifier}
f(Y) \,
\left\{
\def1.7{1.3}
\begin{array}{rl}
> 0 & \quad \textrm{if } Y \in \mathcal L_1 \\
< 0 & \quad \textrm{if } Y \in \mathcal L_2
\end{array}
\right.
\end{eqnarray}
\hfill $\blacksquare$
\end{definition}
\vskip 0.1 true cm
The problem of interest is to construct
correct classifiers. We will investigate two approaches:
\begin{enumerate}
\item[(i)] \emph{Model-based classification}:
The classifier depends on the knowledge of the matrices
$A_i$ and $C_i$, $i = 1,2$.
\item[(ii)] \emph{Data-driven (model-free) classification}:
The classifier does not depend on the knowledge of the matrices
$A_i$ and $C_i$, $i = 1,2$, and has to be determined on the basis of
a given number of \emph{sample} trajectories, that is points in the sets $\mathcal L_1$ and $\mathcal L_2$.
\end{enumerate}
Case (i) reflects the situation where the dynamics of the systems are
known and this information is exploited in the design of the classifier.
On the contrary, case (ii) reflects the situation where the dynamics of the systems are
unknown or this information is not directly exploited in the design of the classifier.
\subsection{Limitations of the classification problem}
Clearly, the knowledge of the system dynamics provides an extra degree of information
that can be used to properly design a classifier. Yet, there are certain limitations
which cannot be overcome even in the ideal situation where
one has perfect knowledge of the dynamics.
In particular, the following result holds true.
\vskip 0.1 true cm
\begin{theorem}[Limitations of the classification problem] \label{thm:feas}
A correct classifier for the dynamical systems in (\ref{eq:sys}) exists only if
$\textrm{rank}\, [\, \mathcal O_{1} \,\,\, \mathcal O_{2}\,] = n_{1}+n_{2}$.
\hfill $\blacksquare$
\end{theorem}
\vskip 0.1 true cm
\emph{Proof of Theorem \ref{thm:feas}.}
By definition, there exists no correct classifier
whenever $\mathcal L_1 \cap \mathcal L_2 \ne \emptyset$,
because this implies the existence of trajectories compatible
with both the systems. This
is equivalent to the fact that the dynamical system
resulting from the parallel interconnection of $\Sigma_1$ and $\Sigma_2$
is observable, that is that the observability matrix of order $N$
of the pair $(C, A)$ with
\begin{eqnarray} \label{eq:obs_form}
A \,= \, \left[
\begin{array}{cc} \,\, A_{1} \,\, & \,\, 0
\\ \,\, 0 \,\, & \,\, A_{2}
\end{array} \right], \quad
C \, = \, \left[
\begin{array}{cc} \, C_{1} \, & \, C_{2}
\end{array} \right]
\end{eqnarray}
has column rank $n_1+n_2$. This gives the result. \hfill $\blacksquare$
\vskip 0.1 true cm
The condition in Theorem \ref{thm:feas} can be satisfied only
if the two systems do not share common eigenvalue-eigenvector
pairs. This condition also
requires $Nm \geq n_1+n_2$, which means
that a large enough observation window must be chosen
to render classification feasible.
We will take
this condition as a standing assumption.
\vskip 0.1 true cm
\emph{Assumption 1.}
$\textrm{rank}\, [\, \mathcal O_1 \,\,\, \mathcal O_2\,] = n_1 + n_2$. \hfill $\blacksquare$
\vskip 0.1 true cm
\section{Support Vector Machines} \label{sec:stat_learning}
In this section, we briefly recall some concepts on SVM
focusing on the case of \emph{separable} data.
This material of this section is adapted from \cite{Burges1998}.
Assume we have $L$ observations $(Y_k,\ell_k)$, $k=1,2,\ldots,L$, each one
consisting of a vector $Y_k \in \mathbb R^d$ plus a \emph{label}
$\ell_k \in \{-1,1\}$ specifying the class to which $Y_k$ belongs.
In connection with the problem introduced in Section II, one can think
of $(Y_k,\ell_k)$ as an observation collected from one of the two
candidate systems $\Sigma_i$, where $Y_k$ is the measurement
and $\ell_k$ specifies which of the two systems has generated $Y_k$.
Consider the problem of classifying the vectors $Y_k$ using
hyperplanes $H(Y,\alpha) = \{Y \in \mathbb R^d:\, w^\top Y + b = 0\}$, where $\alpha=(w,b)$ is
a vector of adjustable weights.
If there exists a vector $\alpha$ satisfying
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:sep_hyp}
\left\{
\def1.7{1.7}
\begin{array}{ll}
w^\top Y_k + b > 0 & \quad \textrm{if } \, \ell_k =1 \\
w^\top Y_k + b < 0 & \quad \textrm{if } \, \ell_k = -1 \\
\end{array}
\right.
\end{eqnarray}}%
for $k=1,2,\ldots,L$,
then the vectors $Y_k$ are called \emph{linearly separable},
and the function
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:lin_classif}
f(Y,\alpha) = w^\top Y + b, \quad \alpha=(w,b)
\end{eqnarray}}%
defines a linear classifier which is correct with respect to the data
$(Y_k,\ell_k)$, $k=1,2,\ldots,L$.
For the linearly separable case, an SVM
searches for the separating hyperplane with largest margin $\rho$, that is it
searches for the value of $\alpha$ which maximizes
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:SVM}
\rho := \min_{k=1,2,\ldots,L} \,\, \frac{|w^\top Y_k + b|}{\|w\|}
\end{eqnarray}}%
This can be cast as a convex program:
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:SVM_convex}
\def1.7{1.7}
\begin{array}{l}
\displaystyle \min_{\alpha} \, \frac{1}{2} \|w\|^2 \\
\textrm{subject to }
\left\{
\def1.7{1.7}
\begin{array}{ll}
w^\top Y_k + b \geq 1 & \quad \textrm{if } \, \ell_k =1 \\
w^\top Y_k + b \leq -1 & \quad \textrm{if } \, \ell_k = -1 \\
\end{array}
\right.
\end{array}
\end{eqnarray}}%
The reason to search for the hyperplane with largest margin
is related to the fact that $f(Y,\alpha)$ is obtained from a finite
set of observations, the so-called \emph{training set}. On the other hand,
one would like $f(Y,\alpha)$ to be able to correctly classify also data
which are not present in the training set. This property is usually called
the \emph{generalization} performance \cite{Burges1998}, and SVM
can guarantee a good generalization performance. We will discuss
this point in more detail in Section V.
\vskip 0.1 true cm
Problem (\ref{eq:SVM_convex}) involves $L$ constraints and $d+1$ unknowns.
When $d > L$ it can be more convenient to resort to a
dual formulation of the problem, called \emph{Wolfe dual}:
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:Wolfe_dual}
\def1.7{1.5}
\begin{array}{l}
\displaystyle \max_{\mu} \,\, \mu^\top \mathbf{1}
-\frac{1}{2} \mu^\top Z \mu \\
\textrm{subject to } \,\, \mu \succeq 0, \, \displaystyle \sum_{k = 1,2,\ldots,L} \mu_k \ell_k = 0
\end{array}
\end{eqnarray}
where $\mu := \textrm{col} (\mu_1,\mu_2,\ldots,\mu_{L})$
is the vector of Lagrange multipliers, $Z=[Z_{kj}]$ is a symmetric $L \times L$
matrix such that $Z_{kj} = \ell_k \ell_j Y_k^\top Y_j$, $k,j=1,2,\ldots,L$,
and where $\mathbf{1}$ is the vector of ones.
Problem (\ref{eq:Wolfe_dual}) involves $L$ constraints and unknowns.
The solution has the form
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:supp_vec}
w = \sum_{k = 1,2,\ldots,L} \mu_k \ell_k Y_k
\end{eqnarray}}%
and each vector $Y_k$
associated to a positive multiplier $\mu_k$ is a \emph{support vector}.
This means that for the optimal linear classifier resulting from (\ref{eq:SVM_convex})
the parameter $w$ is given by a linear combination of the support vectors, which can be then
interpreted as the most representative points in the training dataset.
\subsection{Kernel functions}
Finding a separating surface which is \emph{linear} with respect to the space
$\mathcal Y$ of the input data is not always possible.
One of the most important results about SVM is related to the
possibility of finding \emph{non-linear} separating surfaces in a very straightforward manner.
By looking at the optimization problem (\ref{eq:Wolfe_dual}), one sees that
the data appears only through the products $Y_k^\top Y_j$. One can think of
mapping the input space $\mathcal Y$ into a higher-dimensional space $\mathcal H$
through a function $\Phi: \mathcal Y \rightarrow \mathcal H$, and search for a function
$\kappa: \mathcal Y \times \mathcal Y \rightarrow \mathbb R$
such that
\begin{eqnarray} \label{eq:kernel_def}
\kappa (Y, Z) = \langle \Phi(Y),\Phi(Z) \rangle, \quad \forall \, X,Z \in \mathcal Y
\end{eqnarray}
The space $\mathcal H$ is called the \emph{feature space}, while
$\Phi(Y)$ is called the \emph{feature vector}.
Any function $\kappa$ satisfying (\ref{eq:kernel_def}) is called a \emph{kernel} function.
Kernel functions define separating
surfaces which are {linear} with respect to $\mathcal H$.
The remarkable feature of kernel functions is that there is no need
to use or know the function $\Phi$ in order to compute or use $w$.
In fact, in order to compute the solution of (\ref{eq:Wolfe_dual}) with respect to $\Phi$
one can simply use $Z_{kj} = \ell_k \ell_j \kappa(Y_k, Y_j)$. Moreover,
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{}
w^\top \Phi(Y) = \sum_{k=1,2,\ldots,L} \mu_k \ell_k \kappa (Y_k,Y)
\end{eqnarray}}%
Thus one can use $\kappa$ instead of $\Phi$ also for the classification task.
Kernel functions are also advantageous from the point of view of computations
since $\kappa$ operates in the input space $\mathcal Y$, which has usually lower
dimension than $\mathcal H$. Common kernel functions are
\emph{polynomial}, \emph{Gaussian} and \emph{hyperbolic tangent}
functions \cite{Burges1998}.
In the sequel, we will show that for classifying dynamical systems
\emph{polynomial} kernels are good candidates.
\section{Model-based Classification} \label{sec:MB_class}
We now consider a model-based approach to classification.
The following example shows that no correct
classifier exists which is \emph{linear} in the input space.
\vskip 0.1 true cm
\emph{Example 1.} Consider two systems as in (\ref{eq:sys}), where
$A_1=1$, $A_2=-1$ and $C_1=C_2=1$.
Assumption 1 clearly holds true for $N \geq 2$. However, as depicted in Figure \ref{fig:example},
there exists no linear classifier for the two candidate systems,
and this is independent of the particular choice of $N$. \hfill $\blacksquare$
\vskip 0.1 true cm
\begin{figure}[t]
\begin{tikzpicture}[scale=1.5]
\draw [<->,thick] (0,1) node (yaxis) [above] {\small $y(1)$}
|- (1,0) node (xaxis) [right] {\small $y(0)$};
\draw [thick] (0,-1) node (yaxism) [below] {}
|- (-1,0) node (xaxism) [left] {};
\draw [->,thick] (3,0) -- (4.5,0);
\draw [thick] (1.7,0) -- (3,0);
\draw (-1,-1) coordinate (a_1) -- (1,1) coordinate (a_2);
\draw (-1,1) coordinate (b_1) -- (1,-1) coordinate (b_2);
\draw [thick] (3.05,-0.05) -- (3.05,0.05);
\draw (3.05,-0.1) -- (3.05,-0.1) node [below] {\small $0$};
\draw (4.35,-0.1) -- (4.35,-0.1) node [below] {\small $f(Y)$};
\coordinate (p1) at (0.2,0.2); \coordinate (p2) at (0.4,0.4); \coordinate (p3) at (0.6,0.6);
\coordinate (p4) at (0.8,0.8); \coordinate (p5) at (-0.2,-0.2); \coordinate (p6) at (-0.4,-0.4);
\coordinate (p7) at (-0.6,-0.6); \coordinate (p8) at (-0.8,-0.8);
\coordinate (n1) at (-0.2,0.2); \coordinate (n2) at (-0.4,0.4); \coordinate (n3) at (-0.6,0.6);
\coordinate (n4) at (-0.8,0.8); \coordinate (n5) at (0.2,-0.2); \coordinate (n6) at (0.4,-0.4);
\coordinate (n7) at (0.6,-0.6); \coordinate (n8) at (0.8,-0.8);
\coordinate (apn) at (2.9,0);
\coordinate (ap1) at (3.3,0); \coordinate (ap2) at (3.6,0); \coordinate (ap3) at (3.9,0);
\coordinate (ap4) at (4.2,0);
\coordinate (an4) at (2.8,0);
\coordinate (an3) at (2.5,0); \coordinate (an2) at (2.2,0); \coordinate (an1) at (1.9,0);
%
\fill[red] (p1) circle (1.2pt); \fill[red] (p2) circle (1.2pt); \fill[red] (p3) circle (1.2pt); \fill[red] (p4) circle (1.2pt);
\fill[red] (p5) circle (1.2pt); \fill[red] (p6) circle (1.2pt); \fill[red] (p7) circle (1.2pt); \fill[red] (p8) circle (1.2pt);
\fill[blue] (n1) circle (1.2pt); \fill[blue] (n2) circle (1.2pt); \fill[blue] (n3) circle (1.2pt); \fill[blue] (n4) circle (1.2pt);
\fill[blue] (n5) circle (1.2pt); \fill[blue] (n6) circle (1.2pt); \fill[blue] (n7) circle (1.2pt); \fill[blue] (n8) circle (1.2pt);
\fill[red] (ap1) circle (1.2pt); \fill[red] (ap2) circle (1.2pt); \fill[red] (ap3) circle (1.2pt); \fill[red] (ap4) circle (1.2pt);
\fill[blue] (an1) circle (1.2pt); \fill[blue] (an2) circle (1.2pt); \fill[blue] (an3) circle (1.2pt); \fill[blue] (an4) circle (1.2pt);
\end{tikzpicture}
\caption{\emph{Left}: Pictorial representation of the possible observation
points for Example 1 when $N=2$. The trajectories that can be generated
by the first system correspond to points (red circles) which
always falls in the first or third quadrant of the
Cartesian plane, while the trajectories that can be generated
by the second system correspond to points (blue circles) which
always falls in the second or fourth quadrant of the Cartesian plane.
\emph{Right}: Pictorial representation of $f(Y):=y(0)y(1)$.}
\label{fig:example}
\end{figure}
Example 1 indicates that for dynamical systems there is no correct classifier
which is linear with respect to $Y$. However,
Figure \ref{fig:example} suggests that
a correct classifier for Example 1 exists and is given by
$f(Y)= y(0)y(1)$, which can be rewritten as
$f(Y)=w^\top \Phi$, where
\begin{eqnarray} \label{eq:feature_example}
w^\top = \frac{1}{2} \left[
\begin{array}{c}
0\\
1 \\
1 \\
0 \\
\end{array}
\right ], \quad \Phi = Y \otimes Y
\end{eqnarray}
where $\otimes$ stands for Kronecker product. We will see that
$\Phi$ defines a \emph{polynomial} kernel. Before doing this, we show that
the choice $\Phi = Y \otimes Y$ is general in the sense that it applies
to any linear dynamical system.
Let $\mathcal G_{i} := \mathcal O^\top_{i} \mathcal O_{i}$, $i=1,2$,
be the observability Gramian corresponding to the $i$-th system.
Note that $\mathcal G_{i}$ is nonsingular under Assumption 1.
Also, let
\begin{eqnarray} \label{eq:Q}
\mathcal Q := \mathcal Q_{1} - \mathcal Q_{2}
\end{eqnarray}
where
\begin{eqnarray} \label{eq:Q_i}
\mathcal Q_i := \mathcal O_{i} \mathcal G_{i}^{-1} \mathcal O_{i}^\top, \quad i=1,2
\end{eqnarray}
The following result holds true.
\vskip 0.1 true cm
\begin{theorem}[Model-based classifier] \label{thm:MB_classifier}
Let $ \Phi = Y \otimes Y$ and let $w_M = \textrm{vec}(\mathcal Q)$, where
$\textrm{vec}(\cdot)$ is the vectorization operator.
Under Assumption 1, $f(Y) = w_M^\top \Phi$ is a {correct} classifier
for the dynamical systems in (\ref{eq:sys}).
\end{theorem}
\vskip 0.1 true cm
\emph{Proof of Theorem \ref{thm:MB_classifier}.}
The idea is to show that computing $w_M^\top \Phi$
is equivalent to determining which of the sets $\mathcal L_i$
the vector $Y$ belongs to. Consider the point-set distance
{\setlength\arraycolsep{2pt}
\begin{eqnarray}
\pi_{i}(Y) := \min_{x \in \mathbb R^n} \|\mathcal O_{i} x-Y\|^2, \quad i=1,2
\end{eqnarray}}%
Notice that if $Y \in \mathcal L_1$ then
$\pi_{1}(Y) =0$ and $\pi_{2}(Y) > 0$ in view of Assumption 1.
Likewise, if $Y \in \mathcal L_2$ then $\pi_{1}(Y) > 0$ and $\pi_{2}(Y) = 0$.
Hence, the function
\begin{eqnarray} \label{eq:feature_vector_2}
g(Y) := \pi_{2}(Y) - \pi_{1}(Y)
\end{eqnarray}
defines a {correct} classifier for the dynamical systems in (\ref{eq:sys}).
Notice now that
$\pi_{i}(Y) = \| (I - \mathcal Q_i^\top) Y \|^2$ for all $Y$.
Hence, we get
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{}
g(Y) &= & Y^\top (I- \mathcal Q_{2} ) Y - Y^\top (I - \mathcal Q_{1} ) Y \nonumber \\
&=& Y^\top \mathcal Q Y \nonumber =
\textrm{vec}(\mathcal Q)^\top ( Y \otimes Y ) \nonumber \\
&=& w_M^\top \Phi
\end{eqnarray}}%
where the first equality follows because $\mathcal Q_i$ is idempotent.
Thus $g(\cdot) = f(\cdot)$, which concludes the proof. \hfill $\blacksquare$
\vskip 0.1 true cm
\begin{remark}[Invariance to coordinate transformations]
Notice that $w_M$ is independent of the particular state-space
realization adopted for the dynamical systems since $\mathcal Q_1$
and $\mathcal Q_2$ are projection matrices.
\hfill $\blacksquare$
\end{remark}
\subsection{Form of the model-based classifier: Kernel function and
support vectors interpretation}
Theorem \ref{thm:MB_classifier} could have been stated directly in
terms of $f(Y)=Y^\top \mathcal Q Y$.
Yet, the form $f(Y)=w^\top \Phi$ turns out to be useful because it provides
guidelines for the formulation of the data-driven approach.
In fact, it guarantees the existence of a solution for
the SVM formulation if we use $\Phi = Y \otimes Y$
as input to the training algorithm. Moreover, it is immediate
to verify that
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{}
\Phi^\top \Phi = (Y^\top Y)^2
\end{eqnarray}}%
that is $\Phi$ defines a \emph{homogeneous polynomial kernel}.
This means that in the SVM formulation one can
work directly in the space of $Y$ by emplyoing the kernel $\kappa(Y,Z)= (Y^\top Z)^2$.
This option is possible also for the model-based solution
if we write $w_M$ in terms of support vectors.
This interpretation is simple and worth mentioning.
A (reduced) singular value decomposition of the matrix $\mathcal O_i$
yields $\mathcal O_i = U_i S_i V_i^\top$, where $U_i \in \mathbb R^{Nm \times n_i}$ has orthonormal
columns, $S_i \in \mathbb R^{n_i \times n_i}$ is a diagonal matrix with positive entries
(due to Assumption 1), and $V_i \in \mathbb R^{n_i \times n_i}$ is unitary. Thus we have
$\mathcal Q_i = U_i U_i^\top $.
Let $Y_{i,k}$ be the $k$-th column of $U_i$ and let $\Phi_{i,k} = Y_{i,k} \otimes Y_{i,k}$
be the corresponding feature vector. Hence,
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{}
\sum_{k=1}^{n_i} \Phi_{i,k} &=& \sum_{k=1}^{n_i} Y_{i,k} \otimes Y_{i,k} \nonumber \\
&=& \sum_{k=1}^{n_i} \textrm{vec}( Y_{i,k} Y^\top_{i,k} ) \nonumber \\
&=& \textrm{vec}(U_i U_i^\top) \nonumber \\
&=& \textrm{vec}(\mathcal Q_i)
\end{eqnarray}}%
where the second equality follows from the vectorization rule
$\textrm{vec}(ABC)=(C^\top \otimes A)\textrm{vec}(B)$
for matrices $A$, $B$ and $C$ of appropriate dimension.
Thus,
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{}
w_M &=& \textrm{vec}(\mathcal Q) \nonumber \\
&=& \sum_{k=1}^{n_1} \Phi_{1,k} - \sum_{k=1}^{n_2} \Phi_{2,k}
\end{eqnarray}}%
and the support vectors (\emph{cf.} (\ref{eq:supp_vec})) are
the left singular vectors of the observability matrices $\mathcal O_1$ and $\mathcal O_2$.
\section{Data-driven classification based on \\
Support Vector Machines} \label{sec:DD_class}
The model-based approach suggests an SVM formulation
for the problem of classifying data generated by dynamical systems.
We will first describe the SVM formulation and we will then
make some considerations on the \emph{generalization} performance
of the solution. An interesting result is that the
generalization performance of the data-driven classifier can be quantified
as a function of the dynamics of the systems which generate the training dataset.
\subsection{Data-driven classification based on SVM}
Let $\mathcal L_i^{tr} \subset \mathcal L_i$, $i=1,2$,
be a finite nonempty subset of $\mathcal L_i$ consisting of
all the nonzero trajectories recorded from $\Sigma_i$.
Thus $Y_k \in \mathcal L^{tr} := (\mathcal L_1^{tr} \cup \mathcal L_2^{tr})$,
$k = 1,2,\ldots,L$, $L:=|\mathcal L^{tr}|$,
is the $k$-th training vector. Let $\ell_k=1$ if $Y_k \in \mathcal L_1^{tr}$, and
$\ell_k=-1$ if $Y_k \in \mathcal L_2^{tr}$.
Finally, let $\Phi_k = Y_k \otimes Y_k$ be
the feature vector associated to $Y_k$.
Following Section \ref{sec:stat_learning} and Theorem \ref{thm:MB_classifier}, we formulate the
data-driven approach as the problem
of finding the hyperplane that contains the origin and
separates the {training} datasets with maximum margin,
that is:
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:SVM}
\def1.7{2.5}
\begin{array}{l}
\displaystyle \min_{w} \, \frac{1}{2} \|w\|^2 \\
\textrm{subject to } \,\,
\left\{
\def1.7{1.7}
\begin{array}{ll}
w^\top \Phi_k \geq 1 & \quad \textrm{if } \ell_k =1 \\
w^\top \Phi_k \leq -1 & \quad \textrm{if } \ell_k = -1 \\
\end{array}
\right.
\end{array}
\end{eqnarray}}%
The following result holds true.
\vskip 0.1 true cm
\begin{theorem}[Data-driven classifier] \label{thm:DD_classifier}
Let Assumption 1 be satisfied, and consider an arbitrary training dataset $\mathcal L^{tr}$. Then,
the solution $w_D$ to the optimization problem (\ref{eq:SVM}) exists and is unique.
Hence, $f(Y) = w_D^\top \Phi$ is a {correct} classifier with respect to $\mathcal L^{tr}$.
\end{theorem}
\vskip 0.1 true cm
\emph{Proof of Theorem \ref{thm:DD_classifier}}.
The proof follows from Theorem \ref{thm:MB_classifier}. In fact,
the model-based solution $w_M$ guarantees that
$a_1 :=\min_{\ell_k=1} w_M^\top \Phi_k > 0$
and $a_2 :=\max_{\ell_k=-1} w_M^\top \Phi_k < 0$.
Thus $\overline w_M := w_M/a$ with
$a :=\min \{a_1,-a_2\}$ guarantees the
feasibility of the set of constraints.
Uniqueness follows as the optimization problem
is a convex program.
\hfill $\blacksquare$
\vskip 0.1 true cm
The constraint that the solution must contain the origin is
simply to mimic the model-based solution. This constraint
is actually not needed, and a standard formulation (\ref{eq:SVM_convex})
would still guarantee existence and uniqueness of the solution.
If we constrain the solution to contain the origin the Wolfe dual
becomes
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:Wolfe_dual_simple}
\def1.7{1.5}
\begin{array}{l}
\displaystyle \max_{\mu} \,\, \mu^\top \mathbf{1}
-\frac{1}{2} \mu^\top Z \mu \\
\textrm{subject to } \,\, \mu \succeq 0
\end{array}
\end{eqnarray}
which does not
involve the constraint $\sum_{k=1,2,\ldots,L} \mu_k \ell_k = 0$.
We notice that in this case the dimension of the feature space is $(Nm)^2$.
Nonetheless, by considering a kernel-based implementation one can remain in the
$Nm$-dimensional space of the sequences $Y$.
Theorem \ref{thm:DD_classifier} indicates that one can find
a surface separating the training dataset without information about
the underlying systems except for their linearity, which suggests
the feature space of choice. In the remaining part of this section,
we will discuss on the capability of this SVM classifier to \emph{generalize}
to observations outside the training set.
\subsection{Expected risk}
Ideally, one would like to establish the correctness of the data-driven
classifier in the same sense as Definition \ref{def:class}. This is a non-trivial
problem which, to the best of our knowledge, has not yet been solved.
In the sequel, we consider another way to characterize the
{generalization performance} of the SVM
classifier, based on the notion of \emph{expected risk}. While this
notion does not provide deterministic bounds, it has the merit to capture
the situation where the training dataset is randomly chosen.
Hence, it has the merit to describe cases in which one cannot perform dedicated
experiments on the systems.
Consider a training dataset of $L$ \emph{random i.i.d.} observations drawn according to
a probability distribution $P(Y,\ell)$. Given a classifier $f(Y)$, its \emph{expected risk}
can be defined as \cite{Vapnik1995}:
{\setlength\arraycolsep{2pt}
\begin{eqnarray}
R := \int \frac{1}{2} \left| \ell - \textrm{sgn} ( f(Y) ) \right| dP(Y,\ell)
\end{eqnarray}
where $\textrm{sgn}$ is the sign function. The expected risk quantifies
the capability of a classifier to generalize from the training dataset.
Several studies have been devoted to provide upper bounds
on the expected risk for a given family of classifiers.
An interesting bound for linear classifiers which serves our discussion is reported
hereafter.
\vskip 0.1 true cm
\begin{theorem}[\cite{Bartlett1999}] \label{thm:GTC_v}
Let $Y \in \mathbb R^d$ belong to the sphere of
radius $R$, and consider the class $\mathcal F$ of real-valued functions defined as
$\mathcal F := \{Y \mapsto w^\top Y: \|w\| \leq 1, \|Y\| \leq R\}$. There is a constant $c$
such that, for all probability distributions, with probability at least $1- \eta$ over $L$
randomly i.d.d. vectors, if a classifier has margin at least $\rho$ on all the examples
then its expected error is not larger than
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:GTC_h_DD}
\frac{c}{L} \left( \frac{R^2}{\rho^2} \log^2 L + \log \left( 1/\eta \right) \right)
\end{eqnarray}}%
\hfill $\blacksquare$
\end{theorem}
\vskip 0.1 true cm
The constant $c$ is related to the so-called \emph{fat-shattering}
dimension of linear classifiers, and its explicit expression can be
found in \cite{Bartlett1999}.
Theorem \ref{thm:GTC_v} shows that one can quantify the generalization
performance of a linear classifier as a function of the margin $\rho$ obtained
for the training dataset. We now show that the margin of the SVM
classifier can be related to the margin of the model-based solution.
This permits to quantify the generalization performance of the SVM classifier
in terms of the dynamics of the systems that one wishes to classify.
The analysis which follows holds for normalized data. We will briefly comment
later on the general case.
Consider normalized training data
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:norm_data}
\overline Y_k := \frac{Y_k}{\|Y_k\|}
\end{eqnarray}}%
with feature vector $\overline \Phi_k := \overline Y_k \otimes \overline Y_k$. It holds that
$\| \overline \Phi_k \| =1$. Consider now the optimal solution $w_D$
to (\ref{eq:SVM}) computed with respect to $\overline \Phi_k$,
whose existence and uniqueness is again ensured by the model-based solution.
We can assume without loss of generality that $\|w_D\| \leq 1$.
Let now $\rho_M$ and $\rho_D$ represent the margin corresponding
to the model-based and the data-driven solutions,
respectively,
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:MB_DD_margin}
\rho_i := \min_{k=1,2,\ldots,L} \, \frac{ |w_i^\top \overline \Phi_k |}{\|w_i\|}, \quad i \in \{M,D\}
\end{eqnarray}}%
It holds that
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:rel_MB_DD}
\rho_D \geq \rho_M
\end{eqnarray}}%
irrespective of the training dataset,
because the data-driven solution is the margin maximizer.
The next result shows that, using normalized data, $\rho_M$ is bounded from below by a positive
quantity that depends solely on the dynamics of the systems one wishes to classify.
We refer the reader to \cite{Cock2002} for a definition of
\emph{principal angles}.
\vskip 0.1 true cm
\begin{theorem}[Bound on the data-driven classifier margin] \label{thm:DD_margin}
Let Assumption 1 be satisfied. Consider an arbitrary training dataset
of vectors $Y_k$, and let $\overline \Phi_k := \overline Y_k \otimes \overline Y_k$
where $\overline Y_k$ is as in (\ref{eq:norm_data}). Let
$w_D$ be the unique solution to the optimization problem (\ref{eq:SVM})
computed with respect to $\overline \Phi_k$.
Then, it holds that
{\setlength\arraycolsep{2pt}
\begin{eqnarray}
\rho_D \geq \frac{\beta}{\sqrt{2 \,(n_1+n_2)}}
\end{eqnarray}}%
where $n_1$ and $n_2$ are the
orders of the dynamical systems in (\ref{eq:sys}), and
$\beta$ is
the squared sine of the smallest principal angle between
the subspaces spanned by the columns of the
observability matrices $\mathcal O_1$ and $\mathcal O_2$.
\end{theorem}
\vskip 0.1 true cm
\emph{Proof of Theorem \ref{thm:DD_margin}.}
Since $\rho_D \geq \rho_M$ it is sufficient to bound $\rho_M$.
The term $\|w_M\|$ satisfies
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{}
\|w_M\|^2 &=& \textrm{vec}(\mathcal Q)^\top \textrm{vec}(\mathcal Q) \nonumber \\
&=& \|\mathcal Q\|_F^2 \nonumber \\
&\leq& 2 \,(n_1+n_2)
\end{eqnarray}}%
where $\|\cdot\|_F$ denotes Frobenius norm. The
inequality follows from
$\|\mathcal Q\|_F^2 \leq 2 \|\mathcal Q_1\|_F^2 + 2 \|\mathcal Q_2 \|_F^2$
and $\|\mathcal Q_i\|_F^2=n_i$ because the $\mathcal Q_i$'s are
projection matrices.
Consider now the term $|w_M^\top \overline \Phi_k|$. Assume without loss of
generality that its minimum is attained for some $Y_* \in \mathcal L_1^{tr}$.
It holds that
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{}
\min_{k=1,2,\ldots,L} | w_M^\top \overline \Phi_k | &=& |w_M^\top \overline \Phi_* | \nonumber \\
&=& | \pi_2(\overline Y_*) - \pi_1(\overline Y_*) | \nonumber \\
&=& \pi_2(\overline Y_*)
\end{eqnarray}}%
The third equality comes from the fact that $Y_* \in \mathcal L_1^{tr}$ implies
$\pi_2(\overline Y_*)>0$ and $\pi_1(\overline Y_*)=0$ in view of Assumption 1.
As shown in \cite[Theorem 1]{battSCL},
$\pi_2(\overline Y_*) \geq {\beta} \|\overline Y_*\|^2$.
Hence, the proof follows from $\|\overline Y_*\| =1$.
\hfill $\blacksquare$
\vskip 0.1 true cm
Theorem \ref{thm:DD_margin} permits to bound the risk of the data-driven classifier based on
the dynamics of the systems one wishes to classify, and formalizes the
intuition that the risk bound becomes smaller as the dynamics of the
systems to classify are more distant from one another. In fact,
the higher $\beta$ the larger the coefficient of inclination between the
subspaces spanned by the columns of $\mathcal O_1$ and $\mathcal O_2$,
which is maximal when the two spaces are orthogonal.
Data normalization ensures that $\rho_M$ is bounded away from zero.
This property does not hold in general since trajectories of dynamical systems can be
arbitrarily close to the origin. Nonetheless, one can
obtain a very similar bound by adding to (\ref{eq:GTC_h_DD}) an
extra term which accounts for training data below the margin $\rho$
\cite[Theorem 1.7]{Bartlett1999}.
\section{Discussion}
It is intuitive that incorporating models can be
beneficial to the classification task. This fact is obvious also from the analysis
shown in this paper since under Assumption 1 no classifier can outperform
the model-based classifier when the models are exact and
the data are noise-free. However, as mentioned before,
the model-based approach introduces the non-trivial issue of how to quantify the effect of
modelling inaccuracies. The data-driven bypasses the intermediate step of identification,
and thus it has the potential to be applicable also when accurate models
are difficult to obtain. Hereafter, we briefly elaborate on this point also in connection
with a number of open problems.
\subsection{Linear systems with noisy observations}
When observations are corrupted by noise, identification
may be difficult and require, even for linear systems, many careful provisions \cite{Pillonetto14}.
In contrast, an SVM formulation can address the problem in a rather straightforward manner.
Consider a \emph{soft-margin} SVM \cite{Burges1998}:
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{eq:SVM_soft}
\def1.7{2.5}
\begin{array}{l}
\displaystyle \min_{(w,\xi)} \, \frac{1}{2} \|w\|^2 + \sum_{k=1,2,\ldots,L} C\, \xi_k \\
\textrm{subject to } \,\,
\left\{
\def1.7{1.7}
\begin{array}{ll}
w^\top \Phi_k \geq 1 - \xi_k & \quad \textrm{if } \ell_k =1 \\
w^\top \Phi_k \leq -1 + \xi_k & \quad \textrm{if } \ell_k = -1\\
\end{array}
\right.
\end{array}
\end{eqnarray}}%
where $C$ is a parameter and $\xi := \textrm{col }(\xi_1,\xi_2,\ldots,\xi_L)$ is the vector
of \emph{slack} variables, which account for the fact that noise may render the
data non-separable. On one hand, there exist many studies
aimed at quantifying the generalization performance of SVM also for
soft-margin formulations \cite{Taylor2002}. On the other hand, even with noisy data
one can still give a separation measure between linear systems (the margin $\rho_M$)
as a function of their dynamics and
the \emph{signal-to-noise ratio} \cite[Theorem 2]{battSCL}. This means
that even with noisy data
one can quantify the generalization performance of an SVM classifier along the same lines
as in Section V-B.
We point out that while this reinforces the idea
that for linear systems \emph{polynomial} kernels
are good candidates, it remains unclear if better performance
can be obtained with different kernel functions.
\subsection{Nonlinear systems}
Classification for nonlinear systems is another situation in which an SVM formulation
can bypass difficulties related to system
identification. This is related to the capability of SVM to find
non-linear separating surfaces in a straightforward manner through the kernel trick.
Interestingly, even in the nonlinear case
one can define a separation measure between dynamics \cite[Theorem 3]{battTAC}.
However, in contrast with the linear case where this measure
involves principal angles between observability subspaces,
for nonlinear systems this measure involves \emph{$\mathcal K$-functions},
which are often difficult to relate to the underlying dynamics.
Like for linear systems, a deeper understanding of this point would be beneficial to figure out
which types of kernel functions are most suitable for a given class of nonlinear systems.
In fact, theoretical studies on classification for nonlinear systems are
recent also within computer science, and the approaches appear largely diversified; for example,
see \cite{Shen2017} for an interesting recent account. Yet, also in this context,
the question of which kernel functions are most suitable for a given class of dynamics
is unresolved.
\subsection{Classifiers in-the-loop}
Thanks to their simple form, classifiers have the potential to be used in
real-time applications, thus for control purposes.
This fact has been noted in \cite{Poonawala2017}, where the authors
introduce the term \emph{classifier in-the-loop} to describe a framework
in which a classifier can modify online the control action by looking at the process data.
A notion of generalization is considered, which characterizes the capability of a classifier to work under
small perturbations of the system vector fields, which is a \emph{sensitivity}-type
analysis. While the results are promising, it remains unexplored how to handle more general forms
of uncertainty. Ideally, one should provide bounds on the risk
function of a classifier that hold for all the possible system trajectories,
and relate such bounds with closed-loop stability properties.
A non-trivial difficulty is that much of the theory on the generalization
properties of classifiers have been developed in a probabilistic setting,
while for robust stability it is desirable to guarantee worst-case deterministic bounds.
Interestingly, the architecture considered in \cite{Poonawala2017}
can be regarded as a \emph{supervisory} control system \cite{liberzon}.
In supervisory control, the supervisor selects based on process data
which candidate control law (\emph{hypothesis}) is most appropriate at any given time. This is done by assigning to each candidate
law a score function (\emph{cost function}) that quantifies the performance level
achievable by the control law given the process data,
In supervisory control, one often uses the term \emph{cost detectability} \cite{safo08,TAC13}
to measure the capability of a supervisor to learn from data an appropriate control law
even when the process does not match the models used to design the control laws.
In fact, the supervisor is a classifier and \emph{cost detectability} is a measure of
its generalization performance.
The idea of adaptive control as \emph{learning-from-data}
is indeed not new \cite{safo}, but a firm theoretical link with the realm of machine learning
has not yet been established.
\section{A Numerical Example}
Consider a system with transfer function
{\setlength\arraycolsep{2pt}
\begin{eqnarray} \label{}
G(s) = \frac{s+1}{(s+10)(s^2+s+1)}
\end{eqnarray}}%
where $s$ is the Laplace variable.
To improve performance, the system is controlled with
a proportional controller $K=30$ under negative feedback.
The goal is to design a classifier which can detect the \emph{loss
of control effectiveness}. We denote by $\overline \Sigma_1$
the open-loop system and by $\overline \Sigma_2$
the closed-loop system. Hence, $\overline \Sigma_1$ and $\overline \Sigma_2$
have transfer functions $G(s)$ and $W(s):=KG(s)/(1+KG(s))$, respectively.
Finally, we denote by $\Sigma_1$ and $\Sigma_2$ the corresponding sampled-data systems
under sampling time $T_s$. The systems are as in (\ref{eq:sys}) with $n_1=n_2=3$
and $m=1$.
Using the previous notation, we let $N$ be
the length of the observation sequences, and $L$ the number of training data.
We let $Q$ be the number of data used for validation.
In order for Assumption 1 to be satisfied one needs $N\geq6$.
Under such condition, Assumption 1 holds for a generic choice of $T_s$.
We focus on the SVM classifier because the model-based classifier is always correct
under Assumption 1. We note that classifying the two systems is non-trivial,
as one can observe from Figure 2. For instance, for $T_s=0.1$, in the ideal case of $N=\infty$
one has $\beta=0.004$ in Theorem \ref{thm:DD_margin},
and a \emph{cepstral} distance \cite{Cock2002} equal to $1.045$.
We report in Table I simulations results for various choices of $N$, $L$ and $T_s$,
with $Q=1000$ validation data. The SVM classifier is computed as in Theorem \ref{thm:DD_margin}.
For the training and the validation test, trajectories are generated from random initial conditions with zero mean
and variance $\sigma^2=100$. The error in the validation test is defined as:
{\setlength\arraycolsep{2pt}
\begin{eqnarray}
R_{test} := \sum_{k =1,2,\ldots,Q} \,\,
\frac{1}{2 Q} \left| \ell_k - \textrm{sgn} ( w_D^\top \overline \Phi_k ) \right|
\end{eqnarray}}%
\begin{table}[h!]
\centering
\begin{tabular}
{@{}l*5{>{}l}%
l<{Example text}l@{}}
\toprule[1.5pt]
& \multicolumn{5}{l}{\head{Variation of the parameter $N$\, ($T_s=0.1$, $L=50$)}}\\
& \normal{\head{$N=2$}} & \normal{\head{$N=5$}} & \normal{\head{$N=10$}} & \normal{\head{$N=50$}} & \head{$N=100$}\\
\cmidrule(){2-6}
\multirow{1}{*}{$R_{test}$}
& \normal{$0.4720$} & \normal{$0.0760$} & \normal{$0.0685$} & \normal{$0.0150$} & \normal{$0.0150$} \\
& \normal{ } & \normal{} & \normal{} & \normal{} \\
\toprule[1.5pt]
& \multicolumn{5}{l}{\head{Variation of the parameter $L$\, ($T_s=0.1$, $N=10$)}}\\
& \normal{\head{$L=3$}} & \normal{\head{$L=5$}} & \normal{\head{$L=10$}} & \normal{\head{$L=50$}} & \normal{\head{$L=100$}} \\
\cmidrule(lllll){2-6}
\multirow{1}{*}{$R_{test}$}
& \normal{$0.1480$} & \normal{$0.1480$} & \normal{0.0720} & \normal{$0.0685$} & \normal{0.0620} \\
& \normal{ } & \normal{} & \normal{} & \normal{} \\
\toprule[1.5pt]
& \multicolumn{5}{l}{\head{Variation of the parameter $T_s$\, ($N=10$, $L=50$)}}\\
& \normal{\head{$T_s=0.01$}} & \normal{\head{$T_s=0.05$}} & \normal{\head{$T_s=0.1$}} & \head{$T_s=0.5$} & \head{$T_s=1$} \\
\cmidrule(lllll){2-6}
\multirow{1}{*}{$R_{test}$}
& \normal{$0.4850$} & \normal{$0.0730$} & \normal{$0.0685$} & \normal{$0.0385$} & \normal{$0.0835$} \\
& \normal{ } & \normal{} & \normal{} & \normal{} \\
\toprule[1.5pt]
\end{tabular}
\caption{Numerical results for the SVM classifier with $Q=1000$.}
\end{table}
\begin{figure*}[h!]
\begin{center}
\psfrag{samples}{\footnotesize $y(1)$}
\begin{tabular}{ll}
\includegraphics [width=0.46\textwidth] {open-loop.eps} &
\includegraphics [width=0.46\textwidth] {closed-loop.eps}
\end{tabular}
\caption{Output trajectories of the two systems (Left: open-loop; Right: closed-loop) with
$N=10$ and $T_s=0.1$. The figures report $1000$ normalized trajectories for each system
generated from random initial conditions with zero mean and variance $\sigma^2=100$.}
\end{center}
\label{fig:example2}
\end{figure*}
One sees that the classifier performs well for reasonable
choices of the parameters. In particular:
\begin{enumerate}
\item[(i)] \emph{Dependence on $N$}. As $N$ goes to zero, the performance is clearly that of
a random guess. One the other hand,
remarkably, classification becomes accurate exactly as soon as one approaches the theoretical bound $N\geq6$.
The performance saturates after $N=50$. To further decrease the error we need to increase $L$
(with $L>300$ one can achieve an error below $1\%$).
\item[(ii)] \emph{Dependence on $L$}. The performance variations are less evident in this case.
This suggest that $L$ is less critical than $N$. The intuition is that random initial conditions generically ensure the
excitation of all system dynamics so that even few examples may suffice.
\item[(iii)] \emph{Dependence on $T_s$}. The sampling time does not play a major role as long as
we avoid \emph{over-sampling}, in which case both $A_1$ and $A_2$ tend to the identity matrix,
or \emph{under-sampling}, in which case both $A_1$ and $A_2$ tend to the zero matrix.
\end{enumerate}
\section{Concluding Remarks}
We have considered the problem of classifying trajectories generated by dynamical
systems, looking at a model-based approach, the
common approach in control engineering, as well as at a data-driven approach based
on Support Vector Machines, a popular method in computer science.
The present discussion suggests that both the approaches have distinct merits.
A deeper understanding of the interplay between these two approaches
would help to establish a sound theory for dynamical systems
more general than those considered in this paper.
\bibliographystyle{IEEEtran}
| {
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Q: Google Cloud Project Blocked, Abuse Detected After i started my free trial of google cloud usage, just after when i tried to create a VM instance it gave the error that is written in the title. Then i created another project then i get this error for every project i create.
How can i fix this?
A: The error that is communicated by the "Google Cloud Project Blocked, Abuse Detected" message, can be addressed as follows:
*
*By making use of the email provided for contact with the error.
*By contacting the billing team via the dedicated form: "Google Cloud Platform Billing Support". In case your account has been already suspended, you can submit supporting documents via the "Submit verification documents to reopen your account" page, as needed.
Each one of the above options will lead you to the billing support team. They are ready to help all GCP customers, and able to verify your funding source, confirm its validity, and reinstate normal access to your projects.
If you have multiple projects covered by a unique billing account, any problems with this one account, including blocking, would reflect on all existing projects, and also on eventual future projects opened under the same account.
| {
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https://banyanhill.com/farming-internet-things-iot/
Home » Investment Opportunities » Farming the Internet of Things (IoT)
Farming the Internet of Things (IoT)
Posted by Jeff Yastine | Dec 27, 2016 | Investment Opportunities
I interviewed a lot of farmers in my years as a business reporter. For obvious reasons, you'll never find a more practical-minded bunch of people. One wrong bet can kill a grower's bottom line.
So when it comes to technology, they all have the same attitude: Prove that it's worth the investment of time and money.
But once they have proof something really works, farmers can be the earliest of tech-savvy "early adopters."
They adopted GPS years before consumers did to digitally map their fields, and automatic guided steering was an upgrade on tractors and harvesters years before Tesla unveiled its "autopilot" feature.
And today?
Farmers' choices are worth paying close attention to once again — because they're embracing two of the biggest themes we talk about here at The Sovereign Society…
The first of those themes is the Internet of Things (IoT) — something Paul writes about all the time. His subscribers have seen nice gains in his recommendations.
Planting the IoT Seeds
There may be no industry better suited for the IoT than agriculture, because every farm varies just a little from its next-door neighbor. Soil fertility, elevation, ground slope, moisture content — the list goes on and on — all make a difference.
If you could collect data on all that stuff, it might make the difference between getting a bumper crop or an average crop out of your fields.
Not surprisingly, the big agriculture companies all smell opportunity in the wind. That's why….
Monsanto has been on acquisition spree in recent years, snapping up data and sensor companies like Climate Corp. (2013) and Vitalfields (2016) — not to mention that Germany's Bayer is seeking to acquire Monsanto itself in a record $66 billion offer made earlier this year.
John Deere bought Europe's Monosem. Towed behind a tractor, a Monosem planter uses an array of sensors to place each individual seed at just the right soil depth with just the right dose of fertilizer for maximum growth.
Trimble, best known for its GPS mapping devices, is building a large footprint in "farm tech" through a series of acquisitions (and dropped its old corporate name, Trimble Navigation, earlier this year).
But with all those machines rumbling about the fields, they're also collecting reams of valuable data in the process.
The Most Valuable Commodity of All
As longtime Sovereign Society readers will know, Ted Bauman has warned us about the importance of data privacy for years.
But this is a relatively new question for farmers when it comes to their data and the IoT.
Who gets access? And who potentially stands to make profits from all that very detailed information?
As one example, John Deere makes no bones about the value of farm data. It was a key piece of the company's stated goal back in 2011: to double its sales to $50 billion by 2018.
But farmers, not surprisingly, have other ideas.
The concern about data privacy has spawned a small but growing effort at creating open-sourced DIY "ag tech" products — so farmers aren't held hostage to the protocols of the major farm equipment makers.
And a private agriculture startup by the name of Farmobile looks to take that idea a step further. The company, which has been profiled by The Wall Street Journal, makes a data-recording device that plugs into a tractor's onboard computer system. (It also works with other sensor-laden farm equipment like planters and harvesters.)
More recently, the company launched a "data store" so farmers (only in Minnesota, so far) can literally get paid the value of the bits and bytes generated by their farm equipment.
The upshot is this: The company splits the revenue from the sale of a farm's data evenly with an individual farmer and guarantees $2 per acre. It may not sound like much, but when you consider that the average Midwest farm is roughly 1,000 acres (and farmers often lease even more), the dollar figures add up to a tidy sum.
It shows, in a literal sense, the value of information in the digital farming age.
JL Yastine
Editorial Director, The Sovereign Society
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The January Effect: A Resolution Worth Keeping | {
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{"url":"https:\/\/www.ias.ac.in\/listing\/bibliography\/pram\/SANJEEV_KUMAR","text":"\u2022 SANJEEV KUMAR\n\nArticles written in Pramana \u2013 Journal of Physics\n\n\u2022 Growth of zinc oxide nanostructures\n\nZinc oxide (ZnO) nanowhiskers have been prepared using a multilayer ZnO(50 nm)\/Zn(20 nm)\/ZnO(2\u03bcm) structure on a polished stainless steel (SS) substrate by high rate magnetron sputtering. The formation of uniformly distributed ZnO nanowhiskers with about 20 nm dia. and 2 to 5 \u03bcm length was observed after a postdeposition annealing of the prepared structure at 300\u2013400\u00b0 C. An array of highlyc-axis oriented ZnO columns (70\u2013300 nm in dia. and up to 10 \u03bcm long) were grown on Si substrates by pulsed laser deposition (PLD) at a high pressure (1 Torr), and Raman studies showed the activation of surface phonon modes. The nanosized powder (15\u201320 nm) and nanoparticle ZnO films on glass substrate were also prepared by a chemical route. Nanowhiskers showed enhanced UV light detection characteristics, and the chemically prepared ZnO nanoparticle films exhibited good sensing properties for alcohol\n\n\u2022 A comparative study of model ingredients: Fragmentation in heavy-ion collisions using quantum molecular dynamics model\n\nWe aim to understand the role of NN cross-sections, equation of state as well as different model ingredients such as width of Gaussian, clusterization range and different clusterization algorithms in multifragmentation using quantum molecular dynamics model. We notice that all model ingredients have sizable effect on the fragment pattern.\n\n\u2022 Precision measurement of neutrino oscillation parameters at INO-ICAL detector\n\nA magnetized Iron CALorimeter (ICAL) detector at the India-based neutrino observatory (INO) is used to study neutrino oscillation sensitivity using atmospheric muon neutrino source. The ICAL detector will be able to detect muon tracks and hadron showers produced by neutrino interactions with the iron target. We have performed precision measurement analysis for the atmospheric neutrino oscillation parameters with the muon neutrino events, generated by Monte Carlo NUANCE event generator. A marginalized \ud835\udf122 analysis based on reconstructed neutrino energy and muon zenith angle binning scheme has been performed to determine the sensitivity for the atmospheric neutrino mixing parameters, ${\\rm sin}^{2} \\theta_{23}$ and $|\\Delta m^{2}_{23}|$.\n\n\u2022 Physics potential of the ICAL detector at the India-based Neutrino Observatory (INO)\n\nThe upcoming 50 kt magnetized iron calorimeter (ICAL) detector at the India-based Neutrino Observatory (INO) is designed to study the atmospheric neutrinos and antineutrinos separately over a wide range of energies andpath lengths. The primary focus of this experiment is to explore the Earth matter effects by observing the energy and zenith angle dependence of the atmospheric neutrinos in the multi-GeV range. This study will be crucial toaddress some of the outstanding issues in neutrino oscillation physics, including the fundamental issue of neutrino mass hierarchy. In this document, we present the physics potential of the detector as obtained from realistic detector simulations.We describe the simulation framework, the neutrino interactions in the detector, and the expected responseof the detector to particles traversing it. The ICAL detector can determine the energy and direction of the muons to a high precision, and in addition, its sensitivity to multi-GeV hadrons increases its physics reach substantially. Itscharge identification capability, and hence its ability to distinguish neutrinos from antineutrinos, makes it an efficient detector for determining the neutrino mass hierarchy. In this report, we outline the analyses carried out for the determination of neutrino mass hierarchy and precision measurements of atmospheric neutrino mixing parameters at ICAL, and give the expected physics reach of the detector with 10 years of runtime. We also explore the potential of ICAL for probing new physics scenarios like CPT violation and the presence of magnetic monopoles.\n\n\u2022 # Pramana \u2013 Journal of Physics\n\nCurrent Issue\nVolume 93 | Issue 6\nDecember 2019\n\n\u2022 # Editorial Note on Continuous Article Publication\n\nPosted on July 25, 2019","date":"2019-10-19 02:02:22","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 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\": 0.6223910450935364, \"perplexity\": 3559.0540254456237}, \"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-2019-43\/segments\/1570986688674.52\/warc\/CC-MAIN-20191019013909-20191019041409-00554.warc.gz\"}"} | null | null |
{"url":"http:\/\/doctormath.blogspot.com\/2009\/02\/80085.html","text":"## Tuesday, February 24, 2009\n\n### 80085\n\nWith Valentine's Day just passed and Ash Wednesday lurking around the corner, I know the topics of sex and pregnancy are on a lot of people's filthy guilt-ridden minds these days. To help people understand their risks, and to show I'm not a prude, I'm hosting a little get-together (an orgy, if you will) of questions all about sex. So turn the lights down low, put on some soft music, and enjoy this special \"adults only\" post about what we in the math business call \"multiplication.\"*\n\nDear Dr. Math,\nI read in an article that \"Normally fertile couples have a 25 percent chance of getting pregnant each cycle, and a cumulative pregnancy rate of 75 to 85 percent over the course of one year.\" How do you go from 25% to 85? I don't see the connection between those two numbers.\nName Withheld\n\nAs is often the case, Name, the way to understand the probability of getting pregnant over some number of time intervals (I almost wrote \"periods\" there but then reconsidered) is instead to think about the probability of not getting pregnant during any of those intervals. We can use the fact that the chance of something happening is always 1 minus the chance of it not happening. This turns out to be a generally useful technique whenever you're interested in the occurrence of an event over multiple trials. To take my favorite over-simplified example of flipping a coin, if we wanted to find the chance of flipping an H (almost wrote \"getting heads\"--geez, this is har.., er, difficult) in the first 3 flips, we could go through all of the possible 3-flip sequences and count how many of them had at least one H, or we could just observe that only one sequence doesn't contain an H (namely, TTT). Since the probability of flipping T (\"getting tails\") is $\\frac{1}{2}$ on each flip, the chance of \"doing it three times\" is $\\frac{1}{2^3} = \\frac{1}{8}$. Thus, the probability of at least one H is $1 - \\frac{1}{8} = \\frac{7}{8}$. Phew.\n\nSimilarly here, there are lots of different ways to get pregnant over the course of a year (believe me), but only one way to not get pregnant. If we take the first statistic as correct, that the chance of a normally fertile couple getting pregnant in each cycle is 25%, then we could assume that the chance of not getting pregnant in each cycle was 75%, or 0.75. Assuming a \"cycle\" is 28 days long, there would be 13 cycles per year, so by the same reasoning as above, we could say that the chance of not getting pregnant in a year is $(0.75)^{13}=0.024$, about 2.4%. So, the chance of \"being in the family way\" at some point during the year would be $1-0.024 = 0.976$, or 97.6%.\n\nNow, that doesn't match up with the observed number you quoted, 85%. In the study, of course, all they do is assemble some group of \"normally fertile\" couples and count the number of times they get pregnant in a year. We were trying to solve the problem \"top down\" whereas the data is observed from the \"bottom up.\" What's going on? Well, the problem was our assumption that the different cycles were independent from each other, in the sense that knowing what happened in one cycle doesn't affect our estimation of what will happen in the next. For coin-flipping, this is a reasonable assumption, but for copulation, not so much. It makes sense that there should be some correlation between the different cycles, because the possible causes for infertility one month might continue to be true the next. For example, it could be that either or both partners have some kind of medical condition that makes conception less likely. Or maybe the guy's underwear is too tight, I don't know. But it seems that the assumption of independence probably doesn't hold. Also, it's not entirely clear what's meant by \"normally fertile\" here, since (as far as I know) it's only really possible to know if a couple is \"fertile\" if they've succeeded in having a baby. So, it's possible that the data includes some number of couples who were just less fertile and perhaps didn't know it.\n\nThe correct way to understand these compound probabilities is to consider the probability of not conceiving in one cycle conditional on the event that you had not conceived the cycles previously. Unfortunately, I don't have access to that information from personal experience, nor a good mental model for what numbers would be reasonable. However, it seems like the probability of not conceiving should be higher than ordinary if you know already that you've gone some number of months without conceiving. As a result, the odds of getting pregnant in a year should be lower than our estimate assuming independence, which does in fact agree with the data.\n\nDear Dr. Math,\nPlanned Parenthood's web site says, \"Each year, 2 out of 100 women whose partners use condoms will become pregnant if they always use condoms correctly.\" Is that the same as saying that condoms are 98% effective? If so, does that mean that if you have sex 100 times, you'll likely get somebody pregnant twice? (I mean, if you're a man. If you're a woman I imagine the rate of impregnating your partner will probably slip in the direction of zero.) Yours always,\nName Withheld\n\nOh, you freaky Name Withheld, you've asked the question backwards! In fact, the statistic you give of 2 women out of 100 becoming pregnant in a year is how the effectiveness of condoms is defined. That is, in the birth control industry, specifically, when someone claims that a particular method is \"x% effective,\" it means that if a group of women use that method, over the course of the year about (100-x)% of them will get pregnant. Now, there are a number of assumptions being made here, not the least of which is that those women (and their partners) used the method correctly. Without actually going into people's bedrooms (or living rooms, or kitchens?) and tallying up on a clipboard whether their condom use was \"incorrect\", it's impossible to know for sure. Instead, people who do surveys of this kind have to rely almost exclusively on what people say they did. And let me ask you something: If you accidentally impregnated someone\/got impregnated by someone while nominally using some birth control method, would you say, when asked, that you had been using it \"incorrectly\"? Or would you, as all good carpenters do, blame your tools?\n\nAnother implicit assumption is that the respondents reflect a typical number of sexual encounters in a year. Again, I don't know how they decide what participants to include in this kind of study or how they verify the claims they get, but according to some studies I was able to find, the average \"coital frequency\", as it's romantically known, for both married and single people in the U.S. is somewhere around 7 encounters per month. Therefore, if we treated the experiences as being independent (with the same caveat as in the previous question), we could estimate the probability of unintended pregnancy in a single sexual encounter:\n\nLet's call the probability p. So the chance of not getting pregnant during a given sex act is (1-p). We'll accept the 7 times\/month figure and assume a total of $7*12=84$ sexual encounters per year, all including correct condom usage. As in the coin example, we've assumed independence, so the probability of not getting pregnant over the course of 84 trials is $(1-p)^{84}$, which we're assuming is equal to the stated number of 98%. Therefore, we have:\n$(1-p)^{84}=0.98$\nAnd so $(1-p) = 0.98^{1\/84} = 0.99975$, meaning that p is very small, about 0.02%. Therefore, if you had sex 100 times, as you say (and congrats, btw), you could expect to make an average of 0.02 babies.\n\nSome important notes:\n1) Our assumption of independence here may be more reasonable than in the previous example, because it's possible that whatever factors contribute to a birth control method failing despite proper use may be due more to chance than any kind of recurring trends.\n2) Also, these numbers don't account for the fact that (as we saw above) the chance of getting pregnant in a year even without any protection is something like 85%. So, in a sense, condoms \"only\" reduce the risk of pregnancy from 85% to 2%.\n3) We've only been talking about pregnancy here, not the risks of other things like STDs or panic attacks.\n4) Wear a condom, people!\n\nDear Dr. Math,\nMathematically speaking, what number makes for the best sexual position?\nName Withheld\n\nYou seem to be asking a lot of questions, NW.\n\nPersonally, I've always enjoyed the ln(2\u03c0).\n\n-DrM\n\n*Also acceptable: $\\int e^x$ or \"integration by parts\".\n\nAnonymous said...\n\n\"probability of not conceiving in one cycle conditional on the event that you had not conceived the cycles previously\"\n\nI've been wondering about the percentage chance of getting pregnant in a year question.\n\nIf you got pregnant in the first cycle that would mean that you couldn't get pregnant in any of the later cycles and lower the 97.6% figure. So shouldn't the probability of conceiving go down if you conceived in the cycles previously, not go down if you didn't conceive?\n\ndrmath said...\n\nIt's true that getting pregnant in any cycle makes it impossible to conceive in the subsequent cycles (at least for a while), but that's actually irrelevant to the way that we're calculating the probability. As in the coin example in the first part of this post, it's much simpler to consider the probability of not getting pregnant over the course of the year and then just subtract that from 1 to get the probability of conceiving at some point.\n\nOtherwise, you'd be stuck doing something like the following: let the probability of conceiving in any cycle be p. Again, for the time being, we'll assume independence. So the probability of getting pregnant in the different cycles goes like:\n--cycle 1: probability = p\n--cycle 2: probability = (1-p) * p [we failed in cycle 1 and succeeded in cycle 2.]\n--cycle 3: probability = (1-p)^2 * p\n--cycle 4: probability = (1-p)^3 * p\n...\n--cycle 13: probability = (1-p)^12 * p\n\nNow, you could add up all these probabilities, since the events are mutually exclusive, just as you point out. If you know a little statistics, you might recognize this as (a truncated version of) the geometric distribution. However, with a little algebra, you can show that the sum of these probabilities is exactly 1 - (1-p)^13, as we had already calculated.\n\nThe important point here is the correlation between not conceiving in any given cycle and not conceiving in any other cycle, due to the various medical possibilities I mentioned. This makes the assumption of independence invalid using either method of calculation.\n\n-DrM\n\nAbigail said...\n\nVery complicated mathematic. I will be having difficulty getting pregnant if I have to understand all these. Great stuff anyway!\n\nhbillions said...\n\nWhat's the probability of a fertile virile woman getting pregnant over the course of a 40-year active sex life?","date":"2014-10-24 18:00:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 10, \"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\": 0.712993323802948, \"perplexity\": 691.933170964095}, \"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-2014-42\/segments\/1414119646352.2\/warc\/CC-MAIN-20141024030046-00083-ip-10-16-133-185.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction and main results}
In this paper, we are interested in the existence and dynamics of solutions to the following equation with mixed fractional Laplacians,
\begin{align} \label{fequ}
(-\Delta)^{s_1} u +(-\Delta)^{s_2} u + \lambda u=|u|^{p-2} u,
\end{align}
under the constraint
\begin{align} \label{mass}
\int_{\mathbb{R}^N} |u|^2 \, dx=c>0,
\end{align}
where $N \geq 1$, $0<s_2<s_1<1$, $2+ \frac {4s_1}{N} \leq p< \infty $ if $N \leq 2s_1$, $2+ \frac {4s_1}{N} \leq p< \frac{2N}{N-2s_1}$ if $N >2s_1$, $\lambda \in \mathbb{R}$ appearing as Lagrange multiplier is unknown. The fractional Laplacian $(-\Delta)^s$ is characterized as $\mathcal{F}((-\Delta)^{s}u)(\xi)=|\xi|^{2s} \mathcal{F}(u)(\xi)$ for $\xi \in \mathbb{R}^N$, where $\mathcal{F}$ denotes the Fourier transform. The equation \eqref{fequ} arises from the study of standing waves to the time-dependent equation
\begin{align}\label{evolv pb0}
\left\{
\begin{aligned}
&i\partial_t \psi -(-\Delta)^{s_1} \psi -(-\Delta)^{s_2}\psi =-|\psi|^{p-2}\psi, \\
&\psi(0,x)=\psi_0(x), \quad x \in \mathbb{R}^N,
\end{aligned}
\right.
\end{align}
where $N\geq 1$, $0<s_2<s_1<1$, $2+ \frac {4s_1}{N} \leq p< \infty $ if $N \leq 2s_1$ and $2+ \frac {4s_1}{N} \leq p<\frac{2N}{N-2s_1}$ if $N >2s_1$. Here standing waves to \eqref{evolv pb0} are solutions of the form
$$
\psi(t, x)=e^{i\lambda t} u(x), \quad \lambda \in \mathbb{R}.
$$
It is obvious to see that standing wave $\psi$ is a solution to \eqref{evolv pb0} if and only if $u$ is a solution to \eqref{fequ}.
The equation \eqref{evolv pb0} appears in many fields and has been increasingly attracting the attention of scientists in recent years due to its numerous and important applications. It models many biological phenomena like describing the diffusion in an ecological niche subject to nonlocal dispersals. In the niche, the population is following a certain process so that if an individual exist the niche, it must come to the niche right away by selecting the return point according to the underlying stochastic process. This results in an equation involving mixed fractional Laplacians. The mixed operators are the outcome of the superposition of two long-range L\'evy processes or a classical Brownian motion and a long-range process. The population diffuses according to two or more types of nonlocal dispersals, modeled by L\'evy flights and encoded by two or more fractional Laplacians with two different powers, see \cite{VS} for more detailed accounts. The sum and the difference of two or more fractional Laplacians appear in many other fields, we refer the reader to page 2 of \cite{CBH} and the references therein for more details.
Note that any solution $\psi \in C([0, T), H^{s_1}(\mathbb{R}^N))$ to \eqref{evolv pb0} conserves the mass along time, i.e.
$$
\|\psi(t)\|_2=\|\psi_0\|_2, \quad \forall\,\, t \in [0, T).
$$
The mass often admits a clear physical meaning, for instance it represents the power supply in nonlinear optics or the total number of atoms in Bose-Einstein condensation. Therefore, from a physical point of view, it is interesting to explore standing waves to \eqref{evolv pb0} with prescribed $L^2$-norm. This then leads to the study of solutions to \eqref{fequ}-\eqref{mass}. Such solutions are often called normalized solutions to \eqref{fequ}. In this scenario, the parameter $\lambda \in \mathbb{R}$ is unknown and to be determined as Lagrange multiplier. Here we shall focus on normalized solutions to \eqref{fequ}. It is standard to check that any solution $u \in H^{s_1}(\mathbb{R}^N)$ to \eqref{fequ}-\eqref{mass} corresponds to a critical point of the functional
$$
E(u):=\frac{1}{2} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2\,dx + \frac{1}{2} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2\,dx-\frac{1}{p} \int_{\mathbb{R}^N}|u|^p\,dx
$$
restricted on the constraint
$$
S(c):=\left\{u \in H^{s_1}(\mathbb{R}^N) : \int_{\mathbb{R}^N}|u|^2 dx =c\right\}.
$$
When $2<p<2 + \frac{4s_1}{N}$, by using Gagliardo-Nirenberg inequality \eqref{gn}, we find that $E$ restricted on $S(c)$ is bounded from below for any $c>0$. Therefore, we are able to introduce the following minimization problem,
\begin{align} \label{gmin111}
m(c):=\inf_{u \in S(c)} E(u).
\end{align}
Apparently, minimizers to \eqref{gmin111} are solutions to \eqref{fequ}-\eqref{mass}. In this case, the authors in \cite{HL} established the existence of minimizers to \eqref{gmin111}. However, when $p \geq 2 + \frac{4s_1}{N}$, the study of solutions to \eqref{fequ}-\eqref{mass} is open so far. The aim of the present paper is to make some contributions towards this direction.
Firstly, we shall consider the existence of solutions to \eqref{fequ}-\eqref{mass} for the case $p=2 + \frac{4s_1}{N}$. In this case, by utilizing Gagliardo-Nirenberg inequality \eqref{gn}, we have the following result.
\begin{thm} \label{thm1}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p=2+\frac{4s_1}{N}$. Then there exists a constant $c_{N, s_1}>0$ such that
\begin{align*}
m(c)=\left\{
\begin{aligned}
&0, \qquad 0<&c\leq c_{N, s_1},\\
&-\infty, \qquad & c>c_{N, s_1}.
\end{aligned}
\right.
\end{align*}
In addition, for any $0<c \leq c_{N, s_1}$, $m(c)$ is not attained and there exists no solutions to \eqref{fequ}-\eqref{mass}, where $c_{N,s_1}>0$ is given by
$$
c_{N, s_1}:=\left(\frac{N+2s_1}{N C_{N, s_1}}\right)^{\frac{N}{2s_1}}
$$
and $C_{N, s_1}=C_{N,p,s_1}>0$ is the optimal constant in \eqref{gn} for $p=2+\frac{4s_1}{N}$.
\end{thm}
From Theorem \ref{thm1}, we see that $E$ restricted on $S(c)$ is unbounded from below for any $c>c_{N,s_1}$. This then suggests that it is unlikely to take advantage of \eqref{gmin111} to seek for solutions to \eqref{fequ}-\eqref{mass} for any $c>c_{N,s_1}$. This is also the case when $p>2+\frac{4s_1}{N}$. Indeed, for any $u \in S(c)$ and $t >0$, we define
$$
u_t(x):=t^{\frac N 2} u(tx), \quad x \in \mathbb{R}.
$$
By straightforward calculations, then $\|u_t\|_2=\|u\|_2$ and
\begin{align}\label{scaling}
E(u_t)=\frac{t^{2s_1}}{2} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2\,dx + \frac{t^{2s_2}}{2} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2\,dx-\frac{t^{\frac{N}{2}(p-2)}}{p} \int_{\mathbb{R}^N}|u|^p\,dx,
\end{align}
from which we conclude that $E(u_t) \to -\infty$ as $t \to \infty$, because of $p>2+\frac{4s_1}{N}$. Then there holds that $m(c)=-\infty$ for any $c>0$. In such a situation, deriving the existence of solutions to \eqref{fequ}-\eqref{mass}, we need to introduce the following minimization problem,
\begin{align} \label{min}
\gamma(c):=\inf_{u \in P(c)} E(u),
\end{align}
where $P(c)$ is the so-called Pohozaev manifold defined by
$$
P(c):=\{u \in S(c) : Q(u)=0\}
$$
and
$$
Q(u):=\frac{d}{dt}E(u_t)\mid_{t=1}=s_1\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2\,dx + s_2 \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2\,dx-\frac{N(p-2)}{2p} \int_{\mathbb{R}^N}|u|^p\,dx.
$$
Here $Q(u)=0$ is the Pohozaev identity associated to solutions of \eqref{fequ}-\eqref{mass}, see Lemma \ref{pohozaev}.
To further state the existence results for the case $p \geq 2+\frac{4s_1}{N}$, we define a constant $c_0 \geq 0$ by $c_0=c_{N, s_1}$ if $p=2+\frac{4s_1}{N}$ and $c_0=0$ if $p>2+\frac{4s_1}{N}$, where $c_{N,s_1}>0$ is the constant determined in Theorem \ref{thm1}
\begin{thm}\label{thm2}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2+\frac{4s_1}{N}$. Then there exists a constant $c_1>c_0$ such that, for any $c_0<c<c_1$, \eqref{fequ}-\eqref{mass} has a ground state solution $u_c \in S(c)$ satisfying $E(u_c)=\gamma(c)$. In particular, if $N=1$ and $2s_2 \geq 1$ or $N \geq 1$, $2s_2<N$ and $2< p \leq \frac{2N}{N-2s_2}$, then $c_1=\infty$
\end{thm}
To prove Theorem \ref{thm2}, the essential argument is to demonstrate that $P(c)$ is a natural constraint, by which we can obtain a Palais-Smale sequence belonging to $P(c)$ for $E$ restricted on $S(c)$ at the level $\gamma(c)$ for any $c>c_0$. Later, by using the fact that $E$ restricted on $P(c)$ is coercive, then the Palais-Smale sequence is bounded in $H^{s_1}(\mathbb{R}^N)$. Finally, by verifying that the function $c \mapsto \gamma(c)$ is nonincreasing on $(c_0, \infty)$ and the associated Lagrange multiplier $\lambda_c$ is positive for any $c_0<c<c_1$, then the compactness of the Palais-Smale sequence in $H^{s_1}(\mathbb{R}^N)$ follows. This completes the proof.
\begin{thm} \label{thm6}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2+\frac{4s_1}{N}$. If $u \in S(c)$ is a ground state solution to \eqref{fequ}-\eqref{mass} at the level $\gamma(c)$, then $u$ admits the form $e^{i \theta} |u_c|$ for some $\theta \in \mathbb{S}^1$, where $|u_c| \geq 0$ is radially symmetric and nonincreasing up to translations.
\end{thm}
The proof of Theorem \ref{thm6} is principally based on the variational characteristics of ground state solutions to \eqref{fequ}-\eqref{mass} and P\'olya-Szeg\"o inequality for fractional Laplacian.
\begin{thm} \label{thm3}
Let $N \geq 2$ and $0<s_2<s_1<1$.
\begin{enumerate}
\item [$(\textnormal{i})$] If $p>2+\frac{4s_1}{N}$, then, for any $0<c<c_1$, \eqref{fequ}-\eqref{mass} has infinitely many radially symmetric solutions $\{u_k\} \subset H^{s_1}(\mathbb{R}^N)$ satisfying $E(u_{k+1}) \geq E(u_k)>0$ and $E(u_k) \to \infty$ as $k \to \infty$, where $c_1>0$ is the constant determined in Theorem \ref{thm2}.
\item [$(\textnormal{ii})$] If $p=2+\frac{4s_1}{N} \leq \frac{2N}{N-2s_2}$, then, for any $k \in \mathbb{N}^+$, there exists a constant $c_k>c_{N,s_1}$ such that, for any $c>c_k$, \eqref{fequ}-\eqref{mass} has at least $k$ radially symmetric solutions in $H^{s_1}(\mathbb{R}^N)$.
\end{enumerate}
\end{thm}
To achieve Theorem \ref{thm3}, we shall work in the subspace $H^{s_1}_{rad}(\mathbb{R}^N)$ consisting of radially symmetric functions in $H^{s_1}(\mathbb{R}^N)$.
By applying the Kranosel'skii genus theory and following the strategies of the proof of Theorem \ref{thm2}, we can complete the proof. It is worth mentioning that the discussion of the compactness of Palais-Smale sequence for $E$ restricted on $S(c)$ becomes somewhat simple in $H^{s_1}_{rad}(\mathbb{R}^N)$, because the embedding $H^{s_1}_{rad}(\mathbb{R}^N) \hookrightarrow L^p(\mathbb{R}^N)$ is compact for any $2<p<\frac{2N}{N-2s_1}$ and $N \geq 2$.
\begin{thm}\label{thm4}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2+\frac{4s_1}{N}$.
\begin{enumerate}
\item[$(\textnormal{i})$] The function $c \mapsto \gamma(c)$ is continuous for any $c>c_0$ and it is nonincreasing on $(0, \infty)$. Moreover, $\lim_{c \to c_0^+} \gamma(c)=\infty$.
\item[$(\textnormal{ii})$] The function $c \mapsto \gamma(c)$ is strictly decreasing on $(c_0, c_1)$. Moreover, if $N=1$ and $2s_2 \geq 1$ or $N \geq 1$, $2s_2<N$ and $2 < p < \frac{2N}{N-2s_2}$, then the function $c \mapsto \gamma(c)$ is strictly decreasing on $(0, \infty)$
and $\lim_{c \to \infty} \gamma(c)=0$.
\item[$(\textnormal{iii})$] If $N>\max\left\{2 s_1+2,\frac{2s_1s_2}{s_1-s_2}\right\}$, then there exists a constant $c_{\infty}>0$ such that $\gamma(c)=m$ for any $c \geq c_{\infty}$, where $m>0$ is the ground state energy to \eqref{fequ00}.
\end{enumerate}
\end{thm}
The proofs of the assertions $(\textnormal{i})$ and $(\textnormal{ii})$ of Theorem \ref{thm4} are primarily beneficial from the definition of $\gamma(c)$. To prove the assertion $(\textnormal{iii})$ of Theorem \ref{thm4}, we first need to establish the existence of ground state solutions to the zero mass equation
\begin{align} \label{fequ00}
(-\Delta)^{s_1} u +(-\Delta)^{s_2} u =|u|^{p-2} u
\end{align}
in a proper Sobolev space $H$ defined by the completion of $C^{\infty}_0(\mathbb{R}^N)$ under the norm
$$
\|u\|_H:=\left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2 \,dx\right)^{\frac 12}+\left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u|^2 \,dx\right)^{\frac 12}.
$$
Then we require to show that the solutions belong to $L^2(\mathbb{R}^N)$, see Lemma \ref{l2}.
Let us now mention a few related works with respect to the study of normalized solutions to various nonlinear Schr\"odinger-type equations and systems. For the mass subcritical case, by the well-known Gagliardo-Nirenberg inequality, one derives that the energy functionals restricted on the $L^2$-norm constraints are bounded from below. In this situation, by introducing global minimization problems as the energy functionals restricted on the constraints, one can consider the existence and orbital stability of normalized solutions in the spirit of the Lions concentration compactness principle \cite{Li1, Li}, see for example \cite{AB, CS, CCW, CDSS, CP, G, Gou, GJ2, NW1, NW2, NW3, S} and references therein. Here normalized solutions corresponds to global minimizers.
For the mass critical or supercritical cases, things become quite different and complex. In these cases, the energy functionals restricted on the $L^2$-norm constraints may be unbounded from below, then it is impossible to bring in global minimization problems to investigate the existence of normalized solutions. In this situation, normalized solutions often corresponds to saddle type critical points or local minimizers, the existence of which are guaranteed by minimax arguments. For a long time, the paper \cite{Je} due to Jeanjean is the only one dealing with the existence of normalized solutions when the energy functionals restricted on the constraints are unbounded from below. During recent years, because of its physical relevance and mathematical importance in theories and applications, the study of normalized solutions has received more attention from researchers, see for example \cite{BMRV, BJS, BS1, BS2, BV, BZZ, BJ, BJT, BCGJ, CJ, GJ1, GZ, HT, JS, JL, LY, NTV2, S1, S2} regarding normalized solutions to equations and systems in $\mathbb{R}^N$ and \cite{NTV1, NTV3, PPVV, PG} regarding normalized solutions to equations and systems in bounded domains.
Now we turn to investigate dynamics of solutions to the Cauchy problem for the time-dependent equation \eqref{evolv pb0}. To do this, we first need to establish the local wellposdness of solutions in $H^{s_1}(\mathbb{R}^N)$, whose proof is mainly based on the contraction mapping principle and improved Strichartz estimates.
\begin{thm}\label{pb wellposedness}
Let $N\geq 2$, $\frac 1 2 <s_2<s_1< 1$ and $2< p<\frac{2N}{N-2s_1}$. Then, for any $\psi_0\in H_{rad}^{s_1}(\mathbb{R}^N)$, there exist a constant $T:=T(\|\psi_0\|_{H^{s_1}})>0$ and a unique maximal solution $\psi \in C([0, T), H_{rad}^{s_1}(\mathbb{R}^N))$ to \eqref{evolv pb0} satisfiing the alternative: either $T=+\infty$ or $T<+\infty$ and
$$
\lim_{t \to T^{-}} \|(-\Delta)^{\frac{s_1}{2}} \psi\|_2 =+\infty.
$$
In addition, there holds that
\begin{enumerate}
\item [$(\textnormal{i})$] $\psi \in L_{loc}^{\frac{4s_1p}{N(p-2)}}([0,T),W^{s_1,p}(\mathbb{R}^N))$.
\item [$(\textnormal{ii})$]The solution $\psi(t)$ satisfies the conservation of the mass and the energy, i.e. $\|\psi(t)\|_2=\|\psi_0\|_2$ and $E(\psi(t))=E(\psi_0)$ for any $t \in [0, T)$.
\item [$(\textnormal{iii})$]The solution $\psi(t)$ exists globally in time if $p<2+\frac{4s_1}{N}$ or $p=2+\frac{4s_1}{N}$ and
$$
\|\psi_0\|_2<\left(\frac{N+2s_1}{NC_{N,s_1}}\right)^{\frac{N}{4s_1}},
$$
where $C_{N, s_1}=C_{N,p,s_1}>0$ is the optimal constant appearing in \eqref{gn} for $p=2+\frac{4s_1}{N}$.
\end{enumerate}
\end{thm}
For further clarifications, we need to introduce a function $\phi \in H^{s_1}(\mathbb{R}^N)$ as the ground state solution to the following fractional nonlinear elliptic equation,
\begin{align}\label{psi eqt}
(-\Delta)^{s_1}\phi+\phi=\phi^{p-1}.
\end{align}
In fact, it turns out in \cite{Rup13,Rup16} that $\phi$ is positive, radially symmetric and decreasing. Moreover, whenever $ 2+\frac{4s_1}{N}\leq p <\frac{2N}{N-2s_1}$ and $N \geq 2$, we define
$$
0 \leq s_{c}:=\frac{N}{2}-\frac{2s_1}{p-2} <s_1, \quad \sigma_c:=\frac{s_1-s_c}{s_c}>0.
$$
It should be noted that $s_c>0$ if $p>2+\frac{4s_1}{N}$ and $s_c=0$ if $p=2+\frac{4s_1}{N}$. We also define a functional by
$$
\mathcal{E}(\phi):=\frac 12 \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} \phi |^2 \,dx-\frac 1 p \int_{\mathbb{R}^N} |\phi|^p \,dx.
$$
\begin{thm}\label{blow-up vs global solt}
Let $N\geq 2$, $\frac1 2<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$. Let $\psi \in C([0, T), H^{s_1}_{rad}(\mathbb{R}^N))$ be the solution to \eqref{evolv pb0} with initial datum $\psi_0 \in H^{s_1}_{rad}(\mathbb{R}^N)$ and $\phi \in H^{s_1}_{rad}(\mathbb{R}^N)$ be the ground state solution to \eqref{psi eqt}.
\begin{enumerate}
\item [$(\textnormal{i})$] If $s_c>0$ and $\psi_0 \in H^{s_1}_{rad}(\mathbb{R}^N)$ satisfies
\begin{align}\label{energ u0 inf energ gs}
E(\psi_0)M(\psi_0)^{\sigma_c} <\mathcal{E}(\phi)M(\phi)^{\sigma_c},
\end{align}
\begin{align}\label{mass u0 sup mass gs}
\|(-\Delta)^{\frac{s_1}{2}} \psi_0\|_2\|\psi_0\|_2^{\sigma_c} < \|(-\Delta)^{\frac{s_1}{2}} \phi\|_2\|\phi\|_2^{\sigma_c},
\end{align}
then $\psi(t)$ exists globally in time, i.e. $T=+\infty$.
\item [$(\textnormal{ii})$] If $s_c>0$ and $2<p < 2+4s_1$, either $E(\psi_0)<0$ or $E(\psi_0)\geq 0$ satisifes \eqref{energ u0 inf energ gs} and the following condition,
\begin{align}\label{mass u0 sup mass gs1}
\|(-\Delta)^{\frac{s_1}{2}} \psi_0\|_2\|\psi_0\|_2^{\sigma_c} > \|(-\Delta)^{\frac{s_1}{2}} \phi\|_2\|\phi\|_2^{\sigma_c},
\end{align}
then $\psi(t)$ blows up in finite time and
$$
\limsup_{t\rightarrow T^-} \|(-\Delta)^{\frac{s_1}{2}} \psi\|_2=+\infty.
$$
\item [$(\textnormal{iii})$] If $s_c=0$ and $E(\psi_0)<0$, then $\psi(t)$ either blows up in finite time or blows up in infinite time satisfying there exist $C>0$ and $t^\ast>0$ such that
$$
\|(-\Delta)^{\frac{s_1}{2}} \psi\|_2 + \|(-\Delta)^{\frac{s_2}{2}} \psi\|_2\geq Ct^{s_1}, \quad \forall \,\, t \geq t^*.
$$
\end{enumerate}
\end{thm}
The proof of Theorem \ref{blow-up vs global solt} crucially relies on the variational characteristics of $\phi$ and the analysis of the evolution of the following localized virial type quantity,
$$
M_{\chi_R}[\psi(t)]:=2 Im \int_{\mathbb{R}^N}\overline{\psi}\nabla\chi_R \cdot \nabla \psi\, dx,
$$
where $\chi_R: \mathbb{R}^N \to \mathbb{R}^+$ is a proper cut-off function.
Finally we are going to address orbital instability of ground state solutions to \eqref{fequ}-\eqref{mass} in the following sense.
\begin{defi}
We say that a solution $u \in H^{s_1}(\mathbb{R}^N)$ to \eqref{fequ} is orbitally unstable, if for any $\epsilon > 0$ there exists $ v \in H^{s_1}(\mathbb{R}^N)$ such that $\|v-u\|_{H^{s_1}} \leq \epsilon$ and the solution $\psi (t)$ to \eqref{evolv pb0} with initial datum $\psi(0) = v$ blows up in finite or infinite time.
\end{defi}
\begin{thm}\label{thm5}
Let $N \geq 2$, $\frac 1 2 <s_2<s_1<1$ and $p \geq 2 + \frac{4s_1}{N}$. Then standing waves associated with ground state solutions to \eqref{fequ}-\eqref{mass} are orbitally unstable by blowup in finite or infinite time. In addition, if $2<p<2+4s_1$, then they are orbitally unstable by blowup in finite time.
\end{thm}
{\noindent \bf Structure of the Paper.} The paper is organized as follows. In Section \ref{section2}, we present some preliminary results and give the proof of Theorem \ref{thm1}. In Section \ref{section3}, we consider the existence of ground state solutions to \eqref{fequ}-\eqref{mass} and show the proofs of Theorems \ref{thm2} and \ref{thm6}. In Section \ref{section4}, we aim to prove the existence of bound state solutions to \eqref{fequ}-\eqref{mass} and give the proof of Theorems \ref{thm3}. In Section \ref{section5}, we discuss some properties of the function $c \mapsto \gamma(c)$ and present the proof of Theorem \ref{thm4}. Section \ref{section6} is devoted to the study of the local well-posednesss of solutions to \eqref{evolv pb0} and contains the proof of Theorem \ref{pb wellposedness}. Section \ref{section7} is devoted the proof of Theorem \ref{blow-up vs global solt}. In Section \ref{section8}, orbital instability of ground state solutions to \eqref{fequ}-\eqref{mass} is discussed, i.e. Theorem \ref{thm5} is established. In Appendix, we deduce the Pohozaev identity satisfied by solutions to \eqref{fequ}.
\begin{notation}
Throughout the paper, $L^r(\mathbb{R}^N)$ denotes the usual Lebesgue space equipped with the norm
$$
\|f\|_r:=\left(\int_{\mathbb{R}^N}|f(x)|^r \, dx \right)^{\frac{1}{r}}, \quad 1 \leq r<\infty, \quad \|f\|_\infty:= \underset{x\in \mathbb{R}^N}{\mbox{ess sup}} \, |f(x)|.
$$
Moreover, $W^{s,r}(\mathbb{R}^N)$ denotes the usual Sobolev space equipped with the norm
$$
\|f\|_{W^{s,r}}:=\|f\|_2+ \|(-\Delta)^{\frac{s}{2}}f\|_2, \quad 0<s<1.
$$
In the case $r=2$, we use $H^s(\mathbb{R}^N)$ to denote $W^{s,2}(\mathbb{R}^N)$ and use $H^{s}_{rad}(\mathbb{R}^N)$ to denote the subspace of $H^{s}(\mathbb{R}^N)$, consisting of radially symmetric functions in $H^{s}(\mathbb{R}^N)$. The real number $r^{\prime}:=\frac{r}{r-1}$ is the conjugate exponent associate to a number $r \geq 1$ with the convention $1^\prime=\infty$ and $\infty^\prime=1$.
We also need to introduce some B\"{o}chner spaces which are denoted by $L_T^qL_x^r:=L^q([0,T),L^r(\mathbb{R}^N))$ equipped with the natural norms. If $X$ is an abstract space, then the set of continuous functions defined on $[0,T)$ and valued in $X$ is denoted by $C_T(X):=C([0,T),X)$, if necessary the interval of time may be closed.
If $A$ and $B$ are two nonnegative quantities, we write $A\lesssim B$ to denote $A\leq CB$. We write $A\sim B$ if $A\lesssim B$ and $B\lesssim A$ hold.
Whenever $\varepsilon_n\rightarrow0$ as $n$ goes to infinity, we denote $o_n(1)=\varepsilon_n$.
\end{notation}
\section{Preliminaries and proof of Theorem \ref{thm1}} \label{section2}
In this section, we shall present some preliminary results used to prove our main theorems and give the proof of Theorem \ref{thm1}. First of all, let us display the well-known Gagliardo-Nirenberg inequality in $H^{s_1}(\mathbb{R}^N)$.
\begin{lem} \label{gninequ}
Let $0<s<1$, $2 \leq p< \infty$ if $N<2s$ and $2 \leq p<\frac{2N}{N-2s}$ if $N>2s$, then
\begin{align} \label{gn}
\int_{\mathbb{R}^N} |u|^p\,dx \leq C_{N,p,s} \left(\int_{\mathbb{R}^N} |(-\Delta)^{\frac s 2} u|^2 \,dx \right)^{\frac{N(p-2)}{4s}}\left(\int_{\mathbb{R}^N}|u|^2 \,dx \right)^{\frac p2 -\frac{N(p-2)}{4s}},
\end{align}
where $C_{N,p,s}>0$ denotes the optimal constant.
\end{lem}
\begin{lem} \label{pohozaev}
Let $u \in H^{s_1}(\mathbb{R}^N)$ is a solution to \eqref{fequ}-\eqref{mass}, then $Q(u)=0$, i.e.
$$
s_1\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2\,dx + s_2 \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2\,dx=\frac{N(p-2)}{2p} \int_{\mathbb{R}^N}|u|^p\,dx.
$$
\end{lem}
\begin{proof}
For convenience of readers, the proof of this lemma shalled be postponed to Appendix.
\end{proof}
Making use of Lemmas \ref{gninequ} and \ref{pohozaev}, we are now able to prove Theorem \ref{thm1}.
\begin{proof}[Proof of Theorem \ref{thm1}] In view of \eqref{gn}, we first have that, for any $u \in S(c)$,
$$
E(u) \geq \frac 12 \left(1-\left(\frac{c}{c_{N,s_1}}\right)^{\frac{2s_1}{N}}\right) \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2 \, dx + \frac 12 \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u |^2 \, dx.
$$
This clearly shows that $m(c)\geq 0$ for any $0<c \leq c_{N, s_1}$. On the other hand, from \eqref{scaling}, we can deduce that $E(u_t) \to 0$ as $t \to 0^+$. This leads to $m(c) \leq 0$ for any $c>0$. Therefore, we obtain that $m(c)=0$ for any $0<c \leq c_{N, s_1}$. We next prove that $m(c)$ cannot be attained for any $0<c<c_{N,s_1}$. Let us suppose that $m(c)$ is attained for some $0<c\leq c_{N,s_1}$. Hence there exists $u \in S(c)$ such that $m(c)=E(u)$. From Lemma \ref{pohozaev}, we get that $Q(u)=0$.
Using \eqref{gn}, we then see that
\begin{align}\label{criticalineq}
\begin{split}
s_1\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2\, dx +s_2\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2\, dx
&=\frac{Ns_1}{N+2s_1} \int_{\mathbb{R}^N} |u|^{2+\frac{4s_1}{N}} \,dx \\
& \leq s_1\left(\frac{c}{c_{N, s_1}}\right)^{\frac{2s_1}{N}}\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2\,dx.
\end{split}
\end{align}
This then suggests that $u=0$, because of $0<c\leq c_{N,s_1}$. As a result, we derive that $m(c)$ is not attained for any $0<c \leq c_{N,s_1}$. From the discussions above, we can also conclude that \eqref{fequ}-\eqref{mass} has no solutions for any $0<c \leq c_{N, s_1}$. We now prove that $m(c)=-\infty$ for any $c>c_{N, s_1}$. Let $ u \in H^{s_1}(\mathbb{R}^N)$ be such that the optimal constant $C_{N, s_1}$ in \eqref{gn} is achieved for $p=2+\frac{4s_1}{N}$. This means that
\begin{align} \label{optimal}
\int_{\mathbb{R}^N}|u|^{2+\frac{4s_1}{N}} \,dx =C_{N,s_1} \left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac {s_1} {2}}u|^2 \,dx\right)\left( \int_{\mathbb{R}^N}|u|^2 \, dx \right)^{\frac{2s_1}{N}}.
\end{align}
Define
\begin{align} \label{defw}
w:=c^{\frac 12}\frac{u}{\|u\|_2} \in S(c).
\end{align}
By applying \eqref{optimal}, we can derive that
\begin{align} \label{scaling1}
\begin{split}
E(w_t)&=\frac{c}{2\|u\|_2^2} t^{2s_1}\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2 \, dx +\frac{c}{2\|u\|_2^2} t^{2s_2}\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2 \, dx \\
&\quad -\frac{N}{2N+4s_1}\frac{c^{1+\frac{2s_1}{N}}}{\|u\|_2^{2+\frac{4s_1}{N}}} t^{2s_1} \int_{\mathbb{R}^N}|u|^{2+\frac{4s_1}{N}} \,dx\\
&=\frac{c}{2\|u\|_2^2} \left(1-\left(\frac{c}{c_{N,s_1}}\right)^{\frac{2s_1}{N}}\right) t^{2s_1}\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}}u|^2 \, dx +\frac{c}{2\|u\|_2^2} t^{2s_2} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}}u|^2\, dx.
\end{split}
\end{align}
This indicates that $E(w_t) \to -\infty$ as $t \to \infty$ for any $c>c_{N, s_1}$, due to $0<s_2<s_1<1$. Hence $m(c)=-\infty$ for any $c>c_{N, s_1}$. This completes the proof.
\end{proof}
\begin{lem}\label{pohoz 0}
Let $\phi \in H^{s_1}(\mathbb{R}^N)$ be the ground state solution to \eqref{psi eqt}, then
\begin{align}\label{pohoz 1}
\|(-\Delta)^{\frac {s_1} {2}} \phi\|_2^2=\frac{N(p-2)}{2s_1p-N(p-2)}\|\phi\|_2^2,
\end{align}
\begin{align}\label{pohoz 2}
\|\phi\|_p^p=\frac{2s_1p}{N(p-2)}\|(-\Delta)^{\frac {s_1} {2}} \phi\|_2^2,
\end{align}
\begin{align}\label{best const with GS}
\displaystyle C_{N,p,s_1}=\frac{2s_1p}{N(p-2)}\left(\frac{N(p-2)}{2s_1p-N(p-2)}\right)^{\frac{4s_1-Np+2N}{4s_1}}\|\phi\|_2^{2-p},
\end{align}
where $C_{N,p,s_1}>0$ is the optimal constant in \eqref{gn} with $s=s_1$.
\end{lem}
\begin{proof}
Multiplying \eqref{psi eqt} against $\phi$ and integrating on $\mathbb{R}^N$, one gets that
\begin{align}\label{eq 1}
\|(-\Delta)^{\frac{s_1}{2}}\phi\|_2^2+\|\phi\|_2^2=\|\phi\|_p^p,
\end{align}
On the other hand, from \cite[Lemma 8.1]{Rup16}, one has that
\begin{align}\label{eq 2}
\frac{N-2s_1}{2}\|(-\Delta)^{\frac{s_1}{2}}\phi\|_2^2+\frac{N}{2}\|\phi\|_2^2=\frac{N}{p}\|\phi\|_p^p.
\end{align}
It then follows from \eqref{eq 1} and \eqref{eq 2} that
\begin{align*
\|(-\Delta)^{\frac{s_1}{2}}\phi\|_2^2=\frac{N(p-2)}{2s_1p-N(p-2)}\|\phi\|_2^2.
\end{align*}
This along with \eqref{eq 1} then yields to
\begin{align*}
\|\phi\|_p^p
& = \frac{2s_1p}{N(p-2)}\|(-\Delta)^{\frac{s_1}{2}}\phi\|_2^2.
\end{align*}
From straightforward calculations and the equality
$$
\|\phi\|_{p}^p =C_{N,p,s_1} \|(-\Delta)^{\frac s 2} \phi\|_2^{\frac{N(p-2)}{2s_1}}\|\phi\|_2^{p-\frac{N(p-2)}{2s}},
$$
then \eqref{best const with GS} follows. Thus the proof is completed.
\end{proof}
\begin{comment}
\subsection{Main results for the evolutionary problem}
First, we need to present the definition of admissible pairs.
\begin{defi}
Let $N\geq 2$ and $s\in (0,1]$. Any pair $(q,r)$ of positive real numbers is said to be $s$-admissible, if
$q,r\geq 2$ and
$$\frac{2s}{q}+\frac{N}{r}=\frac{N}{2}.$$
Such set of $s$-admissible pairs is denoted by $\Gamma_s$.
\end{defi}
We denote $S(t)$ the evolution group related to \eqref{evolv pb0}, precisely
$$S(t)u_0:=\mathcal{F}^{-1}(e^{-it(|\xi|^{2s_1}+|\xi|^{2s_2})}\mathcal{F}u_0).$$
Our first main result is about a family of Strichartz estimates without loss of regularity which are useful to control spherically symmetric solutions of the mixed fractional problem \eqref{evolv pb0}.
\begin{thm}\label{strichartz th}
Let $N\geq 2$, $\frac{N}{2N-1}<s_2<s_1< 1$ and $u,u_0,F$ are radially symmetric in space and satisfying:
\begin{align}\label{evolv pb}
\displaystyle
\left\{
\begin{array}{l}
i\partial_tu-(-\Delta)^{s_1}u-(-\Delta)^{s_2}u=F(t,x), \\[2mm]
u(0,x)=u_0(x), x\in \mathbb{R}^N.
\end{array}
\right.
\end{align}
Then
\begin{align}\label{Radial Strichartz}
\|u\|_{L_t^q(L^r)} \lesssim \|u_0\|_2+\|F\|_{L_t^{\tilde{q}^{\prime}}(L^{\tilde{r}^{\prime}})},
\end{align}
if $(q,r)$ and $(\tilde{q},\tilde{r})$ belong to $\Gamma_{s_1}\cup \Gamma_{s_2}$ and, either
$(q,r)\neq (2,\infty)$ or $(\tilde{q}^{\prime},\tilde{r}^{\prime})\neq (2,\infty)$.
\end{thm}
Our second result is the well-posedness of the Cauchy problem \eqref{evolv pb0} in $H_{rd}^{s_1}$ for any exponent $2< p<\frac{2N}{N-2s_1}$.
\begin{thm}\label{pb wellposedness}
Let $N\geq 2,\frac{N}{2N-1}<s_2<s_1< 1$ and $2< p<\frac{2N}{N-2s_1}$. Then, for all $u_0\in H_{rd}^{s_1}$ there exist
$T^\ast:=T^\ast(\|u_0\|_{H^{s_1}})>0$ and a unique maximal solution $u\in C_{T^\ast}(H_{rd}^{s_1})$ to the problem \eqref{evolv pb0}
which satisfies the alternative: either $T^\ast=\infty$ or $T^\ast<\infty$ and
$$\displaystyle \lim_{t\uparrow T^\ast}(\|(-\Delta)^{\frac{s_1}{2}}u\|_2+\|(-\Delta)^{\frac{s_2}{2}}u\|_2)=\infty.$$
In addition,
\begin{enumerate}
\item $\displaystyle u\in L_{loc}^{\frac{4s_1p}{N(p-2)}}([0,T^\ast),W^{s_1,p})$;
\item the solution satisfies the conservation of the mass and the energy;
\item the solution $u$ is global if $p<2+\frac{4s_1}{N}$ or
$$p=2+\frac{4s_1}{N}\text{ and } \|u_0\|_2<(\frac{p}{4C_{N,p,s_1}})^{\frac{2s_1}{2ps_1-Np+2N}}.$$
\end{enumerate}
\end{thm}
The last main result concerning the problem \eqref{evolv pb0} is about sufficient condition for blowup solutions in terms of $\phi$
solution to \eqref{s1 stationary pb}.
\begin{thm}\label{blow-up vs global solt}
Let $N\geq 2,\frac{1}{2}<s_2<s_1<1$ and $0\leq s_{c}:=\frac{N}{2}-\frac{2s_1}{p-2}<s_1$. Let $\phi$ be a solution to
\eqref{s1 stationary pb}, $u_0\in H_{rd}^{s_1}$, and $u\in C_{T^\ast}(H_{rd}^{s_1})$ be a maximal solution
to \eqref{evolv pb0}.
\begin{enumerate}
\item Assume that $p<2+4s_1$. Suppose that either
$E(u_0)<0$ or $E(u_0)\geq 0$ with the two next inequalities
\begin{align}\label{energ u0 inf energ gs}
E(u_0)^{s_c}M(u_0)^{s_1-s_c} <(\frac{Np-2N-4s_1}{2Np-4N-4s_1})^{s_c} E(\phi)^{s_c}M(\phi)^{s_1-s_c};
\end{align}
\begin{align}\label{mass uo sup mass gs}
(\|u_0\|_{\dot{H}^{s_1}}^2+\|u_0\|_{\dot{H}^{s_2}}^2)^{\frac{s_c}{2}}\|u_0\|_2^{s_1-s_c} > \|\phi\|_{\dot{H}^{s_1}}^{s_c}\|\phi\|_2^{s_1-s_c}.
\end{align}
Then,
\begin{enumerate}
\item if $0<s_c<s_1$, then $u$ blows-up in finite time and
$$\displaystyle \limsup_{t\rightarrow T^\ast}(\|u(t)\|_{\dot{H}^{s_1}}+\|u(t)\|_{\dot{H}^{s_2}})=+\infty;$$
\item if $s_c=0$, then $u$ either blows-up in finite time or there exist $C>0$ and $t^\ast>0$ an instant of time such that
$$\forall t\geq t^\ast,\,\,\|u(t)\|_{\dot{H}^{s_1}}+\|u(t)\|_{\dot{H}^{s_2}}\geq Ct^{s_1}.$$
\end{enumerate}
\item Suppose that $E(u_0)\geq 0$ with \eqref{energ u0 inf energ gs} and
\begin{align}\label{mass uo inf mass gs}
(\|u_0\|_{\dot{H}^{s_1}}^2+\|u_0\|_{\dot{H}^{s_2}}^2)^{\frac{s_c}{2}}\|u_0\|_2^{s_1-s_c} < \|\phi\|_{\dot{H}^{s_1}}^{s_c}\|\phi\|_2^{s_1-s_c},
\end{align}
then $T^\ast=\infty$.
\end{enumerate}
\end{thm}
\subsection{Main results for the stationary problem}
The first result reads as follows: we establish the nonexistence of solutions to \eqref{fequ}-\eqref{mass} in the mass critical case $p=2+\frac{4s_1}{N}$.
\begin{thm} \label{thm1}
Let $N \geq 1$ and $p=2+\frac{4s_1}{N}$. Then there exists a constant $c_{N, s_1}>0$ such that
\begin{align*}
m(c):=\inf_{u \in S(c)} E(u)=\left\{
\begin{aligned}
0, \qquad 0<&c\leq c_{N, s_1},\\
-\infty, \qquad & c>c_{N, s_1}.
\end{aligned}
\right.
\end{align*}
In addition, $m(c)$ is not attained and \eqref{fequ}-\eqref{mass} has no solutions for any $0<c \leq c_{N, s_1}$, where
$$
c_{N, s_1}:=\left(\frac{N+2s_1}{N C_{N, s_1}}\right)^{\frac{N}{2s_1}}
$$
and $C_{N, s_1}:=C_{N,p,s_1}>0$ is the optimal constant in \eqref{gn} for $p=2+\frac{4s_1}{N}$.
\end{thm}
Second, we investigate the existence of ground state solutions to \eqref{fequ}-\eqref{mass} in the mass critical and supercritical cases $p\geq 2+\frac{4s_1}{N}$. For this purpose, we introduce the following minimization problem,
\begin{align} \label{min}
\gamma(c):=\inf_{u \in P(c)} E(u),
\end{align}
where $P(c)$ is so-called Pohozaev manifold defined by
$$
P(c):=\{u \in S(c) : Q(u)=0\}.
$$
Let us define the following useful constant
\begin{align}\label{constant c0}
c_0=c_{N, s_1}\text{ if } p=2+\frac{4s_1}{N} \text{ else } c_0=0 \text{ if } p>2+\frac{4s_1}{N},
\end{align}
where the constant $c_{N, s_1}>0$ is determined in Theorem \ref{thm1}. Thus, the following result holds.
\begin{thm}\label{thm2}
Let $p \geq 2+\frac{4s_1}{N}$ and $c \geq c_0$. There exists a constant $c_1>c_0$ such that, for any $c_0<c<c_1$, \eqref{fequ}-\eqref{mass} has a ground state solution $u_c \in S(c)$ satisfying $E(u_c)=\gamma(c)$.
\end{thm}
Next, the existence of infinitely many radially symmetric solutions to \eqref{fequ}-\eqref{mass} is claimed.
\begin{thm} \label{thm3}
Let $p>2+\frac{4s_1}{N}$ and $N \geq 2$. Then there exists a constant $c_1>0$ such that, for any $0<c<c_1$, \eqref{fequ}-\eqref{mass} has infinitely many radially symmetric solutions $(u_k)_{k\geq 1}$ satisfying $E(u_{k+1}) \geq E(u_k)>0$ and $E(u_k) \to \infty$ as $k \to \infty$.
\end{thm}
Finally, our principal aim is to investigate some properties of the function $c \mapsto \gamma(c)$ on $(c_0, \infty)$.
\begin{thm}\label{thm4}
Let $p \geq 2+\frac{4s_1}{N}$. For any $c>c_0$, the function $c \mapsto \gamma(c)$ is continuous and nonincreasing. In addition, $\lim_{c \to c_0^+} \gamma(c)=\infty$ and the following assertions hold,
\begin{enumerate}
\item[$(\textnormal{i})$] If $N=1$ and $2s_2 \geq 1$, then the function $c \mapsto \gamma(c)$ is strictly decreasing on $(0, \infty)$
and $\displaystyle \lim_{c \to \infty} \gamma(c)=0$.
\item[$(\textnormal{ii})$] If $N>\max\{2(s_1+1),\frac{2s_1s_2}{s_1-s_2}\}$ , then there exists a constant $c_{\infty}>0$ such that $\gamma(c)=m$ for any $c \geq c_{\infty}$.
\end{enumerate}
\end{thm}
\end{comment}
\section{Existence and characteristics of ground state solutions} \label{section3}
In this section, we shall present the proofs of Theorems \ref{thm2} and \ref{thm6}. For this aim, we first need to establish some preliminary results. Let us remind that $c_0=c_{N,s_1}$ if $p=2 +\frac{4s_1}{N}$ and $c_0=0$ if $p> 2 +\frac{4s_1}{N}$, where $c_{N,s_1}>0$ is the constant given in Theorem \ref{thm1}.
\begin{lem} \label{nonempty}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$, then $P(c) \neq \emptyset$ for any $c>c_0$.
\end{lem}
\begin{proof}
For the case $p=2+\frac{4s_1}{N}$ and $c>c_{N,s_1}$, it follows from \eqref{scaling1} that $E(w_t)>0$ for any $t>0$ small enough and $E(w_t)<0$ for any $t>0$ large enough, where $w \in S(c)$ is defined by \eqref{defw}. Therefore, one finds that there exists a constant $t_w>0$ such that
$$
t_wQ(w_{t_w})=\frac{d E(w_t)}{d t}{\mid_{t=t_w}}=0.
$$
Hence we have that $w_{t_w} \in P(c)$ and $P(c) \neq \emptyset$ for any $c>c_{N, s_1}$. For the case $p>2+\frac{4s_1}{N}$ and $c>0$, from applying \eqref{scaling}, we can obtain the desired conclusion by a similar way. Thus the proof is completed.
\end{proof}
\begin{lem} \label{coercive}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$, then, for any $c>c_0$, $E$ restricted on $P(c)$ is coercive and bounded from below by a positive constant.
\end{lem}
\begin{proof}
If $u \in P(c)$, then $Q(u)=0$. As a result, there holds that
\begin{align} \label{ide1}
\begin{split}
\hspace{-1cm}E(u)&=E(u)-\frac{2}{N(p-2)}Q(u)\\
&=\frac{N(p-2)-4s_1}{2N(p-2)}\|(-\Delta)^{\frac{s_1}{2}} u\|_2^2 +\frac{N(p-2)-4s_2}{2N(p-2)}\|(-\Delta)^{\frac{s_2}{2}} u\|_2^2.
\end{split}
\end{align}
We first consider the case $p=2+\frac{4s_1}{N}$. In this case, we shall prove that $E$ restricted on $P(c)$ is coercive for any $c>c_{N,s_1}$. To do this, we argue by contradiction that there exists a sequence $\{u_n\} \subset P(c)$ satisfying $\|u_n\|_{H^{s_1}} \to \infty$ as $n \to \infty$ such that $\{E(u_n)\} \subset \mathbb{R}$ is bounded for some $0<c<c_{N,s_1}$. From \eqref{ide1}, we then infer that $\{\|(-\Delta)^{{s_2}/{2}} u_n\|_2\} \subset \mathbb{R}$ is bounded. Next we are going to deduce that $\{\|(-\Delta)^{{s_1}/{2}} u_n\|_2\} \subset \mathbb{R}$ is bounded. If $N=1$ and $2s_2\geq 1$ or $N \geq 1$, $2s_2<N$ and $2 < p \leq \frac{2N}{N-2s_2}$, it then follows from \eqref{gn} in that $\{\|u_n\|_p\} \subset \mathbb{R}$ is bounded, because of $\{\|(-\Delta)^{{s_2}/{2}} u_n\|_2\} \subset \mathbb{R}$ is bounded. Thanks to $Q(u_n)=0$, we then get that $\{\|(-\Delta)^{{s_1}/{2}} u_n\|_2\} \subset \mathbb{R}$ is bounded. If $N \geq 1$, $2s_2<N$ and $p >\frac{2N}{N-2s_2}$, then there exist $p_1, p_2 >0$ with $2<p_2<\frac{2N}{N-2s_2}<p_1$ and $0<\theta<1$ such that $p=\theta p_1 +(1-\theta)p_2$. Using H\"older's inequality, we then derive that
\begin{align} \label{inter}
\|u_n\|_p^p \leq \|u_n\|_{p_1}^{\theta p_1} \|u_n\|_{p_2}^{(1-\theta)p_2}.
\end{align}
On the other hand, applying \eqref{gn}, one gets that
$$
\|u_n\|_{p_1}^{p_1} \leq C_{N,p_1,s_1} \|(-\Delta)^{\frac {s_1} {2}} u_n\|_2^{\frac{N(p_1-2)}{2s_1}}\|u_n\|_2^{p_1-\frac{N(p_1-2)}{2s_1}}
$$
and
$$
\|u_n\|_{p_2}^{p_2} \leq C_{N,p_2,s_2} \|(-\Delta)^{\frac {s_2} {2}} u_n\|_2^{\frac{N(p_2-2)}{2s_2}}\|u_n\|_2^{p_2-\frac{N(p_2-2)}{2s_2}}.
$$
This along with \eqref{inter} results in
\begin{align} \label{inequ1}
\|u_n\|_p^p \leq C\|(-\Delta)^{\frac {s_1} {2}} u_n\|_2^{\frac{\theta N(p_1-2)}{2s_1}} \|(-\Delta)^{\frac {s_2} {2}} u_n\|_2^{\frac{(1-\theta )N(p_2-2)}{2s_2}} \|u_n\|_2^{p-\frac{\theta N(p_1-2)}{2s_1}-\frac{(1-\theta)N(p_2-2)}{2s_2}},
\end{align}
where $ C:=C_{N,p_1,s_1}^{\theta}C_{N,p_2,s_2}^{1-\theta}>0$. Observe that
$$
\theta(p_1-2)=(p-2)-(1-\theta)(p_2-2)<p-2=\frac{4s_1}{N}.
$$
Therefore, there holds that
$$
\frac{\theta N(p_1-2)}{2s_1}<2.
$$
Since $Q(u_n)=0$ and $\{\|(-\Delta)^{{s_2}/{2}} u_n\|_2\} \subset \mathbb{R}$ is bounded, from \eqref{inequ1}, then $\{\|(-\Delta)^{{s_1}/{2}} u_n\|_2\} \subset \mathbb{R}$ is bounded. Hence we reach a contradiction, because $\|u_n\|_{H^{s_1}} \to \infty$ as $n \to \infty$. This in turn implies that $E$ restricted on $P(c)$ is coercive. We now demonstrate that $E$ restricted on $P(c)$ is bounded from below by a positive constant for any $c>c_{N,s_1}$. If $N=1$ and $2s_2\geq 1$ or $N \geq 1$, $2s_2<N$ and $2<p \leq \frac{2N}{N-2s_2}$, it then yields from \eqref{gn} that, for any $u \in P(c)$,
\begin{align} \label{ide11}
\begin{split}
&s_1\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2\, dx +s_2\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2\, dx=\frac{Ns_1}{N+2s_1} \int_{\mathbb{R}^N}|u|^p\,dx \\
&\leq \frac{Ns_1 C_{N,p,s_2}}{N+2s_1} \left(\int_{\mathbb{R}^N} |(-\Delta)^{\frac {s_2} 2} u|^2 \,dx \right)^{\frac{N(p-2)}{4s_2}}\left(\int_{\mathbb{R}^N}|u|^2 \,dx \right)^{\frac p2 -\frac{N(p-2)}{4s_2}}.
\end{split}
\end{align}
Note that
$$
\frac{N(p-2)}{4s_2}>1.
$$
Therefore, by \eqref{ide11}, we get that $\|(-\Delta)^{{s_2}/{2}} u\|_2$ is bounded from below by a positive constant. Coming back to \eqref{ide1}, we then have the desired result. If $N \geq 1$, $2s_2<N$ and $p >\frac{2N}{N-2s_2}$, it then follows from \eqref{criticalineq} that $\|(-\Delta)^{{s_1}/{2}} u\|_2$ is bounded from below by a positive constant, because of $c>c_{N,s_1}$. Let us claim that $\|(-\Delta)^{{s_2}/{2}} u\|_2$ is also bounded from below by a positive constant. Otherwise, we may suppose that there exists $\{u_n\}\subset P(c)$ such that $\|(-\Delta)^{{s_2}/{2}} u_n\|_2=o_n(1)$. This leads to $\|u_n\|_{\frac{2N}{N-2s_1}}=o_n(1)$. If $\{(-\Delta)^{{s_1}/{2}} u_n\|_2\} \subset \mathbb{R}$ is bounded, we then derive from H\"older's inequality that $\|u_n\|_p=o_n(1)$. Since $Q(u_n)=0$, it then gives that $\|(-\Delta)^{{s_1}/{2}} u_n\|_2=o_n(1)$, which is a contradiction. If $\{\|(-\Delta)^{{s_1}/{2}} u_n\|_2\} \subset \mathbb{R}$ is unbounded, we get by the coerciveness of $E$ restricted on $P(c)$ that $E(u_n) \to \infty$ as $n \to \infty$. In view of \eqref{ide1}, we then obtain that $\|(-\Delta)^{{s_2}/{2}} u_n\|_2 \to \infty$ as $n \to \infty$. This is impossible, because we assumed that $\|(-\Delta)^{{s_2}/{2}} u_n\|_2=o_n(1)$. Therefore, the claim holds true. Utilizing \eqref{ide1}, we get the desired result.
Next we consider the case $p>2+\frac{4s_1}{N}$. In this case, there holds that
$$
\frac{N(p-2)}{4s_1}>1.
$$
It is immediate to find from \eqref{ide1} that $E$ restricted on $P(c)$ is coercive for any $c>0$. We now prove that $E$ restricted on $P(c)$ is bounded from below by a positive constant. For any $u \in P(c)$, we know that $Q(u)=0$. It then follows from \eqref{gn} that
\begin{align*}
\hspace{-1cm}s_1\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2\, dx +s_2\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2\, dx&=\frac{Ns_1}{N+2s_1} \int_{\mathbb{R}^N}|u|^p \,dx \\
&\leq C_{N,s_1}c^{\frac p 2 -\frac{N(p-2)}{4s_1}}\left(\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2dx\right)^{\frac{N(p-2)}{4s_1}}.
\end{align*}
This implies that $\|(-\Delta)^{{s_1}/{2}} u\|_2$ is bounded from below by a positive constant. The proof is completed by applying \eqref{ide1}.
\end{proof}
\begin{lem} \label{monotonicity}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$. Let $u \in S(c)$ for $c >c_0$. Assume in addition that $ \sup_{t \geq 0} E(u_t)<\infty$ if $p=2+\frac{4s_1}{N}$. Then there exists a unique $t_u>0$ such that $u_{t_u} \in P(c)$ and $E(u_{t_u})=\sup_{t \geq 0} E(u_t)$. Moreover, the function $t \mapsto E(u_t)$ is concave on $[t_u,\infty)$ and $0<t_u < 1$ if $Q(u) < 0$.
\end{lem}
\begin{proof}
For any $u \in S(c)$, by using \eqref{scaling}, we first have that
\begin{align}\label{derivative} \nonumber
\frac{d}{d t}E(u_t)&=s_1 {t^{2s_1-1}}\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2 \, dx + s_2{t^{2s_2-1}} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2 \, dx -\frac{N(p-2)}{2p}{t^{N(\frac p 2 -1)-1}} \int_{\mathbb{R}^N} |u|^p dx \\
&=\frac 1 t Q(u_t).
\end{align}
If $p=2+\frac{4s_1}{N}$ and $\displaystyle\sup_{t \geq 0} E(u_t)<\infty$, it then follows from \eqref{scaling} that
$$
\frac 12 \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2 \, dx <\frac 1 p \int_{\mathbb{R}^N} |u|^p \, dx.
$$
In light of \eqref{derivative}, we then easily derive there exists a unique $t_u>0$ such that $Q(u_{t_u})=0$. Notice that $Q(u_t)>0$ for any $0<t<t_u$ and $Q(u_t)<0$ for any $t>t_u$, then $E(u_{t_u})=\sup_{t \geq 0} E(u_t)$. Furthermore, if $Q(u) < 0$, we then obtain that $0<t_u < 1$. If $p>2+\frac{4s_1}{N}$, then
$$
\frac {N (p-2)}{2}>2s_1.
$$
In this case, by means of \eqref{derivative}, we can also get the desired result. We now show that the function $t \mapsto E(u_t)$ is concave on $[t_u, \infty)$. Observe that
\begin{align*}
\frac{d^2}{d t^2}E(u_t)&=s_1(2s_1-1) {t^{2s_1-2}}\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2 \, dx + s_2(2s_2-1){t^{2s_2-2}} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2 dx \\
&\quad -\frac{N(p-2)(N(p-2)-2)}{4p}{t^{N(\frac p 2 -1)-2}} \int_{\mathbb{R}^N} |u|^p dx.
\end{align*}
If $2s_1 =1$, we then have that $\frac{d^2}{d t^2}E(u_t)<0$ for any $t >0$. We next consider the case $2s_1 \neq 1$. Let us write $t=\gamma t_u$ for $\gamma >1$, then
\begin{align*}
\frac{d^2}{d t^2}E(u_t)&=\frac{2s_1-1}{\gamma^{2-2s_1} t^2_u} \left(s_1{t^{2s_1}_u}\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2 dx + \frac{s_2(2s_2-1)}{2s_1-1}\gamma^{2(s_2-s_1)}{t^{2s_2}_u} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2 dx \right. \\
& \quad \left.-\frac{N(p-2)(N(p-2)-2)}{4p(2s_1-1)}{t^{N(\frac p 2 -1)}_u} \gamma^{{N(\frac p 2 -1)}-2s_1} \int_{\mathbb{R}^N} |u|^pdx \right)\\
&=:\frac{2s_1-1}{\gamma^{2-2s_1} t^2_u} g(\gamma).
\end{align*}
Since $Q(u_{t_u})=0$, i.e.
$$
s_1{t^{2s_1}_u}\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2 dx + s_2{t^{2s_2}_u} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2 dx=\frac{N(p-2)}{2p}{t^{N(\frac p 2 -1)}_u} \int_{\mathbb{R}^N} |u|^p dx,
$$
then
\begin{align*}
g(\gamma)&=s_2\left(\frac{2s_2-1}{2s_1-1}\gamma^{2(s_2-s_1)}-1\right){t^{2s_2}_u} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2 \, dx \\
&\quad +\frac{N(p-2)}{2p}\left(1-\frac{(N(p-2)-2)}{2(2s_1-1)}\gamma^{{N(\frac p 2 -1)}-2s_1} \right){t^{N(\frac p 2 -1)}_u} \int_{\mathbb{R}^N} |u|^p \,dx.
\end{align*}
If $2s_1>1$, we then deduce that $g(\gamma)<0$ for any $\gamma >1$. If $0<2s_1<1$, we then find that $g(\gamma) \to -\infty$ as $\gamma \to 0^+$, $g(1)>0$ and $g(\gamma) \to \infty$ as $\gamma \to \infty$. This together with the monotonicity of $g$ shows that $g(\gamma)>0$ for any $\gamma >1$. Consequently, we obtain that $\frac{d^2}{d t^2}E(u_t)<0$ for any $t \geq t_u$. This finishes the proof.
\end{proof}
\begin{defi}\label{homotopy} \cite[Definition 3.1]{Gh}
Let $B$ be a closed subset of a set $Y \subset H^{s_1}(\mathbb{R}^2)$. We say that a class $\mathcal{G}$ of compact subsets of $Y$ is a homotopy stable family with the closed boundary $B$ provided that
\begin{enumerate}
\item [\textnormal{(i)}] every set in $\mathcal{G}$ contains $B$;
\item [\textnormal{(ii)}] for any $A \in \mathcal{G}$ and any function $\eta \in C([0, 1] \times Y, Y)$ satisfying $\eta(t, x)=x$ for all $(t, x) \in (\{0\} \times Y) \cup([0, 1] \times B)$, then $\eta(\{1\} \times A) \in \mathcal{G}$.
\end{enumerate}
\end{defi}
Let us remark that $B=\emptyset$ is admissible. For further discussions, we shall introduce some notations. If $p=2+\frac{4s_1}{N}$, we define a functional $F: \mathcal{S}(c) \to R$ by $F(u):=E(u_{t_u})=\max_{t>0}E(u_t)$, where
\begin{align} \label{sc}
\mathcal{S}(c):=\left\{u \in S(c) : \frac 12 \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2 \, dx <\frac 1 p \int_{\mathbb{R}^N} |u|^p dx\right\}.
\end{align}
If $p>2+\frac{4s_1}{N}$, we define a functional $F: S(c) \to R$ by $F(u):=E(u_{t_u})=\displaystyle\max_{t>0}E(u_t)$.
\begin{lem}\label{ps}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$. Let $\mathcal{G}$ be a homotopy stable family of compact subsets of $S(c)$ with closed boundary $B$ and set
\begin{align} \label{ming}
\gamma_{\mathcal{G}}(c):=\inf_{A\in \mathcal{G}}\max_{u \in A} F(u).
\end{align}
Suppose that $B$ is contained on a connected component of $P(c)$ and $\max\{\sup F(B), 0\}<\gamma_{\mathcal{G}}(c)<\infty$. Then there exists a Palais-Smale sequence $\{u_n\} \subset P(c)$ for $E$ restricted on $S(c)$ at the level $\gamma_{\mathcal{G}}(c)$ for any $c>c_0$.
\end{lem}
\begin{proof}
The proof benefits from ingredients developed in \cite{BS1, BS2}. For simplicity, we only show the proof for the case $p>2+ \frac{4s_1}{N}$. Replacing the role of $S(c)$ by $\mathcal{S}(c)$, one can similarly treat the case $p=2+ \frac{4s_1}{N}$. To begin with, we define a mapping $\eta: [0,1] \times S(c) \to S(c)$ by $\eta(s, u)=u_{1-s+st_u}$. From Lemma \ref{monotonicity}, we have that $t_u=1$ if $u \in P(c)$. Thus we see that $\eta(s ,u)=u$ for any $(s, u) \in (\{0\} \times S(c)) \cup([0, 1] \times B)$, because of $B \subset P(c)$. In addition, it is simple to derive that $\eta$ is continuous on $[0,1] \times S(c)$. Let $\{D_n\} \subset \mathcal{G}$ be a minimizing sequence to \eqref{ming}. By Definition \ref{homotopy}, we then get that
$$
A_n:=\eta(\{1\} \times D_n)=\{u_{t_u} : u \in D_n\} \in \mathcal{G}.
$$
Note that $A_n \subset P(c)$, it then holds that
$$
\displaystyle\max_{v \in A_n}F(v)=\displaystyle\max_{u \in D_n}F(u).
$$
Therefore, there exists another minimizing sequence $\{A_n\} \subset P(c)$ to \eqref{ming}. Using \cite[Theorem 3.2]{Gh}, we then deduce that there exists a Palais-Smale sequence $\{\tilde{u}_n\} \subset S(c)$ for $F$ at the level $\gamma_{\mathcal{G}}(c)$ such that $\mbox{dist}_{H^{s_1}}(\tilde{u}_n, A_n)=o_n(1)$. For simplicity, we shall write $t_n=t_{\tilde{u}_n}$ and $u_n=(\tilde{u}_n)_{t_n}$.
We now claim that there exists a constant $C>0$ such that $1/C \leq t_n \leq C$. Indeed, notice first that
$$
t_n^{2s_1}=\frac{\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u_n|^2 \, dx}{\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} \tilde{u}_n|^2 \, dx}.
$$
Since $E(u_n)=F(\tilde{u}_n)=\gamma_{\mathcal{G}}(c)+o_n(1)$ and $\{u_n\} \subset P(c)$, it then follows from Lemma \ref{coercive} that there exists a constant $C_1>0$ such that $1/C_1 \leq \|u_n\|_{H^{s_1}} \leq C_1$. On the other hand, since $\{A_n\} \subset P(c)$ is a minimizing sequence to \eqref{ming}, by Lemma \ref{coercive}, we then have that $\{A_n\}$ is bounded in $H^{s_1}$. Note that $\mbox{dist}_{H^{s_1}}(\tilde{u}_n, A_n)=o_n(1)$, then $\{\tilde{u}_n\}$ is bounded in $H^{s_1}(\mathbb{R}^N)$. In addition, since $A_n$ is compact for any $n\in \mathbb{N}$, then there exists $v_n \in A_n$ such that
$$
\mbox{dist}_{H^{s_1}}(\tilde{u}_n, A_n)=\|\tilde{u}_n-v_n\|_{H^{s_1}}=o_n(1).
$$
Applying again Lemma \ref{coercive}, we then get that
$$
\|\tilde{u}_n\|_{H^{s_1}} \geq \|v_n\|_{H^{s_1}} -\|\tilde{u}_n-v_n\|_{H^{s_1}} \geq \frac{1}{C_2}+o_n(1).
$$
Therefore, the claim follows.
We next show that $\{u_n\} \subset P(c)$ is a Palais-Smale sequence for $E$ restricted on $S(c)$ at the level $\gamma_{\mathcal{G}}(c)$. In the following, we denote by $\|\cdot\|_{*}$ the dual norm of $(T_u S(c))^*$. Observe that
\begin{align*}
\|dE(u_n)\|_*=\sup_{\psi \in T_{u_n}S(c), \|\psi\|_{H^{s_1}}\leq 1}|dE(u_n)[\psi]|=\sup_{\psi \in T_{u_n}S(c), \|\psi\|_{H^{s_1}}\leq 1}|dE(u_n)[(\psi_{\frac{1}{t_n}})_{t_n}]|.
\end{align*}
By straightforward calculations, we can find that the mapping $T_uS(c) \to T_{u_{t_u}}S(c)$ define by $\psi \mapsto \psi_{t_u}$ is an isomorphism. Moreover, we have that $dF(u)[\psi]=dE(u_{t_u})[\psi_{t_u}]$ for any $u \in S(c)$ and $\psi \in T_uS(c)$. As a consequence, we get that
$$
\|dE(u_n)\|_*=\sup_{\psi \in T_{u_n}S(c), \|\psi\|_{H^{s_1}}\leq 1}|dF(\tilde{u}_n)[\psi_{\frac{1}{t_n}}]|.
$$
Since $\{\tilde{u}_n\} \subset S(c)$ is a Palais-Smale sequence for $F$ at the level $\gamma_{\mathcal{G}}(c)$, we then apply the claim to deduce that $\{u_n\} \subset P(c)$ is a Palais-Smale sequence for $E$ restricted on $S(c)$ at the level $\gamma_{\mathcal{G}}(c)$. Thus the proof is completed.
\end{proof}
\begin{lem} \label{pss}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$. Then there exists a Palais-Smale sequence $\{u_n\} \subset P(c)$ for $E$ restricted on $S(c)$ at the level $\gamma(c)$ for any $c>c_0$.
\end{lem}
\begin{proof}
Let $B=\emptyset$ and $\mathcal{G}$ be all singletons in $\mathcal{S}(c)$ if $p=2+\frac{4s_1}{N}$ and all singletons in $S(c)$ if $p>2+\frac{4s_1}{N}$, where $\mathcal{S}(c)$ is defined by \eqref{sc}. Therefore, from \eqref{ming}, there holds that
$$
\gamma_{\mathcal{G}}(c)=\inf_{u \in \mathcal{S}(c)} \sup_{t>0} E(u_t) \,\,\,\mbox{if} \,\, p=2+\frac{4s_1}{N}
$$
and
$$
\gamma_{\mathcal{G}}(c)=\inf_{u \in S(c)} \sup_{t>0} E(u_t) \,\,\,\mbox{if} \,\, p>2+\frac{4s_1}{N}.
$$
We next prove that $\gamma_{\mathcal{G}}(c)=\gamma(c)$. For simplicity, we only consider the case $p>2+\frac{4s_1}{N}$. From Lemma \ref{monotonicity}, we know that, for any $u \in S(c)$, there exists a unique $t_u>0$ such that $u_{t_u} \in P(c)$ and $E(u_{t_u})=\displaystyle\max_{t >0}E(u_t)$. This then implies that
$$
\inf_{u \in S(c)} \sup_{t>0} E(u_t) \geq \inf_{u \in P(c)} E(u).
$$
On the other hand, for any $u \in P(c)$, we have that $E(u)=\displaystyle\max_{t >0}E(u_t)$. This then gives that
$$
\inf_{u \in S(c)} \sup_{t>0} E(u_t) \leq \inf_{u \in P(c)} E(u).
$$
Accordingly, we derive that $\gamma_{\mathcal{G}}(c)=\gamma(c)$. It then follows from Lemma \ref{ps} that the result of this lemma holds true and the proof is completed.
\end{proof}
\begin{lem} \label{lagrange}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$. Let $u_c \in S(c)$ be a solution to the equation
\begin{align} \label{fequ1}
(-\Delta)^{s_1} u_c +(-\Delta)^{s_2} u_c + \lambda_c u_c=|u_c|^{p-2} u_c, \quad c>c_0.
\end{align}
Then there exists a constant $c_1>0$ such that $\lambda_c>0$ for any $c_0<c<c_1$. In particular, if $N=1$ and $2s_2 \geq 1$ or $N \geq 1$, $2s_2<N$ and $2< p \leq \frac{2N}{N-2s_2}$, then $c_1=\infty$.
\end{lem}
\begin{proof}
Since $u_c$ is a solution to \eqref{fequ1}, then $Q(u_c)=0$, see Lemma \ref{pohozaev}. This means that
\begin{align} \label{ph111}
s_1\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_c|^2 \,dx +s_2\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_c|^2 \,dx =\frac{N(p-2)}{2p} \int_{\mathbb{R}^N}|u_c|^p\,dx.
\end{align}
Multiplying \eqref{fequ1} by $u_c$ and integrating on $\mathbb{R}^N$, we get that
\begin{align} \label{integrate}
\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_c|^2 \,dx +\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_c|^2 \,d +\lambda_c \int_{\mathbb{R}^N}|u_c|^2 \,dx =\int_{\mathbb{R}^N}|u_c|^p \,dx .
\end{align}
Combining \eqref{ph111} and \eqref{integrate}, we have that
\begin{align} \label{lc}
\hspace{-0.5cm}\lambda_c c = \left(\frac{2ps_1}{N(p-2)}-1\right) \int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_c|^2 \,dx + \left(\frac{2ps_2}{N(p-2)}-1\right) \int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_c|^2 \,dx.
\end{align}
If $N=1$ and $2s_2\geq 1$ or $N \geq 1$, $2s_2<N$ and $2< p \leq \frac{2N}{N-2s_2}$, then
$$
\frac{2ps_1}{N(p-2)}>\frac{2ps_2}{N(p-2)} \geq 1.
$$
This indicates that $\lambda_c>0$, by \eqref{lc}. In this case, we choose $c_1=\infty$. We now treat the case $N \geq 1$, $N >2s_2$ and $p >\frac{2N}{N-2s_2}$. In virtue of \eqref{gn} and \eqref{ph111}, we derive that
$$
s_1\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_c|^2 \,dx +s_2\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_c|^2 \,dx \leq \widetilde{C}_{N,p,s_1} c^{\frac p 2 -\frac{N(p-2)}{4s_1}}\left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_c|^2 \,dx \right)^{\frac{N(p-2)}{4s_1}},
$$
where $\widetilde{C}_{N,p,s_1}>0$ is defined by
$$
\widetilde{C}_{N,p,s_1}:=\frac{N(p-2)C_{N,p,s_1}}{2p}.
$$
If $p>2+\frac{4s_1}{N}$, from the inequality above, it then leads to $\|(-\Delta)^{{s_1}/{2}} u_c\|_2 \to \infty$ as $c \to 0^+$. In addition, by interpolation inequality, there holds that
\begin{align*}
\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_c|^2 \,dx \leq \left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_c|^2 \,dx \right)^{\frac{s_2}{s_1}} \left(\int_{\mathbb{R}^N}|u_c|^2\,dx \right)^{\frac{s_1-s_2}{s_1}}.
\end{align*}
Due to
$$
\frac{2ps_1}{N(p-2)}>1, \quad s_2<s_1,
$$
we then conclude from \eqref{lc} that $\lambda_c>0$ if $c>0$ small enough. We now treat the case $p=2+\frac{4s_1}{N}$. In this case, from \eqref{ph111} and \eqref{integrate}, we see that
$$
\lambda_c c=(s_1-s_2) \int_{\mathbb{R}^N} |(-\Delta)^{\frac {s_1}{2}} u|^2 \,dx-\frac{N(s_1-s_2)-2s_1s_2}{N+2s_1} \int_{\mathbb{R}^N} |u|^{2+\frac{4s_1}{N}} \,dx.
$$
If $N \geq 1$, $N \geq 2s_2$ and $p>\frac{2N}{N-2s_2}$, i.e. $N(s_1-s_2) > 2s_1 s_2$, by \eqref{gn}, then
$$
\lambda_c c \geq \left((s_1-s_2)-\frac{N(s_1-s_2)-2s_1s_2}{N}\left(\frac{c}{c_{N,s_1}}\right)^{\frac{2s_1}{N}}\right)\int_{\mathbb{R}^N} |(-\Delta)^{\frac {s_1}{2}}u|^2 \,dx,
$$
from which we get that $\lambda_c>0$ if $c_{N,s_1}<c<c_1$, where $c_1>0$ is defined by
$$
c_1:=\left(\frac{N(s_1-s_2)}{N(s_1-s_2)-2s_1s_2}\right)^{\frac{N}{2s_1}} c_{N,s_1}.
$$
This completes the proof.
\end{proof}
\begin{lem} \label{nonincreasing}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$. Then the function $c \mapsto \gamma(c)$ is nonincreasing on $(c_0, \infty)$.
\end{lem}
\begin{proof}
For any $0<c_2<c_1$, we shall prove that $\gamma(c_1) \leq \gamma(c_2)$. By the definition of $\gamma(c)$, we first have that, for any $\epsilon>0$, there exists $u \in P(c_2)$ such that
\begin{align} \label{non1}
E(u) \leq \gamma(c_2) + \frac{\epsilon}{2}.
\end{align}
Let $\chi \in C_0^{\infty}(\mathbb{R}^N, [0,1])$ be a cut-off function such that $\chi(x) =1$ for $|x| \leq 1$ and $\chi(x)=0$ for $|x|\geq 2$. For $\delta>0$ small, we define $u^{\delta}(x):=u(x) \chi(\delta x)$ for $x \in \mathbb{R}^N$. It is easy to check that $u^{\delta} \to u$ in $H^{s_1}(\mathbb{R}^N)$ as $\delta \to 0^+$. Since $Q(u)=0$, we then get that $(u^{\delta})_{t_{u^{\delta}}} \to u$ in $H^{s_1}(\mathbb{R}^N)$ as $\delta \to 0^+$, where $t_{u^{\delta}}>0$ is determined by Lemma \ref{monotonicity} such that $Q((u^{\delta})_{t_{u^{\delta}}})=0$. Therefore, there exists a constant $\delta>0$ small such that
\begin{align} \label{non2}
E((u^{\delta})_{t_{u_{\delta}}}) \leq E(u) + \frac{\epsilon}{4}.
\end{align}
Let $v \in C^{\infty}_0(\mathbb{R}^N)$ be such that $\mbox{supp}\,v \subset B(0, 1+2/\delta) \backslash B(0, 2/\delta)$ and set
$$
\tilde{v}^{\delta}:=\frac{\left(c_1-\|u^{\delta}\|_2^2\right)^{\frac 12}}{\|v\|_2} v.
$$
For $0<t<1$, we define $w^{\delta}_t:=u^{\delta} + (\tilde{v}^{\delta})_t$, where $ (\tilde{v}^{\delta})_t(x):= t^{N/2}\tilde{v}^{\delta}(tx)$ for $x\in \mathbb{R}^N$. Observe that $\mbox{supp}\, u_{\delta} \cap \mbox{supp}\, (\tilde{v}^{\delta})_t =\emptyset$ for any $0<t<1$, then $\|w^{\delta}_t\|_2^2=c_1$. It is not hard to verify that $ (\tilde{v}^{\delta})_t \to 0$ in $\dot{H}^{s_1}(\mathbb{R}^N)$ as $t \to 0^+$. Hence we deduce that there exist $t, \delta>0$ small such that
\begin{align}\label{non3}
\max_{\lambda>0}E(((\tilde{v}^{\delta})_t)_{\lambda}) \leq \frac{\epsilon}{4}.
\end{align}
Consequently, using \eqref{non1}-\eqref{non3}, we have that
\begin{align*}
\gamma(c_1) \leq \max_{\lambda>0} E((w^{\delta}_t)_{\lambda})&=\max_{\lambda>0}\left(E((u^{\delta})_{\lambda}) + E(((\tilde{v}^{\delta})_t)_{\lambda}) \right) \\
&\leq E((u^{\delta})_{t_{u_{\delta}}}) + \frac{\epsilon}{4}\leq E(u)+ \frac{\epsilon}{2} \leq \gamma(c_2) +\epsilon.
\end{align*}
Since $\epsilon>0$ is arbitrary, then $\gamma(c_1) \leq \gamma(c_2)$. Thus the proof is completed.
\end{proof}
\begin{lem}\label{decreasing}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$. If there exists $u \in S(c)$ with $E(u)=\gamma(c)$ satisfying the equation
\begin{align} \label{fequ2}
(-\Delta)^{s_1} u +(-\Delta)^{s_2} u + \lambda u=|u|^{p-2} u,
\end{align}
then $\lambda \geq 0$. If $\lambda>0$, then the function $c \mapsto \gamma(c)$ is strictly decreasing in a right neighborhood of $c$. If $\lambda<0$, then the function $c \mapsto \gamma(c)$ is strictly increasing in a left neighborhood of $c$.
\end{lem}
\begin{proof}
For any $t_1, t_2>0$, we set $u_{t_1,t_2}(x):=t_1^{1/2}t_2^{N/2}u(t_2x)$ for $x \in \mathbb{R}^N$. Then we find that $\|u_{t_1,t_2}\|_2^2 =t_1c$. Define
\begin{align*}
\alpha(t_1,t_2):=E(u_{t_1,t_2})=\frac{t_1^2t_2^{2s_1}}{2}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2\,dx +
\frac{t_1^2t_2^{2s_2}}{2}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_s}{2}} u|^2\,dx-\frac{t_1^pt_2^{\frac{N}{2}(p-2)}}{p} \int_{\mathbb{R}^N}|u|^p\,dx.
\end{align*}
We compute that
\begin{align*}
\frac{\partial}{\partial t_1} \alpha(t_1, t_2)={t_1t_2^{2s_1}}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2\,dx+
{t_1t_2^{2s_2}}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u|^2\,dx -{t_1^{p-1}t_2^{\frac{N}{2}(p-2)}} \int_{\mathbb{R}^N}|u|^p\,dx.
\end{align*}
Note that $u_{t_1, t_2} \to u$ in $H^{s_1}(\mathbb{R}^N)$ as $(t_1, t_2) \to (1, 1)$ and $E'(u)u=-\lambda c$. If $\lambda>0$, then there exists a constant $\delta>0$ small such that, for any $(t_1, t_2) \in (1, 1+\delta) \times [1-\delta, 1+\delta]$,
$$
\frac{\partial}{\partial t_1} \alpha(t_1, t_2) <0.
$$
This leads to $\alpha(t_1, t_2) <\alpha(1, t_2)$ for any $(t_1, t_2) \in (1, 1+\delta) \times [1-\delta, 1+\delta]$. Observe that
\begin{align*}
\frac{\partial}{\partial t_2} \alpha(t_1, t_2)&=s_1{t_1^2t_2^{2s_1-1}}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2\,dx+
s_2{t_1^2t_2^{2s_2-1}}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u|^2\,dx \\
& \quad -\frac{N(p-2)}{2p}{t_1^p t_2^{\frac{N}{2}(p-2)-1}} \int_{\mathbb{R}^N}|u|^p\,dx \\
&=t_1^2\frac{Q(u_{t_2})}{t_2}
\end{align*}
and
\begin{align*}
\frac{\partial^2}{\partial t_2^2} \alpha(t_1, t_2)&=s_1(2s_1-1){t_1^2t_2^{2s_1-2}}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2\,dx+s_2(2s_2-1){t_1^2t_2^{2s_2-2}}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u|^2\,dx \\
& \quad -\frac{N(p-2)(N(p-2)-2)}{4p}{t_1^p t_2^{\frac{N}{2}(p-2)-2}} \int_{\mathbb{R}^N}|u|^p\,dx.
\end{align*}
Then we have that
$$
\frac{\partial}{\partial t_2} \alpha(t_1, t_2) {\mid}_{(1,1)}=0, \quad \frac{\partial^2}{\partial t_2^2} \alpha(t_1, t_2) {\mid}_{(1,1)}<0.
$$
For $\epsilon>0$ small, by the implicit function theorem, then there exists a continuous function $g: [1-\epsilon, 1+\epsilon] \to \mathbb{R} $ with $g(1)=1$ such that $Q(u_{1+\epsilon, g(1+\epsilon)})=0$. Therefore, we conclude that
$$
\gamma((1+\epsilon)c) \leq \alpha(1+\epsilon, g(1+\epsilon))<\alpha(1, g(1+\epsilon)) \leq \alpha(1,1)=E(u)=\gamma(c),
$$
where we used the fact $u \in P(c)$. If $\lambda<0$, we can similarly obtain the desired result. This jointly with Lemma \ref{nonincreasing} implies that $\lambda \geq 0$. Thus the proof is completed.
\end{proof}
\begin{lem}\label{ladecreasing}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p \geq 2 +\frac{4s_1}{N}$. Then the function $c \mapsto \gamma(c)$ is strictly decreasing on $(c_0, c_1)$, where the constant $c_1>0$ is determined in Lemma \ref{lagrange}.
\end{lem}
\begin{proof}
The proof follows directly from Lemmas \ref{lagrange} and \ref{decreasing}.
\end{proof}
We are now ready to prove Theorem \ref{thm2}.
\begin{proof}[Proof of Theorem \ref{thm2}]
In light of Lemma \ref{pss}, we first obtain that there exists a Palais-Smale sequence $\{u_n\} \subset P(c)$ for $E$ restricted on $S(c)$ at the level $\gamma(c)$. From Lemma \ref{coercive}, we have that $\{u_n\}$ is bounded in $H^{s_1}(\mathbb{R}^N)$. Reasoning as the proof of \cite[Lemma 3]{BeLi}, we are able to deduce that $u_n \in H^{s_1}(\mathbb{R}^N)$ satisfies the following equation,
\begin{align} \label{fequ3}
(-\Delta)^{s_1} u_n +(-\Delta)^{s_2} u_n + \lambda_n u_n=|u_n|^{p-2} u_n+o_n(1),
\end{align}
where
$$
\lambda_n:=\frac{1}{c} \left(\int_{\mathbb{R}^N}|u_n|^p\,dx -\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_n|^2\, dx-\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_n|^2\,dx \right).
$$
We claim that $\{u_n\} \subset H^{s_1}(\mathbb{R}^N)$ is non-vanishing. Otherwise, by using \cite[Lemma I.1]{Li}, we have that $\|u_n\|_p=o_n(1)$. Since $Q(u_n)=0$, then there holds that $E(u_n)=o_n(1)$. This is impossible, because of $\gamma(c)>0$ for any $c>c_0$, see Lemma \ref{coercive}. As a result, we know that there exists a sequence $\{y_n\} \subset \mathbb{R}^N$ such that $u_n(\cdot+y_n) \rightharpoonup u$ in $H^{s_1}(\mathbb{R}^N)$ as $n \to \infty$ and $u\neq 0$. Since $\{u_n\}$ is bounded in $H^{s_1}(\mathbb{R}^N)$, then $\{\lambda_n\} \subset \mathbb{R}$ is bounded. Hence, there exists a constant $\lambda\in\mathbb{R}$ such that $\lambda_n \to \lambda$ in $\mathbb{R}$ as $n \to \infty$. Therefore, from \eqref{fequ3}, we get that
\begin{align} \label{fequ4}
(-\Delta)^{s_1} u +(-\Delta)^{s_2} u + \lambda u=|u|^{p-2} u.
\end{align}
This results in $Q(u)=0$, see Lemma \ref{pohozaev}. We next prove that $u \in S(c)$. To do this, let us define $w_n=u_n-u(\cdot-y_n)$. It is immediate to see that $w_n(\cdot+y_n) \rightharpoonup 0$ in $H^{s_1}(\mathbb{R}^N)$ as $n \to \infty$. In addition, there holds that
\begin{align*}
\|(-\Delta)^{\frac{s_i}{2}} u_n\|^2_2=\|(-\Delta)^{\frac{s_i}{2}} w_n\|^2_2+\|(-\Delta)^{\frac{s_i}{2}} u\|^2_2+o_n(1) \quad \mbox{for}\,\, i=1,2
\end{align*}\
and
$$
\|u_n\|_p^p=\|w_n\|_p^p+\|u\|_p^p+o_n(1).
$$
Thus we have that
\begin{align} \label{bl}
\begin{split}
\gamma(c)=E(u_n)+o_n(1) =E(w_n) +E(u)+o_n(1) \geq E(w_n) +\gamma(\|u\|_2^2)+o_n(1),
\end{split}
\end{align}
and
\begin{align} \label{bl1}
Q(w_n)=Q(w_n)+Q(u)=Q(u_n)+o_n(1)=o_n(1).
\end{align}
In view of \eqref{bl1}, then
$$
0 \leq E(w_n)-\frac{2p}{N(p-2)}Q(w_n)=E(w_n) +o_n(1).
$$
Since $0<\|u\|_2^2 \leq c$, by using \eqref{bl} and Lemma \ref{nonincreasing}, we then have that $\gamma(\|u\|_2^2)=\gamma(c)$. This together with Lemmas \ref{lagrange} and \ref{ladecreasing} gives rise to $u \in S(c)$. As a consequence, we get that $\|w_n\|_p=o_n(1)$. From \eqref{fequ3} and \eqref{fequ4}, it then follows that $\|(-\Delta)^{\frac{s_i}{2}} w_n\|^2_2=o_n(1)$ for $i=1,2$. Therefore, we are able to derive that $\gamma(c)=E(u)$. Thus the proof is completed.
\end{proof}
\begin{proof}[Proof of Theorem \ref{thm6}]
Let $u \in S(c)$ be a ground state solution to \eqref{fequ}-\eqref{mass} at the level $\gamma(c)$. We claim that
$$
|u| \in P(c), \quad \|(-\Delta)^{\frac{s_1}{2}} |u|\|_2 = \|(-\Delta)^{\frac{s_1}{2}} u \|_2, \quad \|(-\Delta)^{\frac{s_2}{2}} |u|\|_2 = \|(-\Delta)^{\frac{s_2}{2}} u \|_2.
$$
Indeed, we first observe that $E(|u|) \leq E(u)$ and $Q(|u|) \leq Q(u)=0$. Then, by Lemma \ref{monotonicity}, there exists a unique constant $0<t_{|u|} \leq 1$ such that $|u|_{t_{|u|}} \in P(c)$. Therefore, we conclude that
\begin{align*}
\gamma(c) \leq E(|u|_{t_{|u|}})&=E(|u|_{t_{|u|}})-\frac{2}{N(p-2)}Q(|u|_{t_{|u|}})\\
&=\frac{N(p-2)-4s_1}{2N(p-2)}\|(-\Delta)^{\frac{s_1}{2}} \left(|u|_{t_{|u|}}\right)\|_2^2 +\frac{N(p-2)-4s_2}{2N(p-2)}\|(-\Delta)^{\frac{s_2}{2}} \left( |u|_{t_{|u|}}\right)\|_2^2\\
&=t_{|u|}^{2s_1}\frac{N(p-2)-4s_1}{2N(p-2)}\|(-\Delta)^{\frac{s_1}{2}} |u|\|_2^2 +t_{|u|}^{2s_2}\frac{N(p-2)-4s_2}{2N(p-2)}\|(-\Delta)^{\frac{s_2}{2}} |u|\|_2^2\\
& \leq \frac{N(p-2)-4s_1}{2N(p-2)}\|(-\Delta)^{\frac{s_1}{2}} |u|\|_2^2 +\frac{N(p-2)-4s_2}{2N(p-2)}\|(-\Delta)^{\frac{s_2}{2}} |u|\|_2^2\\
& \leq \frac{N(p-2)-4s_1}{2N(p-2)}\|(-\Delta)^{\frac{s_1}{2}} u\|_2^2 +\frac{N(p-2)-4s_2}{2N(p-2)}\|(-\Delta)^{\frac{s_2}{2}} u\|_2^2 \\
&=E(u)-\frac{2}{N(p-2)}Q(u)=E(u)=\gamma(c).
\end{align*}
This leads to $t_{|u|}=1$ and
$$
\|(-\Delta)^{\frac{s_1}{2}} |u|\|_2 = \|(-\Delta)^{\frac{s_1}{2}} u \|_2, \quad \|(-\Delta)^{\frac{s_2}{2}} |u|\|_2 = \|(-\Delta)^{\frac{s_2}{2}} u \|_2.
$$
Then the claim follows. Hence we have that $u=e^{i \theta} |u|$ for some $\theta \in \mathbb{S}$. From the discussion above, we know that $|u| \in S(c)$ is also a ground state solution to \eqref{fequ}-\eqref{mass} at the level $\gamma(c)$. Let us now denote by $|u|^{\ast}$ the symmetric-decreasing rearrangement of $|u|$. Similarly, we are able to show that
$$
|u|^{\ast} \in P(c) ,\quad \|(-\Delta)^{\frac{s_1}{2}} |u|^{\ast}\|_2 = \|(-\Delta)^{\frac{s_1}{2}} |u| \|_2, \quad \|(-\Delta)^{\frac{s_2}{2}} |u|^{\ast}\|_2 = \|(-\Delta)^{\frac{s_2}{2}} |u| \|_2.
$$
From \cite[Proposition 3]{FSS}, we then derive that $|u|=\rho(|\cdot-x_0|)$ for some $x_0 \in \mathbb{R}^N$, where $\rho$ is a decreasing function. Thus the proof is completed.
\end{proof}
\section{Multiplicity of bound state solutions} \label{section4}
In this section, we aim to prove Theorem \ref{thm3}. To begin with, we need to fix some notations. We denote by $\sigma : H^{s_1}(\mathbb{R}^N) \to H^{s_1}(\mathbb{R}^N)$ the transformation $\sigma(u)=-u$. A set $A \subset H^{s_1}(\mathbb{R}^N)$ is called $\sigma$-invariant if $\sigma(A)=A$. Let $Y \subset H^{s_1}(\mathbb{R}^N)$. A homotopy $\eta: [0,1] \times Y \to Y$ is called $\sigma$-equivariant if $\eta(t,\sigma(u))=\sigma(\eta(t,u))$ for any $(t, u) \in [0,1] \times Y$.
\begin{defi}\label{homotopy1} \cite[Definition 7.1]{Gh}
Let $B$ be a closed $\sigma$-invariant subset of a set $Y \subset H^{s_1}(\mathbb{R}^N)$. We say that a class $\mathcal{F}$ of compact subsets of $Y$ is a $\sigma$-homotopy stable family with the closed boundary $B$ provided that
\begin{enumerate}
\item [\textnormal{(i)}] every set in $\mathcal{F}$ is $\sigma$-invariant;
\item [\textnormal{(ii)}] every set in $\mathcal{F}$ contains $B$;
\item [\textnormal{(iii)}] for any $A \in \mathcal{F}$ and any $\sigma$-equivariant homotopy $\eta \in C([0, 1] \times Y, Y)$ satisfying $\eta(t, x)=x$ for all $(t, x) \in (\{0\} \times Y) \cup([0, 1] \times B)$, then $\eta(\{1\} \times A) \in \mathcal{G}$.
\end{enumerate}
\end{defi}
\begin{lem} \label{ps1}
Let $\mathcal{F}$ be a $\sigma$-homotopy stable family of compact subsets of $S_{rad}(c)$ with a close boundary $B$. Let
$$
\gamma_{\mathcal{F}}(c):= \inf_{A\in \mathcal{F}}\max_{u\in A}F(u).
$$
Suppose that $B$ is contained in a connected component of $P_{rad}(c)$ and $ \max \{\sup E(B),0\}<\gamma_{\mathcal{F}}(c)<\infty$. Then there exists a Palais-Smale sequence $\{u_n\} \subset P_{rad}(c)$ for $E$ restricted on $S_{rad}(c)$ at the level $\gamma_{\mathcal{F}}(c)$.
\end{lem}
\begin{proof}
By applying \cite[Theorem 7.2]{Gh}, the proof is almost identical to the one of Lemma \ref{ps}, then we omit the proof.
\end{proof}
\begin{defi}\label{genus}
For any closed $\sigma$-invariant set $A \subset H^{s_1}(\mathbb{R}^N)$, the genus of $A$ is defined by
$$
\textnormal{Ind}(A):= \min \{n \in \mathbb{N}^+ : \exists \,\, \varphi : A \rightarrow \mathbb{R}^n\backslash \{0\}, \varphi \,\, \text{is continuous and odd}\}.
$$
If there is no $\varphi$ as described above, we set $\textnormal{Ind}(A)= \infty.$ If $A=\emptyset$, we set $\textnormal{Ind}(A)=0$.
\end{defi}
Let $\mathcal{A}$ be a family of compact and $\sigma$-invariant sets contained in $S_{rad}(c)$. For any $k \in \mathbb{N}^+
$, we now define
\begin{align*}
\beta_k(c):=\inf_{A \in \mathcal{A}_{k}}\sup_{u \in A}E(u),
\end{align*}
where the set $\mathcal{A}_k$ is defined by
$$
\mathcal{A}_{k}:=\{A \in \mathcal{A}:\textnormal{Ind}(A) \geq k\}.
$$
\begin{lem} \label{akne}
\begin{enumerate}
\item [\textnormal{(i)}] If $p=2+\frac{4s_1}{N}$, then, for any $k \in \mathbb{N}^+$, there exists a constant $c_k>c_{N,s_1}$ such that $\mathcal{A}_k \neq \emptyset$ for any $c \geq c_k$, where $c_{N, s_1}>0$ is determined in Theorem \ref{thm1}.
\item [\textnormal{(ii)}] If $p >2+\frac{4s_1}{N}$, then, for any $k \in \mathbb{N}^+$, $\mathcal{A}_k \neq \emptyset$ for any $c >0$.
\item [\textnormal{(iii)}] For any $k \in \mathbb{N}^+$, there holds that $\beta_{k+1}(c) \geq \beta_{k}(c)>0$.
\end{enumerate}
\end{lem}
\begin{proof}
Let us first prove $\mbox{(i)}$. For any $k \in \mathbb{N}^+$ and $V_k \subset H^{s_1}_{rad}(\mathbb{R}^N)$ be such that $\mbox{dim} V_k=k$, we define $SV_k(c):=V_k \cap S(c)$. By basic properties of genus, see \cite[Theorem 10.5]{AM}, we have that $\mbox{Ind}(SV_k(c))=k$. Note that all norms are equivalent in finite dimensional subsequence of $H^{s_1}(\mathbb{R}^N)$, then there exists a constant $c_k>c_{N, s_1}$ large enough such that, for any $u \in SV_k(c)$, there holds that $u \in \mathcal{S}(c)$, where $\mathcal{S}(c)$ is defined by \eqref{sc}. It follows that $\sup_{t>0}E(u_t)<\infty$. Thus we apply Lemma \ref{monotonicity} to conclude that, for any $u \in SV_k(c)$ with $c \geq c_k$, there exists a unique $t_u>0$ such that $u_{t_u} \in P(c)$. We now define a mapping $\varphi: SV_k(c) \to P_{rad}(c)$ by $\varphi(u)=u_{t_u}$. It is easy to see that $\varphi$ is continuous and odd. By means of \cite[Lemma 10.4]{AM}, we then obtain that $\mbox{Ind}(\varphi(SV_k(c)))\geq \mbox{Ind}(SV_k(c))=k$. This then suggests that $\mathcal{A}_k \neq \emptyset$. The assertion $\mbox{(ii)}$ can be achieved by using similar arguments. We now prove $\mbox{(iii)}$. Observe that, for any $k \in \mathbb{N}^
+$, $\mathcal{A}_{k+1} \subset \mathcal{A}_k$, then $\beta_{k+1}(c) \geq \beta_{k}(c)$. In addition, by the definition of $\beta_k(c)$, we have that, for any $k \in \mathbb{N}^+$, $\beta_k(c) \geq \gamma(c)>0$. Thus the proof is completed.
\end{proof}
At this point, we are able to present the proof of Theorem \ref{thm3}.
\begin{proof}[Proof of Theorem \ref{thm3}]
Let us first prove the assertion $(\textnormal{i})$. Thanks to Lemma \ref{akne}, we know that, for any $k \in \mathbb{N}^+$, $0<\beta_k(c)<\infty$. From Lemma \ref{ps1}, we have that, for any $k\in \mathbb{N}^+$, there exists a Palais-Smale sequence $\{u_n^k\} \subset P_{rad}(c)$ for $E$ restricted on $S_{rad}(c)$ at the level $\beta_k(c)$. Arguing as the proof of Theorem \ref{thm2}, we can derive that $u_n^k \in H^{s_1}(\mathbb{R}^N)$ satisfies the following equation,
\begin{align} \label{fequ31}
(-\Delta)^{s_1} u_n^k +(-\Delta)^{s_2} u_n^k + \lambda_n^k u_n^k=|u_n^k|^{p-2} u_n^k+o_n(1),
\end{align}
where
$$
\lambda_n^k:=\frac{1}{c} \left(\int_{\mathbb{R}^N}|u_n^k|^p\,dx -\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_n^k|^2\, dx-\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_n^k|^2\,dx \right).
$$
In addition, there exist a constant $\lambda_k \in \mathbb{R}$ such that $\lambda_n^k \to \lambda_k$ as $n \to \infty$ and a nontrivial $u^k \in H^{s_1}(\mathbb{R}^N)$ such that $u_n^k \rightharpoonup u^k$ in $H_{rad}^{s_1}(\mathbb{R}^N)$ as $n \to \infty$. As a consequence, we deduce that $u^k \in H^{s_1}(\mathbb{R}^N)$ satisfies the equation
\begin{align} \label{fequ41}
(-\Delta)^{s_1} u^k +(-\Delta)^{s_2} u^k + \lambda^k u^k=|u^k|^{p-2} u^k.
\end{align}
Taking into account the fact that $H^{s_1}_{rad}(\mathbb{R}^N) \hookrightarrow L^p(\mathbb{R}^N)$ is compact for $N \geq 2$, we then get that $u_n^k \to u^k$ in $L^p(\mathbb{R}^N)$ as $n \to \infty$. Since $Q(u_n^k)=Q(u)=0$, then
$$
\|(-\Delta)^{\frac{s_i}{2}} u_n^k-(-\Delta)^{\frac{s_i}{2}}u^k\|_2=o_n(1), \quad i=1,2.
$$
In view of Lemma \ref{lagrange}, we know that $\lambda_k>0$ for any $c_0<c<c_1$. Applying \eqref{fequ31} and \eqref{fequ41}, we then have that $u_n^k \to u^k$ in $H_{rad}^{s_1}(\mathbb{R}^N)$ as $n \to \infty$. This indicates that $u^k \in S(c)$ is a solution to \eqref{fequ}-\eqref{mass} and $E(u^k)=\beta_k(c)$. Reasoning as the proof of \cite[Proposition 9.33]{Ra}, we can derive that $\beta_k(c) \to \infty$ as $k \to \infty$. Note that if $p=2+\frac{4s_1}{N} \leq \frac{2N}{N-2s_2}$, then $c_1=\infty$, see Lemma \ref{lagrange}. Hence, by a similar way, the assertion $(\textnormal{ii})$ follows. The proof is completed.
\end{proof}
\section{Properties of the function $c \mapsto \gamma(c)$} \label{section5}
In this section, our goal is to prove Theorem \ref{thm4}. We first have the following result.
\begin{lem}\label{continuous}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p\geq 2+\frac{4s_1}{N}$. Then the function $c \mapsto \gamma(c)$ is continuous for any $c>c_0$.
\end{lem}
\begin{proof}
For simplicity, we only consider the case $p>2+\frac{4s_1}{N}$. Let $c>c_0$ and $\{c_n\} \subset (c_0, \infty)$ satisfying $c_n \to c$ as $n \to \infty$, we shall prove that $\gamma(c_n) \to \gamma(c)$ as $n \to \infty$. From the definition of $\gamma(c)$, we know that, for any $\epsilon>0$, there exists $v \in P(c)$ such that
$$
E(v) \leq \gamma(c) + \epsilon/2.
$$
Define
$$
v_n:=\left(\frac{c_n}{c}\right)^{\frac 12} v \in S(c_n).
$$
It is not hard to verify that $v_n \to v$ in $H^{s_1}(\mathbb{R}^N)$ as $n \to \infty$. Therefore, by Lemma \ref{monotonicity}, we can deduce that
\begin{align*}
\gamma(c_n) \leq \max_{\lambda>0} E((v_n)_{\lambda}) \leq \max_{\lambda>0} E(v_{\lambda}) + \frac{\epsilon}{2}=E(v)+\frac{\epsilon}{2} \leq \gamma(c) +\epsilon.
\end{align*}
This implies that
$$
\displaystyle \limsup_{n\to \infty}\gamma(c_n) \leq \gamma(c).
$$
By a similar way, we can prove that
$$
\gamma(c) \leq \displaystyle\liminf_{n\to \infty}\gamma(c_n).
$$
Thus proof is completed.
\end{proof}
\begin{lem} \label{limit1}
Let $N \geq 1$, $0<s_2<s_1<1$ and $p\geq 2+\frac{4s_1}{N}$. Then $\gamma(c) \to \infty$ as $c \to c_0^+$.
\end{lem}
\begin{proof}
Let $\{c_n\} \subset (c_0, \infty)$ satisfy $c_n \to c_0$ as $n \to \infty$. In view of Theorem \ref{thm2}, we have that there exists $\{u_n\}\subset P(c_n)$ such that $E(u_n)=\gamma(c_n)$. Record that
\begin{align} \label{ide111}
\begin{split}
\gamma(c_n)=E(u_n)&=E(u_n)-\frac{2}{N(p-2)}Q(u_n) \\
&=\frac{N(p-2)-4s_1}{2N(p-2)}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_n|^2 \,dx+\frac{N(p-2)-4s_2}{2N(p-2)}\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_n|^2 \,dx.
\end{split}
\end{align}
Let us first treat the case $p=2+\frac{4s_1}{N}$. Suppose by contradiction that $\{\gamma(c_n)\} \subset \mathbb{R}$ is bounded. Therefore, by arguing as the proof of Lemma \ref{coercive}, we are able to deduce that $\{u_n\} \subset H^{s_1}(\mathbb{R}^N)$ is bounded. Since $Q(u_n)=0$, by using \eqref{gn}, we obtain that
\begin{align*}
s_1\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_n|^2 \,dx +s_2\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_n|^2 \,dx
&=\frac{Ns_1}{N+2s_1} \int_{\mathbb{R}^N}|u_n|^{2+\frac{4s_1}{N}}\,dx \\
&\leq s_1\left(\frac{c_n}{c_{N, s_1}}\right)^{\frac{2s_1}{N}}
\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_n|^2 \,dx.
\end{align*}
Note that $c_n \to c_{N, s_1}^+$ as $n \to \infty$, it then follows that $\|(-\Delta)^{{s_2}/{2}} u_n\|_2=o_n(1)$. Therefore, from \eqref{ide111}, we find that $\gamma(c_n)=o_n(1)$. It is impossible, see Lemmas \ref{coercive} and \ref{nonincreasing}. Then we get that $\gamma(c) \to \infty$ as $c \to c_{N, s_1}$.
Next we handle the case $p>2+\frac{4s_1}{N}$. In this case, by applying \eqref{gn}, we have that
\begin{align*}
s_1\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_n|^2 \,dx +s_2\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u_n|^2 \,dx
&=\frac{N(p-2)}{2p}\int_{\mathbb{R}^N}|u_n|^p \,dx \\
&\leq C_{N,p,s_1}c^{\frac p2 -\frac{N(p-2)}{4s_1}}
\left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u_n|^2 \,dx \right)^{\frac{N(p-2)}{4s_1}}.
\end{align*}
This readily infers that $\|(-\Delta)^{{s_1}/{2}} u_n\|_2\to \infty$ as $n \to \infty$. Utilizing \eqref{ide111}, we then get the desired result. Thus the proof is completed.
\end{proof}
\begin{lem} \label{limit2}
Let $N=1$, $2s_2 \geq 1$ and $p\geq 2+4s_1$ or $N \geq 1$, $2s_2<N$ and $2 + \frac{4s_2}{N}< p < \frac{2N}{N-2s_2}$. Then $\gamma(c) \to 0$ as $c \to \infty$.
\end{lem}
\begin{proof}
We first consider the case $p=2+\frac{4s_1}{N}$. Observe that
$$
E(w_t)=\frac{c}{2\|u\|_2^2} \left(1-\left(\frac{c}{c_{1,s_1}}\right)^{\frac{2s_1}{N}}\right) t^{2s_1}\int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}}u|^2 \, dx +\frac{c}{2\|u\|_2^2} t^{2s_2} \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}}u|^2 \, dx,
$$
where $w$ is defined by \eqref{defw}. Then we have that
$$
0<\gamma(c) \leq \sup_{t>0} E(w_t)=\frac{s_1-s_2}{s_1}\left(\frac{s_2}{s_1}\right)^{\frac{s_2}{s_1-s_2}}\frac{\frac{c}{2\|u\|_2^2} \left( \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_2}{2}} u|^2 \,dx\right)^{\frac{s_1}{s_1-s_2}}}{\left(\left(\left(\frac{c}{c_{N,s_1}}\right)^{\frac{2s_1}{N}}-1\right) \int_{\mathbb{R}^N} |(-\Delta)^{\frac{s_1}{2}} u|^2 \,dx\right)^{\frac{s_2}{s_1-s_2}}}.
$$
This immediately yields that $\gamma(c) \to 0$ as $c \to \infty$, because of
$$
\frac{2s_1s_2}{N(s_1-s_2)}>1.
$$
Next we consider the case $p>2+\frac{4s_1}{N}$. For any $u \in S(1)$, we see that $c^{1/2} u \in S(c)$. From Lemma \ref{monotonicity}, we then know that there exists a constant $t_c>0$ such that $Q((c^{1/2}u)_{t_c})=0$. This means that
\begin{align*}
&t^{2(s_1-s_2)}_c s_1\int_{\mathbb{R}} |(-\Delta)^{\frac{s_1}{2}} u|^2 dx + s_2\int_{\mathbb{R}}|(-\Delta)^{\frac{s_2}{2}} u|^2dx=(c t_c^{2s_2})^{\frac {N(p-2)-4s_2}{4s_2}} c^{\frac p2-\frac{N(p-2)}{4s_2}}\frac{N(p-2)}{2p} \int_{\mathbb{R}}|u|^p dx.
\end{align*}
Therefore, we derive that $ct_c^{2s_2} \to 0$ as $c \to \infty$. Observe that
\begin{align*}
\gamma(c) \leq E((c^{1/2}u)_{t_c})&=E((c^{1/2}u)_{t_c})-\frac{2}{N(p-2)}Q((c^{1/2}u)_{t_c})\\
&=c t_c^{2s_1}\frac{N(p-2)-4s_1}{2N(p-2)} \int_{\mathbb{R}} |(-\Delta)^{\frac{s_1}{2}} u|^2 \,dx + c t_c^{2s_2}\frac{N(p-2)-4s_2}{2N(p-2)} \int_{\mathbb{R}} |(-\Delta)^{\frac{s_2}{2}} u|^2\, dx.
\end{align*}
Then we conclude that $\gamma(c) \to 0$ as $c \to \infty$. Thus the proof is completed.
\end{proof}
To further reveal some properties of the function $c \mapsto \gamma(c)$ as $c \to \infty$, we need to investigate the following zero mass equation,
\begin{align} \label{zfequ}
(-\Delta)^{s_1} u +(-\Delta)^{s_2} u =|u|^{p-2} u,
\end{align}
where $N>2s_2$ and $p\geq 2+\frac{4s_1}{N}$. The Sobolev space related to \eqref{zfequ} is defined by
$$
H:=\left\{u \in \dot{H}^{s_2}(\mathbb{R}^N) : \int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2 \,dx <\infty\right\}
$$
equipped with norm
$$
\|u\|_H:=\left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2 \,dx\right)^{\frac 12}+\left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u|^2 \,dx\right)^{\frac 12}, \quad u \in H.
$$
It is standard to check that $H$ is a reflexive Banach space.
\begin{lem} \label{embedding}
Let $N>\max\{2s_1,\frac{2s_1s_2}{s_1-s_2}\}$, $0<s_2<s_1<1$ and $p \geq 2+\frac{4s_1}{N}$. Then there holds that
$$
\int_{\mathbb{R}^B}|u|^p \,dx \leq C_{N, s_1,s_2} \left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u|^2 \,dx\right)^{^{\frac{N(1-\theta)}{N-2s_2}}}\left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2 \,dx\right)^{^{\frac{N\theta}{N-2s_1}}}, \quad u \in H,
$$
where $C_{N,s_1,s_2}>0$ is a constant and $0<\theta<1$ satisfying that
$$
p=\frac{2N(1-\theta)}{N-2s_2}+\frac{2N\theta}{N-2s_1}.
$$
\end{lem}
\begin{proof}
Since $N>2s_2$ and $N>\frac{2s_1s_2}{s_1-s_2}$, then
$$
2+\frac{4s_1}{N} >\frac{2N}{N-2s_2}.
$$
Due to $N>2s_1$ and $p<\frac{2N}{N-2s_1}$, then there exists a constant $0<\theta<1$ such that
$$
p=\frac{2N(1-\theta)}{N-2s_2}+\frac{2N\theta}{N-2s_1}.
$$
By using H\"older's inequality, we have that
$$
\int_{\mathbb{R}^N}|u|^p\,dx \leq \left(\int_{\mathbb{R}^N}|u|^{\frac{2N}{N-2s_2}} \,dx \right)^{1-\theta} \left(\int_{\mathbb{R}^N}|u|^{\frac{2N}{N-2s_1}} \,dx \right)^{\theta} .
$$
In view of Sobolev inequalities, we know that
$$
\int_{\mathbb{R}^N}|u|^{\frac{2N}{N-2s_2}} \,dx \leq C_{N, s_2}\left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u|^2\,dx\right)^{\frac{N}{N-2s_2}}
$$
and
$$
\int_{\mathbb{R}^N}|u|^{\frac{2N}{N-2s_1}} \,dx \leq C_{N, s_1}\left(\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2\,dx\right)^{\frac{N}{N-2s_1}}.
$$
Therefore, the result of the lemma follows immediately and the proof is completed.
\end{proof}
Taking into account Lemma \ref{embedding}, we are able to seek for solutions to \eqref{zfequ} in $H$. Indeed, solutions to \eqref{zfequ} correspond to critical points of the following energy functional,
$$
E(u)=\frac 12 \int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2 \, dx+\frac 12 \int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u|^2 \, dx-\frac 1p \int_{\mathbb{R}^N} |u|^p \, dx.
$$
\begin{lem}
Let $N>\max\{2s_1,\frac{2s_1s_2}{s_1-s_2}\}$, $0<s_2<s_1<1$ and $p \geq 2+\frac{4s_1}{N}$. Then there exists a ground state solution to \eqref{zfequ} in $H$, namely the ground state energy $m$ is achieved, where
\begin{align} \label{defm}
m:=\left\{E(u) : u \in H\backslash\{0\}, E^\prime(u)=0\right\}.
\end{align}
\end{lem}
\begin{proof}
To prove this, it is equivalent to show that the functional $J$ restricted on $M$ admits a minimizer in $H$, where
$$
J(u):=\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_1}{2}} u|^2 \, dx+\int_{\mathbb{R}^N}|(-\Delta)^{\frac{s_2}{2}} u|^2 \, dx, \quad M:=\left\{u \in H: \int_{\mathbb{R}^N} |u|^p\,dx=1 \right\}.
$$
Let $\{u_n\} \subset M$ be a minimizing sequence. Without restriction, we may assume that $\{u_n\}$ is radially symmetric. Otherwise, we shall use its symmetric-decreasing rearrangement to replace $\{u_n\}$. Note that the embedding $H_{rad}\hookrightarrow L^p(\mathbb{R}^N)$ is compact for $N \geq 2$, where $H_{rad}$ denotes the subspace consisting of radially symmetric functions in $H$. Hence we easily obtain the existence of minimizers and the proof is completed.
\end{proof}
\begin{lem} \label{l2}
Let $N>\max\{2s_1+2,\frac{2s_1s_2}{s_1-s_2}\}$, $0<s_2<s_1<1$ and $p \geq 2+\frac{4s_1}{N}$. Then any solution to \eqref{zfequ} belongs to $L^2(\mathbb{R}^N)$.
\end{lem}
\begin{proof}
By using scaling techniques, it suffices to demonstrate that any solution to the equation
\begin{align} \label{zfequ1}
\left(\frac{k_{s_2}}{k_{s_1}}\right)^{\alpha s_1}(-\Delta)^{s_1} u +\left(\frac{k_{s_2}}{k_{s_1}}\right)^{\alpha s_2}(-\Delta)^{s_2} u =|u|^{p-2} u, \quad u \in H
\end{align}
belongs to $L^2(\mathbb{R}^N)$, where
$$
k_s:=2^{1-2s} \frac{\Gamma(1-s)} {\Gamma(s)} ,\quad \alpha=\frac{1}{s_1-s_2}.
$$
Indeed, if $u \in H$ is a solution to \eqref{zfequ}, then $\tilde{u} \in H$ is a solution to \eqref{zfequ1}, where $\tilde{u}$ is defined by
$$
\tilde{u}(x):=u\left({k_{s_1}^{\frac{\alpha}{2}}}/{k_{s_2}^{\frac{\alpha}{2}}}x\right), \quad x \in \mathbb{R}^N.
$$
For our purpose, by making use of the harmonic extension theory from \cite{CS}, we need to introduce the following extended problem
\begin{align}\label{fequ11}
\displaystyle
\left\{
\begin{aligned}
&-\mbox{div}(y^{1-2s_1} \nabla w+y^{1-2s_2} \nabla w)=0 \,\, \, &\mbox{in} \,\, \mathbb{R}^{N+1}_+,\\
&-\frac{\partial w}{\partial {\nu}}=k_{s_1,s_2}|u|^{p-2}u \,\,\, &\mbox{on} \,\, \mathbb{R}^N \times \{0\},
\end{aligned}
\right.
\end{align}
where
$$
\frac{\partial w}{\partial {\nu}}:= \lim_{y \to 0^+} y^{1-2s_1} \frac{\partial w}{\partial y}(x, y)+y^{1-2s_2} \frac{\partial w}{\partial y}(x, y) =- \frac{1}{k_{s_1}} (- \Delta )^{s_1} u(x)- \frac{1}{k_{s_2}} (- \Delta )^{s_2} u(x)
$$
and
$$
k_{s_1,s_2}:=\left(\frac{k_{s_1}^{s_2}}{k_{s_2}^{s_1}}\right)^{\alpha}.
$$
Let $\varphi \in C^{\infty}_0(\mathbb{R}^{N+1}_+ \backslash \mathcal{B}^+(0, R), \mathbb{R})$ be a cut-off function such that $\varphi(x, y)=1$ for $|(x, y)| \geq 2R$, where
$$
\mathcal{B}^+(0, R):=\{(x, y) \in \mathbb{R}^{N+1}_+: |(x, y)| <R\}
$$
and $R>0$ is a constant to be determined later. For $R_1>2R$, we define $\psi:=\varphi h_{R_1}$, where $h_{R_1}$ is given by
\begin{align*}
h_{R_1}(x, y):=\left\{
\begin{aligned}
&|(x, y)|^{s_2} &\quad \mbox{for} \,\, 2 R \leq |(x, y)|<R_1,\\
&R_1^{s_2} \left(1+\tanh((|(x, y)|-R_1)/R_1)\right) & \mbox{for} \,\, |(x, y)| \geq R_1.
\end{aligned}
\right.
\end{align*}
As a direct consequence, we see that
\begin{align} \label{cutoff}
\sup_{|(x, y)| \geq 2R} \frac{|(x,y)||\nabla \psi(x ,y)|}{\psi(x, y)}=1.
\end{align}
Multiplying \eqref{fequ11} by $\psi^2 w$ and integrating on $\mathbb{R}^{N+1}_+$, we have that
\begin{align*}
\int_{\mathbb{R}^{N+1}_+} \left(y^{1-2s_1} \nabla w +y^{1-2s_2} \nabla w \right) \cdot \nabla(w \psi^2) \, dx dy=k_{s_1,s_2}\int_{\mathbb{R}^N} |u|^p |\psi(\cdot, 0)|^2 \, dx.
\end{align*}
Observe that
$$
|\nabla(w \psi)|^2=\nabla w \cdot \nabla(w \psi^2) + |w|^2|\nabla \psi|^2.
$$
It then follows that
\begin{align} \label{estimate} \nonumber
\int_{\mathbb{R}^{N+1}_+} y^{1-2s_1} |\nabla (w \psi)|^2 +y^{1-2s_2} |\nabla (w \psi)|^2 \, dx &=\int_{\mathbb{R}^{N+1}_+} \left(y^{1-2s_1} |w|^2+ y^{1-2s_2} |w|^2 \right) |\nabla \psi|^2 \, dxdy \\
&\quad + \int_{\mathbb{R}^N} |u|^p |\psi(\cdot, 0)|^2 \, dx.
\end{align}
Applying H\"older's inequality, the definition of $\varphi$ and trace inequalities, we know that
\begin{align*}
\int_{\mathbb{R}^N} |u|^p |\psi(\cdot, 0)|^2 \, dx &\leq \left(\int_{\mathbb{R}^N} |u \psi(\cdot, 0)|^{p}\,dx \right)^{\frac2p} \left(\int_{\mathbb{R}^N \backslash B(0, R)} |u|^p \, dx\right)^{\frac{p-2}{p}}
\end{align*}
and
\begin{align*}
\int_{\mathbb{R}^N} |u \psi(\cdot, 0)|^{p}\,dx
&\leq \left(\int_{\mathbb{R}^N}|u \psi(\cdot, 0)|^{\frac{2N}{N-2s_1}}\,dx\right)^{\theta} \left(\int_{\mathbb{R}^N}|u \psi(\cdot, 0)|^{\frac{2N}{N-2s_2}}\,dx\right)^{1-\theta}\\
&\leq \widetilde{C}\left(\int_{\mathbb{R}^{N+1}_+} y^{1-2s_1} |\nabla (w\psi)|^2 \,dxdy\right)^{\frac{\theta N}{N-2s_1}} \left(\int_{\mathbb{R}^{N+1}_+} y^{1-2s_2} |\nabla (w\psi)|^2\, dxdy \right)^{\frac{(1-\theta)N}{N-2s_2}},
\end{align*}
where $0<\theta<1$ and
$$
p=\frac{2N\theta}{N-2s_1}+\frac{2N(1-\theta)}{N-2s_2}
$$
and $\widetilde{C}=C_{N,s_1,s_2}>0$ is a constant.
Define
$$
\delta(R):=\widetilde{C}k_{s_1,s_2}\left(\int_{\mathbb{R}^N \backslash B(0, R)} |u|^p \, dx\right)^{\frac{p-2}{p}},
$$
and note that $\delta(R) \to 0$ as $R \to \infty$. It then follows from \eqref{estimate} and Young's inequality that
\begin{align} \label{estimate1}
\begin{split}
&\left(1-\delta(R)\right)\int_{\mathbb{R}^{N+1}_+} y^{1-2s_1} |\nabla (w\psi)|^2 +y^{1-2s_2} |\nabla (w\psi)|^2 \, dx \\
&\leq \int_{\mathbb{R}^{N+1}_+} \left(y^{1-2s_1} |w|^2+ y^{1-2s_2} |w|^2 \right) |\nabla \psi|^2 \, dxdy.
\end{split}
\end{align}
Let us now estimate the terms in the right side hand of \eqref{estimate1}. Using \eqref{cutoff} and \cite[Theorem 1.1]{T}, we have that
\begin{align*}
\int_{\mathbb{R}^{N+1}_+} y^{1-2s_1} |w|^2 |\nabla \psi|^2 dxdy
&\leq \int_{\mathcal{B}^+(0, 2R)} y^{1-2s_1} |w|^2 dxdy
+\int_{\mathbb{R}^{N+1}_+ \backslash \mathcal{B}^+(0, 2R)} y^{1-2s_1} \frac{|w \psi |^2}{|(x, y)|^{2}} dxdy \\
& \leq C_1(R) +\frac {4}{(b-2s_1-1)^2}\int_{\mathbb{R}^{N+1}_+} y^{1-2s_1} |\nabla (w\psi)|^2 dxdy,
\end{align*}
where $b>0$ is a constant satisfying $1+2s_1 < b < N+1$. Similarly, we can obtain that
\begin{align*}
\int_{\mathbb{R}^{N+1}_+} y^{1-2s_2} |w|^2 |\nabla \psi|^2 dxdy &\leq \int_{\mathcal{B}^+(0, 2R)} y^{1-2s_2} |w|^2 dxdy
+\int_{\mathbb{R}^{N+1}_+ \backslash \mathcal{B}^+(0, 2R)} y^{1-2s_2} \frac{|w\psi|^2}{|(x, y)|^{2}}dxdy \\
& \leq C_2(R) +\frac {4}{(b-2s_2-1)^2}\int_{\mathbb{R}^{N+1}_+} y^{1-2s_2} |\nabla (w\psi)|^2 dxdy,
\end{align*}
where $1+2s_2<1+2s_1 < b < N+1$. Choosing $b$ close to $N+1$ with $N>2s_1+2$ such that
$$
\frac {4}{(b-2s_1-1)^2}<1, \quad \frac {4}{(b-2s_2-1)^2}<1,
$$
and taking $R>0$ large enough, we then get from \eqref{estimate1} that
$$
\int_{\mathbb{R}^{N+1}_+} y^{1-2s_1} |\nabla (w\psi)|^2 +y^{1-2s_2} |\nabla (w\psi)|^2 \, dx \leq C(R).
$$
Applying again \cite[Theorem 1.1]{T}, we then have that
$$
\int_{\mathbb{R}^N \backslash B(0, 2R)}\frac{|u \psi(\cdot, 0)|^2}{|x|^{2s_1}} +\frac{|u \psi(\cdot, 0)|^2}{|x|^{2s_2}} \, dx \leq C
$$
uniformly with respect to $R_1$. Observe that
$$
\frac{|u \psi(\cdot, 0)|^2}{|x|^{2s_1}} +\frac{|u \psi(\cdot, 0)|^2}{|x|^{2s_2}} \to |u|^2 \quad \mbox{a.e.} \,\,\, |x| \geq 2R\,\,\, \mbox{as}\,\, R_1 \to \infty.
$$
It then yields from Faton's Lemma that $u \in L^2(\mathbb{R}^N \backslash B(0, 2R))$. This indicates that $u \in L^2(\mathbb{R}^N)$ and the proof is completed.
\end{proof}
\begin{lem} \label{limit3}
Let $N>\max\{2s_1+2,\frac{2s_1s_2}{s_1-s_2}\}$, $0<s_2<s_1<1$ and $p \geq 2+\frac{4s_1}{N}$. Then there exists a constant $c_{\infty}>0$ such that $\gamma(c) = m$ for any $c \geq c_{\infty}$, where $m$ is defined by \eqref{defm}.
\end{lem}
\begin{proof}
Note first that
$$
m=\left\{E(u) : u \in H \backslash\{0\}, Q(u)=0\right\}.
$$
Then we have that $\gamma(c) \geq m$ for any $c >c_0$. From Lemma \ref{l2}, we know that there exists $u \in H^{s_1}(\mathbb{R}^N)$ such that $E(u)=m$ and $Q(u)=0$. Consequently, we obtain that $\gamma(c_{\infty})=m$, where $c_{\infty}:=\|u\|_2^2$. Combining Lemma \ref{nonincreasing}, we then derive that $\gamma(c)=m$ for any $c \geq c_{\infty}$. Thus the proof is completed.
\end{proof}
From the lemmas above, we are now able to give the proof of Theorem \ref{thm4}.
\begin{proof}[Proof of Theorem \ref{thm4}]
The proof of Theorem \ref{thm4} follows directly from Lemmas \ref{lagrange}, \ref{nonincreasing}, \ref{decreasing}, \ref{continuous}, \ref{limit1}, \ref{limit2} and \ref{limit3}.
\end{proof}
\section{Local well-posedness of solutions to the Cauchy problem} \label{section6}
In this section, we shall demonstrate Theorem \ref{pb wellposedness}. First we need to present the definition of admissible pairs. For convenience, in the remaining sections, we shall replace the notation $\psi(t)$ by $u(t)$ to denote solutions to \eqref{evolv pb0}.
\begin{defi}
Let $N\geq 2$ and $s\in (0,1]$. Any pair $(q,r)$ of positive real numbers is said to be $s$-admissible, if
$q,r\geq 2$ and
$$\frac{2s}{q}+\frac{N}{r}=\frac{N}{2}.$$
Such a set of $s$-admissible pairs is denoted by $\Gamma_s$.
\end{defi}
The first main result in this section is with respect to a family of Strichartz estimates without loss of regularity, which are useful to control radially symmetric solutions of \eqref{evolv pb0}.
\begin{thm}\label{strichartz th}
Let $N\geq 2$, $\frac 12 <s_2<s_1< 1$, $u, u_0$ and $F$ are radially symmetric in space and satisfy the equation
\begin{align}\label{evolv pb}
\left\{
\begin{aligned}
&i\partial_tu-(-\Delta)^{s_1}u-(-\Delta)^{s_2}u=F(t,x), \\
&u(0,x)=u_0(x), \quad x\in \mathbb{R}^N.
\end{aligned}
\right.
\end{align}
Then
\begin{align}\label{Radial Strichartz}
\|u\|_{L_t^q L^r_x} \lesssim \|u_0\|_2+\|F\|_{L_t^{\tilde{q}^{\prime}}L_x^{\tilde{r}^{\prime}}},
\end{align}
if $(q,r)$ and $(\tilde{q},\tilde{r})$ belong to $\Gamma_{s_1}\cup \Gamma_{s_2}$ and either
$(q,r)\neq (2,\infty)$ or $(\tilde{q}^{\prime},\tilde{r}^{\prime})\neq (2,\infty)$.
\end{thm}
To prove Theorem \ref{strichartz th}, we first need to introduce some notations and preliminary results. Let us introduce a nonnegative smooth even function $\varphi:\mathbb{R}^N\to [0,1]$ such that $\mbox{supp} \, \varphi \subset \{x\in \mathbb{R}^N : |x|\leq 2\}$ and $\varphi(x)=1$ if $|x|\leq 1$.
Let $\psi (x):=\varphi(x)-\varphi(2x)$ and $P_k$ be the Littelwood-Paley projector for $k\in \mathbb{Z}$, namely
$$
P_kf:= \mathcal{F}^{-1}\psi(2^{-k}|\xi|)\mathcal{F}f.
$$
Recall that
$$
\|f\|_p^2\sim \sum_{k\in\mathbb{Z}}\|P_kf\|_p^2\,\,\, \text{and} \,\,\, \|f\|_{H^s}^2\sim \sum_{k\in\mathbb{Z}}2^{2s}\|P_kf\|_2^2.
$$
It is clear to see that the function $\phi(r):=r^{2s_1}+r^{2s_2}$ for any $r\in \mathbb{R}_+$ satisfies the following conditions introduced in \cite{GuPe08,GuWa14}.
(H1) There exists $m_1 > 0$ such that for any $\alpha \geq2$ and $\alpha \in \mathbb{N}$,
$$
|\phi^{\prime}(r)|\sim r^{m_1-1}\,\,\, \text{ and }\,\,\, |\phi^{(\alpha)}(r)|\lesssim r^{m_1-\alpha}, \quad r\geq 1.
$$
(H2) There exists $m_2 > 0$ such that for any $\alpha \geq2$ and $\alpha \in \mathbb{N}$,
$$
|\phi^{\prime}(r)|\sim r^{m_2-1}\,\,\, \text{ and }\,\,\, |\phi^{(\alpha)}(r)|\lesssim r^{m_2-\alpha}, \quad 0<r< 1.
$$
(H3) There exists $\alpha_1>0$ such that
$$
|\phi^{\prime\prime}(r)|\sim r^{\alpha_1-2}, \quad r\geq 1.
$$
(H3) There exists $\alpha_2>0$ such that
$$
|\phi^{\prime\prime}(r)|\sim r^{\alpha_2-2}, \quad 0<r< 1.
$$
Precisely, for our case one has $m_1=\alpha_1=2s_1$ and $m_2=\alpha_2=2s_2$. Let us now denote
\begin{align*
m(k)=\alpha(k):=
\left\{
\begin{aligned}
&2s_1, &\text{ for }k\geq 0,\\
&2s_2, &\text{ for }k< 0.
\end{aligned}
\right.
\end{align*}
Thus, according to \cite[Theorem 1.2]{GuWa14}, the following result holds.
\begin{lem}\label{propos}
Suppose $N\geq 2, k\in \mathbb{Z}$, $(4N+2)/(2N-1)\leq q\leq +\infty$ and $u_0 \in L^2(\mathbb{R}^N)$ is radially symmetric. Then
$$
\|S(t)P_ku_0\|_{L_{t,x}^q(\mathbb{R}^{N+1})} \lesssim 2^{\left(\frac{N}{2}-\frac{N+m(k)}{2}\right)k}\|u_0\|_2,
$$
where $S(t)$ denotes the evolution group related to \eqref{evolv pb}, namely
$$
S(t)u_0:=\mathcal{F}^{-1}(e^{-it(|\xi|^{2s_1}+|\xi|^{2s_2})}\mathcal{F}u_0).
$$
\end{lem}
\begin{defi}
Let $N\geq 2$. The exponent pair $(q,r)$ is said to be $N$-D radial Schr\"{o}dinger-admissible, if $q,r\geq 2$ and
$$
\frac{4N+2}{2N-1}\leq q\leq \infty, \quad \frac{2}{q}+\frac{2N-1}{r}\leq N-\frac{1}{2}
$$
or
$$
2\leq q<\frac{4N+2}{2N-1},\quad \frac{2}{q}+\frac{2N-1}{r}\leq N-\frac{1}{2}.
$$
\end{defi}
In a similar way as the proof of \cite[theorem 1.5]{GuWa14}, from Lemma \ref{propos}, one can derive the following interesting result.
\begin{lem} \label{lem6.1}
Let $N\geq 2, k\in \mathbb{Z}, \frac{1}{2}<s_2<s_1<1$ and let
\begin{align}\label{Csq}
C_{s_1,s_2}^{q,r}(k):=
\left\{
\begin{aligned}
&2^{k\left(\frac{N}{2}-\frac{2s_1}{q}-\frac{N}{r}\right)}, &\text{ for }k\geq 0,\\
&2^{k\left(\frac{N}{2}-\frac{2s_2}{q}-\frac{N}{r}\right)}, &\text{ for }k< 0.
\end{aligned}
\right.
\end{align}
Then for any radial function $u_0\in L^2(\mathbb{R}^N)$, there holds that
\begin{align}\label{strichartz pk}
\|S(t)P_ku_0\|_{L_t^q L^r_x(\mathbb{R} \times \mathbb{R}^N)} \lesssim C_{s_1,s_2}^{q,r}(k)\|u_0\|_2,
\end{align}
if $(q,r)$ is $N$-D radial Schr\"{o}dinger-admissible.
\end{lem}
\begin{lem}\label{lemme1}\cite[Lemma 3.2]{GuWa14}
Assume $1\leq q,r \leq \infty$, $\frac{1}{q}+\frac{1}{q^{\prime}}=\frac{1}{r}+\frac{1}{r^{\prime}}=1$ and $k\in \mathbb{Z}$. If for any $u_0\in L_{rad}^2(\mathbb{R}^N)$ there exists $C(k)>0$ such that
$$
\|S(t)P_ku_0\|_{L_t^qL^r_x}\lesssim C(k)\|u_0\|_2,
$$
then for any $f\in L_t^{q^\prime}L^{r^\prime}_x$ and $f$ is radially symmetric in space, there holds that
$$
\left\|\int_{\mathbb{R}}S(-\tau)P_kf(\tau,\cdot)\,d\tau\right\|_2 \lesssim C(k)\|f\|_{L_t^{q^\prime}L^{r^\prime}_x}.
$$
\end{lem}
\begin{lem}\label{lemma2}(Christ-Kiselev \cite{CK})
Assume $1\leq p_1,q_1,p_2,q_2\leq \infty$ with $p_1>p_2$. If for any $f\in L_t^{p_2}L^{q_2}_x$ radially symmetric in space, there exists $C(k)>0$ such that
$$
\left\|\int_{\mathbb{R}}S(t-\tau)P_kf(\tau,\cdot)d\tau\right\|_{L_t^{p_1}L^{q_1}_x}\lesssim C(k) \|f\|_{L_t^{p_2}L^{q_2}_x},
$$
then
$$
\left\|\int_0^tS(t-\tau)P_kf(\tau,\cdot)d\tau\right\|_{L_t^{p_1}L^{q_1}_x}\lesssim C(k) \|f\|_{L_t^{p_2}L^{q_2}_x}
$$
holds with the same bound $C(k)$ and for any $f\in L_t^{p_1}L^{q_1}_x$ radially symmetric in space.
\end{lem}
Now, based on Lemmas \ref{lem6.1} \ref{lemme1} and \ref{lem6.4}, we are able to prove the following family of Strichartz estimates of solutions to \eqref{evolv pb}.
\begin{lem} \label{lem6.4}
Let $N\geq 2$, $\frac 12<s_2<s_1< 1$, $u, u_0$ and $F$ are radially symmetric in space and satisfy \eqref{evolv pb}. Then
\begin{align}\label{Strichartz estimate}
\|u\|_{L_t^q L^r_x} \lesssim \left\|C_{s_1,s_2}^{q,r}(k)\left\|P_k^2u_0\right\|_2\right\|_{l_k^2}+\left\|C_{s_1,s_2}^{\tilde{q},\tilde{r}}(k)\|P_kF\|_{L_t^{\tilde{q}^{\prime}}L^{\tilde{r}^{\prime}}_x}\right\|_{l_k^2},
\end{align}
if $(q,r)$ and $(\tilde{q}^{\prime},\tilde{r}^{\prime})$ are $N$-D radial Schr\"{o}dinger-admissible pairs, either $(\tilde{q}^{\prime},\tilde{r}^{\prime})\neq (2,\infty)$ or $(q,r)\neq (2,\infty)$, where $C_{s_1,s_2}^{q,r}>0$ is defined by \eqref{Csq}.
\end{lem}
\begin{proof}
In view of Duhamel's principle, we first have that
$$
u=S(t)u_0-i\int_0^tS(t-\tau)F(\tau,\cdot)\,d\tau.
$$
Let $P_k^2$ be the Littelwood-Paley projector associated to $\psi^2$. Hence
\begin{align*}
P_k^2f = \mathcal{F}^{-1} \psi^2(2^{-k}|\xi|)\mathcal{F}f= \mathcal{F}^{-1} \psi(2^{-k}|\xi|)\psi(2^{-k}|\xi|)\mathcal{F}f = \mathcal{F}^{-1} \psi(2^{-k}|\xi|)\mathcal{F}P_kf= P_kP_kf.
\end{align*}
Similarly, one gets that $P_k^3=P_kP_k^2$. Note that
$$
P_k^3u=S(t)P_k^3u_0-i\int_0^tS(t-\tau)P_k^3F(\tau,\cdot)\,d\tau.
$$
It then yields that
\begin{align}\label{ineq}
\left\|P_k^3u\right\|_{L_t^q L^r_x} \lesssim \left\|S(t)P_k^3u_0\right\|_{L_t^q L^r_x}+\left\|\int_0^tS(t-\tau)P_k^3F(\tau,\cdot)\,d\tau\right\|_{L_t^qL^r_x}.
\end{align}
According to Lemmas \ref{lem6.1} and \ref{lemme1}, we have that
$$
\left\|\int_{\mathbb{R}}S(-\tau)P_k^2F(\tau,\cdot)\,d\tau\right\|_2\lesssim C_{s_1,s_2}^{\tilde{q},\tilde{r}}(k)\|P_kF\|_{L_t^{\tilde{q}^\prime}L^{\tilde{r}^\prime}_x}.
$$
Therefore, from Lemma \ref{lem6.1}, we derive that
\begin{align*}
\left\|\int_{\mathbb{R}}S(t-\tau)P_k^3 F(\tau,\cdot) \,d\tau\right\|_{L_t^q L^r_x}
& = \left\|S(t)P_k\int_{\mathbb{R}}S(-\tau)P_k^2 F(\tau,\cdot) \, d\tau\right\|_{L_t^q L^r_x}\\
& \lesssim \left \|\int_{\mathbb{R}}S(-\tau)P_k^2 F(\tau,\cdot) \, d\tau \right \|_2 \lesssim C_{s_1,s_2}^{\tilde{q},\tilde{r}}(k)\|P_kF\|_{L_t^{\tilde{q}^\prime}L^{\tilde{r}^\prime}_x}.
\end{align*}
It then follows from Lemma \ref{lemma2} that
\begin{align}\label{ineq0}
\left\|\int_0^t S(t-\tau)P_k^3 F(\tau,\cdot) \,d\tau\right\|_{L_t^qL^r_x}\lesssim C_{s_1,s_2}^{\tilde{q},\tilde{r}}(k)\|P_kF\|_{L_t^{\tilde{q}^\prime}L^{\tilde{r}^\prime}_x}.
\end{align}
Coming back to \eqref{ineq} and using Lemma \ref{lem6.1} and \eqref{ineq0} results in
$$
\left\|P_k^3u\right\|_{L_t^q L^r_x} \lesssim C_{s_1,s_2}^{q,r}(k)\left\|P_k^2u_0\right\|_2+C_{s_1,s_2}^{\tilde{q},\tilde{r}}(k)\|P_kF\|_{L_t^{\tilde{q}^\prime} L^{\tilde{r}^\prime}_x},
$$
from which we then conclude that
$$
\|u\|_{L_t^q L^r_x} \lesssim \left\|\left\|P_k^3u\right\|_{L_t^q L^r_x}\right\|_{l_2^k}\lesssim \left\|C_{s_1,s_2}^{q,r}(k)\|P_k^2u_0\|_2\right\|_{l_2^k}+\left\|C_{s_1,s_2}^{\tilde{q},\tilde{r}}(k)\|P_kF\|_{L_t^{\tilde{q}^\prime}L^{\tilde{r}^\prime}_x}\right\|_{l_2^k}.
$$
Thus the proof is completed.
\end{proof}
We are now ready to prove Theorem \ref{strichartz th}.
\begin{proof}[Proof of Theorem \ref{strichartz th}]
If $(q,r)\in \Gamma_{s_2}$, then \eqref{Csq} becomes
$$
C_{s_1,s_2}^{q,r}(k):=
\left\{
\begin{aligned}
&2^{\frac{2k}{q}(s_2-s_1)}, &\text{ for }k\geq 0,\\
&1, &\text{ for }k< 0.
\end{aligned}
\right.
$$
It then leads to
\begin{align*}
\left\|C_{s_1,s_2}^{q,r}(k)\left\|P_k^2u_0\right\|_2\right\|_{l_2^k}^2
& \lesssim \sum_{k<0} \left\|P_k^2u_0\right\|_2^2+ \sum_{k\geq0} 2^{\frac{4k}{q}(s_2-s_1)}\left\|P_k^2u_0\right\|_2^2\\
& \lesssim \sum_{k\in \mathbb{Z}} \left\|P_k^2u_0\right\|_2^2 \sim \|u_0\|_2^2.
\end{align*}
In the case when $(q,r)\in \Gamma_{s_1}$, one obtains that
$$
C_{s_1,s_2}^{q,r}(k):=
\left\{
\begin{aligned}
&1, &\text{ for }k\geq 0,\\
&2^{\frac{2k}{q}(s_1-s_2)}, &\text{ for }k< 0.
\end{aligned}
\right.
$$
As a consequence, there holds that
\begin{align*}
\left\|C_{s_1,s_2}^{q,r}(k)\left\|P_k^2u_0\right\|_2\right\|_{l_2^k}^2
&\lesssim \sum_{k<0} 2^{\frac{4k}{q}(s_1-s_2)}\left\|P_k^2u_0\right\|_2^2+\sum_{k\geq0}\left\|P_k^2u_0\right\|_2^2\\
&\lesssim \sum_{k\in \mathbb{Z}} \left\|P_k^2u_0\right\|_2^2\sim \|u_0\|_2^2.
\end{align*}
Similarly, whenever $(\tilde{q},\tilde{r})$ belongs to $\Gamma_{s_1}\cup \Gamma_{s_2}$, one also gets that
$$
\left\|C_{s_1,s_2}^{\tilde{q},\tilde{r}}(k)\|P_kF\right\|_{L_t^{\tilde{q}^\prime}L^{\tilde{r}^\prime}_x}\|_{l_2^k}^2\lesssim \|\|P_kF\|_{L_t^{\tilde{q}^\prime}L^{\tilde{r}^\prime}_x}\|_{l_2^k}^2\lesssim \|F\|_{L_t^{\tilde{q}^\prime}L^{\tilde{r}^\prime}_x}^2.
$$
Making use of Lemma \ref{lem6.4}, we then have the desired conclusion. Thus the proof is completed.
\end{proof}
Let us now present chain rules for fractional Laplacian adapted to prove Theorem \ref{pb wellposedness}.
\begin{lem}\label{chain rules}
Let $s\in (0,1]$ and $1<p, p_i, q_i<\infty$ satisfying $\frac{1}{p}=\frac{1}{p_i}+\frac{1}{q_i}$ and i=1,2.
\begin{itemize}
\item [$(\textnormal{i})$] There holds that
$$
\|(-\Delta)^{\frac{s}{2}}(uv)\|_{p}\lesssim \|(-\Delta)^{\frac{s}{2}}u\|_{p_1}\|v\|_{q_1}+\|u\|_{p_2}\|(-\Delta)^{\frac{s}{2}}v\|_{q_2}.
$$
\item [$(\textnormal{i})$] If $G\in C^1(\mathbb{C})$, then
$$
\|(-\Delta)^{\frac{s}{2}}G(u)\|_{p}\lesssim \|G^\prime(u)\|_{p_1}\|(-\Delta)^{\frac{s}{2}}u\|_{q_1}.
$$
\end{itemize}
\end{lem}
\begin{proof}[Proof of Theorem \ref{pb wellposedness}]
To prove Theorem \ref{pb wellposedness}, we shall employ the contraction mapping principle. Let us first introduce some notations. Denote
$$
(q_j,r):=\left(\frac{4s_jp}{N(p-2)},p\right) \in \Gamma_{s_j}, \quad j=1,2.
$$
For $T,R>0$, we define
$$
Y_T:=C_T(H_{rad}^{s_1}(\mathbb{R}^N))\cap L_T^{q_1}(W^{s_1,r}(\mathbb{R}^N)) \,\,\, \text{ and }\,\,\, B_T(R):=\{u\in Y_T : \|u\|_{T}\leq R\},
$$
where
$$
\|u\|_{T}:=\|u\|_{L_T^\infty H^{s_1}\cap L_T^{q_1} W^{s_1,r}}.
$$
The closed ball $B_T(R)$ is equipped with the complete distance
$$
d(u,v):=\|u-v\|_{L_T^\infty L^2_x\cap L_T^{q_1} L^r_x}.
$$
Given $u_0\in H_{rad}^{s_1}(\mathbb{R}^N)$, we define a mapping by
$$
\Phi(u)(t):=S(t)u_0+i\int_0^tS(t-s)|u(\tau)|^{p-2}u(\tau)\,d\tau.
$$
In the following, we are going to prove the existence of $T>0$ sufficiently small such that $\Phi$ defines a contraction mapping on $B_T(R)$. For any $u,v \in B_T(R)$, applying Strichartz estimate \eqref{Radial Strichartz}, one has that
$$
d(\Phi(u),\Phi(v))\lesssim \||u|^{p-2}u-|v|^{p-2}v\|_{L_T^{q_1^\prime}L^{r^\prime}_x}
$$
The mean value theorem gives that
$$
||u|^{p-2}u-|v|^{p-2}v|\lesssim (|u|^{p-2}+|v|^{p-2})|u-v|.
$$
From H\"{o}lder's inequality and the Sobolev embedding $H^{s_1}(\mathbb{R}^N)\hookrightarrow L^r(\mathbb{R}^N)$ for any $2 \leq r \leq \frac{2N}{N-2s_s}$, we then obtain that
\begin{align*}
d(\Phi(u),\Phi(v)) & \lesssim \||u|^{p-2}+|v|^{p-2}\|_{L_T^{\frac{2s_1p}{2s_1p-N(p-2)}}L^{\frac{p}{p-2}}_x}\|u-v\|_{L_T^{q_1}L^r_x}\\
& \lesssim T^{\frac{2s_1p-N(p-2)}{2s_1p}}\||u|^{p-2}+|v|^{p-2}\|_{L_T^{\infty}L^{\frac{p}{p-2}}_x}\|u-v\|_{L_T^{q_1}L^r_x}\\
& \lesssim T^{\frac{2s_1p-N(p-2)}{2s_1p}}\left(\|u\|_{L_T^\infty L^p_x}^{p-2}+\|v\|_{L_T^\infty L^p_x}^{p-2}\right)\|u-v\|_{L_T^{q_1}L^r_x}\\
& \lesssim T^{\frac{2s_1p-N(p-2)}{2s_1p}}\left(\|u\|_{L_T^\infty H^{s_1}}^{p-2}+\|v\|_{L_T^\infty H^{s_1}}^{p-2}\right)\|u-v\|_{L_T^{q_1}L^r_x}.
\end{align*}
This infers that
\begin{align}\label{phi contract}
d(\Phi(u),\Phi(v))\lesssim T^{\frac{2s_1p-N(p-2)}{2s_1p}}R^{p-2}d(u,v).
\end{align}
Note that the condition $2<p<\frac{2N}{N-2s_1}$ implies that $2s_1p-N(p-2)>0$. Next suppose
$\|S(\cdot)u_0\|_{T}<\frac{\widetilde{C}R}{2}$ and denote
$$
\theta :=\frac{2s_1p}{2s_1p-N(p-2)},
$$
where $\widetilde{C}>0$ is a small constant determined later. Taking $v=0$ and $T>0$ small enough in \eqref{phi contract}, one derives that
\begin{align*}
\|\Phi(u)\|_{L_T^\infty L^2_x\cap L_T^{q_1} L^r_x}
& \lesssim \frac{\widetilde{C}R}{2}+ T^{\frac{2s_1p-N(p-2)}{2s_1p}}R^{p-1}.
\end{align*}
Moreover, using Strichartz estimate \eqref{Radial Strichartz}, the chain rules, see Lemma \ref{chain rules}, H\"{o}lder's inequality and
Sobolev embedding, one gets that
\begin{align*}
\|\Phi(u)\|_{L_T^\infty \dot{H}^{s_1} \cap L_T^{q_1} \dot{W}^{s_1,r}}
& \lesssim \|S(\cdot)u_0\|_T+\|(-\Delta)^{\frac{s_1}{2}}(|u|^{p-2}u)\|_{L_T^{q_1^\prime} L^{r^\prime}_x}\\
& \lesssim \frac{\widetilde{C}R}{2}+ \|(-\Delta)^{\frac{s_1}{2}} u\|_{L_T^{q_1} L^{r}_x}\|u\|_{L_T^{\theta} L^{r}_x}^{p-2}\\
& \lesssim \frac{\widetilde{C}R}{2}+ \| u\|_{L_T^{q_1} W^{s_1,r}}\|u\|_{L_T^{\theta} H^{s_1}}^{p-2}\\
& \lesssim \frac{\widetilde{C}R}{2}+ T^{\frac{p-2}{\theta}}\| u\|_{L_T^{q_1} W^{s_1,r}}\|u\|_{L_T^\infty H^{s_1}}^{p-2}\\
& \lesssim \frac{\widetilde{C}R}{2}+ \frac{\widetilde{C}^{p-1}T^{\frac{p-2}{\theta}}R^{p-1}}{2^{p-1}}.
\end{align*}
In conclusion, by taking $\widetilde{C}>0$ small enough, we obtain that $\Phi$ is a contraction mapping on $B_T(R)$ for some $T>0$ small enough. This then leads to the local existence of solutions to \eqref{evolv pb0}. Uniqueness of maximal solutions to \eqref{evolv pb0} follows from \eqref{phi contract} for small time. Then, by using standard translation argument, one obtains uniqueness of solutions for all existing time.
Now, we focus on our attention to prove the conservation laws. Let $u\in C_{T}(H^{s_1}(\mathbb{R}^N))$ be a maximal solution to the evolving problem \eqref{evolv pb0}. Since $u(t)\in H^{s_1}(\mathbb{R}^N)$, then we can multiply the equation in \eqref{evolv pb0} by $i\bar{u}(t)$ and integrate over $\mathbb{R}^N$ to find that
$$
\frac{d}{dt}\|u(t)\|_2^2=0,\quad \forall \,\, t\in [0,T).
$$
This implies the conservation of mass.
To see the conservation of energy, let us introduce the operator
$$
J_{\varepsilon}:=(I+\varepsilon(-\Delta)^{s_1}+\varepsilon(-\Delta)^{s_2})^{-1},\quad \varepsilon>0.
$$
Using standard functional arguments in\cite{Caz89}, one can verify that
\begin{itemize}
\item [$(\textnormal{i})$] $J_{\varepsilon}$ defines a bounded mapping from $H^{-s_1}(\mathbb{R}^N)$ into $H^{s_1}(\mathbb{R}^N)$.
\item [$(\textnormal{ii})$] If $f\in L^p(\mathbb{R}^N)$, then $J_{\varepsilon}f\in L^p(\mathbb{R}^N)$ and $\|J_{\varepsilon}f\|_{L^p}\lesssim \|f\|_{L^p}$ for some $p\in [1,\infty)$.
\item [$(\textnormal{iii})$] If $X$ is either of the space $H^{s_1}(\mathbb{R}^N), L^2(\mathbb{R}^N), H^{-s_1}(\mathbb{R}^N)$, then for every $f\in X$, there holds that
$J_{\varepsilon}f\rightarrow f$ in $X$ as $\varepsilon \to 0^+$.
\end{itemize}
At this point, the energy conservation follows easily by adaptation of the arguments for Strichartz solutions developed in \cite{Oz06}.
Let us now prove the third assertion. Define
$$
X(t):=\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2^2+\|(-\Delta)^{\frac{s_2}{2}}u(t)\|_2^2, \quad t \in [0, T).
$$
Taking into account of the conservation laws and applying Gagliardi-Nirenberg inequality \eqref{gn}, we have that
\begin{align*}
E(u_0)=E(u(t))
& \geq \frac{1}{2}X(t)-\frac{C_{N,p,s_1}}{p}\|u_0\|_2^{p-\frac{N(p-2)}{2s_1}}
\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_{2}^{\frac{N(p-2)}{2s_1}}\\
& \geq X(t)\left(\frac{1}{2}-\frac{C_{N,p,s_1}}{p}\|u_0\|_2^{p-\frac{N(p-2)}{2s_1}}
X(t)^{\frac{N(p-2)-4s_1}{4s_1}}\right).
\end{align*}
It then follows that $ \sup_{[0,T)}X(t)<\infty$ if $p<2+\frac{4s_1}{N}$ or $p=2+\frac{4s_1}{N}$ and
$$
\|u_0\|_2<\left(\frac{N+2s_1}{NC_{N,s_1}}\right)^{\frac{N}{4s_1}}.
$$
This completes the proof.
\end{proof}
\section{Blowup versus global existence of solutions to the Cauchy problem} \label{section7}
In this section, our aim is to prove Theorem \ref{blow-up vs global solt}, namely we shall derive general criteria with respect to the existence of global/non-global solutions to \eqref{evolv pb0}. For this, we need to introduce at first virial type inequality in the spirit of the recent work \cite{BoHiLe2016}.
Let us first introduce $\chi\in C_0^\infty(\mathbb{R}^N, \mathbb{R}^+)$ as a radial cut-off function satisfying
\begin{align}
\chi(r)=\chi(|x|):=
\left\{
\begin{aligned}
&\frac{1}{2}|x|^2,&\text{ for } |x|\leq 1, \\
&C,&\text{ for } |x|\geq 10,
\end{aligned}
\right.
\quad \text{ and }\,\,\,\chi^{\prime\prime}(r)\leq 1, \quad \forall \,\, r \geq 0.
\end{align}
For $R>0$, we define
$$
\chi_R:=R^2\chi\left(\frac{\cdot}{R}\right).
$$
It is simple to check that $\chi_R$ satisfies the following properties,
\begin{align}\label{bound psi}
\chi_R^{\prime\prime}(r)\leq 1, \quad \chi_R^{\prime}(r)\leq r, \quad \Delta \chi_R(r)\leq N, \quad r \geq 0.
\end{align}
The localized virial type quantity is defined by
$$
M_{\chi_R}[u]:=2 Im \int_{\mathbb{R}^N}\overline{u}\nabla\chi_R \cdot \nabla u \,dx.
$$
\begin{lem}\label{Virial}
Let $N\geq 2$, $\frac1 2<s_2<s_1<1$ and $2<p<\frac{2N}{N-2s_1}$. Assume that $u\in C_T(H_{rad}^{s_1}(\mathbb{R}^N))$ is a solution
to \eqref{evolv pb0}.
\begin{enumerate}
\item [$(\textnormal{i})$] For every $R>0$ and $\varepsilon>0$ small enough, then there holds that
\begin{align*}
\frac{d}{dt}M_{\chi_R}[u]
& \leq 2N(p-2)E(u_0)-(N(p-2)-4s_1)\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^2-(N(p-2)-4s_2)\|(-\Delta)^{\frac{s_2}{2}}u\|_{2}^2\\
& \quad +C\left(R^{-2s_2}+R^{-\frac{(p-2)(N-1)}{2}+\varepsilon s_1}\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^{\frac{p-2}{2s_1}+\varepsilon}\right).
\end{align*}
\item [$(\textnormal{ii})$] If $p=2+\frac{4s_1}{N}$ and $E(u_0)<0$ , then for some $R$ sufficiently large, there holds that
$$
\frac{d}{dt}M_{\chi_R}[u] < 4s_1E(u_0).
$$
\end{enumerate}
\end{lem}
\begin{proof}
The proof here is an adaptation of the one mentioned in \cite{BoHiLe2016}. To begin with, let us first introduce a self-adjoint differential operator
$$
\Gamma_\chi:=-i(\nabla \cdot \nabla \chi +\nabla \chi \cdot\nabla).
$$
It acts on a function $f$ as follows,
$$
\Gamma_\chi f=-i(\nabla\cdot ((\nabla\chi)f)+\nabla\chi \cdot \nabla f).
$$
One can check that
$$
M_{\chi_R}[u(t)]=\langle u(t),\Gamma_{\chi_R} u(t)\rangle.
$$
For $m>0$, we also introduce the function
$$
u_m:=\sqrt{\frac{\sin(\pi s)}{\pi}}\frac{1}{m-\triangle}u=\sqrt{\frac{\sin(\pi s)}{\pi}}\mathcal{F}^{-1}(\frac{\mathcal{F}u}{|\cdot|^2+m}).
$$
If $[X,Y]:=XY-YX$ denotes the commutator of $X$ and $Y$, then, by taking the time derivative and using \eqref{evolv pb0}, one gets that
\begin{align*}
\frac{d}{dt}M_{\chi_R}[u(t)]
=\langle u(t), [(-\Delta)^{s_1}+(-\Delta)^{s_2},i\Gamma_{\chi_R}]u(t)\rangle
+ \langle u(t), [-|u|^{p-2}u,i\Gamma_{\chi_R}]u(t)\rangle.
\end{align*}
According to computations developed in \cite{BoHiLe2016}, one has that
\begin{align*}
\frac{d}{dt}M_{\chi_R}[u(t)]
& \leq 4s_1\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^2+4s_2\|(-\Delta)^{\frac{s_2}{2}}u\|_{2}^2
- \frac{2(p-2)}{p}\int_{\mathbb{R}^N}|u|^p\Delta \psi_R \,dx+C\left(R^{-2s_1}+R^{-2s_2}\right)\\
& \leq 4s_1\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^2+4s_2\|(-\Delta)^{\frac{s_2}{2}}u\|_{2}^2- \frac{2N(p-2)}{p}\int_{\mathbb{R}^N}|u|^p\,dx\\
& \quad +C\left(R^{-2s_1}+R^{-2s_2}+R^{-\frac{(p-2)(N-1)}{2}+\varepsilon s_1}\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^{\frac{p-2}{2s_1}+\varepsilon}\right),
\end{align*}
for any $0<\varepsilon <\frac{(2s_1-1)(p-2)}{2s_1}$ and some constant $C:=C(\|u_0\|_2,N,\varepsilon,s_1,p)>0$. Hence, by
conservation of energy, one obtains the virial type inequality in the energy subcritical case.
Now suppose $p=2+\frac{4s_1}{N}$ and denote $\chi_1:=1-\chi_R^{\prime\prime}$ and $\chi_2:=N-\Delta \chi_R(r)$. Recall that $\chi_1$ and $\chi_2$ are nonnegative by \eqref{bound psi}. Using similar computations from \cite{BoHiLe2016}, we derive that
\begin{align*}
\frac{d}{dt}M_{\chi_R}[u(t)]
& \leq 4s_1\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^2+4s_2\|(-\Delta)^{\frac{s_2}{2}}u\|_{2}^2 -4\int_{0}^{\infty}m^{s_1}\int_{\mathbb{R}^N}\chi_1|\nabla u_m|^2\,dxdm\\
& \quad -\frac{4s_1N}{N+2s_1}\int_{\mathbb{R}^N}|u|^p\,dx+\frac{4s_1N}{N+2s_1}\int_{|x|\geq R}\chi_2|u|^p\,dx +O(R^{-2s_1}+R^{-2s_1})\\
& \leq 8s_1E(u_0)-4\int_{0}^{\infty}m^{s_1}\int_{\mathbb{R}^N}\chi_1|\nabla u_m|^2\,dxdm +\frac{4s_1N}{N+2s_1}\int_{\mathbb{R}^N}\chi_2|u|^p\,dx +O(R^{-2s_1}).
\end{align*}
Estimating the term $\int_{\mathbb{R}^N}\chi_2|u|^p\,dx$ in the same way as in \cite{BoHiLe2016} and using properties of $\chi_R$ and $E(u_0)<0$, we then obtain
$$
\frac{d}{dt}M_{\chi_R}[u] < 4s_1E(u_0).
$$
Thus the proof is completed.
\end{proof}
In the following, we are going to present some useful auxiliary results employed to establish Theorem \ref{blow-up vs global solt}.
\begin{lem}\label{lem A1}\cite[Lemma A.1]{BoHiLe2016}
Let $N\geq 1$ and $\chi$ be a real valued function such that $\nabla \chi \in W^{1,\infty}(\mathbb{R}^N)$. Then for any $u\in H^{\frac{1}{2}}(\mathbb{R}^N)$, there holds that
\begin{align*
\left|\int_{\mathbb{R}^N}\bar{u}\nabla \chi \cdot \nabla u\,dx\right|\leq C\left(\||\nabla|^{\frac{1}{2}}u\|_2^2+\|u\|_2\||\nabla|^{\frac{1}{2}}u\|_2\right),
\end{align*}
where the constant $C>0$ depends only on $N$ and $\|\nabla \chi\|_{W^{1,\infty}}$.
\end{lem}
\begin{lem}\label{lem bup}
Let $N \geq 2$, $\frac 1 2 <s_2<s_1<1$ and $p \geq 2 + \frac{4s_1}{N}$. Let $u_0\in H_{rad}^{s_1}(\mathbb{R}^N)$ be such that $E(u_0)\neq 0$ and $u\in C_{T}(H_{rad}^{s_1}(\mathbb{R}^N))$ be the maximal solution of \eqref{evolv pb0} with initial datum $u_0$. If there exist $R>0$, $t_0>0$ and $C>0$ such that
\begin{align}\label{ineq bup}
M_{\chi_R}[u(t)]\leq -C\int_{t_0}^t\left(\|(-\Delta)^{\frac{s_1}{2}}u(\tau)\|_2+\|(-\Delta)^{\frac{s_2}{2}}u(\tau)\|_2\right)^2\,d\tau,
\end{align}
holds for any $t\geq t_0$. Then $u(t)$ cannot exist globally in time, i.e. $T<+\infty$.
\end{lem}
\begin{proof}
In light of Lemma \ref{lem A1}, the definition of $M_{\chi_R}[u]$ and the conservation of mass, we first get that
$$
|M_{\chi_R}[u(t)]|\leq C\left(\||\nabla|^{\frac{1}{2}}u\|_2^2+\||\nabla|^{\frac{1}{2}}u\|_2\right).
$$
Due to $s_1>\frac{1}{2}$, then the following interpolation estimate holds,
$$
\||\nabla|^{\frac{1}{2}}u\|_2\leq \|(-\Delta)^{\frac{s_1}{2}}u\|_2^{\frac{1}{2s_1}}\|u\|_2^{1-\frac{1}{2s_1}}.
$$
Thus
\begin{align}\label{MR inf frac u}
|M_{\chi_R}[u(t)]|\leq C\left(\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2^{\frac{1}{s_1}}+\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2^{\frac{1}{2s_1}}\right).
\end{align}
On the other hand, we claim that
\begin{align}\label{bound below}
\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2+\|(-\Delta)^{\frac{s_2}{2}}u(t)\|_2 \gtrsim 1, \quad \forall \,\, t \in [0, T).
\end{align}
Indeed, suppose that there exists a sequence of time $\{t_n\} \subset \mathbb{R}^+$ such that
$$
\|(-\Delta)^{\frac{s_1}{2}}u(t_n)\|_2+\|(-\Delta)^{\frac{s_2}{2}}u(t_n)\|_2=o_n(1).
$$
From Gagliardo-Nirenberg inequality \eqref{gn}, one then obtains that$\|u(t_n)\|_p=o_n(1)$. Hence $E(u(t_n))=o_n(1)$. This contradicts $E(u(t_n))=E(u_0) \neq 0$. Thus the claim follows. Combining \eqref{MR inf frac u} and \eqref{bound below} then implies that
\begin{align}\label{MR inf s}
|M_{\chi_R}[u(t)]|\leq C\left(\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2+\|(-\Delta)^{\frac{s_2}{2}}u(t)\|_2\right)^{\frac{1}{s_1}}.
\end{align}
Therefore, from the assumption \eqref{ineq bup}, we deduce that
$$
M_{\chi_R}[u(t)]\leq -C\int_{t_0}^t|M_{\psi_R}[u(\tau)]|^{2s_1}\,d\tau, \quad \forall \,\, t \geq t_0.
$$
By straightforward calculations, we then find that
$$
M_{\chi_R}[u(t)] \leq -C|t-t_1|^{1-2s_1}
$$
for some $0<t_1<\infty$. Consequently, we have that $M_{\chi_R}[u(t)] \rightarrow -\infty$ as $t \to t_1$, which implies that $u(t)$ cannot be global and then $T<+\infty$. This completes the proof.
\end{proof}
\begin{lem}\label{invariant condits}
If $s_c>0$, then the following conditions are invariant under the flow of \eqref{evolv pb0}.
\begin{enumerate}
\item [$(\textnormal{i})$] \eqref{energ u0 inf energ gs} and \eqref{mass u0 sup mass gs}.
\item [$(\textnormal{ii})$] \eqref{energ u0 inf energ gs} and \eqref{mass u0 sup mass gs1}.
\end{enumerate}
\end{lem}
\begin{proof}
From the conservation laws, it follows that \eqref{energ u0 inf energ gs} is invariant under the flow of \eqref{evolv pb0}. Next we shall prove that \eqref{mass u0 sup mass gs} and \eqref{mass u0 sup mass gs1} are invariant under the flow of \eqref{evolv pb0}. In view of Gagliardo-Nirenberg inequality \eqref{gn}, we first have that
\begin{align} \label{invariant1}
\begin{split}
\hspace{-1cm}E(u(t))M(u(t))^{\sigma_c}&=\frac 12 \left(\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2^2+\|(-\Delta)^{\frac{s_2}{2}}u(t)\|_2^2\right) \|u(t)\|_2^{2\sigma_c}-\frac 1 p \|u(t)\|_p^p\|u(t)\|_2^{2\sigma_c} \\
& \geq \frac 12 \left(\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2 \|u(t)\|_2^{\sigma_c}\right)^2 -\frac {C_{N,p,s_1}}{p} \left(\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2 \|u(t)\|_2^{\sigma_c}\right)^{\frac{N(p-2)}{2s_1}} \\
&=:f(\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2 \|u(t)\|_2^{\sigma_c}),
\end{split}
\end{align}
where $f : \mathbb{R}^+ \to \mathbb{R}$ is defined by
\begin{align} \label{deff}
f(x):=\frac 12 x^2 -\frac{C_{N,p,s_1}}{p}x^{\frac{N(p-2)}{2s_1}}.
\end{align}
Direct computations and Lemma \ref{pohoz 0} show that $f$ has a unique critical point
\begin{align} \label{critical}
x_0:=\left(\frac{2ps_1}{C_{N,p,s_1}N(p-2)}\right)^{\frac{2s_1}{N(p-2)-4s_1}}=\|(-\Delta)^{\frac{s_1}{2}} \phi\|_2\|\phi\|_2^{\sigma_c}
\end{align}
and
$$
\max_{x>0} f(x)=f(x_0)=\frac{N(p-2)-4s_1}{2N(p-2)} \left(\frac{2ps_1}{C_{N,p,s_1}N(p-2)}\right)^{\frac{4s_1}{N(p-2)-4s_1}}=\mathcal{E}(\phi)M(\phi)^{\sigma_c}.
$$
Therefore, by the conservation laws and \eqref{energ u0 inf energ gs}, we have that
$$
f(\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2 \|u(t)\|_2^{\sigma_c}) < \mathcal{E}(\phi)M(\phi)^{\sigma_c}=f(\|(-\Delta)^{\frac{s_1}{2}} \phi\|_2\|\phi\|_2^{\sigma_c}).
$$
It then follows from \eqref{mass u0 sup mass gs} and \eqref{mass u0 sup mass gs1} along with continuity arguments that \eqref{mass u0 sup mass gs} that \eqref{mass u0 sup mass gs1} are invariant under the flow of \eqref{evolv pb0}.
Thus the proof is completed.
\end{proof}
\begin{comment}
Denote
$$
X(t):=\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2^2+\|(-\Delta)^{\frac{s_2}{2}}u(t)\|_2^2 \,\,\, \text{ and } \,\,\,K:=\frac{2C_{N,p,s_1}}{p}\|u_0\|^{p-\frac{N(p-2)}{2s_1}}, \quad t \in [0, T).
$$
Using the conservation laws and Gagliardo-Nirenberg inequality \eqref{gn}, we first get that
\begin{align*}
2E(u_0)=2E(u(t)) & =\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2^2+\|(-\Delta)^{\frac{s_2}{2}}u(t)\|_2^2 -\frac{2}{p}\|u\|_p^p \\
& \geq X(t)-\frac{2C_{N,p,s_1}}{p}\|u(t)\|_2^{p-\frac{N(p-2)}{2s_1}}\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_2^{\frac{N(p-2)}{2s_1}}\\
& \geq X(t)-KX(t)^{\frac{N(p-2)}{4s_1}}.
\end{align*}
Thus
\begin{align}\label{fct X(t) inf energ}
X(t)-KX(t)^{\frac{N(p-2)}{4s_1}}\leq 2E(u_0), \quad \forall \,\,t\in [0, T).
\end{align}
Elementary computations show that the function $f:x \mapsto x-Kx^{\frac{N(p-2)}{4s_1}}$ has a global maximum on $\mathbb{R}_+$ at the point
$$
x_m=\left(\frac{4s_1}{KN(p-2)}\right)^{\frac{4s_1}{N(p-2)-4s_1}}
$$
with the maximum value
$$
f(x_m)= \frac{N(p-2)-4s_1}{N(p-2)}x_m.
$$
From \eqref{pohoz 1} and \eqref{pohoz 2}, we derive that
\begin{align*}
2E(\phi)
&=\|(-\Delta)^{\frac{s_2}{2}}\phi\|_2^2+\frac{Np-2N-4s_1}{N(p-2)}\|(-\Delta)^{\frac{s_1}{2}}\phi\|_2^2\\
&\leq \frac{2(Np-2N-2s_1)}{N(p-2)}\|(-\Delta)^{\frac{s_1}{2}}\phi\|_2^2=\frac{2(Np-2N-2s_1)}{2s_1p-Np+2N}\|\phi\|_2^2.
\end{align*}
Using the previous relation, the condition \eqref{energ u0 inf energ gs} becomes
$$2E(u_0)<\frac{Np-2N-4s_1}{2s_1p-Np+2N}M(\phi)^{\frac{s_1}{s_c}}M(u_0)^{\frac{s_c-s_1}{s_c}}.$$
By using \eqref{best const with GS}, we have
\begin{align*}
f(x_m)
&=\frac{Np-2N-4s_1}{N(p-2)}x_m= \frac{Np-2N-4s_1}{N(p-2)}(\frac{4s_1}{KN(p-2)})^{\frac{4s_1}{N(p-2)-4s_1}}\\
&= \frac{Np-2N-4s_1}{2s_1p-Np+2N}M(\phi)^{\frac{s_1}{s_c}}M(u_0)^{\frac{s_c-s_1}{s_c}}>2E(u_0).
\end{align*}
On the other hand, one has
$$x_m= \frac{N(p-2)}{Np-2N-4s_1}f(x_m)=\frac{N(p-2)}{2s_1p-Np+2N}M(\phi)^{\frac{s_1}{s_c}}M(u_0)^{\frac{s_c-s_1}{s_c}}.$$
From the inequality \eqref{fct X(t) inf energ}, we also have
\begin{align}\label{infer f(xm)}
f(\|u(t)\|_{\dot{H}^{s_1}}^2+\|u(t)\|_{\dot{H}^{s_2}}^2)\leq 2E(u_0)<f(x_m).
\end{align}
\begin{itemize}
\item The assumption \eqref{mass uo inf mass gs} gives
\begin{align*}
\|u_0\|_{\dot{H}^{s_1}}^2+\|u_0\|_{\dot{H}^{s_2}}^2
& < \|\phi\|_{\dot{H}^{s_1}}^2(\frac{M(\phi)}{M(u_0)})^{\frac{s_1-s_c}{s_c}} \\
& < \frac{N(p-2)}{2s_1p-Np+2N}M(\phi)^{\frac{s_1}{s_c}}M(u_0)^{\frac{s_1-s_c}{s_c}}=x_m.
\end{align*}
Since $u\in C_{T^\ast}(\dot{H}^{s_1})$, according to \eqref{infer f(xm)} with a continuity argument, we must have
$\|u(t)\|_{\dot{H}^{s_1}}^2+\|u(t)\|_{\dot{H}^{s_2}}^2< x_m$, for all time $t\in [0,T^\ast)$.
\item Similarly, from \eqref{mass uo sup mass gs}, one has $\|u_0\|_{\dot{H}^{s_1}}^2+\|u_0\|_{\dot{H}^{s_2}}^2>x_m$. Together
\eqref{infer f(xm)} with a continuity argument, imply that $\|u(t)\|_{\dot{H}^{s_1}}^2+\|u(t)\|_{\dot{H}^{s_2}}^2> x_m$ holds
for any time $t\in[0,T^\ast)$. Consequently, assumptions \eqref{energ u0 inf energ gs} and \eqref{mass uo inf mass gs}, as well
as \eqref{energ u0 inf energ gs} and \eqref{mass uo sup mass gs} are invariant under the flow of \eqref{evolv pb0}.
\end{itemize}
\end{comment}
\begin{proof}[Proof of Theorem \ref{blow-up vs global solt}]
Let $u\in C_T(H_{rad}^{s_1}(\mathbb{R}^N))$ be a maximal solution to \eqref{evolv pb0} with initial datum $u_0 \in H^{s_1}_{rad}(\mathbb{R}^N)$. As a consequence of the conservation laws and Lemma \ref{invariant condits}, then the assertion $(\textnormal{i})$ follows immediately. Next we shall prove the assertion $(\textnormal{ii})$. Let us first consider the case $E(u_0)<0$. In this case, by Lemma \ref{Virial}, we obtain that
\begin{align*}
\frac{d}{dt}M_{\chi_R}[u]
&\leq N(p-2)E(u_0)-(N(p-2)-4s_1) \left( \|(-\Delta)^{\frac{s_1}{2}}u\|_2^2+\|(-\Delta)^{\frac{s_2}{2}}u\|_2^2 \right)\\
&\quad +C\left(R^{-2s_2}+R^{-\frac{(p-2)(N-1)}{2}+\varepsilon s_1}\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^{\frac{p-2}{2s_1}+\varepsilon}\right).
\end{align*}
Since $2<p<2+4s_1$, then we can choose $\varepsilon$ sufficiently small such that
$$
0<\frac{p-2}{2s_1}+\varepsilon<2.
$$
From the conservation laws and Gagliardo-Nirenberg inequality \eqref{gn}, we see that
$$
\|(-\Delta)^{\frac {s_1}{2}} u(t)\|_2+\|(-\Delta)^{\frac {s_2}{2}} u(t)\|_2 \gtrsim 1, \quad \forall \,\, t \in [0, T),
$$
Therefore, for any $R>0$ large enough, there holds that
\begin{align*}
\frac{d}{dt}M_{\chi_R}[u] \leq -\frac{N(p-2)-4s_1}{2} \left( \|(-\Delta)^{\frac{s_1}{2}}u\|_2^2+\|(-\Delta)^{\frac{s_2}{2}}u\|_2^2 \right).
\end{align*}
Suppose $T=+\infty$ and integrate above inequality on time, then there exists $t_0>0$ sufficiently large such that $M_{\chi_R}[u(t)] < 0$ for any $t\geq t_0$. Therefore, we derive that
$$
M_{\chi_R}[u(t)] \leq -\frac{N(p-2)-4s_1}{4}\int_{t_0}^{t}\left(\|(-\Delta)^{\frac{s_1}{2}}u(\tau)\|_{2}+\|(-\Delta)^{\frac{s_2}{2}}u\|_2^2\right)^2\,d\tau, \quad \forall \,\, t\geq t_0.
$$
In view of Lemma \ref{lem bup}, then the solution $u$ cannot exist for all time and $T$ must be finite.
Now we consider the case that $E(u_0) \geq 0$ and the assumptions \eqref{energ u0 inf energ gs} and \eqref{mass u0 sup mass gs1} hold. Note first that, by the Gagliardo- Nirenberg inequality \eqref{gn} and the conservation of mass, then
\begin{align*}
E(u(t)) &\geq \frac 12 \|(-\Delta)^{\frac{s_1}{2}}u(t)\|_{2}^2-\frac 1p \|u(t)\|^p_p \\
&\geq \frac 12 \|(-\Delta)^{\frac{s_1}{2}}u(t)\|_{2}^2-\frac{C_{N,p,s_1}}{p} \|u(t)\|_2^{p-\frac{N(p-2)}{2s_1}} \|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^{\frac{N(p-2)}{2s_1}} \\
&=\frac 12 \|(-\Delta)^{\frac{s_1}{2}}u(t)\|_{2}^2-\frac{C_{N,p,s_1}}{p} \|u_0\|_2^{p-\frac{N(p-2)}{2s_1}} \|(-\Delta)^{\frac{s_1}{2}}u(t)\|_{2}^{\frac{N(p-2)}{2s_1}} \\
&=:g(\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_{2}),
\end{align*}
where $g: \mathbb{R}^+ \to \mathbb{R}$ is defined by
$$
g(x):=\frac 12 x^2-\frac{C_{N,p,s_1}}{p} \|u_0\|_2^{p-\frac{N(p-2)}{2s_1}} x^{\frac{N(p-2)}{2s_1}}.
$$
In light of Lemma \ref{pohoz 0}, it is straightforward to compute that $g$ has a unique critical point
$$
x_1:=\left(\frac{2ps_1}{C_{N,p,s_1}N(p-2)}\right)^{\frac{2s_1}{N(p-2)-4s_1}} \|u_0\|_2^{-\frac{N(p-2)-2ps_1}{N(p-2)-4s_1}}=\|(-\Delta)^{\frac{s_1}{2}} \phi\|_2\|\phi\|_2^{\sigma_c}\|u_0\|_2^{-\sigma_c}
$$
and
\begin{align*}
\max_{x>0} g(x)=g(x_1)&=\frac{N(p-2)-4s_1}{2N(p-2)}\left(\frac{2ps_1}{C_{N,p,s_1}N(p-2)}\right)^{\frac{4s_1}{N(p-2)-4s_1}} \|u_0\|_2^{\frac{-2N(p-2)-4ps_1}{N(p-2)-4s_1}}\\
&=\mathcal{E}(\phi)M(\phi)^{\sigma_c}\|u_0\|_2^{-2\sigma_c}.
\end{align*}
From \eqref{energ u0 inf energ gs} and \eqref{mass u0 sup mass gs1}, we see that
$$
E(u_0)<g(x_1), \quad \|(-\Delta)^{\frac {s_1}{2}} u_0\|_2 >x_1.
$$
Therefore, by continuity arguments, we have that $\|(-\Delta)^{\frac {s_1}{2}} u(t)\|_2 >x_1$ for any $t \in [0, T)$. Let $0<\mu<1$ be such that
\begin{align}\label{Eu0 inf Ephi}
E(u_0)M(u_0)^{\sigma_c}< (1-\mu)\mathcal{E}(\phi)M(\phi)^{\sigma_c}.
\end{align}
This shows that
\begin{align*}
E(u_0)< (1-\mu)\mathcal{E}(\phi)M(\phi)^{\sigma_c}M(u_0)^{-\sigma_c}&=(1-\mu)\frac{N(p-2)-4s_1}{2N(p-2)}x_1^2 \\
&<(1-\mu)\frac{N(p-2)-4s_1}{2N(p-2)}\|(-\Delta)^{\frac {s_1}{2}} u(t)\|_2^2,
\end{align*}
from which we derive that
\begin{align}\label{last ineq}
(1-\mu)(N(p-2)-4s_1)\left(\|(-\Delta)^{\frac {s_1}{2}} u(t)\|_2^2+\|(-\Delta)^{\frac {s_2}{2}} u(t)\|_2^2\right)>2N(p-2)E(u_0).
\end{align}
Since $2<p<2+4s_1$, then we choose $\varepsilon>0$ small enough such that
$$
0<\frac{p-2}{2s_1}+\varepsilon<2.
$$
Note that
$$
\|(-\Delta)^{\frac {s_1}{2}} u(t)\|_2+\|(-\Delta)^{\frac {s_2}{2}} u(t)\|_2 \gtrsim 1, \quad \forall \,\, t \in [0, T).
$$
By Lemma \ref{Virial}, then
\begin{align*}
\frac{d}{dt}M_{\chi_R}[u(t)]
&\leq 2N(p-2)E(u_0)-(N(p-2)-4s_1)\left(\|(-\Delta)^{\frac {s_1}{2}} u(t)\|_2^2+\|(-\Delta)^{\frac {s_2}{2}} u(t)\|_2^2\right)\\
&+C\left(R^{-2s_2}+R^{-\frac{(p-2)(N-1)}{2}+\varepsilon s_1}\|(-\Delta)^{\frac{s_1}{2}}u(t)\|_{2}^{\frac{p-2}{2s_1}+\varepsilon}\right)\\
& \leq -\frac{\mu(N(p-2)-4s_1)}{2}\left(\|(-\Delta)^{\frac {s_1}{2}} u(t)\|_2^2+\|(-\Delta)^{\frac {s_2}{2}} u(t)\|_2^2\right) +o_R(1)\\
& \leq -\frac{\mu(N(p-2)-4s_1)}{4}\left(\|(-\Delta)^{\frac {s_1}{2}} u(t)\|_2+\|(-\Delta)^{\frac {s_2}{2}} u(t)\|_2\right)^2.
\end{align*}
Using Lemma \ref{lem bup}, we then have desired conclusion. Now we turn to prove the assertion $(\textnormal{iii})$.
In virtue of Lemma \ref{Virial}, we first have that
$$
\frac{d}{dt}M_{\chi_R}[u(t)]\leq 4s_1E(u_0), \quad \forall \,\, t\in [0,T).
$$
Suppose that $u(t)$ exists globally in time, then there exists a constant $t^*>0$ large such that
$$
M_{\chi_R}[u(t)] \leq -C t, \quad \forall \,\, t \geq t^*,
$$
This jointly with \eqref{MR inf s} then yields that
$$
\|(-\Delta)^{\frac {s_1}{2}} u(t)\|_2+\|(-\Delta)^{\frac {s_2}{2}} u(t)\|_2\geq Ct^{s_1}, \quad \forall \,\, t\geq t_*.
$$
Thus the proof is completed.
\end{proof}
\section{Orbital instability of ground state solutions} \label{section8}
In this section, we shall discuss orbital instability of ground state solutions to \eqref{fequ}-\eqref{mass} and present the proof of Theorem \ref{thm5}.
\begin{proof}[Proof of Theorem \ref{thm5}] Let $u_c \in S(c)$ be a ground state solution to \eqref{fequ}-\eqref{mass} at the level $\gamma(c)>0$.
In view of Theorem \ref{thm6}, we may assume that $u_c$ is radially symmetric. Define
$$
\mathcal{Q}_c:=\{v \in S(c) : E(v) < E(u_c), Q(v)<0\}.
$$
Note first that $u_0:=(u_c)_{\tau} \in \mathcal{Q}_c$ for ant $\tau >1$, by Lemma \ref{monotonicity}. It then implies that $\mathcal{Q}_c \neq \emptyset$. Record that $u_0 \to u_c$ in $H^{s_1}(\mathbb{R}^N)$ as $\tau \to 1^+$. This suggests that $E(u_0) \to \gamma(c)$ as $\tau \to 1^+$. Let $u \in C([0, T), H_{rad}^{s_1}(\mathbb{R}^N))$ be the solution to \eqref{evolv pb0} with initial datum $u_0 \in H^{s_1}_{rad}(\mathbb{R}^N)$. In the following, we are going
to demonstrate that $u(t)$ blows up in finite or infinite time. Observe first that $\mathcal{Q}_c$ is invariant under the flow of \eqref{evolv pb0}. Indeed, if not, by the conservation laws, then there exists $0<t_0<T$ such that $E(u(t_0))<E(u_c)$ and $Q(u(t_0))=0$. Hence
$$
\gamma(c) \leq E(u(t_0))<E(u_c).
$$
This is impossible, because of $E(u_c)=\gamma(c)$. For simplicity, we shall write $u=u(t)$. Due to $Q(u)<0$, it then follows from Lemma \ref{monotonicity} that there exists a constant $0<\tau_u<1$ such that $Q(u_{\tau_u})=0$. In addition, we know that the function $\tau \mapsto E(u_{\tau})$ is concave on $[\tau_u, 1]$. This then results in
$$
E(u_{\tau_u})-E(u) \leq (\tau_u-1) \frac{d}{d \tau} E(u_{\tau}) \mid_{\tau=1}=(\tau_u -1) Q(u).
$$
Since $Q(u)<0$ and $\gamma(c) \leq E(u_{\tau_u})$, by the conservation of energy, then
$$
Q(u) < (1-\tau_u) Q(u) \leq E(u)-E(u_{\tau_u}) \leq E(u)-\gamma(c)=E(u_0)-\gamma(c):=\delta<0,
$$
where $\delta>0$ is a constant.
If $2<p<2+4s_1$, then we can choose $\epsilon>0$ small enough such that
$$
0<\frac{p-2}{2s_1} +\epsilon<2.
$$
In addition, by the conservation laws $E(u)=E(u_0) \neq 0$, we have that
$$
\|(-\Delta)^{\frac {s_1}{2}} u\|_2^2+\|(-\Delta)^{\frac {s_2}{2}} u\|_2^2 \gtrsim 1.
$$
Using Lemma \ref{Virial}, Young's inequality and taking $R>0$ large enough, we then obtain that
\begin{align} \label{evolution}
\begin{split}
\frac{d}{dt}M_{\chi_R}[u]
&\leq 2N(p-2)E(u)-(N(p-2)-4s_1)\left(\|(-\Delta)^{\frac {s_1}{2}} u\|_2^2+\|(-\Delta)^{\frac {s_2}{2}} u\|_2^2\right)\\
&\quad +C\left(R^{-2s_2}+R^{-\frac{(p-2)(N-1)}{2}+\varepsilon s_1}\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^{\frac{p-2}{2s_1}+\varepsilon}\right)\\
& = 4Q(u)+C\left(R^{-2s_2}+R^{-\frac{(p-2)(N-1)}{2}+\varepsilon s_1}\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}^{\frac{p-2}{2s_1}+\varepsilon}\right)\\
& \leq -\frac{\delta}{2}\left(\|(-\Delta)^{\frac {s_1}{2}} u\|_2^2+\|(-\Delta)^{\frac {s_2}{2}} u\|_2^2\right).
\end{split}
\end{align}
Thus, by Lemma \ref{lem bup}, we get that $u(t)$ cannot exist globally in time, i.e. $T<+\infty$. Let us now treat the case $p \geq 2+4s_1$. In this case, if $\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}$ is unbounded, then $u(t)$ blows up in finite time or infinite time. If $\|(-\Delta)^{\frac{s_1}{2}}u\|_{2}$ is bounded, namely $u(t)$ exists globally in time, by \eqref{evolution}, then for $R>0$ large enough,
$$
\frac{d}{dt}M_{\chi_R}[u] \leq -2\delta.
$$
Arguing as the proof of the assertion $(\textnormal{iii})$ of Theorem \ref{blow-up vs global solt}, we are able to achieve that there exists a constant $t^*>0$ large enough such that
\begin{align} \label{inst}
\|(-\Delta)^{\frac {s_1}{2}} u\|_2+\|(-\Delta)^{\frac {s_2}{2}} u\|_2\geq Ct^{s_1}, \quad \forall \,\, t\geq t_*.
\end{align}
Note that
$$
\|(-\Delta)^{\frac {s_2}{2}} u\|_2 \leq \|(-\Delta)^{\frac {s_1}{2}} u\|_2^{\frac{s_2}{s_1}} \|u\|_2^{1-\frac {s_2}{s_1}}=\|(-\Delta)^{\frac {s_1}{2}} u\|_2^{\frac{s_2}{s_1}} \|u_0\|_2^{1-\frac {s_2}{s_1}},
$$
where we used the conservation of mass. In virtue of \eqref{inst}, it then follows that $\|(-\Delta)^{\frac {s_1}{2}} u\|_2$ is unbounded. This contradicts with the assumption. Thus we have the desired conclusion and the proof is completed.
\end{proof}
\section{Appendix} \label{section9}
\begin{proof}[Proof of Lemma \ref{pohozaev}]
Utilizing scaling techniques, we only need to deduce Pohozaev identity of solutions to the following equation,
\begin{align} \label{zfequ11}
\left(\frac{k_{s_2}}{k_{s_1}}\right)^{\alpha s_1}(-\Delta)^{s_1} u +\left(\frac{k_{s_2}}{k_{s_1}}\right)^{\alpha s_2}(-\Delta)^{s_2} u + \lambda u=|u|^{p-2} u, \quad u \in H^{s_1}(\mathbb{R}^N),
\end{align}
where
$$
k_s=2^{1-2s} \frac{\Gamma(1-s)} {\Gamma(s)}, \quad \alpha=\frac{1}{s_1-s_2}.
$$
For this, by the harmonic extension theory from \cite{CS}, we are able to introduce the following extended problem,
\begin{align}\label{fequ111}
\left\{
\begin{aligned}
&-\mbox{div}(y^{1-2s_1} \nabla w+y^{1-2s_2} \nabla w)=0 \,\,\, &\mbox{in} \,\,\, \mathbb{R}^{N+1}_+, \\
&-\frac{\partial w}{\partial {\nu}}= k_{s_1, s_2} (|u|^{p-2}u-\lambda u) \,\,\, &\mbox{on} \,\, \mathbb{R}^N \times \{0\}.
\end{aligned}
\right.
\end{align}
where
$$
\frac{\partial w}{\partial {\nu}}:= \lim_{y \to 0^+} y^{1-2s_1} \frac{\partial w}{\partial y}(x, y)+y^{1-2s_2} \frac{\partial w}{\partial y}(x, y) =- \frac{1}{k_{s_1}} (- \Delta )^{s_1} u(x)- \frac{1}{k_{s_2}} (- \Delta )^{s_2} u(x)
$$
and
$$
k_{s_1,s_2}:=\left(\frac{k_{s_1}^{s_2}}{k_{s_2}^{s_1}}\right)^{\alpha}.
$$
Multiplying \eqref{fequ111} by $(x, y) \cdot \nabla w$ and integrating on $\mathcal{B}^+(0, R)$, we get that
$$
\int_{\mathcal{B}^+(0, R)}\mbox{div}(y^{1-2s_1} \nabla w+y^{1-2s_2} \nabla w) ((x, y) \cdot \nabla w) \,dxdy=0,
$$
where
$$
\mathcal{B}^+(0, R):=\{(x, y) \in \mathbb{R}^{N+1}_+: |(x, y)| <R\}.
$$
Taking into account the divergence theorem, we find that
\begin{align} \label{ph1}
\begin{split}
&-\int_{\mathcal{B}^+(0, R)}(y^{1-2s_1} \nabla w+y^{1-2s_2} \nabla w)\cdot \nabla ((x, y) \cdot \nabla w)\,dxdy \\
&= k_{s_1, s_2} \int_{B(0, R)} (|u|^{p-2}u-\lambda u)(x \cdot \nabla u) \, dx -R \int_{\partial^+\mathcal{B}^+(0, R)} y^{1-2s_1} |\nabla w|^2 + y^{1-2s_2} |\nabla w|^2\,dS,
\end{split}
\end{align}
where $B(0, R):=\partial \mathcal{B}^+(0, R) \cap \mathbb{R}^N$ and $\partial^+\mathcal{B}^+(0, R):=\partial \mathcal{B}^+(0, R) \cap \mathbb{R}^{N+1}_+$. We are going to compute every term in \eqref{ph1}. Let us start with treating the first term in the right side hand of \eqref{ph1}. By the divergence theorem, then
\begin{align*}
k_{s_1, s_2} \int_{B(0, R)} (\lambda u -|u|^{p-2}u)(x \cdot \nabla u) \, dx&=\frac {\lambda k_{s_1, s_2}}{2} \int_{B(0, R)} x \cdot \nabla \left(|u|^2\right) \, dx -\frac {k_{s_1, s_2}}{p} \int_{B(0, R)} x \cdot \nabla \left(|u|^p\right) \, dx \\
&=-\frac{\lambda k_{s_1, s_2} N}{2} \int_{B(0, R)} |u|^2 \, dx +\frac {k_{s_1, s_2}N} {p} \int_{B(0, R)} |u|^p \, dx \\
&\quad +\frac{\lambda k_{s_1, s_2} R}{2} \int_{\partial B(0, R)} |u|^2\,dS- \frac {k_{s_1, s_2}R} {p} \int_{\partial B(0, R)} |u|^p \, dS.
\end{align*}
We next deal with the term in the left side hand of \eqref{ph1}. By the divergence theorem, then
\begin{align*}
&\int_{\mathcal{B}^+(0, R)} y^{1-2s_1} \nabla w \cdot \nabla ((x, y) \cdot \nabla w) \,dxdy\\
&=\frac 12 \int_{\mathcal{B}^+(0, R)} y^{1-2s_1} (x ,y) \cdot \nabla \left(|\nabla w|^2\right) \, dxdy
+\int_{\mathcal{B}^+(0, R)} y^{1-2s_1} |\nabla w|^2 \,dxdy\\
&=-\frac{N-2s_1}{2} \int_{\mathcal{B}^+(0, R)} y^{1-2s_1} |\nabla w|^2\,dxdy
+ \frac R 2 \int_{\partial^+\mathcal{B}^+(0, R)} y^{1-2s_1} |\nabla w|^2 \,dS.
\end{align*}
Similarly, we can deduce that
\begin{align*}
&\int_{\mathcal{B}^+(0, R)}(y^{1-2s_2} \nabla w) \cdot \nabla ((x, y) \cdot \nabla w)\,dxdy\\
&=-\frac{N-2s_2}{2} \int_{\mathcal{B}^+(0, R)} y^{1-2s_2} |\nabla w|^2\,dxdy
+ \frac R 2 \int_{\partial^+\mathcal{B}^+(0, R)} y^{1-2s_2} |\nabla w|^2\,dS.
\end{align*}
Since $u \in H^{s_1}(\mathbb{R}^N)$ and $\nabla w \in L^2(y^{1-2s_1}, \mathbb{R}^{N+1}_+) \cap L^2(y^{1-2s_2}, \mathbb{R}^{N+1}_+)$, then there exists a sequence $\{R_n\} \subset \mathbb{R}$ such that
$$
R_n \left(\int_{\partial B(0, R_n)} |u|^2\,dS+ \int_{\partial B(0, R_n)} |u|^p \,dS \right)=o_n(1)
$$
and
$$
R_n \left(\int_{\partial^+\mathcal{B}^+(0, R_n)} y^{1-2s_1} |\nabla w|^2 \,dS+ \int_{\partial^+\mathcal{B}^+(0, R_n)} y^{1-2s_2} |\nabla w|^2 \,dS \right)=o_n(1).
$$
Making use of \eqref{ph1} with $R=R_n$ and taking $n \to \infty$, we then derive
\begin{align} \label{ph111}
\begin{split}
&\frac{N-2s_1}{2}\int_{\mathbb{R}^{N+1}_+} y^{1-2s_1} |\nabla w|^2 \, dxdy +\frac{N-2s_2}{2}\int_{\mathbb{R}^{N+1}_+} y^{1-2s_2} |\nabla w|^2\,dxdy \\
&=- \frac {\lambda k_{s_1, s_2} N} {2} \int_{\mathbb{R}^N} |u|^2 \,dx + \frac {k_{s_1, s_2}N} {p} \int_{\mathbb{R}^N} |u|^p\,dx.
\end{split}
\end{align}
On the other hand, multiplying \eqref{fequ111} by $w$ and integrating on $\mathbb{R}^{N+1}_+$, we obtain that
\begin{align} \label{ph112}
\hspace{-1cm}\int_{\mathbb{R}^{N+1}_+}y^{1-2s_1}|\nabla w|^2\,dxdy +\int_{\mathbb{R}^{N+1}_+}y^{1-2s_2}|\nabla w|^2\,dxdy
=-k_{s_1, s_2} \lambda \int_{\mathbb{R}^N} |u|^2\,dx + k_{s_1, s_2}\int_{\mathbb{R}^N} |u|^p\,dx.
\end{align}
Therefore, by combining \eqref{ph111} and \eqref{ph112}, we conclude that any solution $u \in H^{s_1}(\mathbb{R}^N)$ to \eqref{fequ111} satisfies the following identity,
$$
s_1\int_{\mathbb{R}^{N+1}_+}y^{1-2s_1}|\nabla w|^2\,dxdy +s_2 \int_{\mathbb{R}^{N+1}_+}y^{1-2s_2}|\nabla w|^2\,dxdy =\frac{k_{s_1, s_2}N(p-2)}{2p}\int_{\mathbb{R}^N}|u|^p\,dx.
$$
This completes the proof.
\end{proof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,802 |
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <unistd.h>
#include <fcntl.h>
#include <ctype.h>
#include <sys/types.h>
#include <sys/stat.h>
#include <errno.h>
#include <stdint.h>
#include <stdarg.h>
#include "superblocks.h"
/**
* SECTION:superblocks
* @title: Superblocks probing
* @short_description: filesystems and raids superblocks probing.
*
* The library API has been originally designed for superblocks probing only.
* This is reason why some *deprecated* superblock specific functions don't use
* '_superblocks_' namespace in the function name. Please, don't use these
* functions in new code.
*
* The 'superblocks' probers support NAME=value (tags) interface only. The
* superblocks probing is enabled by default (and controlled by
* blkid_probe_enable_superblocks()).
*
* Currently supported tags:
*
* @TYPE: filesystem type
*
* @SEC_TYPE: secondary filesystem type
*
* @LABEL: filesystem label
*
* @LABEL_RAW: raw label from FS superblock
*
* @UUID: filesystem UUID (lower case)
*
* @UUID_SUB: subvolume uuid (e.g. btrfs)
*
* @LOGUUID: external log UUID (e.g. xfs)
*
* @UUID_RAW: raw UUID from FS superblock
*
* @EXT_JOURNAL: external journal UUID
*
* @USAGE: usage string: "raid", "filesystem", ...
*
* @VERSION: filesystem version
*
* @MOUNT: cluster mount name (?) -- ocfs only
*
* @SBMAGIC: super block magic string
*
* @SBMAGIC_OFFSET: offset of SBMAGIC
*
* @FSSIZE: size of filessystem [not-implemented yet]
*
* @SYSTEM_ID: ISO9660 system identifier
*
* @PUBLISHER_ID: ISO9660 publisher identifier
*
* @APPLICATION_ID: ISO9660 application identifier
*
* @BOOT_SYSTEM_ID: ISO9660 boot system identifier
*/
static int superblocks_probe(blkid_probe pr, struct blkid_chain *chn);
static int superblocks_safeprobe(blkid_probe pr, struct blkid_chain *chn);
static int blkid_probe_set_usage(blkid_probe pr, int usage);
/*
* Superblocks chains probing functions
*/
static const struct blkid_idinfo *idinfos[] =
{
/* RAIDs */
&linuxraid_idinfo,
&ddfraid_idinfo,
&iswraid_idinfo,
&lsiraid_idinfo,
&viaraid_idinfo,
&silraid_idinfo,
&nvraid_idinfo,
&pdcraid_idinfo,
&highpoint45x_idinfo,
&highpoint37x_idinfo,
&adraid_idinfo,
&jmraid_idinfo,
&bcache_idinfo,
&drbd_idinfo,
&drbdproxy_datalog_idinfo,
&lvm2_idinfo,
&lvm1_idinfo,
&snapcow_idinfo,
&verity_hash_idinfo,
&luks_idinfo,
&vmfs_volume_idinfo,
/* Filesystems */
&vfat_idinfo,
&swsuspend_idinfo,
&swap_idinfo,
&xfs_idinfo,
&xfs_log_idinfo,
&ext4dev_idinfo,
&ext4_idinfo,
&ext3_idinfo,
&ext2_idinfo,
&jbd_idinfo,
&reiser_idinfo,
&reiser4_idinfo,
&jfs_idinfo,
&udf_idinfo,
&iso9660_idinfo,
&zfs_idinfo,
&hfsplus_idinfo,
&hfs_idinfo,
&ufs_idinfo,
&hpfs_idinfo,
&sysv_idinfo,
&xenix_idinfo,
&ntfs_idinfo,
&refs_idinfo,
&cramfs_idinfo,
&romfs_idinfo,
&minix_idinfo,
&gfs_idinfo,
&gfs2_idinfo,
&ocfs_idinfo,
&ocfs2_idinfo,
&oracleasm_idinfo,
&vxfs_idinfo,
&squashfs_idinfo,
&squashfs3_idinfo,
&netware_idinfo,
&btrfs_idinfo,
&ubifs_idinfo,
&bfs_idinfo,
&vmfs_fs_idinfo,
&befs_idinfo,
&nilfs2_idinfo,
&exfat_idinfo,
&f2fs_idinfo
};
/*
* Driver definition
*/
const struct blkid_chaindrv superblocks_drv = {
.id = BLKID_CHAIN_SUBLKS,
.name = "superblocks",
.dflt_enabled = TRUE,
.dflt_flags = BLKID_SUBLKS_DEFAULT,
.idinfos = idinfos,
.nidinfos = ARRAY_SIZE(idinfos),
.has_fltr = TRUE,
.probe = superblocks_probe,
.safeprobe = superblocks_safeprobe,
};
/**
* blkid_probe_enable_superblocks:
* @pr: probe
* @enable: TRUE/FALSE
*
* Enables/disables the superblocks probing for non-binary interface.
*
* Returns: 0 on success, or -1 in case of error.
*/
int blkid_probe_enable_superblocks(blkid_probe pr, int enable)
{
if (!pr)
return -1;
pr->chains[BLKID_CHAIN_SUBLKS].enabled = enable;
return 0;
}
/**
* blkid_probe_set_superblocks_flags:
* @pr: prober
* @flags: BLKID_SUBLKS_* flags
*
* Sets probing flags to the superblocks prober. This function is optional, the
* default are BLKID_SUBLKS_DEFAULTS flags.
*
* Returns: 0 on success, or -1 in case of error.
*/
int blkid_probe_set_superblocks_flags(blkid_probe pr, int flags)
{
if (!pr)
return -1;
pr->chains[BLKID_CHAIN_SUBLKS].flags = flags;
return 0;
}
/**
* blkid_probe_reset_superblocks_filter:
* @pr: prober
*
* Resets superblocks probing filter
*
* Returns: 0 on success, or -1 in case of error.
*/
int blkid_probe_reset_superblocks_filter(blkid_probe pr)
{
return __blkid_probe_reset_filter(pr, BLKID_CHAIN_SUBLKS);
}
/**
* blkid_probe_invert_superblocks_filter:
* @pr: prober
*
* Inverts superblocks probing filter
*
* Returns: 0 on success, or -1 in case of error.
*/
int blkid_probe_invert_superblocks_filter(blkid_probe pr)
{
return __blkid_probe_invert_filter(pr, BLKID_CHAIN_SUBLKS);
}
/**
* blkid_probe_filter_superblocks_type:
* @pr: prober
* @flag: filter BLKID_FLTR_{NOTIN,ONLYIN} flag
* @names: NULL terminated array of probing function names (e.g. "vfat").
*
* %BLKID_FLTR_NOTIN - probe for all items which are NOT IN @names;
*
* %BLKID_FLTR_ONLYIN - probe for items which are IN @names
*
* Returns: 0 on success, or -1 in case of error.
*/
int blkid_probe_filter_superblocks_type(blkid_probe pr, int flag, char *names[])
{
return __blkid_probe_filter_types(pr, BLKID_CHAIN_SUBLKS, flag, names);
}
/**
* blkid_probe_filter_superblocks_usage:
* @pr: prober
* @flag: filter BLKID_FLTR_{NOTIN,ONLYIN} flag
* @usage: BLKID_USAGE_* flags
*
* %BLKID_FLTR_NOTIN - probe for all items which are NOT IN @usage;
*
* %BLKID_FLTR_ONLYIN - probe for items which are IN @usage
*
* Returns: 0 on success, or -1 in case of error.
*/
int blkid_probe_filter_superblocks_usage(blkid_probe pr, int flag, int usage)
{
unsigned long *fltr;
struct blkid_chain *chn;
size_t i;
fltr = blkid_probe_get_filter(pr, BLKID_CHAIN_SUBLKS, TRUE);
if (!fltr)
return -1;
chn = &pr->chains[BLKID_CHAIN_SUBLKS];
for (i = 0; i < chn->driver->nidinfos; i++) {
const struct blkid_idinfo *id = chn->driver->idinfos[i];
if (id->usage & usage) {
if (flag & BLKID_FLTR_NOTIN)
blkid_bmp_set_item(chn->fltr, i);
} else if (flag & BLKID_FLTR_ONLYIN)
blkid_bmp_set_item(chn->fltr, i);
}
DBG(LOWPROBE, ul_debug("a new probing usage-filter initialized"));
return 0;
}
/**
* blkid_known_fstype:
* @fstype: filesystem name
*
* Returns: 1 for known filesytems, or 0 for unknown filesystem.
*/
int blkid_known_fstype(const char *fstype)
{
size_t i;
if (!fstype)
return 0;
for (i = 0; i < ARRAY_SIZE(idinfos); i++) {
const struct blkid_idinfo *id = idinfos[i];
if (strcmp(id->name, fstype) == 0)
return 1;
}
return 0;
}
/**
* blkid_superblocks_get_name:
* @idx: number >= 0
* @name: returns name of supported filesystem/raid (optional)
* @usage: returns BLKID_USAGE_* flags, (optional)
*
* Returns: -1 if @idx is out of range, or 0 on success.
*/
int blkid_superblocks_get_name(size_t idx, const char **name, int *usage)
{
if (idx < ARRAY_SIZE(idinfos)) {
if (name)
*name = idinfos[idx]->name;
if (usage)
*usage = idinfos[idx]->usage;
return 0;
}
return -1;
}
/*
* The blkid_do_probe() backend.
*/
static int superblocks_probe(blkid_probe pr, struct blkid_chain *chn)
{
size_t i;
int rc = BLKID_PROBE_NONE;
if (!pr || chn->idx < -1)
return -EINVAL;
blkid_probe_chain_reset_vals(pr, chn);
if (pr->flags & BLKID_FL_NOSCAN_DEV)
return BLKID_PROBE_NONE;
if (pr->size <= 0 || (pr->size <= 1024 && !S_ISCHR(pr->mode)))
/* Ignore very very small block devices or regular files (e.g.
* extended partitions). Note that size of the UBI char devices
* is 1 byte */
return BLKID_PROBE_NONE;
DBG(LOWPROBE, ul_debug("--> starting probing loop [SUBLKS idx=%d]",
chn->idx));
i = chn->idx < 0 ? 0 : chn->idx + 1U;
for ( ; i < ARRAY_SIZE(idinfos); i++) {
const struct blkid_idinfo *id;
const struct blkid_idmag *mag = NULL;
blkid_loff_t off = 0;
chn->idx = i;
id = idinfos[i];
if (chn->fltr && blkid_bmp_get_item(chn->fltr, i)) {
DBG(LOWPROBE, ul_debug("filter out: %s", id->name));
rc = BLKID_PROBE_NONE;
continue;
}
if (id->minsz && id->minsz > pr->size) {
rc = BLKID_PROBE_NONE;
continue; /* the device is too small */
}
/* don't probe for RAIDs, swap or journal on CD/DVDs */
if ((id->usage & (BLKID_USAGE_RAID | BLKID_USAGE_OTHER)) &&
blkid_probe_is_cdrom(pr)) {
rc = BLKID_PROBE_NONE;
continue;
}
/* don't probe for RAIDs on floppies */
if ((id->usage & BLKID_USAGE_RAID) && blkid_probe_is_tiny(pr)) {
rc = BLKID_PROBE_NONE;
continue;
}
DBG(LOWPROBE, ul_debug("[%zd] %s:", i, id->name));
rc = blkid_probe_get_idmag(pr, id, &off, &mag);
if (rc < 0)
break;
if (rc != BLKID_PROBE_OK)
continue;
/* final check by probing function */
if (id->probefunc) {
DBG(LOWPROBE, ul_debug("\tcall probefunc()"));
rc = id->probefunc(pr, mag);
if (rc != BLKID_PROBE_OK) {
blkid_probe_chain_reset_vals(pr, chn);
if (rc < 0)
break;
continue;
}
}
/* all cheks passed */
if (chn->flags & BLKID_SUBLKS_TYPE)
rc = blkid_probe_set_value(pr, "TYPE",
(unsigned char *) id->name,
strlen(id->name) + 1);
if (!rc)
rc = blkid_probe_set_usage(pr, id->usage);
if (!rc && mag)
rc = blkid_probe_set_magic(pr, off, mag->len,
(unsigned char *) mag->magic);
if (rc) {
blkid_probe_chain_reset_vals(pr, chn);
DBG(LOWPROBE, ul_debug("failed to set result -- ignore"));
continue;
}
DBG(LOWPROBE, ul_debug("<-- leaving probing loop (type=%s) [SUBLKS idx=%d]",
id->name, chn->idx));
return BLKID_PROBE_OK;
}
DBG(LOWPROBE, ul_debug("<-- leaving probing loop (failed=%d) [SUBLKS idx=%d]",
rc, chn->idx));
return rc;
}
/*
* This is the same function as blkid_do_probe(), but returns only one result
* (cannot be used in while()) and checks for ambivalen results (more
* filesystems on the device) -- in such case returns -2.
*
* The function does not check for filesystems when a RAID or crypto signature
* is detected. The function also does not check for collision between RAIDs
* and crypto devices. The first detected RAID or crypto device is returned.
*
* The function does not probe for ambivalent results on very small devices
* (e.g. floppies), on small devices the first detected filesystem is returned.
*/
static int superblocks_safeprobe(blkid_probe pr, struct blkid_chain *chn)
{
struct blkid_prval vals[BLKID_NVALS_SUBLKS];
int nvals = BLKID_NVALS_SUBLKS;
int idx = -1;
int count = 0;
int intol = 0;
int rc;
if (pr->flags & BLKID_FL_NOSCAN_DEV)
return BLKID_PROBE_NONE;
while ((rc = superblocks_probe(pr, chn)) == 0) {
if (blkid_probe_is_tiny(pr) && !count)
return BLKID_PROBE_OK; /* floppy or so -- returns the first result. */
count++;
if (chn->idx >= 0 &&
idinfos[chn->idx]->usage & (BLKID_USAGE_RAID | BLKID_USAGE_CRYPTO))
break;
if (chn->idx >= 0 &&
!(idinfos[chn->idx]->flags & BLKID_IDINFO_TOLERANT))
intol++;
if (count == 1) {
/* save the first result */
nvals = blkid_probe_chain_copy_vals(pr, chn, vals, nvals);
idx = chn->idx;
}
}
if (rc < 0)
return rc; /* error */
if (count > 1 && intol) {
DBG(LOWPROBE, ul_debug("ERROR: superblocks chain: "
"ambivalent result detected (%d filesystems)!",
count));
return -2; /* error, ambivalent result (more FS) */
}
if (!count)
return BLKID_PROBE_NONE;
if (idx != -1) {
/* restore the first result */
blkid_probe_chain_reset_vals(pr, chn);
blkid_probe_append_vals(pr, vals, nvals);
chn->idx = idx;
}
/*
* The RAID device could be partitioned. The problem are RAID1 devices
* where the partition table is visible from underlaying devices. We
* have to ignore such partition tables.
*/
if (chn->idx >= 0 && idinfos[chn->idx]->usage & BLKID_USAGE_RAID)
pr->prob_flags |= BLKID_PROBE_FL_IGNORE_PT;
return BLKID_PROBE_OK;
}
int blkid_probe_set_version(blkid_probe pr, const char *version)
{
struct blkid_chain *chn = blkid_probe_get_chain(pr);
if (chn->flags & BLKID_SUBLKS_VERSION)
return blkid_probe_set_value(pr, "VERSION",
(unsigned char *) version, strlen(version) + 1);
return 0;
}
int blkid_probe_sprintf_version(blkid_probe pr, const char *fmt, ...)
{
struct blkid_chain *chn = blkid_probe_get_chain(pr);
int rc = 0;
if (chn->flags & BLKID_SUBLKS_VERSION) {
va_list ap;
va_start(ap, fmt);
rc = blkid_probe_vsprintf_value(pr, "VERSION", fmt, ap);
va_end(ap);
}
return rc;
}
static int blkid_probe_set_usage(blkid_probe pr, int usage)
{
struct blkid_chain *chn = blkid_probe_get_chain(pr);
char *u = NULL;
if (!(chn->flags & BLKID_SUBLKS_USAGE))
return 0;
if (usage & BLKID_USAGE_FILESYSTEM)
u = "filesystem";
else if (usage & BLKID_USAGE_RAID)
u = "raid";
else if (usage & BLKID_USAGE_CRYPTO)
u = "crypto";
else if (usage & BLKID_USAGE_OTHER)
u = "other";
else
u = "unknown";
return blkid_probe_set_value(pr, "USAGE", (unsigned char *) u, strlen(u) + 1);
}
int blkid_probe_set_id_label(blkid_probe pr, const char *name,
unsigned char *data, size_t len)
{
struct blkid_chain *chn = blkid_probe_get_chain(pr);
struct blkid_prval *v;
if (!(chn->flags & BLKID_SUBLKS_LABEL))
return 0;
v = blkid_probe_assign_value(pr, name);
if (!v)
return -1;
if (len >= BLKID_PROBVAL_BUFSIZ)
len = BLKID_PROBVAL_BUFSIZ - 1; /* make a space for \0 */
memcpy(v->data, data, len);
v->data[len] = '\0';
/* remove white spaces */
v->len = blkid_rtrim_whitespace(v->data) + 1;
if (v->len > 1)
v->len = blkid_ltrim_whitespace(v->data) + 1;
if (v->len <= 1)
blkid_probe_reset_last_value(pr); /* ignore empty */
return 0;
}
int blkid_probe_set_label(blkid_probe pr, unsigned char *label, size_t len)
{
struct blkid_chain *chn = blkid_probe_get_chain(pr);
struct blkid_prval *v;
if (len > BLKID_PROBVAL_BUFSIZ)
len = BLKID_PROBVAL_BUFSIZ;
if ((chn->flags & BLKID_SUBLKS_LABELRAW) &&
blkid_probe_set_value(pr, "LABEL_RAW", label, len) < 0)
return -1;
if (!(chn->flags & BLKID_SUBLKS_LABEL))
return 0;
v = blkid_probe_assign_value(pr, "LABEL");
if (!v)
return -1;
if (len == BLKID_PROBVAL_BUFSIZ)
len--; /* make a space for \0 */
memcpy(v->data, label, len);
v->data[len] = '\0';
v->len = blkid_rtrim_whitespace(v->data) + 1;
if (v->len == 1)
blkid_probe_reset_last_value(pr);
return 0;
}
int blkid_probe_set_utf8label(blkid_probe pr, unsigned char *label,
size_t len, int enc)
{
struct blkid_chain *chn = blkid_probe_get_chain(pr);
struct blkid_prval *v;
if ((chn->flags & BLKID_SUBLKS_LABELRAW) &&
blkid_probe_set_value(pr, "LABEL_RAW", label, len) < 0)
return -1;
if (!(chn->flags & BLKID_SUBLKS_LABEL))
return 0;
v = blkid_probe_assign_value(pr, "LABEL");
if (!v)
return -1;
blkid_encode_to_utf8(enc, v->data, sizeof(v->data), label, len);
v->len = blkid_rtrim_whitespace(v->data) + 1;
if (v->len == 1)
blkid_probe_reset_last_value(pr);
return 0;
}
int blkid_probe_sprintf_uuid(blkid_probe pr, unsigned char *uuid,
size_t len, const char *fmt, ...)
{
struct blkid_chain *chn = blkid_probe_get_chain(pr);
int rc = -1;
va_list ap;
if (len > BLKID_PROBVAL_BUFSIZ)
len = BLKID_PROBVAL_BUFSIZ;
if (blkid_uuid_is_empty(uuid, len))
return 0;
if ((chn->flags & BLKID_SUBLKS_UUIDRAW) &&
blkid_probe_set_value(pr, "UUID_RAW", uuid, len) < 0)
return -1;
if (!(chn->flags & BLKID_SUBLKS_UUID))
return 0;
va_start(ap, fmt);
rc = blkid_probe_vsprintf_value(pr, "UUID", fmt, ap);
va_end(ap);
/* convert to lower case (..be paranoid) */
if (!rc) {
size_t i;
struct blkid_prval *v = __blkid_probe_get_value(pr,
blkid_probe_numof_values(pr));
if (v) {
for (i = 0; i < v->len; i++)
if (v->data[i] >= 'A' && v->data[i] <= 'F')
v->data[i] = (v->data[i] - 'A') + 'a';
}
}
return rc;
}
/* function to set UUIDs that are in suberblocks stored as strings */
int blkid_probe_strncpy_uuid(blkid_probe pr, unsigned char *str, size_t len)
{
struct blkid_chain *chn = blkid_probe_get_chain(pr);
struct blkid_prval *v;
if (str == NULL || *str == '\0')
return -1;
if (!len)
len = strlen((char *) str);
if (len > BLKID_PROBVAL_BUFSIZ)
len = BLKID_PROBVAL_BUFSIZ;
if ((chn->flags & BLKID_SUBLKS_UUIDRAW) &&
blkid_probe_set_value(pr, "UUID_RAW", str, len) < 0)
return -1;
if (!(chn->flags & BLKID_SUBLKS_UUID))
return 0;
v = blkid_probe_assign_value(pr, "UUID");
if (v) {
if (len == BLKID_PROBVAL_BUFSIZ)
len--; /* make a space for \0 */
memcpy((char *) v->data, str, len);
v->data[len] = '\0';
v->len = len + 1;
return 0;
}
return -1;
}
/* default _set_uuid function to set DCE UUIDs */
int blkid_probe_set_uuid_as(blkid_probe pr, unsigned char *uuid, const char *name)
{
struct blkid_chain *chn = blkid_probe_get_chain(pr);
struct blkid_prval *v;
if (blkid_uuid_is_empty(uuid, 16))
return 0;
if (!name) {
if ((chn->flags & BLKID_SUBLKS_UUIDRAW) &&
blkid_probe_set_value(pr, "UUID_RAW", uuid, 16) < 0)
return -1;
if (!(chn->flags & BLKID_SUBLKS_UUID))
return 0;
v = blkid_probe_assign_value(pr, "UUID");
} else
v = blkid_probe_assign_value(pr, name);
blkid_unparse_uuid(uuid, (char *) v->data, sizeof(v->data));
v->len = 37;
return 0;
}
int blkid_probe_set_uuid(blkid_probe pr, unsigned char *uuid)
{
return blkid_probe_set_uuid_as(pr, uuid, NULL);
}
/**
* blkid_probe_set_request:
* @pr: probe
* @flags: BLKID_PROBREQ_* (deprecated) or BLKID_SUBLKS_* flags
*
* Returns: 0 on success, or -1 in case of error.
*
* Deprecated: Use blkid_probe_set_superblocks_flags().
*/
int blkid_probe_set_request(blkid_probe pr, int flags)
{
return blkid_probe_set_superblocks_flags(pr, flags);
}
/**
* blkid_probe_reset_filter:
* @pr: prober
*
* Returns: 0 on success, or -1 in case of error.
*
* Deprecated: Use blkid_probe_reset_superblocks_filter().
*/
int blkid_probe_reset_filter(blkid_probe pr)
{
return __blkid_probe_reset_filter(pr, BLKID_CHAIN_SUBLKS);
}
/**
* blkid_probe_invert_filter:
* @pr: prober
*
* Returns: 0 on success, or -1 in case of error.
*
* Deprecated: Use blkid_probe_invert_superblocks_filter().
*/
int blkid_probe_invert_filter(blkid_probe pr)
{
return __blkid_probe_invert_filter(pr, BLKID_CHAIN_SUBLKS);
}
/**
* blkid_probe_filter_types
* @pr: prober
* @flag: filter BLKID_FLTR_{NOTIN,ONLYIN} flag
* @names: NULL terminated array of probing function names (e.g. "vfat").
*
* Returns: 0 on success, or -1 in case of error.
*
* Deprecated: Use blkid_probe_filter_superblocks_types().
*/
int blkid_probe_filter_types(blkid_probe pr, int flag, char *names[])
{
return __blkid_probe_filter_types(pr, BLKID_CHAIN_SUBLKS, flag, names);
}
/**
* blkid_probe_filter_usage
* @pr: prober
* @flag: filter BLKID_FLTR_{NOTIN,ONLYIN} flag
* @usage: BLKID_USAGE_* flags
*
* Returns: 0 on success, or -1 in case of error.
*
* Deprecated: Use blkid_probe_filter_superblocks_usage().
*/
int blkid_probe_filter_usage(blkid_probe pr, int flag, int usage)
{
return blkid_probe_filter_superblocks_usage(pr, flag, usage);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 410 |
{"url":"https:\/\/www.studysmarter.us\/textbooks\/physics\/physics-for-scientists-and-engineers-a-strategic-approach-with-modern-physics-4th\/traveling-waves\/q-45-figure-p1645-is-a-history-graph-at-x-0-m-of-a-wave-trav\/","text":"Suggested languages for you:\n\nQ. 45\n\nExpert-verified\nFound in: Page 452\n\n### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics\n\nBook edition 4th\nAuthor(s) Randall D. Knight\nPages 1240 pages\nISBN 9780133942651\n\n# FIGURE P16.45 is a history graph at x = 0 m of a wave traveling in the positive x-direction at 4.0 m\/s. a. What is the wavelength? b. What is the phase constant of the wave? c. Write the displacement equation for this wave.\n\na. The wavelength of the wave is .\n\nb. The phase constant of the wave is .\n\nc. The displacement of the wave is .\n\nSee the step by step solution\n\n## Given information\n\nA history graph at x = 0 m of a wave traveling in the positive x-direction is shown below\n\n## Part a\n\nFrom the history graph, it can be observed that and .\n\nThe wavelength of the wave is given by .\n\nSubstitute the given values\n\nTherefore, the wavelength of the wave is .\n\n## Part b\n\nA phase constant can be obtained by .\n\nSubstitute the given values\n\nTherefore, the phase constant of the wave is .\n\n## Part c\n\nThe equation of the displacement of the wave is given by .\n\nSubstitute the given values\n\nTherefore, the displacement equation for this wave is .","date":"2022-12-01 07:46:23","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\": 0.8637042045593262, \"perplexity\": 1209.4720182633896}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710801.42\/warc\/CC-MAIN-20221201053355-20221201083355-00049.warc.gz\"}"} | null | null |
REACHING A MEDICAL EMERGENCY IN RAPID TIME CAN BE THE DIFFERENCE BETWEEN LIFE AND DEATH. THAT'S WHERE YOUR LOCAL AIR AMBULANCE COMES IN.
WNAA was launched in 2003 followed by DLRAA in 2008 expanding our services to fly patients over 5 counties. Our two helicopters provide a rapid response to trauma and medical emergencies over an area of 3850 square miles covering many of the UK's major road networks including the M1, M6, M69 and M42.
With an average response of just 13 minutes, between them, our aircrafts attend on average 6 missions a day between the hours of 7am – 5pm. Our Critical Care Cars then work throughout the night attending medical emergencies that occur within these regions creating a service that operates 24/7, 365 days a year.
If you're local, you may well have seen us in the skies above you. What many people don't realise when seeing our air ambulances or visiting our shops is that we're a non-government funded charity, so we're only able to continue with our services because of generous donations.
Fundraising: There are so many ways to fundraise, whether it's through cake sales, swap shops or even the marathons. Any donations raised, no matter how big or small means we can keep our services going. Find out more about the fundraising opportunities here.
Shop with Us: We're proud of our stores, one is even award-winning because we care about the stock we receive. From quality homeware to pre-loved clothes, when you purchase from us you're supporting our services as well as getting something in return. Discover your nearest shop here and pop in to see what we have to offer.
Volunteer: We wouldn't be where we are today without the dedication and time given by our incredible volunteers. Giving time to help raise awareness of our charity is something that we always need. Whether it's some of your time weekly or once a month, whatever you can give can make the world of difference to what we do here at The Air Ambulance Service.
Donate: Donations are what we need more than anything and there are so many ways you can do this. Giving clothes to keep our shops stocked, dropping spare change into one of our many collection points or simply donating online, everything helps to keep us flying. To find out where and how your donations go to help us save lives, read more here.
Whether you're an ongoing supporter of or thinking of choosing us as your charity to support, thank you on behalf of all us at The Air Ambulance Service. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,564 |
BAND OF HEATHENS
THE DOUBLE DOWN- LIVE IN DENVER VOL 1 & 2
This Austin, Texas based six-piece is at its best live as evidenced by the fact that this two disc set noses its live release count ahead of its studio output. On this broad ranging set recorded over the course of two consecutive nights, the band jumps from rock to blues to country to rootsy Americana with a great mix of tunes that sound familiar yet are all originals. "You're Gonna Miss Me" kicks off disc one with a loose limbed jam that recalls Little Feat and even the Spin Doctors with its funky guitar and keyboard grooves. "Somebody Tell the Truth" travels the same path with a long guitar solo evoking the Dead. "Golden Calf" shows another side of the band entirely with its foreboding, mysterious feel. "Say" starts out like a slice of pop but then morphs into Americana and features some earnest vocals that recall any number of rock anthems. "Let Your Heart Not Be Troubled" and "What's This World" feature the band in Eagles territory with rich harmonies, earnest sentiments and a Southern California country vibe while "LA County Blues" gets closer to the soaring richness of the Jayhawks which is achieved again on the introspective "Nothing to See Here" that starts acoustic and lean and builds into a rocking wall of sound. "Right Here With Me" and "Should Have Known" lope along at an unhurried pace but with a sinewy groove that would fit well on a JJ Grey & Mofro disc. Disc two features shorter tracks with slashing guitar that recalls Exile era Stones, "Jackson Station" and "I Ain't Running", southern soul rock, "Talking out Loud" and "The Other Broadway", atmospheric rock that would fit neatly on a Mark Knopfler solo disc, "Judas 'Scariot Blues", acoustic powered jams, "Nine Steps Down", organ-drenched gospel, "Shine a Light", and a swampy ode to the "Second Line" that could have been laid down by the Subdudes. "Gris Gris Satchel" sounds straight out of the Band's early catalog while the military cadence of "Free Again" is an ironic counter-point to the lyrics. Even though the material on this sprawling set is wide-ranging the band effortlessly negotiates all the twists and turns with glorious vocal harmonies and stellar instrumental interplay. Flat out terrific, this is American roots rock at its best. Smitty
all reviews | all rock reviews
More reviews tagged #Rock
K. D. LANG
House of Spirits
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No Cites Left
AARON FREEMAN
Marvelous Clouds
Everything But the Girl
Adapt or Die - Ten Years of Remixes
THE VOLEBEATS | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,145 |
\chapter{The fluid/gravity correspondence}
\copyrightline{Chapter of the book \textit{Black Holes in Higher Dimensions} to
be published by Cambridge University Press (editor: G. Horowitz)}
\contributor{Veronika E Hubeny \affiliation{Durham Univeristy}}
\contributor{Shiraz Minwalla \affiliation{Tata Institute of Fundamental Research}}
\contributor{Mukund Rangamani\affiliation{Durham Univeristy}}
\section{Introduction}
\label{s:intro}
In this chapter we will study a particular long wavelength limit of
Einstein's equations with a negative cosmological constant in $d+1$ dimensions.
In such a limit we find that Einstein's equations reduce to the equations of fluid dynamics
(relativistic generalizations of the famous Navier-Stokes equations) in
$d$ dimensions. While the motivation for our study lies within the AdS/CFT correspondence of string theory, the fluid/gravity correspondence stands on its own and can be viewed as a map between two classic dynamical systems.
\subsection{Prelude: CFT stress tensor dynamics from gravity }
\label{s:prelude}
An important consequence of the AdS/CFT correspondence [Ch.AdSCFT] is that the dynamics of the stress(-energy-momentum) tensor in a large class of $d$-dimensional strongly coupled quantum field theories is governed by the dynamics of Einstein's equations with negative cosmological constant in $d+1$ dimensions. To begin with, we shall try to provide the reader with some intuition for this statement and argue that searching for a tractable corner of this connection leads one naturally to the fluid/gravity correspondence.
In its most familiar example, the AdS/CFT correspondence [Ch.AdSCFT]
asserts that $SU(N)$ ${\cal N}=4$ Super Yang-Mills (SYM) theory is dual to Type IIB string theory on AdS$_5 \times {\bf S}^5$. It has long been known that in the 't Hooft limit,
which involves taking $N\to \infty$ keeping the coupling $\lambda$ fixed, the gauge theory becomes effectively classical. However, it was widely believed that for any non-trivial gauge theory the resulting classical system would be too complicated to be tractable. The remarkable observation of Maldacena in 1997 was that this field theory intuition is spectacularly wrong. Indeed, not only is the classical system governing ${\cal N}=4$ SYM tractable, it is actually a well known theory, viz., classical Type IIB string theory.
Now, even classically, string theory has complicated dynamics; however in the strong gauge coupling ($\lambda \to \infty$) regime, it reduces to the dynamics of Type IIB supergravity (by decoupling the massive string states). More interestingly, Type IIB supergravity on AdS$_5\times {\bf S}^5$ admits several consistent truncations. The simplest and most universal of these is the truncation to Einstein's equations with negative
cosmological constant,
\begin{equation}\label{Eeq}
E_{\mu\nu} \equiv R_{\mu\nu} - \frac{1}{2} \, R \, g_{\mu\nu} + \Lambda \, g_{\mu\nu} =0 \ , \qquad \Lambda \equiv -\frac{d \, (d-1)}{2\, R_\text{AdS}^2} \ .
\end{equation}
(Note that the AdS curvature radius $R_\text{AdS}$ can be scaled away by a change of units ; we therefore set $R_\text{AdS}$ to unity in the rest of this chapter). Having thus motivated the study of the most beautiful equation of physics, namely Einstein's equations of general relativity, we now confront the question: What does this imply for the field theory?
Recall that according to the AdS/CFT dictionary there is a one-to-one map between single particle states in the classical Hilbert space of string theory and single-trace operators in the gauge theory. For instance the bulk graviton maps to the stress tensor of the boundary theory. Taking the collection of such single trace operators as a whole, one can try to formulate dynamical equations for their quantum expectation values in the field theory. While this can be done in principle, the resulting system is non-local in terms of the intrinsic field theory variables themselves.
However, because we can associate the quantum operators (and their expectation values) of the gauge theory at strong coupling to the classical fields of string theory/supergravity, we know that the set of classical equations we are looking for are just the local equations of Type IIB supergravity on AdS$_5 \times {\bf S}^5$. This reduction, whilst retaining lots of interesting physics, still turns out to be too complicated from the field theory perspective. For one, the space of single trace operators is still infinite dimensional (at infinite $N$), and relatedly attempting to classify the solution space of Type IIB supergravity is a challenging problem. However, the fact that on the string side we can reduce the system to \eqref{Eeq}, implies that there is a decoupled sector of stress tensor dynamics in ${\cal N}=4$ SYM at large $\lambda$.\footnote{While this is always true in two dimensional field theories, such a decoupling is not generic in higher dimensional field theories (in fact it is not true of ${\cal N}=4$ Yang Mills at weak coupling), and is in itself a surprising and interesting
fact about the ${\cal N}=4$ dynamics at strong coupling. }
Actually, there is an infinite number of conformal gauge theories which have a gravitational dual that truncates consistently at the two-derivative level to Einstein's equations with a negative cosmological constant; ${\cal N}=4$ SYM theory is just a particularly simple member of this class. Thus \eqref{Eeq} describes the {\it universal decoupled} dynamics of the stress tensor for an infinite number of different gauge theories. In the first part of this chapter
we will focus on the study of this universal sector. Later we will generalize to the
study of bulk equations with more fields, thereby obtaining richer dynamics at the expense of universality.
Given this association between the dynamics of quantum field theory stress tensors to the dynamics of gravity in negatively curved backgrounds, it is natural to ask -- can we do more? Can we for instance classify all possible behaviors of stress tensors? On the gravity side we would have to classify all possible solutions to \eqref{Eeq}; this is a laudable goal and various chapters in this book are aimed at addressing this question using different approaches. We are going to focus on one that naturally follows from the basic organizing principle of physics: separation of scales.
It is well known that in many situations in physics (as well as chemistry, biology, etc.),
complicated UV dynamics results in relatively simple IR dynamics. Perhaps the first systematic exposition of this ubiquitous fact was in the context of finite temperature physics. It has been known for almost 200 years now that the dynamics of nearly equilibrated systems at high enough temperature may be described by an effective theory called hydrodynamics.
The key dynamical equation of hydrodynamics is the conservation of the stress tensor
\begin{equation}
\nabla_{\! a} \, T^{ab} = 0 \ ,
\label{Tcons}
\end{equation}
where $\nabla_{\! a}$ is the covariant derivative compatible with the background metric $\gamma_{ab}$ on which this fluid lives. As this equation is an autonomous dynamical system involving just the stress tensor, it should lie within the sector of universal decoupled stress tensor dynamics.
Given that the AdS/CFT correspondence asserts that this universal sector
is governed by \eqref{Eeq}, we are led to conclude that
\eqref{Eeq} must, in an appropriate high temperature
and long distance limit which we refer to as the {\it long wavelength regime}, reduce to the equations of $d$-dimensional hydrodynamics. Indeed, this expectation has been independently verified in
\cite{Bhattacharyya:2008jc} and the resulting map between gravity and
fluid dynamics has come to be known as the {\it fluid/gravity correspondence}. In particular, the specific fluid
dynamical equations, dual to long wavelength gravity in the universal sector, have been determined up to the second order in a gradient expansion (cf.\ \S\ref{s:sten2}). Given any solution to the
these fluid dynamical equations, the fluid/gravity map {\it explicitly} determines
a solution to Einstein's equations \eqref{Eeq} to the appropriate
order in the derivative expansion. The solutions in gravity are simply inhomogeneous, time-dependent black holes, with slowly varying but otherwise generic horizon profiles.
The main focus of the present chapter is to explain and present the fluid/gravity map at the full non-linear level following \cite{Bhattacharyya:2008jc} and subsequent work.
The connection between these two systems was established and extensively studied
much earlier at the linearized level in the AdS/CFT context (following the seminal work
\cite{Policastro:2001yc}). The first hints of the connection between fluid dynamics and gravity at the non-linear level were obtained in attempts to construct non-linear solutions dual to a particular boost invariant flow \cite{Janik:2005zt}, which provided inspiration for the fluid/gravity map. Such a map was also suggested by the observation that the properties of large
rotating black holes in global AdS space are reproduced by the equations
of non-linear fluid dynamics \cite{Bhattacharyya:2007vs}. We refer the reader to \cite{Rangamani:2009xk} for a list of developments and references.
\subsection{Preview of the fluid/gravity correspondence}
\label{s:ipreview}
Having provided the reader with a broad, albeit abstract, rationale to associate the dynamics of Einstein's equations to that of a quantum field theoretic stress tensor, we now provide some specifics that set the stage for our discussion.
According to the gauge/gravity dictionary, distinct asymptotically AdS bulk geometries correspond to distinct states in the boundary gauge theory.
The pure AdS geometry, i.e., the maximally symmetric negatively curved spacetime, corresponds to the vacuum state of the gauge theory. A large\footnote{
Recall that AdS is a space of constant negative curvature, which introduces a length scale, called the AdS scale $R_{\rm AdS}$, corresponding to the radius of curvature.
The black hole size is then measured in terms of this AdS scale; large black holes have horizon radius $r_+ > R_{\rm AdS}$. We will be focus on the large black hole limit $r_+ \gg R_{\rm AdS}$, and therefore consider the {\it planar} Schwarzschild-AdS black holes.
} Schwarzschild-AdS black hole corresponds to a thermal density matrix in the gauge theory. This can be easily conceptualized in terms of the late-time configuration a generic state evolves to: in the bulk, the combined effect of gravity and negative curvature tends to make a generic configuration collapse to form a black hole which settles down to the Schwarzschild-AdS geometry, while in the field theory, a generic excitation will eventually thermalize.
Note that although the underlying theory is supersymmetric, the correspondence applies robustly to non-supersymmetric states such as the black holes mentioned above. In this sense, supersymmetry is {\it not} needed for the correspondence.
On the boundary, the essential physical properties of the gauge theory state (such as local energy density, pressure, temperature, entropy current, etc.) are captured by the expectation value of the {\it boundary stress tensor}, which in the bulk is related to normalizable metric perturbations about a given state. It can be extracted via a well-defined Brown-York type procedure \cite{Balasubramanian:1999re} as we review later (see \eqref{BYstress}).
At the risk of being repetitive we urge the reader to note the distinction between the two separate stress tensors that will enter our analysis. In our framework, the {\it bulk}\ stress tensor appearing on the r.h.s.\ of the bulk Einstein's equation is zero if we are only interested in the universal sub-sector discussed above. On the other hand, the {\it boundary} stress tensor $T^{ab}$ is non-zero; it is a measure of the normalizable fall off of the bulk metric at the boundary. Note that the boundary stress tensor does not
curve the boundary spacetime \`a la Einstein's equations since the boundary metric $\gamma_{ab}$ is non-dynamical and fixed. We will discuss generalizations that allow for non-trivial bulk matter in \S\ref{s:extensions} when we move outside the universal stress tensor sector.
To describe gravity duals of fluid flows, a useful starting point is the map between the boundary and bulk dynamics in global thermal equilibrium. In the field theory, one characterizes thermal equilibrium by a choice of static frame and a temperature field. On the gravity side, the natural candidates to characterize the equilibrium solution are static (or more generally stationary) black hole spacetimes, as can be seen by demanding regular solutions with periodic Euclidean time circle. The temperature of the fluid is given by the Hawking temperature of the black hole, while the fluid dynamical velocity is captured by the horizon boost velocity of the black hole. For planar Schwarzschild-AdS black holes the temperature grows linearly with horizon size; the AdS asymptotics thus ensures thermodynamic stability as well as providing a natural long wavelength regime.
Now let us try to gently move away from the equilibrium configuration.
Starting with the stationary black hole (namely the boosted planar Schwarzschild-AdS$_{d+1}$) solution, we wish to use it to build solutions where the fluid dynamical temperature and velocity are slowly-varying functions of the boundary directions. Intuitively, this mimics patching together pieces of black holes with slightly different temperatures and boosts in a smooth way so as to get a regular solution of \eqref{Eeq}. In order to obtain a true solution of Einstein's equations, the patching up procedure cannot be done arbitrarily; one is required at the leading order to constrain the velocity and temperature fields to obey the equations of ideal fluid dynamics.\footnote{These constraints are actually the radial momentum constraints for gravity in AdS and imply \eqref{Tcons}. In contrast to the conventional ADM decomposition, we imagine foliating the spacetime with timelike leaves and `evolve' into the AdS bulk radially.} Further, the solution itself is corrected order
by order in a derivative expansion, a process that likewise corrects the fluid equations. All these steps may be implemented\footnote{In the technical implementation of this program, it is important that one respect boundary conditions. We require that the
bulk metric asymptote to $\gamma_{ab}$ (up to a conformal factor) and further be manifestly regular in the part of the spacetime outside of any event horizon.} in detail in a systematic boundary gradient expansion. The final output is
a map between solutions to negative cosmological constant gravity and
the equations of fluid dynamics in one lower dimension, i.e.
the fluid/gravity map.
A noteworthy aspect of this construction is that Einstein's equations become tractable due to the long wavelength regime without losing non-linearity. From the boundary standpoint, one encounters domains of nearly constant fluid variables; these domains can then be extended radially from the boundary into the bulk and in each such bulk `tube', illustrated in Figure \ref{PDtube}, we are guaranteed to have a solution which is close to the equilibrium form. Lest the reader be led astray, we should note that the solutions we construct are perturbative and hence approximate.
Nevertheless, they are `generic' slowly-varying asymptotically-AdS black hole geometries, with no Killing fields.
\begin{figure}[h!]
\begin{center}
\includegraphics[scale=0.55]{Sads_penD}
\hspace{1.5cm}
\includegraphics[scale=0.29]{tubes}
\end{center}
\caption{Penrose diagram of the uniform planar black hole (\ref{sads1}) and the causal structure of the spacetimes dual to fluid dynamics illustrating the tube structure. Dashed line in the second figure denotes the future event horizon, while the shaded tube indicates the region of spacetime over which the solution is well approximated by a corresponding uniform black hole.}
\label{PDtube}
\end{figure}
A remarkable outcome of the association between generic black holes and fluid flows is that it automatically provides a sensible entropy current with non-negative divergence for hydrodynamics. On the gravitational side, entropy is naturally associated to the area of the event horizon; by pulling back this area form to the boundary, we can equip our fluid with a canonical entropy current.
We now turn to the technical aspects of the fluid/gravity map. Following a review of fluid dynamics and the perturbative construction of gravitational solutions, we finally present the main results (in particular the bulk metric and the boundary stress tensor, to second order in boundary derivatives) in \S\ref{s:secord}. The subsequent sections are devoted to describing some implications and extensions of the basic construction.
\section{Relativistic fluid dynamics}
\label{s:fd}
To set the stage, let us start by reviewing fluid dynamics, explicating the use of gradient expansion as an organizational principle.
At high temperatures every non-trivial quantum field theory (and every
experimentally realizable system) equilibrates into a fluid phase, i.e.,
a translationally invariant phase in which adiabatic displacement of
neighboring elements requires no force.
Weakly interacting fluids are composed of
a collection of a large number of
long lived partonic excitations which continually collide with each other.
The time and space intervals between successive collisions of a given
parton are called the mean free time, $t_{\rm m}$, and the mean free length, $\ell_{\rm m}$,
respectively.\footnote{
In a relativistic system of massless particles, like
${\cal N}=4$ SYM, $t_{\rm m} \sim \ell_{\rm m}$. We will assume this is the case
in our discussions below.} Such fluids are
characterized by a parton density function in phase space, and the
time evolution of this function is governed by the well known
Boltzmann transport equations of statistical physics. These equations have
an interesting property: arbitrary initial density functions
relax to local thermal
equilibrium over a time scale of order the mean free time. In other words, for $t \gg t_{\rm m}$, the parton distribution in
momentum space approximately reduces, at every point $x$, to an
equilibrium distribution. However the parameters\footnote{
For simplicity, in this discussion we assume that the system has
no conserved charges other than the stress-energy-momentum tensor, and no other
Goldstone-like light degrees of freedom. We discuss generalizations
below.}
characterizing this equilibrium configuration, the
temperature field $T(x)$ and fluid velocity field $u^a(x)$, vary on a length scale that is large compared to
$\ell_{\rm m}$. $T(x)$ and $u^a(x)$ are the effective dynamical variables of
the system at later times; their evolution as a function of time is governed
by the equations of fluid dynamics.
Now it turns out that the equations of fluid dynamics
may also be derived in a much simpler and more general
manner, and so apply even at strong coupling.
The main assumption that underlies fluid
dynamics is that systems always equilibrate locally over a finite
time scale that we continue to refer to as $t_{\rm m}$. While this assumption is
true of the Boltzmann transport equations, it is believed to hold more
generally also for strongly coupled fluids. It follows immediately
that $T(x)$ and $u^a(x)$ are the effective variables for dynamics at length
and time scales large compared to $\ell_{\rm m}$ and $t_{\rm m}$. As we will now see,
the equations of fluid dynamics follow inevitably out of this conclusion.
\subsection{The equations of fluid dynamics and constitutive relations}
The stress tensor in any $d$-dimensional quantum field theory on a background with metric $\gamma_{ab}$ obeys the $d$ conservation equations
\begin{equation}
\nabla_{\! a} T^{ab}=0.
\label{stc}
\end{equation}
These equations do not constitute a well defined initial value problem
for the stress tensor in general as, in $d \geq 2$, we have more variables
(the $\frac{1}{2}\, d(d+1)$ independent components of the
stress tensor) than equations.\footnote{
For the special case of conformal field theories the number of variables is reduced by one, as the trace of the stress tensor vanishes. In this case, at $d=2$, we have as many variables as equations. This observation underlies the special simplicity of CFTs in $d=2$.}
In the fluid dynamical limit, however, the stress tensor is determined as a
function of $d$ variables, $T(x)$ and $u^a(x)$. Consequently,
\eqref{stc}, supplemented with a formula for $T^{ab}$ as a function
of thermodynamical fields, constitute a complete set of dynamical
equations. These are the equations of fluid dynamics.
A constitutive relation that expresses $T^{ab}$ as a function of $T(x)$, $u^a(x)$,
and their derivatives turns \eqref{stc} into a concrete set of fluid dynamical
equations. In thermal equilibrium the stress tensor $T^{ab}$
is given by
\begin{equation} \label{Teq}
T^{ab}= \left( P + \rho \right)\, u^a \, u^b + P\, \gamma^{ab}
\end{equation}
where $P$ is the pressure of the fluid and $\rho$ is its energy density. Recall
that both $\rho$ and $P$ are known functions of temperature
(determined by the thermodynamic equation of state of the fluid).
For a fluid in {\it local} thermal equilibrium,
\eqref{Teq} generalizes to
\begin{equation} \label{const}
T^{ab}(x)= \left[ P(x) + \rho(x) \right] u^a(x) \, u^b(x)
+ P(x) \, \gamma^{ab} + \Pi^{ab}(x)
\end{equation}
where $P(x)=P(T(x))$, $\rho(x)=\rho(T(x))$ and
$\Pi^{ab}(x)$ represents the contributions of derivatives of $T(x)$
and $u^a(x)$ to the stress tensor. This dissipative part $\Pi^{ab}$ may then be
expanded as
\begin{equation}\label{pexp}
\Pi^{ab}= \sum_{n=1}^\infty \ell_{\rm m}^n \, \Pi_{(n)}^{ab}
\end{equation}
where $\Pi_{(n)}^{ab}$ is defined to be of $n^{\rm th}$ order in derivatives of the
fluid dynamical fields. Note that magnitude of $\Pi_{(n)}^{ab}$
relative to the ideal fluid stress tensor is approximately $(\ell_{\rm m}/L)^n$
where $L$ characterizes the length scale of
variation of the temperature and velocity fields; consequently terms at
higher values of $n$ are increasingly subdominant in the fluid dynamical limit.
The explicit form of the functions $\Pi_{(n)}^{ab}$ can only be
derived from a detailed study of the dynamics of the specific system. However
the allowed forms for constitutive relations are significantly constrained
by symmetry and other general considerations. At first order, for instance,
it is possible to assert on very general grounds that
%
\begin{equation}\label{constraints}
\begin{split}
\Pi_{(1)}^{\langle a b \rangle} \equiv
P^a_{\ c}\, P^b_{\ d}\, \Pi_{(1)}^{c d} - \frac{1}{d-1}\,P^{ab}\, P_{cd}\, \Pi_{(1)}^{cd} &
= -2\,\eta\, \sigma^{ab} \\
\frac{1}{d-1}\, \Pi_{(1)}^{ab} P_{ab} - \frac{\partial P}{\partial\rho} \, ( u_a \,u_b \,\Pi_{(1)}^{ab})& = - \zeta \, \theta
\end{split}
\end{equation}
where
\begin{equation}\label{pdef}
P^{ab} \equiv u^{a}u^{b} + \gamma^{ab}
\end{equation}
is the projector onto space in the local fluid rest frame,
\begin{equation}
\label{E:sigmadef}
\sigma^{ab} =
\nabla^{\langle a } \, u^{ b \rangle}
\equiv
P^{a c}\, P^{b d}\,
\left( \nabla_{\! (c} \, u_{d)} - \frac{1}{d-1}\,
P_{c d} \,\theta\right)
\end{equation}
is the fluid shear tensor, $\theta \equiv \nabla_{\! c} \, u^c $ is the expansion, and the brackets around the indices ${\langle a b \rangle}$ denote the symmetric transverse traceless part of the expression. Here $\eta$ and $\zeta$ are arbitrary functions of the temperature, referred to as the shear and bulk viscosity, respectively.
The equation \eqref{constraints} is a physically complete specification of the
constitutive relations at first order, even though it leaves $P_{\ c}^a \, \Pi_{(1)}^{c d} \, u_d$ and one linear combination of
$\Pi_{(1)}^{ab}\, P_{ab}$ and $u_a\, u_b\, \Pi_{(1)}^{ab}$ unspecified.
This is because $T(x)$ and $u^a(x)$ have no intrinsic
definition out of equilibrium. All equations of fluid dynamics must be `field
redefinition invariant' (invariant under redefinitions of $T(x)$ and $u^a(x)$
that reduce to identity in equilibrium), and it turns out that the l.h.s.\ of
\eqref{constraints} are the only field redefinition invariant data
in $\Pi_{(1)}^{ab}$. The other components of $\Pi_{(1)}^{ab}$ can be modified at
will by an appropriate field redefinition, and have no physical significance.
The r.h.s.\ of the two equations in \eqref{constraints} represent the most general
inequivalent `tensor' and `scalar' data that can be constructed
from a single derivative of fluid dynamical fields compatible with the conservation equation at first order which imply that $u^a \, \nabla_{\! a} \, T\propto \theta$.
It is sometimes convenient to fix the field redefinition ambiguity by
giving the fields $u^a(x)$ and $T(x)$ unambiguous (but arbitrary) meaning.
In the so-called `Landau Frame' this is achieved by asserting that, at each
point,
\begin{equation}\label{landauframe}
T^{a}_{\ b}(x) \, u^b(x) = -\rho(x) \, u^a(x) \ .
\end{equation}
This relation defines $u^a$ by identifying it with the unique timelike
eigenvector of the stress tensor at any point, and defines the temperature
by identifying the corresponding eigenvalue with the energy density.%
\footnote{
Note that the equations \eqref{landauframe} are true in
equilibrium.}
In the Landau frame, which we adopt for most of this chapter, \eqref{constraints} simplify to
\begin{equation}\label{constn}
\Pi_{(1)}^{ab}= -2\, \eta \,\sigma^{ab} -\zeta \, \theta \, P^{a b} \ .
\end{equation}
As the equations of fluid dynamics are both local and
thermodynamical in nature, they must respect a local form of the second law of thermodynamics. It follows that the equations
of fluid dynamics must be accompanied by an entropy current whose divergence
is pointwise non-negative in every conceivable fluid flow. At first order, for a charge-free fluid, the constraints imposed by this requirement are a
relatively mild set of inequalities on $\eta$ and $\zeta$:
It turns out that the entropy current is constrained to take the form
\begin{equation}\label{canent}
J_s^a = s \,u^{a} - \frac{1}{T}\; u_{b} \,\Pi_{(1)}^{a b} \,,
\end{equation}
where $s$ is the entropy density. It is possible to demonstrate that
the current in \eqref{canent} is field redefinition invariant to first
order. Note that the second term on the r.h.s.\ of \eqref{canent} vanishes in the Landau frame. Using the Euler relation ($\rho+P=s \, T$) and the Gibbs-Duhem relation ($dP=s \, dT$) of thermodynamics along with the equations of motion, it follows that the divergence of this entropy current is given by
\begin{equation}\label{diventcan}
\nabla_{\! a} J_s^a = -\nabla_{a} \left( \frac{u_{b}}{T} \right) \Pi_{(1)}^{a b} \,.
\end{equation}
Using \eqref{constraints} (or more simply \eqref{constn} in the Landau frame),
it is easy to verify that positivity of the entropy current requires that
$\eta \geq 0$ and $\zeta \geq 0$. At higher orders in the derivative expansion
(for uncharged fluids) and even at first order for more complicated fluids
(e.g.\ charged fluids and superfluids) the requirement of positivity of the
entropy current imposes more than a set of inequalities on transport
coefficients; it forces linear combinations of otherwise
arbitrary transport coefficients to vanish \cite{Bhattacharya:2011tr}.
In the rest of this chapter we will be especially interested in the fluid
dynamics of conformal field theories. These theories enjoy three key
simplifications. First, as they have no dimensionless parameters, the
dependence of all physical quantities (e.g.\ $P$, $\rho$, $\eta$) on temperature
follows on dimensional grounds. In particular,
\begin{equation}
P=\alpha\, T^d, ~~~\rho=(d-1)\, \alpha \, T^d, ~~~\eta= \eta' \, T^{d-1}
\label{cftPetc}
\end{equation}
where $\alpha$ and $\eta'$ are dimensionless constants.
Second, the stress tensor in any CFT is necessarily traceless. It in particular follows from this condition that $\zeta=0$. Finally, the stress tensor in such theories must transform
covariantly under Weyl transformations. This imposes additional restrictions
on the stress tensor at higher orders in the derivative expansion. In summary,
for a conformal fluid, the stress tensor up to first order has the form
\begin{equation}\label{ft}
T^{ab}= \alpha\, T^{d} \left(d \, u^a u^b + \gamma^{ab} \right)
- \eta' \, T^{d-1} \sigma^{ab}
\end{equation}
where $\alpha$ and $\eta'$ are pure numbers and $\eta' \geq 0$.
The constraints on allowed forms of the constitutive relations at higher order are more complicated. The most general allowed equations of second order fluid dynamics have largely (but perhaps not completely) been worked out in \cite{Romatschke:2009kr}. In the
following we will determine the second order fluid equations for ${\cal N}=4$
Yang Mills at strong coupling using the fluid/gravity duality.
\subsection{The Navier-Stokes scaling limit}
\label{s:nsscale}
An interesting fact about the equations of relativistic (or any other
compressible) fluid dynamics is that they reduce to a universal form under
a combined low amplitude and long wavelength scaling.
Consider a uniform fluid at rest, perturbed so that the amplitude in velocity fluctuations
is small (scales like $\epsilon$) and the amplitude in temperature
fluctuations is smaller (scales like $\epsilon^2$). We also require that
the wavelength of spatial fluctuations is large (scales like $1/\epsilon$)
and that their temporal scale even larger (scales like $1/\epsilon^2$).
We then take the strict $\epsilon \to 0$ limit. In this limit:
\begin{itemize}
\item[1)] The fluid is non-relativistic, as all velocities are parametrically
smaller than the speed of light.
\item[2)] The fluid is incompressible, as all velocities are parametrically
smaller than the speed of sound (recall that a sound wave is a compression
wave, and that fluid flows at velocities smaller than the speed of sound
are effectively incompressible).
\item[3)] The temporal component of the energy conservation equations reduces,
at leading order ${\cal O}(\epsilon^2)$ to the continuity equation
${\vec \nabla} \cdot {\vec v}=0$. We use the symbol ${\vec v}$ for the non-relativistic spatial velocity.
\item[4)] The spatial component of the energy conservation equations
reduce at leading order, ${\cal O}(\epsilon^3)$, to the famous (non-relativistic) Navier-Stokes equations
\begin{equation}\label{ns}
{\dot {\vec v}} + {\vec v} \cdot { \vec \nabla } \, {\vec v}= -{\vec \nabla} P
+ \nu \, \nabla^2 {\vec v}
\end{equation}
with kinematic viscosity
$$\nu=\frac{\eta}{\rho_0 + P_0}.$$
where $\rho_0$ and $P_0$ are the background values of the density and
pressure of the fluid.
\end{itemize}
Note that the Navier-Stokes equations are homogeneous neither in amplitude of
fluctuations (the convective term is non-linear), nor in derivatives (the
viscous term is quadratic in derivatives). All terms retained in
\eqref{ns} are equally important in the $\epsilon \to 0$ limit; in particular, the parameter $\nu$ may be set to unity by a uniform rescaling of space and time. In contrast, the viscosities $\eta, \zeta$ give a subleading correction to ideal
fluid dynamics in the derivative expansion of relativistic fluid dynamics.
Taking the spatial divergence of \eqref{ns} one sees
that the pressure may be solved for in terms of the velocity field {\it on any
given time slice}; so the pressure is not an independent degree of freedom.
The initial data of the Navier-Stokes equations comprise just the components
of a divergence-free velocity field specified on any time slice. This reduction is not surprising
since the sound waves are being projected out in this limit.
The incompressible Navier-Stokes equations \eqref{ns} describe a wide
variety of sometimes extremely complicated phenomena like turbulence.
Despite the fact that these equations have been studied for almost 200 years,
their non-linear phenomenology remains rather poorly understood.
One of the hopes of the fluid/gravity correspondence is to shed a new (geometric) light on some of these issues.
\section{Perturbative construction of gravity solutions}
\label{s:pertthy}
We have seen that fluid dynamics can be treated systematically as the theory of long wavelength fluctuations about thermal equilibrium. We are now going to construct gravitational solutions dual to fluid flows by formalizing this intuition to set up an algorithmic procedure to construct slowly varying dynamical black hole spacetimes as solutions to \eqref{Eeq}.
\subsection{Global thermal equilibrium from gravity}
\label{s:}
The starting point from the gravitational perspective is a solution that corresponds to global thermal equilibrium. For the moment let us consider a conformal field theory on Minkowski space $\gamma_{ab} = \eta_{ab}$. From the gauge/gravity correspondence we know that the dual geometry in the bulk is the planar Schwarzschild-AdS$_{d+1}$ geometry, whose metric in static coordinates (with $x^a = \{t,y^i\}$) is given by
\begin{equation}
ds^2 = -r^2\, f(r/T) \, dt^2 + \frac{dr^2}{r^2\, f(r/T) }+ r^2\, \delta_{ij} \, dy^i\, dy^j \ , \qquad \
f(r) \equiv 1-\left(\frac{4\pi}{d\, r}\right)^d\!.
\label{sads1}
\end{equation}
This is a one-parameter family of solutions, parameterized in terms of the black hole temperature $T$, which determines the horizon radius, $r_+ \equiv \frac{4 \pi \, T}{d}$, where $f$ vanishes. It is easy to generate a $d$-parameter family of solutions by boosting (\ref{sads1}) along the translationally invariant spatial directions $y^i$, leading to a solution parameterized by a (normalized) timelike velocity field $u^a$. The parameters which characterize the bulk solution are precisely the basic hydrodynamical degrees of freedom, viz., temperature $T$ and velocity $u^a$
of the black hole. It is easy to see that the solution induces on the Minkowski boundary of the AdS$_{d+1}$ spacetime a stress tensor which precisely takes the ideal fluid form of \eqref{Teq} with thermodynamic parameters specified by \eqref{cftPetc}. The normalization constant $\alpha$ is fixed by the gravitational theory to be $\alpha = \frac{\pi^d}{16\pi\,G_N^{(d+1)}}$.
Consider this $d$-parameter family of boosted planar Schwarzschild-AdS$_{d+1}$ geometries, each of which holographically map to an ideal (conformal) fluid living on ${\bf R}^{d-1,1}$ (endowed with the Minkowski metric). This fluid is in global thermal equilibrium and one should be able to describe the long wavelength but arbitrary-amplitude fluctuations away from equilibrium via hydrodynamics. This class of fluctuations has a bulk geometric avatar; we now describe an algorithmic procedure that enables us to construct such asymptotically locally AdS$_{d+1}$ black hole geometries which are generically inhomogeneous and dynamical. This procedure crucially relies on the fact that hydrodynamics, as indeed any effective field theory, can be systematically studied in a gradient expansion.
\subsection{The perturbation theory}
\label{s:perthy}
We start by considering perturbations to the {\it seed} geometry characterizing equilibrium. Take the boosted planar Schwarzschild-AdS$_{d+1}$ spacetime (\ref{sads1}), for convenience rewritten in ingoing coordinates so as to remove the coordinate singularity on the horizon, and replace the parameters $u_a$ and $T$ by functions of the boundary coordinates $x^a$,
\begin{equation}
ds^2 =-2\,u_{a}(x)\,dx^{a} \,dr -r^2\, f\left( r/T(x) \right) \,
u_{a}(x) \, u_{b} (x) \, dx^{a}\, dx^{b} +
r^2\, P_{ab}(x) \, dx^{a} \, dx^{b} \ ,
\label{boostedg0}
\end{equation}
with $f(r)$ as specified in (\ref{sads1}) and $P_{ab}$ given by
(\ref{pdef}) with $\gamma_{ab}= \eta_{ab}$.
This metric, which we henceforth denote as $g^{(0)}_{\mu\nu}(T(x), u^a(x))$, is not a solution to Einstein's equations. It however has two felicitous features: (i) it is regular for all $r>0$ and (ii) if the functions $T(x)$ and $u^a(x)$ are chosen so as to have small derivatives, then it can be approximated in local domains by a corresponding boosted black hole solution.
These observations lead us to consider an iterative procedure to correct (\ref{boostedg0}) order by order in a gradient expansion.
We will find that we however cannot specify just any slowly varying $T(x)$ and $u^a(x)$ (recall that $x^a$ included the temporal direction).
A true solution to Einstein's equations is obtained only when the functions $T(x)$ and $u^a(x)$ in addition to being slowly varying satisfy a set of equations which happen to be precisely the conservation equations of fluid dynamics. Let us record that we have fixed gauge by setting $g_{rr}=0$ and $g_{ra}=-u_a$.
Since we want to keep track of the derivatives with respect to the boundary coordinates, it is useful to introduce a book-keeping parameter $\varepsilon$ and regard the variables of the problem as functions of rescaled boundary coordinates $\varepsilon x^a$. At the end of the day $\varepsilon$ may be set to unity. With this in mind, let us consider the corrections to the seed metric in a gradient expansion:
\begin{equation}
g_{\mu\nu} = \sum_{k=0}^\infty \, \varepsilon^k g^{(k)}_{\mu\nu}(T(\varepsilon x) ,u^a(\varepsilon x) ) \ ,
\ u^a = \sum_{k=0}^\infty \varepsilon^k u^{a\,(k)}(\varepsilon x) \ ,
\ T = \sum_{k=0}^\infty \varepsilon^k T^{(k)}(\varepsilon x)
\label{gbuexpn}
\end{equation}
where the correction pieces $g_{\mu\nu}^{(k)}$, $u^{a\,(k)}$ and $T^{(k)}$ are to be determined by solving Einstein's equations to the $k^{\rm th}$ order in the gradient expansion. The ansatz (\ref{gbuexpn}) should therefore be inserted into the Einstein's equations (\ref{Eeq}) and the result expanded in powers of $\varepsilon$.
Let us examine the resulting structure in abstraction first. For the sake of argument, assume that we have determined $g_{\mu\nu}^{(m)}$ for $m \leq n-1$ and $T^{(m)}$ and $u^{a\,(m)}$ for $m \leq n-2$. At order $\varepsilon^n$ one finds that Einstein's equations reduce to a set of {\em inhomogeneous linear differential equations} whose structure can be schematically written as
\begin{equation}
{\mathbb H} \left[g^{(0)}(T^{(0)}, u^{a\,(0)}) \right] \, g^{(n)} = \;s_n
\label{homoop}
\end{equation}
where we have dropped the spacetime indices for notational clarity
(c.f.,\ \cite{Bhattacharyya:2008jc,Rangamani:2009xk} for the explicit equations). Since each derivative with respect to $x^a$ is accompanied by a power of $\varepsilon$, it follows that the linear operator ${\mathbb H}$ is constructed purely from the data of the equilibrium Schwarzschild-AdS$_{d+1}$ geometry. This means that ${\mathbb H}$ is at most a second-order differential operator with respect to the radial variable $r$. Moreover, it has to be independent of $n$. Thus the perturbation theory in $\varepsilon$ is ultra-local in the boundary coordinates, implying that we can solve the equations of motion of the bulk spacetime point by point on the boundary!
On the right hand side of (\ref{homoop}) we collect all order $\varepsilon^{n}$ terms which do not have explicit radial derivatives into a source term $s_n$, which is then a complicated construct involving contributions from different orders in perturbation theory. It is a local expression of $(n-m)^{\rm th}$ order in boundary derivatives of $T^{(m)}$ and $u^{a\,(m)}$ for $m \leq n-1$, and ascertaining it is the most substantial part of the computation.
The reader may be puzzled by the following aspect of \eqref{homoop}: while we have $\frac{d(d+1)}{2}$ equations, we have only $\frac{d(d-1)}{2}$ variables after fixing the gauge redundancy. This implies that a subset of Einstein's equations has a distinguished status as constraint equations, while the remainder are the physical dynamical equations.
To understand this let us examine the differential equations (\ref{homoop}) by invoking the canonical split of our bulk coordinates $X^\mu = (r, x^a)$. The $E_{ra}$ equations are the momentum constraint equations for `evolution' in the radial direction.
These equations are special in several ways. To start with, they need only
be satisfied on a single $r$ slice; the `dynamical' equations ($E_{ab}$) then
ensure that they will be solved on every $r$ slice. For this reason, it is
consistent to study these equations just at the boundary, where they turn out
to reduce merely to the equations of conservation of the boundary stress
tensor
\begin{equation}
\nabla_a T_{(n-1)}^{\; a b}=0 \ .
\label{cst}
\end{equation}
(See \S\ref{s:sten2} for the definition of the boundary stress tensor.)
Note that at $n^{\rm th}$ order the equations \eqref{cst} depend only on the
boundary stress tensor built out of the spacetime metric at order $n-1$. This is because \eqref{cst} has an explicit boundary derivative which
carries its own effective power of $\varepsilon$. The net upshot is that
the unknown metric $g^{(n)}$ does not enter the equations \eqref{cst} at all
(the operator ${\mathbb H}$ in \eqref{homoop} vanishes for these solutions).
Hence, \eqref{cst} is instead a constraint on the solution already obtained
at one lower order in perturbation theory. As we will see below, the solution
for $g^{(n)}$ of the dynamical equations at each order in perturbation theory
is uniquely obtained in terms of the
previous order solution, and so, ultimately, in terms of the velocity
and temperature fields that enter the starting ansatz (the zeroth-order term
in perturbation theory). Consequently, \eqref{cst}
is an equation which constrains the starting velocity and temperature
fields, and turns out to be the equation of boundary fluid dynamics.
The remaining equations $E_{rr}$ (the `Hamiltonian constraint' for radial evolution) and $E_{ab}$ are dynamical equations with the operator ${\mathbb H}$ being a second order differential operator in $r$. Exploiting the spatial rotational symmetry of the seed solution, these equations can be decoupled and solved by quadratures,
\begin{equation}
g^{(n)} = {\rm particular} (s_n) + {\rm homogeneous}({\mathbb H}) \ .
\label{}
\end{equation}
A unique solution to the dynamical equations
is obtained upon specification of boundary conditions: normalizability at infinity and regularity in the interior for all $r > 0$. These turn out to specify the solution completely\footnote{Modulo the fact that the operator ${\mathbb H}$ has zero modes which are to be accounted for by re-definitions of the background values of $T$ and $u^a$.} and one ends up with a regular black hole geometry at each given order in the $\varepsilon$ expansion.
In summary, at any order in the perturbative expansion one solves the constraint
equations, enforcing fluid dynamical equations on the `initial' data. One then
solves for the corrected metric. This correction feeds into the constraint
equations giving corrected equations of fluid dynamics, and so on. The process
may be iterated to any desired order, thereby yielding
a systematic derivative expansion of the equations of fluid dynamics.
\section{Results at 2nd order}
\label{s:secord}
Having seen abstractly the iterative procedure which perturbatively corrects the seed metric to obtain a solution to Einstein's equations at arbitrary order in the gradient expansion, we now turn to the results of this construction (for now still considering only energy-momentum transport on the boundary). While our discussion so far has been restricted to the case of a flat boundary metric $\gamma_{ab} = \eta_{ab}$, the observation we made about the ultra-locality of the perturbation theory allows us to immediately generalize to slowly-varying curved boundary metrics. Given a metric $\gamma_{ab}$ on the boundary, we can exploit the freedom to pass over to a Gaussian normal coordinate chart about the point under consideration, and account for the curvatures which arise starting with the second order in the $\varepsilon$ expansion via the computation of appropriate source terms. We will therefore present the results below for this more general setting. Before we do so, we will take the opportunity to review a beautiful technical framework developed by \cite{Loganayagam:2008is} to simplify the results for conformal fluids.
\subsection{Weyl-covariant formalism}
\label{s:weylc}
The vacuum AdS$_{d+1}$ spacetime is dual to the vacuum state of a conformal field theory. If we are interested in the hydrodynamic description of the latter on a background manifold ${\cal B}_d$, then rather than focusing on the metric $\gamma_{ab}$ of this geometry, we can consider the conformal class of metrics $\left({\cal B}_d, {\cal C}\right)$. On this conformal class there is a natural derivative operator, defined through a Weyl connection, which efficiently keeps track of Weyl transformation properties of various operators. This is all the more natural in the context of fluid dynamics where there is a distinguished vector field, the velocity $u^a$, defined to be the (normalized) timelike eigenvector of the stress tensor.
Let us first start with local Weyl rescalings of the boundary metric which transforms homogeneously, i.e.,
\begin{equation}
\gamma_{ab} = e^{2\phi}\; \widetilde{\gamma}_{ab} \qquad \Leftrightarrow \qquad
\gamma^{ab} = e^{-2\phi}\;\widetilde{\gamma}^{ab} ,
\label{conftransf}
\end{equation}
We will call a tensor ${\cal Q}$ with components ${\cal Q}_{a_1 \cdots a_n}^{\ b_1 \cdots b_m}$ conformally covariant and of weight $w$ if it transforms homogeneously under Weyl rescalings of the metric, i.e., ${\cal Q} = e^{-w\,\phi} \, \widetilde{{\cal Q}}$ under (\ref{conftransf}).
The velocity field $u^a$ transforms as a weight $1$ tensor while the stress tensor $T^{ab}$ of a conformal fluid has weight $(d+2)$ in $d$-spacetime dimensions.
One defines a class of torsionless connections, called the Weyl connections, characterized by a connection one form ${\cal A}_a$, whose associated covariant derivative $\nabla^{\text{Weyl}}$ captures the fact that the metric transforms homogeneously under conformal transformations (with weight $-2$). In particular, for every metric in the conformal class ${\cal C}$,
\begin{equation}
\nabla^{\rm Weyl}_a \gamma_{bc} = 2 \, {\cal A}_a\, \gamma_{bc} \,.
\label{wcmet}
\end{equation}
Given this derivative structure, we can go ahead and define a Weyl covariant derivative ${\cal D}_a = \nabla^{\rm Weyl}_a + w \, {\cal A}_a$
which is metric compatible and whose action on tensors transforming homogeneously with weight $w$ (i.e., ${\cal Q}^{a\cdots}_{b \cdots} = e^{-w\, \phi} \, \widetilde{{\cal Q}}^{a\cdots}_{b \cdots}$) is given by
\begin{eqnarray}
{\cal D}_c {\cal Q}^{a\cdots}_{b \cdots} &\equiv& \nabla_c {\cal Q}^{a\cdots}_{b \cdots} + w\, {\cal A}_c\,{\cal Q}^{a\cdots}_{b \cdots}\nonumber \\
&& +\left( \gamma_{c d} \, {\cal A}^a - \delta^a_c \, {\cal A}_d - \delta^a_d \,{\cal A}_c\right) \, {\cal Q}^{d\cdots}_{b \cdots} + \cdots \nonumber \\
&&- \left( \gamma_{cb}\, {\cal A}^d - \delta^d_c \, {\cal A}_b - \delta^d_b \, {\cal A}_c\right) \, {\cal Q}^{a\cdots}_{d \cdots} -\cdots \ .
\label{weylcd}
\end{eqnarray}
The connection has been defined so that the Weyl covariant derivative of a conformally covariant tensor transforms homogeneously with the same weight as the tensor itself.
In hydrodynamics we will require that the Weyl covariant derivative of the fluid velocity be transverse and traceless,
\begin{equation}
u^a \, {\cal D}_a u^b = 0 \ , \qquad {\cal D}_a u^a = 0 \ ,
\label{}
\end{equation}
which enables one to uniquely determine the connection one-form ${\cal A}_a$ to be the distinguished vector field
\begin{equation}
{\cal A}_a= u^c\, \nabla_{\! c} \, u_a - \frac{1}{d-1} \, u_a
\, \nabla_{\!c} \, u^c = a_a - \frac{1}{d-1}\, \theta \, u_a \ ,
\label{cadef}
\end{equation}
built from the fluid velocity field.
One can rewrite the various quantities appearing in the gradient expansion of the stress
tensor in this Weyl covariant notation. For instance, at first order in derivatives, we have the shear and vorticity constructed from the velocity field:
\begin{equation}
\sigma^{ab} = {\cal D}^{(a} u^{b)} \ , \qquad
\omega^{ab} = -{\cal D}^{[a} u^{b]} \ ,
\label{udecdefs2}
\end{equation}
both of which have weight $w =3$. The fluid dynamical equations, viz., stress tensor conservation, are simply ${\cal D}_a \, T^{ab} = 0$ in this Weyl covariant language (which is equivalent to (\ref{stc}) since (\ref{weylcd}) with $w=d+2$ gives
${\cal D}_a \, T^{ab} = \nabla_{\!a}\, T^{ab} + T_a^{\ a} \, {\cal A}^b$ and the conformal fluid stress tensor must be traceless).
\subsection{Generic asymptotically AdS black hole metric}
\label{s:met2}
We now have at our disposal all the technical machinery necessary to present the results for the gravity dual of non-linear fluid dynamics. By a suitable choice of gauge (a slight generalization of the Eddington-Finkelstein coordinates), one can express the bulk metric $g_{\mu\nu}$ in the form
\begin{equation}
ds^2 = - 2 \, u_a(x) \, dx^a \,\left( dr + {\mathfrak V}_b(r,x)\,\,dx^b\right)+ {\mathfrak G}_{ab}(r,x) \, dx^a\, dx^b \ ,
\label{formmetw}
\end{equation}
where the fields ${\mathfrak V}_a$ and ${\mathfrak G}_{ab}$ are functions of $r$ and $x^a$ which admit an expansion in the boundary derivatives. In the parameterization used in \cite{Bhattacharyya:2008mz} one finds the metric functions are given up to second order in derivatives as:
\begin{equation}
\begin{aligned}
{\mathfrak V}_a & = r\, {\cal A}_a - {\cal S}_{ac}\,u^c - {\mathfrak v}_1(r/T)\, P^{\; b}_a\, {\cal D}_c \, \sigma^{c}_{\ b} \\
&\qquad +u_a \, \left[\frac{1}{2}\, r^2 \, f(r/T) + \frac{1}{4}\, \left(1-f(r/T)\right) \, \omega_{cd}\, \omega^{cd} + {\mathfrak v}_2(r/T) \, \frac{\sigma_{cd}\, \sigma^{cd}}{d-1}\right] \\
{\mathfrak G}_{ab} &= r^2\, P_{ab} - \omega_{a}^{\ c}\,\omega_{cb}+ 2\, (r/T)^2\, {\mathfrak g}_1(b\,r)\, \left[\frac{4\pi T}{d}\, \sigma_{ab} + {\mathfrak g}_1(r/T) \, \sigma_a^{\ c}\,\sigma_{cb} \right] \\
&\qquad - {\mathfrak g}_2(b\,r) \,\frac{\sigma_{cd}\, \sigma^{cd}}{d-1} \, P_{ab}
- {\mathfrak g}_3(r/T) \, \left[{\mathfrak T}_{1ab} + \frac{1}{2}\, {\mathfrak T}_{3ab} + 2\,{\mathfrak T}_{2ab} \right] \\
&\qquad + {\mathfrak g}_4(r/T)\, \left[{\mathfrak T}_{1ab} + {\mathfrak T}_{4ab} \right] .
\end{aligned}
\label{met2w}
\end{equation}
Here ${\cal S}_{ab} = \frac{1}{d-2}\left({\cal R}_{ab}-\frac{{\cal R} \, }{2(d-1)}\, \gamma_{ab}\right)$ is the Schouten tensor of the boundary metric, where
the Weyl covariant curvature tensors are
\begin{equation}
\begin{split}
{\cal R}_{ab} &= R_{ab} -(d-2)\left(\nabla_{\! a} \, {\cal A}_b + {\cal A}_a \, {\cal A}_b -{\cal A}^2 \, \gamma_{ab} \right)-g_{ab}\nabla_{\! c} \, {\cal A}^c - {\cal F}_{ab}\\
{\cal R} & \equiv {\cal R}_{a}^{\ a} = R -2\, (d-1) \, \nabla_{\! c} \, {\cal A}^c + (d-2)(d-1) \, {\cal A}^2 \
\end{split}
\label{ricEin:eq}
\end{equation}
with ${\cal F}_{ab} \equiv \nabla_{\! a} \, {\cal A}_b - \nabla_{\! b} \, {\cal A}_a $.
Apart from the shear and vorticity tensors (\ref{udecdefs2}) constructed from the fluid velocity, we also encounter four of the five second order tensors which form a Weyl covariant basis,
\begin{equation}
\begin{aligned}
&{\mathfrak T}_1^{ab} =2\, u^c \, {\cal D}_c \sigma^{ab} \ , \quad
{\mathfrak T}_2^{ab} = C^{acbd}\,u_c \,u_d \ , \\
&{\mathfrak T}_3^{ab} =4\,\sigma^{c\langle a}\, \sigma^{b\rangle}_{\ c} \ , \quad
{\mathfrak T}_4^{ab} = 2\, \sigma ^{c\langle a}\, \omega^{b\rangle}_{\ c} \ , \quad {\mathfrak T}_5^{ab}= \omega ^{c\langle a}\, \omega ^{b\rangle}_{\ c} \ .
\end{aligned}
\label{winv2der}
\end{equation}
Note that the tensor ${\mathfrak G}_{ab}$ is clearly transverse, since it is built out of operators that are orthogonal to the velocity, and it can be inverted via the relation
$\left({\mathfrak G}^{-1}\right)^{ac} \, {\mathfrak G}_{cb} = P^a_{\ b}\, $. The induced metric on the boundary in these coordinates takes the form:
\begin{equation}
\gamma_{ab} = \lim_{r\to \infty} \, \frac{1}{r^2} \, \left({\mathfrak G}_{ab} -2\, u_{(a}\, {\mathfrak V}_{b)} \right) ,
\label{bdymet2w}
\end{equation}
which is crucially used to raise and lower the boundary indices.
Finally, the various functions ${\mathfrak g}_{i}$ and ${\mathfrak v}_{i}$ appearing in the metric are given in terms of definite integrals once one has inverted the operator ${\mathbb H}$:
\begin{equation}
\begin{aligned}
{\mathfrak g}_1(y) &= \int_y^\infty\, d\zeta\, \frac{\zeta^{d-1}-1}{\zeta\, \left(\zeta^d -1\right)} \\
{\mathfrak g}_2(y) &= 2\,y^2 \, \int_y^\infty \frac{d\xi}{\xi^2} \int_\xi^\infty\, d\zeta\,\zeta^2 \, {\mathfrak g}_1'(\zeta)^2 \\
{\mathfrak g}_3(y) & =y^2 \, \int_y^\infty\, d\xi\, \frac{\xi^{d-2}-1}{\xi \, \left(\xi^d -1\right)} \\
{\mathfrak g}_4(y)& = y^2 \, \int_y^\infty\, \frac{d\xi}{\xi \, \left(\xi^d -1\right)}
\int_1^\xi\,d\zeta\, \zeta^{d-3}\bigg(1+ (d-1)\,\zeta\,{\mathfrak g}_1(\zeta) + 2\, \zeta^2\,{\mathfrak g}'_1(\zeta)\bigg) \\
{\mathfrak v}_1(y) &=\frac{2}{y^{d-2}} \, \int_y^\infty \, d\xi \; \xi^{d-1}\int_\xi^\infty\, d\zeta\, \frac{\zeta-1}{\zeta^3\, \left(\zeta^d-1\right)}\\
{\mathfrak v}_2(y) &= \frac{1}{2\, y^{d-2}} \, \int_y^\infty\; \frac{d\xi}{\xi^2}\,\bigg[1-\xi\,(\xi-1) \,{\mathfrak g}'_1(\xi) -2 \,(d-1)\,\xi^{d-1} \\
&\qquad + \left(2\, (d-1)\,\xi^d - (d-2)\right) \, \int_\xi^\infty\, d\zeta\, \zeta^2\,{\mathfrak g}'_1(\zeta)^2 \bigg] .
\end{aligned}
\label{fmetfnsw}
\end{equation}
The asymptotic behavior of these functions ${\mathfrak g}_i(r/T)$ and ${\mathfrak v}_i(r/T)$ is important for the stress tensor computation of \S\ref{s:sten2} and can be found in \cite{Bhattacharyya:2008mz}.
\subsection{Event horizon and entropy current}
\label{s:eventhor}
The metric (\ref{formmetw}), (\ref{met2w}) solves Einstein's equations to second order in the gradient expansion, provided the first order stress tensor
(which takes the form (\ref{ft}) with the coefficients extracted from the 1st order bulk metric, and given explicitly below in \S\ref{s:sten2}) satisfies the hydrodynamic conservation equations. While this already establishes a firm connection between solutions of Einstein's equations and those of fluid dynamics (in one lower dimension), it is imperative to establish that the bulk geometry we describe is regular everywhere outside the curvature singularity at $r=0$.
Although one can utilize the behavior of the metric functions and iteratively argue that the sources are regular order by order in perturbation theory, it is convenient to establish once and for all that what one has constructed is a black hole spacetime with a regular event horizon. Doing so involves ascertaining the location of the event horizon. A-priori, this sounds like a tall order, especially given that explicit solution is contingent on having solved the fluid equations. Moreover, as is well known, the event horizon is a teleological concept (it is the boundary of the past of future null infinity) whose determination requires knowing the entire future history of the spacetime. However, with one key assumption of late-time relaxation which is natural from fluid dynamics, it turns out to be possible to determine the location of the event horizon {\it locally} within our gradient expansion. Apart from showing regularity, this has the additional virtue of enabling us determine a natural entropy current for fluid dynamics \cite{Bhattacharyya:2008xc}.
Since generic flows of dissipative fluids tend to approach global equilibrium at late times, it follows that the corresponding event horizon has to approach the radial position determined by the local late-time temperature of the fluid. In particular, we look for a null co-dimension one surface given by the equation $S_{\cal H}(r,x) = r - r_{\cal H}(x)=0$ with the correct asymptotics.
The function $r_{\cal H}(x)$ should be parameterized within the gradient expansion $r_{\cal H}(x) = \frac{4 \pi \, T(x)}{d} + \sum_k \, \varepsilon^k \, r_{(k)}(x)$. The corrections $r_{(k)}(x)$ are determined by solving the null condition $g^{\mu\nu} \, \partial_\mu S_{\cal H} \, \partial_\nu S_{\cal H} =0$. The resulting equations are algebraic for $r_{(k)}$ and to second order in gradients one finds that, for the solution (\ref{formmetw})-(\ref{fmetfnsw}),
\begin{equation}
r_{\cal H}(x) = \frac{4 \pi \, T(x)}{d}+ \frac{d}{4 \pi \, T(x)}\, \left(\aleph_1 \, \sigma_{ab}\, \sigma^{ab} + \aleph_2 \, \omega_{ab}\, \omega^{ab} + \aleph_3\, {\cal R}\right)
\label{}
\end{equation}
with
\begin{equation}
\begin{aligned}
\aleph_1 &= \frac{2\,(d^2 +d-4)}{d^2\,(d-1)\,(d-2)} - \frac{2 \,{\mathfrak v}_2(1)}{d\,(d-1)}\\
\aleph_2 &= -\frac{d+2}{2\,d\,(d-2)} \ , \qquad \aleph_3 = -\frac{1}{d\,(d-1)\,(d-2)} \ .
\end{aligned}
\label{alephdef}
\end{equation}
This indeed establishes that the solutions we have constructed in \S\ref{s:met2} to 2nd order qualify to be called inhomogeneous, dynamical black holes.
Note that in general, beyond the leading order, the horizon position and generators are not simply given by the corresponding fluid temperature and velocity (for example, while the horizon generators must be vorticity-free, $\omega_{ab}$ need not vanish for the boundary fluid). In some sense, while the black hole horizon is distinguished in the bulk, physics appears simpler when expressed in terms of the fluid data living on the boundary.
Having determined the event horizon of the gravity solution, we immediately have access to an important hydrodynamic quantity, viz., the {\em entropy current}. For a black hole spacetime it is natural to view the area of the event horizon as an entropy {\it a la} Bekenstein-Hawking \cite{Bekenstein:1973ur,Hawking:1974sw}. In fact, by suitably foliating the event horizon with spatial slices (propagated forward by the null generator), we can equivalently talk about an area $(d-1)$-form $a_{\cal H}$ on these slices. Since we imagine the dual fluid living on the boundary of the spacetime, it is natural to pull-back this area form out to the boundary. A canonical choice is to pull-back along radially ingoing null geodesics \cite{Bhattacharyya:2008xc}, which is quite easy to implement for the metric (\ref{formmetw}), where the lines of $x^a = {\rm constant}$ are precisely such geodesics. We then have a $(d-1)$-form on the boundary which can be dualized to a one-form or equivalently a current $J^a_s$, which is the entropy current on the boundary. Not only does this definition agree with the equilibrium notion of entropy of the fluid, but also thanks to the area theorem of black hole horizons, we are immediately guaranteed that this current has manifest non-negative divergence as demanded by the second law. The hydrodynamic entropy current takes the general form
\begin{equation}
\begin{split}
\, J^a_s &= s\,u^a + \frac{s\, d^2}{(4 \pi \, T)^2} \, u^a \,\left(A_1 \,\sigma_{cd}\,\sigma^{cd}+A_2 \,\omega_{cd}\,\omega^{cd} +A_3 \,\mathcal{R}\,\right)\\
&\quad + \frac{s\, d^2}{(4 \pi \, T)^2} \,\left( B_1 \,{\cal D}_c \, \sigma^{ac} + B_2 \,{\cal D}_c \, \omega^{ac} \right) + \cdots
\end{split}
\label{ecurw}
\end{equation}
where $s$ is the entropy density and $A_{1,2,3}$, $B_{1,2}$ are a-priori arbitrary numerical coefficients. While ${\cal D}_a J^a_s \geq 0$ only demands that $B_1 +2 \,A_3 =0$, the gravity solution (\ref{formmetw}) fixes all the coefficients in (\ref{ecurw}) explicitly.
In particular, we obtain
\begin{equation}
\begin{split}
&s = \frac{1}{4\,G_N^{(d+1)}} \left(\frac{4\pi\, T}{d}\right)^{\! \! d-1} \ , \qquad
A_1 = \frac{2}{d^2}\, (d+2) -\left( \frac{1}{2}\, {\mathfrak g}_2(1) +\frac{ 2}{d}\, {\mathfrak v}_2(1)\right) ,\\
&A_2 = -\frac{1}{2\,d} \ , \qquad B_1 = -2 \, A_3 = \frac{2}{d\, (d-2)} \ , \qquad B_2 = \frac{1}{d-2} \ .
\end{split}
\label{sdengr}
\end{equation}
We should note here that there is an ambiguity in pulling back the area-form from the event horizon to the boundary, for one can supplement the pull-back map with a boundary diffeomorphism, which affects the coefficient $A_1$ above. Since this just relabels boundary points in the gradient expansion, one is tempted to think of this ambiguity as unphysical. However, it is rather curious that if one tries to pull-back the area form from quasi-local horizons one encounters a shifted value of $A_1$ \cite{Booth:2011qy}, which suggests that there is perhaps more to this ambiguity than meets the eye.
\subsection{Stress tensor of dissipative fluid}
\label{s:sten2}
Given an asymptotically locally AdS$_{d+1}$ metric, one can construct a quasi-local boundary tensor which is manifestly conserved and is associated with the stress-energy-momentum tensor of the conformal field theory \cite{Henningson:1998gx, Balasubramanian:1999re}. To perform the computation one regulates the bulk spacetime by introducing an explicit cut-off at $r = r_\infty$. The boundary stress tensor is given in terms of the extrinsic curvature $K_{ab}$ of this surface, defined in terms of its unit outward pointing normal $n^a$ as $
K_{ab} = \gamma_{ac}\, \nabla^c n_b$. In addition to the extrinsic curvature one also has contributions from the counter-terms necessary to obtain a finite boundary stress tensor. Denoting the curvatures of the boundary metric by $^\gamma \!R $ etc., this is given (to 2nd order) as
\begin{equation}
T_{ab} = \lim_{r_\infty \to \infty}\; \frac{-\,r_\infty^{d}}{8\pi \, G_N^{(d+1)}} \, \left[ K_{ab} - K \, \gamma_{ab} + (d-1)\, \gamma_{ab} - \frac{1}{d-2}\, \left( ^{\gamma}\!R_{ab} -\frac{1}{2}\, \, ^{\gamma}\!R \, \gamma_{ab}\right)\right]
\label{BYstress}
\end{equation}
For the gravity duals to fluid dynamics constructed in \S\ref{s:met2}, one finds that the boundary stress tensor takes the form \eqref{const} with the dissipative part, at the first and second order, given by this gravitational construction to be
\begin{eqnarray}
\Pi_{(1)}^{ab} &=& -2\, \eta\,\sigma^{ab} \nonumber \\
\Pi_{(2)}^{ab} &=& \tau_\pi\,\eta\, {\mathfrak T}_1^{ab} + \kappa\,{\mathfrak T}_2^{ab} + \lambda_1\, {\mathfrak T}_3^{ab} + \lambda_2\, {\mathfrak T}_4^{ab} + \lambda_3\, {\mathfrak T}_5^{ab} \ .
\label{fld2}
\end{eqnarray}
where the tensors ${\mathfrak T}_i^{ab}$ were defined earlier in (\ref{winv2der}). With the tensor structure determined, one is just left with fixing the six transport coefficients, $\eta$, $\tau_\pi$, $\kappa$, and $\lambda_i$ for $i = \{1,2, 3\}$, which completely characterizes the flow of a non-linear viscous fluid with a gravitational dual. The transport coefficients for conformal fluids in $d$-dimensional boundary turn out to be
\begin{equation}
\begin{aligned}
&\eta = \frac{1}{16 \pi\, G_N^{(d+1)}} \, \left(\frac{4\pi}{d}\, T\right)^{d-1}
\ , \\
&\tau_\pi = \frac{d}{4\pi\, T} \, \left[1 + \frac{1}{d}\, {\rm Harmonic}\left(\frac{2}{d} -1\right) \right] , \qquad \kappa = \frac{d}{2\pi\, (d- 2)} \,\frac{\eta}{T} \ , \\
& \lambda_1 = \frac{d}{8\pi}\, \frac{\eta}{T} \ , \qquad
\lambda_2 = \frac{1}{2\pi}\, \text{Harmonic}\left(\frac{2}{d} -1\right) \, \frac{\eta}{T}\ , \qquad \lambda_3=0 \ .
\end{aligned}
\label{transpgend}
\end{equation}
where ${\rm Harmonic}(x)$ is the harmonic number function. Setting $d=4$ in the above expressions and using the fact that $\text{Harmonic}(-\frac{1}{2}) = -2 \,\log(2)$ together with the replacement $\frac{1}{16\pi \, G_N^{(5)}} = \frac{1}{8\pi^2} \, N^2$, one can obtain the transport coefficients for $SU(N)$ ${\cal N}=4$ Super Yang-Mills theory \cite{Baier:2007ix,Bhattacharyya:2008jc}. This has been used for real data analysis from e.g.\ RHIC.
One immediate consequence of (\ref{transpgend}) and (\ref{sdengr}) is that our fluid saturates the famous bound on the viscosity to entropy density ratio, $\frac{\eta}{s} \ge \frac{1}{4\pi}$, \cite{Kovtun:2004de}. This bound is saturated by a large class of two-derivative theories of gravity, and it is indeed experimentally satisfied by all presently-known systems in nature. Intriguingly, cold atoms at unitarity and quark-gluon plasma both come near to saturating this bound \cite{Schafer:2009dj}. Its status in more general theories is currently under active debate \cite{Buchel:2008vz}.
Moreover, (\ref{transpgend}) reveals further intriguing relations between the coefficients, which hint at the specific nature of any conformal fluid which admits a gravitational dual.
For example, the result that $\lambda_3 = 0$ is universal but non-trivial from the fluid standpoint. We also see that $2 \, \eta \, \tau_\pi = 4 \lambda_1 + \lambda_2$ for all $d$; this in fact was shown to hold quite generally in a large class of two-derivative theories of gravity (including matter couplings) \cite{Haack:2008cp}.
\section{Specific fluid flows and their gravitational analog}
\label{s:applications}
The construction presented above can be generalized in many interesting ways; however before indicating the most important of these in \S\ref{s:extensions}, we first pause to discuss some of the special cases of the framework explained in the preceding section. One of the reasons to discuss these special cases is that while we have demonstrated the existence of a map from the equations governing fluid dynamics to those governing the dynamics of gravity, we did not at any stage solve the fluid equations explicitly. The felicitous feature of our construction was the ultra-locality along the boundary directions which allowed us to implement the construction in terms of local solutions to the conservation equations. Construction of novel fluid flows and generic behavior of the relativistic conservation equations are interesting (and perhaps hard) questions. Nevertheless there are some corners where we can gain analytic control which serves not only as a check that the fluid/gravity solution set is non-empty, but also provides a point of contact with previous studies of the hydrodynamic regime in the AdS/CFT literature.
\subsection{Linearized setting: quasinormal modes}
\label{s:}
Above we have established a map between any solution of the equations of
fluid dynamics and long wavelength solutions of Einstein gravity with a
negative cosmological constant. In order to find explicit
gravitational solutions we need a class of explicit solutions to the
equations of fluid dynamics. In this subsection and the next we will
study such examples.
It is of course easy to solve the equations of fluid dynamics, derived above,
when linearized about static equilibrium. Utilizing translational invariance,
we search for solutions of the form
$$u^a= \delta^a_t + \delta^a_j \, \delta v^j \, e^{i (\omega t + k^i y_i)} \,, \qquad T= T_0 + \delta T \,
e^{i (\omega t + k^i y_i)} \,,$$
with purely spatial velocity fluctuations $\delta v^j$. The resulting linear equations require that the matrix of coefficients $M(\omega, k)$ annihilate the length-$d$ column vector with entries $\delta v^i$ and $\delta T$. So the spectrum $\omega(k)$ is obtained as the roots of the $d^{\rm th}$ order polynomial $\text{det}(M)= 0$.
At leading (ideal fluid) order, the $d$
roots to this equation turn out to be $\omega = \pm \frac{k}{\sqrt{d-1}}$
(the sound modes of the fluid) and $\omega=0$ with degeneracy $d-2$
(the shear modes of the fluid). These modes and their corresponding
eigenvectors receive corrections at higher orders in the derivative
expansion; in particular the shear modes pick up nontrivial $k$
dependence, $\omega \propto i\,k^2$, at first order. The explicit
solutions are easily determined (see \cite{Bhattacharyya:2008jc}).
Employing the fluid/gravity map then yields explicit linearized
solutions of the Einstein equations \eqref{Eeq} about the planar black hole background, whose study in fact predates
the fluid/gravity map by almost 10 years.
The spectral problem of linearized fluctuations about a black hole solution is of course a well-studied topic (cf., \cite{Berti:2009kk}). It is known that due to the presence of a horizon, black holes admit no
normal modes. Instead, by imposing regularity at the future event horizon, one finds quasinormal modes, i.e., modes which have complex frequencies characterizing decay of perturbations at late times. Mathematically these are related to the poles of the retarded Green's function computed in the black hole background.
In terms of the gauge/gravity perspective, such quasinormal modes describe the timescale for return to thermal equilibrium in the field theory \cite{Horowitz:1999jd}. Asymptotically AdS black holes host an infinite family of
quasinormal modes.
All except $d$ of these are `massive';
their frequency remains finite (and has a finite imaginary part or decay
rate $\propto T$) even in the limit $k \to 0$. However, planar black holes admit exactly $d$ special `massless' quasinormal
modes. These so-called hydrodynamic modes can have arbitrarily low
frequency at long spatial wavelengths and therefore fall within the
long wavelength regime. These are precisely the
sound and shear modes described above.
The fact that the dispersion relations of the massless quasinormal modes agrees
with hydrodynamic dispersion relations was first demonstrated in the
pioneering works \cite{Policastro:2002se,Policastro:2002tn}, who mapped the Schwarzschild-AdS quasinormal modes to sound and shear modes of the dual field theory (perturbed from thermal equilibrium).
\subsection{Rotating black holes in global AdS space}
\label{s:}
A second class of examples which accord analytic control are explicit solutions corresponding to stationary configurations in hydrodynamics. While on flat space there are no interesting stationary flows other than a uniformly boosted fluid (whose dual is the seed solution we started with), it turns out that by a suitable choice of background geometry one can derive nontrivial flows. We now describe one such flow on the Einstein Static Universe (${\mathbb R} \times {\bf S}^{d-1}$) which allows one to make contact with rotating black holes in asymptotically (globally) AdS spacetimes.
Fluid flows of a conformal relativistic $d$-dimensional fluid on spatial ${\bf S}^{d-1}$ conserve angular momentum in addition to energy. The angular momentum on ${\bf S}^{d-1}$ is a rank-$d$ antisymmetric matrix, which can be brought to canonical form by an $SO(d)$
similarity transform (a rotation) and is therefore labeled by its $[d/2]$ inequivalent
eigenvalues. For every physically allowed choice of these $[d/2]$ angular momenta
together with the energy, an arbitrary fluid flow eventually settles down into an equilibrium stationary configuration.
The stationary configurations of viscous conformal fluids on spheres
turn out to be extremely simple. The velocity field is simply that of
a rigid rotation. Focusing on the case of $d=2n$ for concreteness,
the metric of a unit ${\bf S}^{2n-1}$ may be written in terms of the direction cosines $\mu_i$ as
\begin{equation}\label{metric}
ds_{{\bf S}^{2n-1}}^2=\sum_{i=1}^n \mu_i^2 \, d \phi_i^2 + d\mu_i^2 \ ,
\qquad {\rm where} \qquad \sum_{i=1}^n \mu_i^2=1 \,.
\end{equation}
In these coordinates the velocity and temperature
fields of stationary flows take the form
\begin{equation}\label{vf}
u_s^a \, \partial_a= \gamma \left( \partial_t + \sum_{i=1}^n \omega_i \,
\partial_{\phi_i} \right) \,, \quad
T_s = \gamma\, T_0\ , \quad \gamma = \left(1-\sum_{i=1}^m \omega_i^2 \mu_i^2\right)^{\! \! -\frac{1}{2}}
\end{equation}
This flow is Weyl equivalent to a uniform velocity and temperature configuration on a confomally rescaled spacetime \cite{Bhattacharyya:2007vs}, i.e.,
\begin{equation}\label{vfw}
ds^2=\gamma^{2}\, \left(-dt^2+ ds_{{\bf S}^{2n-1}}^2\right) , \quad
u_s^a \, \partial_a = \partial_t + \sum_{i=1}^n \omega_i
\partial_{\phi_i} \,, \quad
T_s = T_0 \ .
\end{equation}
It is not difficult to verify that \eqref{vfw} provides a non-dissipative solution to the equations of fluid dynamics at least
to second order (the solution is non-dissipative because it is stationary;
equivalently the divergence of the entropy current vanishes). The constant
parameters $\omega_i$ and $T_0$ of this solution turn out to have
thermodynamical significance: they are simply the angular velocity (chemical
potential for angular momentum) and temperature of the fluid configuration.
According to the AdS/CFT correspondence, the dual description of a
conformal field theory on ${\mathbb R} \times {\bf S}^{d-1}$ is simply asymptotically
global AdS$_{d+1}$ space. If we pump a large amount of energy and angular
momentum into global AdS$_{d+1}$ space and let the system relax, we expect
the eventual equilibrium configuration to be that of a large rotating black
hole. This reasoning leads to a prediction: the fluid/gravity map applied
to \eqref{vfw} should produce the (independently known) metric of large
rotating AdS$_{d+1}$ black hole, expanded to second order in the derivative
expansion. This prediction\footnote{
The first observation that the properties of large rotating black holes
should be reproduced from fluid dynamics was made in
\cite{Bhattacharyya:2007vs}, a precursor to the fluid/gravity map.
Rotating black holes were further studied in \cite{Bhattacharyya:2008ji}
in 4 dimensions, and fully analyzed in $d$ dimensions in
\cite{Bhattacharyya:2008mz}. Here for illustration we give the
general result of \cite{Bhattacharyya:2008mz}, who find the explicit
coordinate transformation to rewrite the rotating black hole solution
in AdS$_{d+1}$ of \cite{Gibbons:2004uw} in fluid variables.} has been verified in detail
in the following manner. It is possible to transform the exactly known
metric of the rotating AdS$_{d+1}$ black holes to the fluid/gravity gauge described in
\S\ref{s:pertthy} above. This maneuver in fact turns out
to greatly simplify the rotating black hole metric which takes the
form (\ref{formmetw}) with
\begin{eqnarray} \label{bhm}
{\mathfrak V}_a(r,x) & =& r\, {\cal A}_a - {\cal S}_{ac}\,u^c
- \frac{(4 \pi \, T)^d \, r^2 \, u_a}{2 \, d^2 \, \det \left[ r \,
\delta^{b}_{\ c} - \omega^{b}_{\ c} \right]} \ , \nonumber \\
{\mathfrak G}_{ab}(r,x) & =& r^2\, P_{ab} - \omega_{a}^{\ c}\,\omega_{cb} \ .
\label{KerrAdSmet}
\end{eqnarray}
The above is an exact rewriting of the rotating AdS black holes (in even dimensions) of \cite{Gibbons:2004uw}.
The metric \eqref{bhm} may be expanded in derivatives simply
by expanding the inverse determinant in powers of $\omega$. By truncating this expansion at second order we recover exactly the metric dual to the
fluid flow \eqref{vfw}. It is rather remarkable the full black hole solution can be written economically within the fluid/gravity metric ansatz, perhaps suggesting greater utility for metrics of the form \eqref{formmetw}.
\subsection{Non-relativistic fluids}
\label{s:nonrelfg}
While relativistic fluids are interesting in astrophysical or high energy plasma physics contexts, most fluids we encounter in everyday situations are non-relativistic. Furthermore, for many practical applications one is usually interested in their dynamics in the incompressible regime, which is attained by projecting out the sound mode. It is natural to ask whether this regime is accessible to fluid/gravity; an affirmative answer is suggested by the discussion in \S\ref{s:nsscale}, namely one only needs to implement the Navier-Stokes scaling limit directly in the fluid/gravity solutions. This procedure has been carried out in \cite{Bhattacharyya:2008kq} to obtain the gravitational dual of non-relativistic incompressible fluid flows. In principle this provides a geometric window to explore phenomenologically interesting fluid flows.
\section{Extensions beyond conformal fluids}
\label{s:extensions}
The fluid/gravity correspondence was originally derived for the case of conformal fluids which are related to gravitational dynamics in an asymptotically AdS spacetime. Conformal
theories are rather special and `ordinary' fluids one encounters everyday deviate significantly from this behavior. Hence it would be useful to look for extensions of the basic framework which allows for these generalizations. As already indicated earlier, this can be done at the expense of complicating the system of gravitational equations, and accompanying loss of universality. Nevertheless, forays into these areas have revealed very interesting lessons about fluid dynamics in general that transcend the fluid/gravity correspondence. In this section we take stock of some of these developments.
\subsection{Non-conformal fluids}
\label{s:nonconf}
The first generalization we consider is provided by a handy trick to obtain a particular class of non-conformal theories.
It turns out that by exploiting the gauge/gravity duality for a special class of theories, viz., theories that naturally arise on the world-volume of D$p$-branes, one finds a surprisingly tractable class of non-conformal fluids.
Let us first consider the special case of the D4-brane which is a solution of the equations of 10-dimensional IIA supergravity. IIA supergravity is the dimensional reduction of 11-dimensional supergravity on ${\bf S}^1$, and the D4-brane solution is the dimensional reduction of a M5 brane solution that wraps the ${\bf S}^1$. The near horizon
geometry of the M5 brane solution is AdS$_7 \times {\bf S}^4$, and the 11-dimensional equations admit a consistent truncation to 7-dimensional equations of motion \eqref{Eeq} involving gravitational dynamics with a negative cosmological constant. Compactifying further on an ${\bf S}^1$ and restricting to the zero momentum sector on this circle, yields a further consistent truncation of this
seven dimensional set of equations. The resulting 6-dimensional equations are simply the Einstein-dilaton equations about the D4-brane background. It follows that the Einstein-dilaton
equations constitute a consistent truncation of the equations of IIA
supergravity about the D4 near-horizon background (as is easily independently
verified).
It turns out that the fluid dynamics dual to the
long wavelength fluctuations about the thermal M5 brane solution is simply
that computed in \S\ref{s:pertthy}, for the special case $d=6$.
We want to focus on gravitational solutions corresponding to fluid flows independent of one of the boundary directions $x^i$ (the direction of the ${\bf S}^1$ in the paragraph above). These lie within the six dimensional consistent truncation described above. But these are simply the gravitational solutions dual to fluid flows on the world volume theory of the D4-brane. In other words, the fluid dynamics of the D4-brane world volume theory is a dimensional
reduction of the conformal fluid dynamics on the world volume of the M5 brane.
Moreover the gravitational duals to D4-brane fluid flows are very easily
obtained from the KK reduction of the results of \S\ref{s:pertthy}.
Note that the dimensional reduction of conformal fluid dynamics results in
non-conformal fluid dynamics (e.g. the dimensional reduction of a traceless
stress tensor generically has non-vanishing trace).
It is an interesting and surprising fact that the discussion of the previous
paragraph generalizes to D$p$-branes for all $p$ at the purely algebraic level.
In every case one can find a consistent truncation of the Einstein-dilaton
system which, in a purely formal manner, can be regarded as the reduction of
negative cosmological constant Einstein gravity in a higher
(sometimes fractional) dimension \cite{Kanitscheider:2009as}. This observation immediately yields the fluid descriptions of arbitrary D$p$-brane backgrounds as a dimensional reduction
of the conformal fluid dynamics derived in \S\ref{s:pertthy}.
\subsection{Theories with a deconfinement transition}
\label{s:plasma}
So far, we have studied the fluid dynamical description of field theories
that are `deconfined' at every temperature, i.e., the free energy is ${\cal O}(N^2)$. Consider, however, a theory
like pure Yang Mills at large $N$ which undergoes a first order deconfinement
phase transition at finite temperature. Such a system has a dual description
in terms of a black hole only above the deconfinement temperature; the
low temperature phase is given by a gas of glueballs, and is thermodynamically
indistinguishable from the vacuum at leading order in $N$ (free energy is ${\cal O}(1)$).
The Scherk-Schwarz reduction of ${\cal N}=4$ Yang Mills on a circle of radius $R$ (with
anti-periodic boundary conditions for fermions) is a simple
example of such a theory. At strong coupling this theory undergoes a
first order deconfinement transition at $T\, R= 2 \pi$. The gravity
dual of the high temperature phase is simply the ${\bf S}^1$ compactification of
the AdS$_5$ planar black hole. The gravity dual of the low temperature phase
is a so-called AdS-soliton (a double analytic continuation of the planar Schwarzschild-AdS black hole, in which the role of time and the ${\bf S}^1$ direction are interchanged).
At temperatures much higher than the phase transition, the effective 3-dimensional low
energy theory is simply the dimensional reduction of the 4-dimensional conformal fluid
system derived in earlier subsections (just as in \S\ref{s:nonconf}).
However, at the phase transition temperature we have a new phenomenon; there
exists a new static solution of the equations of motion, a co-dimension
one domain wall that interpolates between the AdS-soliton and the
${\bf S}^1$ compactification of the planar AdS$_5$ black hole. Unfortunately this
solution has been constructed only numerically \cite{Aharony:2005bm}. The domain wall is
static in these solutions because of a pressure balance on the two sides
(recall that the free energy, and hence the pressure, of the two phases are equal at a
phase transition temperature). This configuration is that of a fluid
with a boundary; the effective low energy fluctuations of this system
consist of boundary modes (like waves on the surface of water) in addition
to the bulk modes discussed so far in this chapter. At the ideal fluid
level the action for boundary degrees of freedom is captured by a single
parameter, the surface tension of the boundary (computed from the numerical solution).
Already using the ideal
fluid action including boundary terms, it has proved possible to construct
many stationary solutions of the fluid equations. These solutions, called
plasma-balls and plasma-rings, have dual descriptions as black holes, black
rings, and (in higher dimensions) black objects of more exotic topology \cite{Lahiri:2007ae}.
The effective action for surface degrees of freedom has not been worked out
at higher orders in the derivative expansion, and appears to be an
interesting exercise.
One particularly interesting static solution of the equations of ideal
fluid dynamics including boundary terms is the plasma-tube; a configuration
consisting of a domain wall that interpolates from the vacuum to the high
temperature phase at the phase transition temperature, followed by a second
parallel domain wall at separation $L$ that interpolates back to the vacuum.
Such a fluid configuration is the two dimensional analogue of a 3-dimensional
cylindrical tube of fluid, and is well known to undergo a famous fluid
dynamical instability (to droplet formation) called the Rayleigh instability.
For real fluids such as water, the endpoint of the Rayleigh instability is a
series of disconnected droplets. Now the gravitational dual of the plasma tube
is an infinitely long black string in 5-dimensional gravity. This solution has the
well known Gregory-Laflamme instability [Ch.GL] which, apparently, is dual to the
Rayleigh instability in the long wavelength limit. The boundary
dual of a series of disconnected droplets, on the other hand, is a series of
disconnected black holes. This discussion at least strongly suggests that
the end point of the Gregory-Laflamme instability consists of localized
black holes \cite{Cardoso:2006ks}. Note that the fluid description breaks down near the `pinch off' point; the actual description of topology change in this process requires
the use of the full field theory (e.g.\ details of interactions between water
molecules in the case of water).
\subsection{Charged fluids and anomalies}
\label{s:}
Under the AdS/CFT correspondence a global symmetry in the boundary maps to a
gauge symmetry in the bulk. This suggests that there should
be a duality between the long wavelength asymptotically AdS planar black hole
solutions of the Einstein-Maxwell theory (with negative cosmological constant) and the equations of charged fluid
dynamics. This is a useful extension as
fluids of interest in experimental situations conserve one or more
$U(1)$ charges in addition to energy and momentum. For instance, the flow
of air in the atmosphere conserves air molecule number.
It is conceptually straightforward to generalize the set-up of
section \S\ref{s:pertthy} to the study of locally thermalized charged planar black holes.
The starting point is the construction of spacetimes that tubewise approximate
Reissner-Nordstr\"om AdS black hole solutions with locally varying
temperature, chemical potential and velocity. A perturbation expansion
entirely analogous to the one outlined in \S\ref{s:pertthy} then constructs
the gravitational solutions to the Einstein-Maxwell-Chern-Simons theory
(which forms a consistent truncation of IIB supergravity on AdS$_5 \times
{\bf S}^5$) dual to charged fluid flows order by order in the derivative expansion \cite{Erdmenger:2008rm,Banerjee:2008th}. This procedure also determines the equations of charged fluid dynamics to order by order in the derivative expansion. The results of this analysis turned out to throw up a surprise purely from the viewpoint of charged first
order fluid dynamics, as we now explain.
The equations of charged fluid dynamics are the conservation of the charge
current
\begin{equation}\label{ccc}
\nabla_{\! a} \, J^a=0
\end{equation}
together with the conservation of the stress tensor \eqref{stc}.
Concrete fluid dynamical equations require constitutive relations that
express the field redefinition invariant parts of the stress tensor and
charge current in terms of expressions of first order in the derivative
of fluid fields. The charge current for charge density $q$ takes the form
\begin{equation}\label{ccf}
J^a= q \, u^a + J^a_{diss} \ ,
\end{equation}
where $J^a_{diss}$ represents the contribution of terms with one or more
derivatives of the fluid fields to the charge current, and is to be viewed as the
charge current analogue of $\Pi^{ab}$; similarly to \eqref{pexp} we
expand
\begin{equation}\label{jexp}
J^a_{diss}= \sum_{n=1}^\infty \ell_{\rm m}^n \, j_{(n)}^a \ .
\end{equation}
Standard textbook analyses assert that
the most general allowed form at first order for the constitutive relations
of a relativistic charged fluid are the first equation of \eqref{constraints} along with
\begin{equation}\label{consCan1}
P^a_{\ c}\,
\left( j^c_{(1)} + \frac{q}{\rho + P} (u_b \,\Pi_{(1)}^{bc}) \right) = \kappa \, V_1^a \ , \quad V_1^a\equiv -P^{ab} \nabla_{b}\frac{\mu}{T} + \frac{F^{ab}u_{b}}{T}
\end{equation}
while the second equation of \eqref{constraints} gets modified to
\begin{equation}\label{consCan2}
\frac{1}{d-1}\, \Pi_{(1)}^{ab} P_{ab} - \frac{\partial P}{\partial\rho} \, ( u_a \,u_b \,\Pi_{(1)}^{ab})+\frac{\partial P}{\partial q} (u_a j_{(1)}^a ) = - \beta \, \nabla_{\! c} \, u^c \ .
\end{equation}
In \eqref{consCan1} $F^{ab}$ is the non-dynamical background electromagnetic field that
couples to the $U(1)$ current $J^a$ in \eqref{ccc} and $\mu$ is the
chemical potential of the fluid. Provided that
$$ \eta \geq 0, ~~~ \kappa \geq 0, ~~~ \beta \geq 0 ,$$
these expressions are consistent with the positivity of divergence of
the fluid entropy current
\begin{equation}\label{canentc}
J_{can}^a = s \, u^{a} - \frac{1}{T} \, u_{b} \, \Pi_{(1)}^{ab} - \frac{\mu}{T} \, j^{a}_{(1)} \,,
\end{equation}
using the alleged relation
\begin{equation}\label{diventcanc}
\nabla_{a} J^a_{can} = -\nabla_{a} \left( \frac{u_{b}}{T} \right) \Pi_{(1)}^{ab}
- \left( \nabla_{a} \left( \frac{\mu}{T}\right) - \frac{F_{ab}u^{b}}{T}\right) j^{a}_{(1)}.
\end{equation}
However it was found by explicit computation that the fluid dual to
the asymptotically AdS-Einstein-Maxwell-Chern-Simons system has constitutive
relations that differ from those of \eqref{consCan1} in the following
fashion: the r.h.s.\ of \eqref{consCan1} includes new
terms proportional to fluid vorticity $\omega^a$ and rest frame magnetic field $B^a$ where
$$\omega^{a} =
\frac{1}{2}\epsilon^{ab c d} \, u_b \, \partial_{c} u_{d} \ , \qquad B^{a} = \frac{1}{2}\epsilon^{ab c d} \, u_b \, F_{cd}\ . $$
In a beautiful paper \cite{Son:2009tf} pointed out the reason for the
appearance of these new terms. When the $U(1)$ current
has a global $U(1)^3$ triangle anomaly (as is true of the field theory dual to a
bulk system with a 5-dimensional Chern-Simons term), \eqref{diventcanc} has an
additional term on its r.h.s.\ proportional to this anomaly. This term spoils
the positivity of the divergence of the canonical entropy current in the
presence of such a field. It is however consistent with the positivity
of the divergence of a modified entropy current provided that modifications
are also made to the r.h.s.\ of \eqref{consCan1}.
More concretely, positivity of the entropy current in every conceivable
circumstance requires that, in addition to the first equation of \eqref{constraints} and \eqref{consCan2},
\begin{equation}\label{conssSS}
\begin{split}
J^a_S&=J^a_{can}+ \sigma_{\omega} \, \omega^{a} + \sigma_B \, B^{a}\\
P^a_{\ c}\,
\left( j^c_{(1)} + \frac{q}{\rho + P} (u_b \,\Pi_{(1)}^{bc}) \right)
&= \kappa \, V_1^a + \tilde{\kappa}_{\omega} \, \omega^a
+\tilde{\kappa}_B \, B^a
\end{split}
\end{equation}
where
\begin{equation}\label{res}\begin{split}
\sigma_{\omega}&=c \, \frac{\mu^3}{3T} + T \, \mu \, k_2 + T^2 \, k_1\\
\sigma_B&=c \, \frac{\mu^2}{2T} + \frac{T}{2} \, k_2\\
\tilde{\kappa}_{\omega}&=c \left( \mu^2 -\frac{2}{3} \, \frac{q}{\rho +P} \, \mu^3 \right) + T^2 \left(1-\frac{2q}{\rho +P} \, \mu \right) k_2 - \frac{2q}{\rho +P} \, k_1 \\
\tilde{\kappa}_{B}&=c\left( \mu -\frac{1}{2} \, \frac{q}{\rho_n+P} \, \mu^2 \right) - \frac{T^2}{2}\frac{q}{\rho+P} \, k_2 \\
\end{split}
\end{equation}
and $k_1$ and $k_2$ are integration constants. Further imposition of CPT invariance forces $k_2$ to vanish.
This explanation accounts for the additional transport coefficients
in the AdS/CFT duality, but applies more generally to every fluid flow
with a $U(1)^3$ anomaly. The effect of these new transport coefficients may
well turn out to have experimentally measurable effects in the relativistic heavy ion collisions
or in neutron or quark stars.
\subsection{Holographic superfluid hydrodynamics}
\label{s:}
It was pointed out by \cite{Gubser:2008px} that charged asymptotically
AdS$_5$ planar black holes are sometimes unstable in the presence of charged scalar fields. The endpoint of this instability is a hairy black hole: a black hole
immersed in a charged scalar condensate. The AdS/CFT correspondence maps
the hairy black hole to a phase in which a global $U(1)$
symmetry is spontaneously broken by the vacuum expectation value of a charged
scalar operator (see [Ch.CM] for further discussion). In condensed matter physics a phase with a spontaneously broken global $U(1)$ symmetry is referred to as a superfluid.
The variables of relativistic
superfluid dynamics consist of two velocity fields, the normal fluid velocity
$u^a$ and a superfluid velocity field $u^a_s$, together with a temperature
and chemical potential field. The superfluid velocity is the unit vector
in the direction of $-\xi_{a}$ where $\xi_a$ is
the gradient of the phase of the scalar
condensate. Conservation of the stress
tensor and charge current together with the assertion that
$\xi_a$ is curl free constitute the equations of superfluid
dynamics. These equations form a closed dynamical system once
they are supplemented with constitutive relations that express
the stress tensor, charge current and the component of $\xi_a$
along the normal velocity, as functions of the fluid dynamical variables.
It has proved possible to apply the fluid/gravity map to hairy black holes
to derive the constitutive relations for holographic superfluids, with
interesting results. The theory of perfect superfluids was worked out by
Landau and Tisza in the 1940s. In a beautiful recent work \cite{Sonner:2010yx} have used the equations
of Einstein gravity to re-derive Landau-Tisza equations for superfluids that admit a holographic description.
The theory of first order dissipative corrections to the equations of
Landau-Tisza superfluidity was most completely spelled out in \cite{Putterman:1974uq}. Calculations
done within the fluid/gravity framework have led to the realization that
the 13 parameter Clark-Putterman equations derived therein miss one parameter (under the
assumption of parity invariance for the superfluids) and 6 more parameters
(if the superfluids are not assumed to preserve parity). A completely
satisfactory framework for superfluid hydrodynamics has been developed only
very recently \cite{Bhattacharya:2011tr}, and the fluid/gravity map has played a major role in
this development.
\section{Relation to other developments}
\label{s:otherdev}
Having surveyed the fluid/gravity correspondence and its various applications, we finally describe connections with other approaches.
\subsection{Implications for Israel-Stewart formalism}
\label{s:}
One useful application of the fluid/gravity correspondence is an improvement on the `causal relativistic hydrodynamics', also known as the Israel-Muller-Stewart formalism \cite{Israel:1976tn,Israel:1979wp}. To appreciate the context, recall that a conventional theory of relativistic dissipative (i.e., irreversible) hydrodynamics, which is first order in time derivatives, is described in terms of a parabolic system of differential equations, leading to instantaneous propagation of signals. While these apparently a-causal modes lie outside of the long wavelength regime of validity of the hydrodynamical formulation as discussed in \cite{Geroch:2001xs}, they nevertheless lead to conceptual and computational problems.
To capture the dissipative physics, \cite{Israel:1976tn} observed that second order terms are needed in the entropy current. These render the system hyperbolic, thereby
providing a good initial value formulation. However, the particular terms added are not all the possible ones consistent with the symmetries, so as such, the construction is somewhat ad-hoc. Indeed, \cite{Baier:2007ix} observed in the context of conformal fluid, that the terms added do not maintain conformal invariance of the system, manifesting the incompleteness of the approach.
The fluid/gravity construction in effect prescribes the correct completion to render the full system causal, as well as manifestly consistent with the symmetries. We expect that due to the gravitational dual, causality will be guaranteed at all orders in the derivative expansion.
\subsection{The black hole membrane paradigm}
\label{s:membrane}
Perhaps the most salient feature of the fluid/gravity correspondence is the fact that the horizon dynamics (which in this case prescribes the dynamics of the entire spacetime) is governed by hydrodynamics. At the face of it, such type of relation is not new; in fact for several decades
relativists have explored the idea that spacetime, or important aspects thereof like black hole horizons, might resemble a fluid.
Early indications include black hole thermodynamics \cite{Bekenstein:1973ur,Hawking:1974sw} developed in the 70's, analog models of black holes \cite{Unruh:1980cg} initiated in the early 80's, and most strikingly the black hole Membrane Paradigm \cite{Thorne:1986iy,Damour:1978cg} formulated in the late-70's. The latter realizes the idea that for external observers, black holes behave much like a fluid membrane, endowed with physical properties such as viscosity, conductivity, and so forth. In particular, the dynamics of this membrane is governed by the familiar laws of fluid dynamics, namely the compressible Navier-Stokes equations.
Motivated by the superficial similarity between the membrane paradigm and the fluid/gravity correspondence, recently \cite{Eling:2009sj,Bredberg:2011jq} have attempted to formulate a precise derivation of the former. In \cite{Eling:2009sj} Einstein's equations in the bulk are projected onto a null hypersurface and then expanded in gradients along the hypersurface. On the other hand \cite{Bredberg:2011jq} show that one can systematically find a solution to vacuum Einstein's equations which describes the near-horizon geometry of a generic non-degenerate black hole in the long wavelength regime.
Within the fluid/gravity correspondence, the entire spacetime evolution is mapped to the dynamics of a conformal fluid, which, albeit reminiscent of the membrane paradigm, has one important twist: the membrane lives on the {\it boundary} of the spacetime (which is unambiguously defined and admits a fluid description with well-defined dynamics), and gives a perfect mirror of the full bulk physics. This ``membrane at the end of the universe" picture is a natural consequence of the holographic nature of the fluid/gravity correspondence.
\subsection{Blackfolds}
\label{s:blackfolds}
As in the fluid/gravity correspondence and the membrane paradigm type ideas, the blackfold approach to constructing higher-dimensional black holes
(discussed in [ch.BF] of this book) likewise asserts that the effective theory describing the long wavelength dynamics of black hole horizons can be expressed in terms of fluid dynamics.
However, there are several important differences between these descriptions.
Since the blackfold `fluid' pertains to the effective world-volume dynamics of an extended black object as seen from far away, the intrinsic dynamics typically has to be supplemented by extrinsic dynamics, describing how the blackfold embeds in the ambient spacetime.
On the other hand, in the fluid/gravity correspondence the fluid resides on the boundary of asymptotically (locally) AdS spacetime, so there is no issue with extrinsic dynamics.
Moreover, although the blackfold formalism is most naturally formulated in asymptotically flat spacetime, by a suitable separation of scales, one can in principle consider blackfolds with any asymptotics.
In contrast, the fluid/gravity correspondence concerns asymptotically AdS black holes.
On the other hand, unlike all the above-mentioned approaches, fluid/gravity is the only one where there is a known physical microscopic origin to the fluid:
it is the effective behavior of the dual field theory residing on the AdS boundary.
\section{Summary}
\label{s:summary}
The fluid/gravity correspondence provides a natural way to map solutions of fluid dynamics into those of gravity, enabling one to construct time-dependent, inhomogeneous black hole solutions to Einstein's equations, retaining full non-linearity. An interesting aspect of the construction is the manner in which classical gravity can be moulded to fit naturally with effective field theory intuition to extract approximate solutions. While the construction itself arose from the gauge/gravity correspondence, it is clear that it can be implemented in greater generality.
Apart from providing interesting insights into the dynamics of gravity, the map has played an important role in clarifying various issues in fluid dynamics. The role of quantum anomalies in hydrodynamical transport, and generalizations of fluid dynamics to systems with spontaneously broken symmetries, are two examples where the fluid/gravity map has served to elucidate the underlying physics cleanly. The physical points seem much simpler to understand from the gravitational perspective; aided by this intuition one can re-evaluate the hypotheses of traditional descriptions of fluids.
The fluid/gravity map suggests several extremely interesting technical, as
well as conceptual, questions for the future. Some of these are:
Does the gravitational viewpoint shed any light on
turbulent fluid flows, or questions about singularities that develop in
finite time from smooth initial data in fluid dynamics?
Is there a path integral formulation of fluid dynamics
at finite $N$, and how does it map to the path integral of bulk gravity?
Are the corrections to the classical equations of gravity constrained
by the requirement of positivity of divergence of an `entropy current' on
an event horizon (analogously to, and perhaps even dual to, fluid dynamics)?
It seems likely that many interesting results remain to be discovered
in this general area.
\section{Epilogue: Einstein and Boltzmann}
\label{s:ebotlz}
As we have emphasized throughout, the equations of fluid dynamics, for which
we have an independent field theory intuition, are dual to a long wavelength
limit of Einstein's equations \eqref{Eeq}. It is then natural to ask what is the field theoretical
interpretation of the full dynamical system of equations \eqref{Eeq}?
We believe that these equations may be conceptually thought of as the strong
coupling analogue of (a decoupled sector of) the Boltzmann transport equations.
It is well known that the linearization of the Boltzmann transport equations
about equilibrium yields an infinite set of `quasinormal modes', i.e.,
solutions to the equations of motion that all decay to zero (returning the
system back to equilibrium) at late times. Exactly $d$ of these
quasinormal modes are massless (in the sense that they are static in the
infinite wavelength limit). In textbooks on statistical
mechanics, fluid dynamics is sometimes derived as the non-linear theory
of this finite set of Boltzmann `quasinormal modes'.
The remaining quasinormal modes are `fast modes' that
decay away on a time scale set by the mean free path of kinetic theory.
Similarly, the linearization of the equations of gravity about
the planar black hole has $d$ massless quasinormal modes and an infinite
set of massive quasinormal modes. In direct analogy with the work on the
Boltzmann equations, the fluid/gravity correspondence constructs the equations
of fluid dynamics as the non-linear theory of these massless modes (effectively
by integrating out the massive modes, order by order).
For this reason it is natural to think of the full set of Einstein's equations
in the presence of an event horizon
(including all quasinormal mode degrees of freedom)
as the strong coupling analogue of the Boltzmann transport equations.
An important property of the Boltzmann transport equations is that they are
irreversible; they obey the Boltzmann $H$-theorem (which asserts that a
certain functional of kinetic variables called $H$ always increases
in time and is maximum in equilibrium). In direct analogy, Einstein's equations,
together with the assumption of regularity of future event horizons (and physical energy conditions),
always obey the classic area increase theorem of general relativity.
This suggests that the better analogy is between the Boltzmann transport
equations and Einstein's equations {\it plus the condition of regularity
of the future event horizon}. The last condition breaks the time reversal
invariance of Einstein's equations. In fact, the requirement that the future event horizon stay regular was a crucial element in our implementation of the fluid/gravity map. The
Boltzmann theorem has a local analogue in fluid dynamics; it maps to
the statement that the equations of fluid dynamics are accompanied
by a local entropy current that whose divergence is everywhere non-negative.
The area increase theorem of general relativity can be used to
construct such an entropy current for the fluid dynamics generated from the
fluid/gravity map.
Just like the Boltzmann equations, the system of gravitational
equations \eqref{Eeq} can be used to study the approach to equilibrium from a highly non equilibrated starting point. In simple studies of equilibration using
Einstein's equations \cite{Chesler:2008hg,Bhattacharyya:2009uu}, the equilibration time, measured by the time taken for fluid dynamics to take over as the effective description,
turns out to be extremely rapid. In more complicated
situations the equilibration process displays sharp phase transitions
associated with Choptuik phenomena. Indeed the equations
\eqref{Eeq} undoubtedly contain a host of dynamical delights for the
intrepid gravitational and statistical physicist; it seems clear that
the fluid/gravity map is merely the tip of an iceberg's worth of connections
between gravity and statistical physics.
\providecommand{\href}[2]{#2}\begingroup\raggedright | {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,060 |
{"url":"https:\/\/www.gamedev.net\/forums\/topic\/184813-memory-leaking\/","text":"\u2022 Announcements\n\nArchived\n\nThis topic is now archived and is closed to further replies.\n\nMemory Leaking\n\nRecommended Posts\n\nIn the TTT demo of James Trotter I saw a file containing memory leaking,''memoryleaks.log'' and I thought he personally made the log(manually) and I browsed the source and didnt found anything to prove that . Therefore I guess its something that MSVC++ (6) can generate for you right ? Can anyone tell me what should I do to generate that file ? Thanks in advance\n\nShare on other sites\nI would recommend you to use a memory manager. I used the mmgr memory manager by Paul Nettle - its excellent.\n\nftp:\/\/ftp.flipcode.com\/code\/mmgr.zip\n\nShare on other sites\nVC6 has no built-in facility for creating a log file of this nature, but it does have a built-in facility for detecting memory leaks. Search MSDN for an article entitled 'Detecting and Isolating Memory Leaks Using Microsoft Visual C++', or click here.\n\nAn addendum - If you're using Windows 2K or XP, the OS's performance monitor is an excellent tool for monitoring memory\/resource consumption and locating leaks. See this article.\n\n[edited by - Ferdinand the Bull on October 11, 2003 9:16:58 AM]\n\nShare on other sites\nYes, that was Paul Nettle's memory manager. It's really excellent! Although I've had a couple of problems with it... It doesn't like iostream much, and tends to crash when I include the header... I think it does the same with a couple of STL objects, but I'm not sure.\n\nHehe, well I really didn't have time to fix that little problem , so please forgive me..\n\n[edited by - James Trotter on October 12, 2003 4:31:58 PM]\n\n\u2022 Partner Spotlight\n\n\u2022 Forum Statistics\n\n\u2022 Total Topics\n627682\n\u2022 Total Posts\n2978622\n\n\u2022 9\n\u2022 14\n\u2022 12\n\u2022 10\n\u2022 12","date":"2017-10-20 09:01:14","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\": 0.26241958141326904, \"perplexity\": 4058.663174517294}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-43\/segments\/1508187823997.21\/warc\/CC-MAIN-20171020082720-20171020102720-00809.warc.gz\"}"} | null | null |
{"url":"https:\/\/brilliant.org\/problems\/and-here-is-an-easy-one\/","text":"# And here is an easy one\n\nNumber Theory Level pending\n\nIn a book with page numbers from 1 to 100, some pages are torn off. The sum of the numbers on the remaining pages is 4949. How many pages are torn off?\n\n\u00d7","date":"2017-01-20 20:24:38","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\": 0.8051775097846985, \"perplexity\": 358.51042540157687}, \"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-2017-04\/segments\/1484560280872.69\/warc\/CC-MAIN-20170116095120-00109-ip-10-171-10-70.ec2.internal.warc.gz\"}"} | null | null |
The Annual March for Life will be on January 22, 2012 at our State Capitol. Bishop Quinn, Fr. Colletti and young people from FOCUS and our Universities in Winona will be in Washington, DC for its march for Life on Monday January 23.
Info on the March to the State Capitol is in the Gathering Space at Cathedral.
There is also a petition you can sign to help advance the Pain Capable Unborn Child Protection Act. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,253 |
The term hill-slope enclosure describes a type of late prehistoric earthwork found across South West England and also in Wales. Normally formed from a single bank, or ditch and bank, enclosing an area of less than 1 hectare, and not on the summit of a hill. They are often found on a spur of a larger hill or range of hills.
The original purpose of the hill-slope enclosure is obscure but it is thought that they were not primarily defensive structures. Surveys and excavations have revealed low densities of postholes and storage pits suggesting they functioned as defensible farmsteads and permanent livestock enclosures.
They may also have served different purposes at different times and they may have had symbolic and religious significance which is now impossible to determine.
References
Archaeological sites in the United Kingdom | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,105 |
Q: Java code running twice I have 2 Notes servers running from a load balancer. The database uses directory services to authenticate to LDAP.
I have java code that checks LDAP to check if user's password is expired. If the password is expired the code redirects to a password change screen. This code runs in the before page load event. Since all pages are NOT public access a Notes generated login occurs before anything takes place.
The password change screen first ties to authenticate the user in LDAP then changes the password. But if I immediately change my password after the initial Note login then I get an authentication error.
If I change the password back to the same thing then I get no authentication error then everything works fine.
So I suspected that the java code was running twice. The notes log should only running once. But when our LDAP team turned on logging, they could see that the password attribute was being changed twice (when I changed to the same password). So what was happening with the failure is that, the password was changed successfully but when the second time the code ran, it was using the "old" password and it was this error that was returned to the browser.
Now here is where it really gets strange. If I do a Notes authentication, then wait one full minute before password change, the code only runs once.
Or if I go to one of the servers, the code only runs once.
Code runs twice only if I go through the load balancer or if I try changing my password, immediately after logging in.
Any idea what on earth could be going on here?
Update: The issue seems to be coming from our reverse proxy server. The way our site is configured is Browser->Reverve Proxy->Load Balancer->(Notes Server 1, Notes Server 2).
If I go to the Load Balancer then the code only runs once.
While I might not be seeing logging in notes.nsf, I can see it running twice when I look direct at teh console.
Update: Reverse Proxy is running on Apache. Not sure the version.
A: My previous password change page was refreshing the whole page when I pressed submit. For some reason this was causing the page to be submitted twice. I changed things to a partial refresh and now all works well. Don'tknow why the refresh would not like the full refresh. But it works now. :)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,769 |
Q: Convert string with HASH MD5 to ToBase64String this is my problem,
i have this code that accepts clean text with passwords and returns Base64MD5 hashes
private static string GetMd5Base64Pass(string userpwd)
{
MD5 md5 = new MD5CryptoServiceProvider();
return Convert.ToBase64String(md5.ComputeHash(Encoding.ASCII.GetBytes(userpwd)));
}
And i need to reuse it to accept MD5 string hashes and return in Base64MD5.
i tried to do this:
private static string GetMd5Base64PassMD5(string userpwd)
{
MD5 md5 = new MD5CryptoServiceProvider();
return Convert.ToBase64String(Encoding.ASCII.GetBytes(userpwd));
}
but the returns are completely different.
already tried to convert the string to bytearray, didn't work.
I need to insert one string with 32bits MD5, and return it in Base64String.
thks
------------------------------ Edited
Example:
Password is 123123:
MD5 is: 4297f44b13955235245b2497399d7a93
Base64String of MD5 is: Qpf0SxOVUjUkWySXOZ16kw==
I need to get
this: Qpf0SxOVUjUkWySXOZ16kw==
from
this hash string
4297f44b13955235245b2497399d7a93
A: public static string ConvertHexStringToBase64(string hexString)
{
byte[] buffer = new byte[hexString.Length / 2];
for (int i = 0; i < hexString.Length; i++)
{
buffer[i / 2] = Convert.ToByte(Convert.ToInt32(hexString.Substring(i, 2), 16));
i += 1;
}
string res = Convert.ToBase64String(buffer);
return res;
}
this receives md5 string hashes and transforms it to Base64 Hex
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,003 |
Q: Experience with iLugger? I have an iMac and I use it for development and video editing. I am looking for greater portability and I'm considering a MacBook or MacBook Pro. My other option is an iLugger.
I'm looking for owners of iLugger to share their experiences with iLugger and if it is a worthy buy.
A: I love my iLugger!!!! You get exactly what you pay for. The only con I can say is the weight upon your shoulder, when using the shoulder strap.. Looks like they added wheels now, so this definitely is a good buy.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,660 |
\section{Viability, feasibility and optimality}\label{sec:survivability}
We consider a continuous time environment in which an agent selects actions that result in a time varying set of penalties. Use $t$ to denote time and let $X\subseteq \mathbb{R}^n$ be a closed convex set from which the agent selects action $x\in X $. The penalties incurred at time $t$ for selected action $x$ are given by the value $f(t,x)$ of the vector function $f:\reals\times\reals^n \to \reals^m$. We interpret the vector penalty function $f$ as a definition of the environment. Our interest is in situations where the agent is faced with an environment $f$ and must choose an action $x\in X$ -- or perhaps a trajectory $x(t)$ -- that guarantees nonpositive penalties $f(t,x(t))\leq 0$ for all times $t$ not exceeding a time horizon $T$. Since the existence of this trajectory depends on the specific environment we define a viable environment as one in which it is possible to select an action with nonpositive penalty for times $0\leq t\leq T$ as we formally specify next.
\begin{definition}[\textbf{Viable environment}]\label{def_viable_environment}
We say that an environment $f:\reals\times\reals^n \to \reals^m$ is viable over the time horizon $T$ for an agent that selects actions $x\in X$ if there exists a feasible action $x^\dagger\in X$ such that
\begin{equation}\label{eqn_def_viable_environment}
f(t,x^\dagger) \leq 0, \quad \text{for all\ } t \in[0,T] .
\end{equation}
The set $X^\dagger:=\{x^\dagger \in X: f(t,x^\dagger) \leq 0,\ \text{for all\ } t \in[0,T]\}$ is termed the feasible set of actions.
\end{definition}
Since for a viable environment it is possible to have multiple feasible actions it is desirable to select one that is optimal with respect to some criterion of interest. Introduce then the objective function $f_0:\reals\times\reals^n \to \reals$, where for a given time $t \in [0,T]$ and action $x\in X$ the agent suffers a loss $f_0(t,x)$. The optimal action is defined as the one that minimizes the accumulated loss $\int_0^T f_0(t,x) \,dt$ among all viable actions, i.e.,
\begin{alignat}{2}\label{eqn_optimal_strategy}
x^* :=\ &\argmin_{x\in X} \int_0^T f_0(t,x) \,dt \\ \nonumber
&\st\ f(t,x) \leq 0,\ \text{for all\ } t \in [0,T] .
\end{alignat}
For the definition in \eqref{eqn_optimal_strategy} to be valid the function $f_0(t,x)$ has to be integrable with respect to $t$. In subsequent definitions and analyses we also require integrability of the environment $f$ as well as convexity with respect to $x$ as we formally state next.
\begin{assumption} \label{as:integrability}
The functions $f(t,x)$ and $f_0(t,x)$ are integrable with respect to $t$ in the interval $[0,T]$.
\end{assumption}
\begin{assumption}\label{as:convexity}
The functions $f(t,x)$ and $f_0(t,x)$ are convex with respect to $x$ for all times $t\in[0,T]$.
\end{assumption}
If the environment $f(t,x)$ and functions $f_0(t,x)$ are known beforehand, finding the action in a viable environment that minimizes the total aggregate cost is equivalent to solving the convex optimization problem in \eqref{eqn_optimal_strategy} for which a number of algorithms are known. Here, we consider the problem of adapting a strategy $x(t)$ when the functions $f(t,x)$ and $f_0(t,x)$ are {\it arbitrary} and {\it revealed causally.} I.e., we want to choose the action $x(t)$ using observations of viability $f(t,x)$ and cost $f_0(t,x)$ in the open interval $[0,t)$. This implies that $f(t,x(t))$ and $f_0(t,x(t))$ are not observed before choosing $x(t)$. The action $x(t)$ is chosen ex ante and the corresponding viability $f(t,x(t))$ and cost $f_0(t,x(t))$ are incurred ex post. Further observe that the constraints and objective functions may change abruptly if the number of discontinuities in these are finite for finite $T$. This makes the problem different from time varying optimization in which the goal is to track the optimal argument of $f_0(t,x)$ subject to the constraint $f(t,x)\leq 0$ under the assumption that these functions change continuously and at a sufficiently small rate
\cite{popkov2005gradient,fazlyab2015interior,zavala2010real}.
\subsection{Regret and fit}
We evaluate the performance of trajectories $x(t)$ through the concepts of regret and fit. To define regret we compare the accumulated cost $\int_0^T f_0(t,x(t)) \,dt$ incurred by $x(t)$ with the cost incurred by the optimal action $x^*$ defined in \eqref{eqn_optimal_strategy},
\begin{equation}\label{eqn_continuous_regret}
\ccalR_T := \int_0^T f_0(t,x(t)) \,dt - \int_0^T f_0(t,x^*) \,dt .
\end{equation}
Analogously, we define the fit of the trajectory $x(t)$ as the accumulated penalties $f(t,x(t))$ incurred for times $t\in[0,T]$,
\begin{equation}\label{eqn_def_fit}
\ccalF_{T} := \int_0^T f(t,x(t)) \,dt.
\end{equation}
The regret $\ccalR_T$ and fit $\ccalF_{T}$ can be interpreted as performance losses associated with online causal operation as opposed to offline clairvoyant operation. If $\ccalF_{T}$ is positive in a viable environment we are in a situation in which, had the environment be known a priori, we could have selected an action $x^\dagger$ with $f(t,x^\dagger) \leq 0$. The fit measures how far the trajectory $x(t)$ comes from achieving that goal. As in the case of the fit, if the regret $\ccalR_T$ is large we are in a situation in which prior knowledge of environment and cost would had resulted in the selection of the action $x^*$ -- and in that sense $\ccalR_T$ indicates how much we regret not having had that information available.
Because of the cumulative nature of fit, it is possible to achieve small fit by alternating between actions for which the constraint functions take positive and negative values. This is valid when cumulative constraints are an appropriate model, which happens for quantities that can be stored or preserved in some sense -- such as energy budgets enforced through average power constraints. For situations where this is not appropriate, we define the saturated fit in which constraint slacks are saturated to a small constant $\delta$. Formally, let $\delta>0$ be a positive constant and define the function $\bar{f}_{\delta}(t,x)) = \max\left\{f(t,x),-\delta \right\}$. Then, the $\delta$-saturated fit is defined as
\begin{equation}\label{eqn_saturated_fit}
\bar\ccalF_{T} = \int_0^T \bar{f}_{\delta}(t,x(t)) \, dt.
\end{equation}
Since $\bar{f}_{\delta}(t,x)$ is the pointwise maximum of two convex functions with respect to the actions, it is a convex function itself and $\bar\ccalF_{T}$ is not different than the fit for the environment defined by $\bar{f}_{\delta}(t,x)$. By taking small values of $\delta$ we can reduce the negative portion of the fit to be as small as desired.
A good learning strategy is one in which $x(t)$ approaches $x^*$. In that case, the regret and fit grow for small $T$ but eventually stabilize or, at worst, grow at a sublinear rate. Considering regret $\ccalR_T$ and fit $\ccalF_{T}$ separately, this observation motivates the definitions of feasible trajectories strongly feasible trajectories, and strong optimal trajectories that we formally state next.
\begin{definition}\label{def_0ptimality_and_viability}
Given an environment $f:\reals\times\reals^n \to \reals^m$, a cost $f_0:\reals\times\reals^n \to \reals$, and a trajectory $x(t)$ we say that:
\begin{mylist}
\item[\bf Feasibility.] The trajectory $x(t)$ is feasible in the environment if the fit $\ccalF_{T}$ grows sublinearly with $T$. I.e., if there exist a function $h(T)$ with $\limsup_{T\to\infty} h(T)/T = 0$ and a constant vector $C$ such that for all times $T$ it holds,
\begin{equation}\label{eqn_def_weak_survival}
\ccalF_{T} := \int_0^T f(t,x(t)) \,dt \leq C h(T).
\end{equation}
\item[\bf Strong Feasibility.] The trajectory $x(t)$ is strongly feasible in the environment if the fit $\ccalF_{T}$ is bounded for all $T$. I.e., if there exists a constant vector $C$ such that for all times $T$ it holds,
\begin{equation}\label{eqn_def_survival}
\ccalF_{T} := \int_0^T f(t,x(t)) \,dt \leq C.
\end{equation}
\item[\bf Strong optimality.] The trajectory $x(t)$ is strongly optimal in the environment if the regret $\ccalR_{T}$ is bounded for all $T$. I.e., if there exists a constant $C$ such that for all times $T$ it holds,
\begin{equation}\label{eqn_def_0ptimality}
\ccalR_{T} := \int_0^T f_0(t,x(t)) \,dt - \int_0^T f_0(t,x^*) \,dt \leq C.
\end{equation}
\end{mylist} \end{definition}
Having the regret satisfy $\ccalR_{T}\leq C$ irrespectively of $T$ is an indication that $f_0(t,x(t))$ is close to $f_0(t,x^*)$ so that the integral stops growing. This is not necessarily so because we can also achieve small regret by having $f_0(t,x(t))$ oscillate above and below $f_0(t,x^*)$ so that positive and negative values of $f_0(t,x(t)) - f_0(t,x^*)$ cancel out. In general, the possibility of having small regret by a trajectory that does not approach $x^*$ is a limitation of the concept of regret. Alternatively, we can think of the optimal offline policy $x^*$ as fixing a budget for cost accumulated across time. An optimal online policy meets that budget up to a constant $C$ -- perhaps by overspending at some times and underspending at some other times.
Likewise, when the fit satisfies $\ccalF_{T}\leq C$ irrespectively of $T$, it suggests that $x(t)$ approaches the feasible set. This need not be true as it is possible to achieve bounded fit by having $f(t,x(t))$ oscillate around $0$. Thus, as in the case of regret, we can interpret strongly feasible trajectories as meeting the {\it accumulated} budget $\int_0^T f(t,x(t))\,dt\leq 0$ up to a constant term $C$. This is in contrast with feasible actions $x^\dagger$ that meet the budget $f(t,x^\dagger)\leq0$ for all times. Feasible trajectories differ from strongly feasible trajectories in that the fit is allowed to grow at a sublinear rate. This means that feasible trajectories do not meet the {\it accumulated} budget within a constant $C$ but do meet the {\it time averaged} budget $(1/T)\int_0^T f(t,x(t))\,dt\leq0$ within that constant. The notion of optimality -- as opposed to strong optimality -- could have been defined as a case in which regret is bounded by a sublinear function of $T$. This is not necessary here because our results state strong optimality.
In this work we solve three different problems: (i) Finding strongly optimal trajectories in unconstrained environments. (ii) Finding strongly feasible trajectories. (iii) Finding feasible, strongly optimal trajectories. We develop these solutions in sections \ref{sec:continuous_regret}, \ref{subsec:non_opti}, and \ref{subsec:otpi}, respectively. Before that, we present two pertinent remarks and we clarify concepts with the introduction of an example.
\begin{remark}[\bf Not every trajectory is strongly feasible]
In definition \eqref{eqn_def_survival} we consider the integral of a measurable function in a finite interval, hence it is always bounded by a constant. Yet if the latter depends on the time horizon $T$, the trajectory is not strongly feasible, because it is not uniformly bounded for all time horizons $T$. The same remark is valid for the definitions of strongly optimal and feasible.
\end{remark}
\begin{remark}[\bf Connection with Stochastic Optimization]
One can think about the online learning framework as a generalization of the stochastic optimization setting (see e.g. \cite{robbins1951stochastic,borkar2008stochastic}). In the latter, the objective and constraint functions depend on a random vector $\theta \in \mathbb{R}^p$. Formally, the cost is a function $f_0: \mathbb{R}^n\times \mathbb{R}^p \to \mathbb{R}$ and the constraints are given by a multivalued function $f: \mathbb{R}^n\times \mathbb{R}^p \to \mathbb{R}^m$. The constrained stochastic optimization problem can be then formulated as
\begin{equation}\label{eqn_stochastic_problem}
\begin{split}
x^*:=&\argmin \, \E{f_0(x,\theta)} \\
&\;\, \mbox{s.t.} \quad \quad \E{f(x,\theta)} \leq 0,
\end{split}
\end{equation}
where the above expectations are with respect to the random vector $\theta$. When the process that determines the temporal evolution of the random vector $\theta_t$ is stationary, the expectations can be replaced by time averages. In that sense problem \eqref{eqn_stochastic_problem} is equivalent to the problem of generating trajectories that are feasible and optimal in the sense of Definition \ref{def_0ptimality_and_viability}.
\end{remark}
\subsection{The shepherd problem}\label{sec_shepherd_problem}
Consider a target tracking problem in which an agent -- the shepherd -- follows a group of $m$ targets -- the sheep. Specifically, let $z(t) = [z_1(t),z_2(t)]^T \in\reals^2$ denote the position of the shepherd at time $t$. To model smooth paths for the shepherd introduce a polynomial parameterization so that each of the position components $z_k(t)$ can be written as
\begin{equation}\label{eqn_shepherd_position}
z_k(t) = \sum_{j=0}^{n-1} x_{kj} p_j(t),
\end{equation}
where $p_j(t)$ are polynomials that parameterize the space of possible trajectories. The action space of the shepherd is then given by the vector $x=[x_{10},\ldots,x_{1,n-1},x_{20},\ldots,x_{2,n-1}]^T\in\reals^{2n}$ that stacks the coefficients of the parameterization in \eqref{eqn_shepherd_position}.
Further define $y_i(t)=[y_{i1}(t), y_{i2}(t)]^T$ as the position of the $i$th sheep at time $t$ for $i=1,\ldots,m$ and introduce a maximum allowable distance $r_i$ between the shepherd and each of the sheep . The goal of the shepherd is to find a path $z(t)$ that is within distance $r_i$ of sheep $i$ for all sheep. This can be captured by defining an $m$-dimensional environment $f$ with each component function $f_i$ defined as
\begin{equation}\label{eqn_sheep_environment}
f_i(t,x) = \| z(t) - y_i(t) \|^2 - r_i^2 \quad \mbox{for all} \quad i=1..m.
\end{equation}
That the environment defined by \eqref{eqn_sheep_environment} is viable means that it is possible to select a vector of coefficients $x$ so that the shepherd's trajectory given by \eqref{eqn_shepherd_position} stays close to all sheep for all times. To the extent that \eqref{eqn_shepherd_position} is a loose parameterization -- we can approximate arbitrary functions with sufficiently large index $n$, if the time horizon is fixed and not allowed to tend to infinity --, this simply means that the sheep are sufficiently close to each other at all times. E.g., if $r_i=r$ for all times, viability is equivalent to having a maximum separation between sheep smaller than $2r$.
As an example of a problem with an optimality criterion say that the first target -- the black sheep -- is preferred in that the shepherd wants to stay as close as possible to it. We can accomplish that by introducing the objective function
\begin{equation}\label{eqn_black_sheep}
f_0(t,x) = \| z(t) - y_1(t) \|^2 .
\end{equation}
Alternatively, we can require the shepherd to minimize the work required to follow the sheep. This behavior can be induced by minimizing the integral of the acceleration which in turn can be accomplished by defining the optimality criterion [cf. \eqref{eqn_optimal_strategy}],
\begin{equation}\label{eqn_minimum acceleration}
f_0(t,x) = \big\|\ddot z(t)\big\|
= \Bigg\| \bigg[ \sum_{j=0}^{n-1} x_{1j} \ddot p_j(t),\
\sum_{j=0}^{n-1} x_{2j} \ddot p_j(t) \bigg] \Bigg\|.
\end{equation}
Trajectories $x(t)$ differ from actions in that they are allowed to change over time, i.e., the constant values $x_{kj}$ in \eqref{eqn_shepherd_position} are replaced by the time varying values $x_{kj}(t)$. A feasible or strongly feasible trajectory $x(t)$ means that the shepherd is repositioning to stay close to all sheep. An optimal trajectory with respect to \eqref{eqn_black_sheep} is one in which he does so while staying as close as possible to the black sheep. An optimal trajectory with respect to \eqref{eqn_minimum acceleration} is one in which the work required to follow the sheep is minimized. In all three cases we apply the usual caveat that small fit and regret may be achieved with stretches of underachievement following stretches of overachievement.
\section{Unconstrained regret in continuous time. }\label{sec:continuous_regret}
Before considering the feasibility problem we consider the following unconstrained minimization problem. Given an unconstrained environment ($f(t,x) \equiv 0$) our goal is to generate strong optimal trajectories $x(t)$ in the sense of Definition \ref{def_0ptimality_and_viability}, selecting actions from a closed convex set $X$, i.e., $x(t) \in X$ for all $t\in [0,T]$. Given the convexity of the objective function with respect to the action, as per Assumption \ref{as:convexity}, it is natural to consider a gradient descent controller. To avoid restricting attention to functions that are differentiable with respect to $x$, we work with subgradients. For a convex function $g:X\to \mathbb{R}$ a subgradient $g_x$ satisfies the
\begin{equation}\label{eqn_def_subgradient}
g(y) \geq g(x) + g_x(x)^T(y-x) \quad \mbox{for all} \quad y\in X.
\end{equation}
In general, subgradients are defined at all points for all convex functions. At the points where the function $f$ is differentiable the subgradient and the gradient coincide. In the case of vector functions $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$ we group the subgradients of each component into a matrix $f_x(x)\in\reals^{n\times m}$ defined as
\begin{equation}\label{eqn_subgradient_f}
f_x(x) = \left[ \begin{array}{c c c c} f_{1,x}(x) & f_{2,x}(x) & \cdot\cdot\cdot & f_{m,x}(x) \end{array}\right],
\end{equation}
where $f_{i,x}(x)$ is a subgradient of $f_i(x)$.
In addition, since the action must always be selected from the set $X$ we define the controller in a way that the actions are the solution of a projected dynamical system over the set $X$. The solution has been studied in
\cite{Zhang95} and we define the notion as follow.
\begin{definition}[Projected dynamical system]\label{def_projected_dynamical_system}
Let $X$ be a closed convex set.
\begin{mylist}
\item[\bf Projection of a point.] For any $z \in R^n$, there exits a unique element in $X$, denoted $P_X(z)$ such that
\begin{equation}\label{eqn_proj_over_X}
P_X(z) = \argmin_{y \in X} \|y-z \|.
\end{equation}
\item[\bf Projection of a vector at a point.]Let $x \in X$ and $v$ a vector, the projection of $v$ over the set $X$ at the point $x$ is
\begin{equation}
\Pi_X(x,v) = \lim_{\delta \to 0^+}\left(P_X(x+\delta v) -x\right) / \delta.
\end{equation}
\item[\bf Projected dynamical system.]Given a closed convex set $X$ and a vector field $F(t,x)$ which takes elements from $\mathbb{R}\times X$ into $\reals^n$ the projected differential equation associated with $X$ and $F$ is defined to be
\begin{equation}
\dot{x}(t) = \Pi_X\left(x,F(t,x)\right).
\end{equation}
\end{mylist}
\end{definition}
In the above projection if the point $x$ is in the interior of $X$ then the projection is not different from the original vector field, i.e., $\Pi_X(x,F(t,x)) = F(t,x)$. On the other hand if the point $x$ is in the border of $X$, then the projection is just the component of the vector field that is tangential to the set $X$ at the point $x$. Let's consider for instance the case where the set $X$ is a box in $R^n$. Let $X = [a_1,b_1] \times ... \times [a_n,b_n]$ where $a_1 .. a_n$ and $b_1 ... b_n$ are real numbers. Then for each component of the vector field we have that
\begin{equation}
\Pi_X\left(x,F(t,x)\right)_i=\left\{ \begin{array}{l} 0 \quad \mbox{if} \quad x_i = a_i \quad \mbox{and} \quad F(t,x)_i < 0, \\
0 \quad \mbox{if} \quad x_i = b_i \quad \mbox{and} \quad F(t,x)_i > 0 ,\\
F(t,x)_i \quad \mbox{otherwise}.
\end{array}
\right.
\end{equation}
Therefore, when the projection is included, the proposed controller takes the form of the following projected dynamical system:
\begin{equation}\label{eqn_gradient_controller}
\dot{x} = \Pi_X\left(x,-\varepsilon f_{0,x}(t,x)\right),
\end{equation}
where $\varepsilon>0$ is the gain of the controller. Before stating the first theorem we need a Lemma concerning the relation between the original vector field and the projected vector field. This lemma is used in the proofs of theorems \ref{theo:first_theo}, \ref{theo:not_opti} and \ref{theo:opti}.
\begin{lemma}\label{lemma:big_lemma}
Let $X$ be a convex set and $x_0 \in X$ and $x \in X$. Then
\begin{equation}\label{eqn_big_lemma}
(x_0-x)^T \Pi_X(x_0,v) \leq (x_0-x)^T v.
\end{equation}
\end{lemma}
\begin{proof}
See Apendix \ref{ap_big_lema_proof}.
\end{proof}
Let's define an Energy function $V_\bbarx:\reals^n \to \reals$ as
\begin{equation}\label{eqn_Lyapunov_opti}
V_\bbarx(x) = \frac{1}{2} (x-\bbarx)^T(x-\bbarx).
\end{equation}
Where $\bbarx \in X \subset \reals^n$ is an arbitrary fixed action. We are now in conditions to present the first theorem, which states that the solution of the gradient controller defined in \eqref{eqn_gradient_controller} is a strongly optimal trajectory, i.e., with bounded regret for all $T$.
\begin{theorem}\label{theo:first_theo} Let $f_0: \reals\times X \to \reals$ be cost function satisfying assumptions 1 and 2, with $X \subseteq \reals^n$ convex. The solution $x(t)$ of the online projected gradient controller in \eqref{eqn_gradient_controller} is strongly optimal in the sense of Definition \ref{def_0ptimality_and_viability}. In particular, the regret $\ccalR_T$ can be bounded by
\begin{equation}\label{eqn_theo_first_theo}
\ccalR_{T} \leq V_{x^*}\left(x(0)\right) / \varepsilon, \quad \text{for all\ } T\\
\end{equation}
where $V_\bbarx$ is the Energy function in \eqref{eqn_Lyapunov_opti}.\end{theorem}
\begin{proof}
Consider an action trajectory $x(t)$, an arbitrary given action $\bbarx \in X$, and the corresponding energy function $V_\bbarx(x(t))$ as per \eqref{eqn_Lyapunov_opti}. The derivative $\dot V_\bbarx(x(t))$ of the energy function with respect to time is then given by
\begin{equation}\label{eqn_theo_opti_pf_21}
\dot{V}_\bbarx(x(t)) = (x(t) - \bbarx)^T\dot{x}(t).
\end{equation}
If the trajectory $x(t)$ follows from the online projected gradient dynamical system in \eqref{eqn_gradient_controller} we can substitute the trajectory derivative $\dot x$ by the vector field value and reduce \eqref{eqn_theo_opti_pf_21} to
\begin{equation}\label{eqn_theo_opti_pf_22}
\dot{V}_\bbarx(x(t)) = (x(t) - \bbarx)^T \Pi_X \left(x(t),-\varepsilon f_{0,x}(t,x(t))\right).
\end{equation}
Use now the result in Lemma \ref{lemma:big_lemma} with $v=-\varepsilon f_{0,x}(t,x(t))$ to remove the projection operator from \eqref{eqn_theo_opti_pf_22} and write
\begin{equation}\label{eqn_theo_opti_pf_23}
\dot{V}_\bbarx(x(t)) \leq -\varepsilon (x(t)-\bbarx)^Tf_{0,x}(t,x(t)).
\end{equation}
Using the defining equation of a subgradient \eqref{eqn_def_subgradient}, we can upper bound the inner product $-(x(t)-\bbarx )^T f_{0,x}(t,x(t))$ by the difference $f_0(t,\bbarx) - f_0(t,x(t))$ and transform \eqref{eqn_theo_opti_pf_23} into
\begin{equation}
\dot{V}_\bbarx(x(t))\leq \varepsilon\left(f_0(t,\bbarx) - f_0(t,x(t))\right).
\end{equation}
Rearranging terms in the preceding inequality and integrating over time yields
\begin{equation}\label{eqn_theo1basic}
\int_0^T f_0(t,x(t)) \,dt - \int_0^T f_0(t,\bbarx) \,dt
\leq -\frac{1}{\varepsilon}\int_0^T \dot{V}_\bbarx(x(t))\,dt .
\end{equation}
Since the primitive of $\dot{V}_\bbarx(x(t))$ is $V_\bbarx(x(t))$ we can evaluate the integral on the right hand side of \eqref{eqn_theo1basic} and further use the fact that $V_\bbarx (x) \geq 0$ for all $x\in\reals^n$ to conclude that
\begin{equation}\label{eqn_theo1_aux}
-\int_0^T \dot{V}_\bbarx(x(t)) dt
\ = \ V_\bbarx(x(0)) - V_\bbarx (x(T))
\ \leq\ V_\bbarx\left(x(0)\right) .
\end{equation}
Combining the bounds in \eqref{eqn_theo1basic} and \eqref{eqn_theo1_aux} we have that
\begin{equation}\label{eqn_theo1almost}
\int_0^T f_0(t,x(t)) \,dt-\int_0^T f_0(t,\bbarx) \,dt
\leq V_\bbarx(x(0)) / \varepsilon .
\end{equation}
Since the above inequality holds for an arbitrary point $\bbarx \in \reals^n$ it holds for $\bbarx=x^*$ in particular. When making $\bbarx=x^*$ in \eqref{eqn_theo1almost} the left hand side reduces to the regret $\ccalR_T$ associated with the trajectory $x(t)$ [cf. \eqref{eqn_continuous_regret}] and in the right hand side we have $V_\bbarx(x(0))/ \varepsilon = V_{x^*}(x(0))/ \varepsilon$. Eq. \eqref{eqn_theo_first_theo} follows because \eqref{eqn_theo1almost} is true for all times $T$. This implies that the trajectory is strongly optimal according to \eqref{eqn_def_0ptimality} in Definition \ref{def_0ptimality_and_viability}. \end{proof}
The strong optimality of the online projected gradient controller in \eqref{eqn_gradient_controller} that we claim in Theorem \ref{theo:first_theo} is not a straightforward generalization of the optimality of gradient controllers in constant convex potentials. The functions $f_0$ are allowed to change arbitrarily over time and are not observed until after the cost $f_0(t,x(t))$ has been incurred.
Since the initial value of the Energy function $V_{x^*}(x(0))$ is the square of the distance between $x(0)$ and $x^*$, the bound on the regret in \eqref{eqn_theo_first_theo} shows that the closer we start to the optimal point the smaller the accumulated cost is. Likewise, the larger the controller gain $\varepsilon$, the smaller the bound on the regret is. Theoretically, we can make this bound arbitrarily small. This is not possible in practice because larger $\varepsilon$ entails trajectories with larger derivatives which cannot be implemented in systems with physical constraints. In the example in Section \ref{sec_shepherd_problem} the derivatives of the state $x(t)$ control the speed and acceleration of the shepherd. The physical limits of these quantities along with an upper bound on the cost gradient $f_{0,x}(t,x)$ can be used to estimate the largest allowable gain $\varepsilon$.
Another observation regarding the bound on the regret is that it does not depend on the function that we are minimizing --except for the location of the point $x^*$. For instance by scaling a function the bound on the regret is kept constant if the same gain $\varepsilon$ can be selected. This is not surprising since a scaling in the function implies a bigger cost but it also entails a larger action derivative, which allows to track better changes on the function. However, if a bound on the maximum allowed gain exists then the regret bound cannot be invariant to scalings.
\begin{remark}\normalfont
In discrete time systems where $t$ is a natural variable and the integrals in \eqref{eqn_continuous_regret} are replaced by sums, online gradient descent algorithms are used to reduce regret; see e.g. \cite{Zinkevich03,hazan2007logarithmic}. The online gradient controller in \eqref{eqn_gradient_controller} is a direct generalization of online gradient descent to continuous time. This similarity notwithstanding, the result in Theorem \ref{theo:first_theo} is stronger than the corresponding bound on the regret in discrete time which states a sublinear growth at a rate not faster than $\sqrt{T}$ if the cost function is convex \cite{Zinkevich03}, and $\log{T}$ if the cost function is strictly convex \cite{hazan2007logarithmic}. The key where this difference lies is in the fact that discrete time algorithms have to "pay" to switch from the action at time $t$ to the action at time $t+1$. In the proofs of \cite{Zinkevich03,hazan2007logarithmic} a term related to the norm square of the gradient is present in the upper bound on the regret while in continuous time this term is absent. The bound on the norm of the gradient is related to the selecting a different action. As in the case of fictitious plays that lead to no regret in the continuous time but not in discrete time (see e.g.\cite{viossat2013no,hart2001general,young1993evolution}) the bounds on the regret in continuous time are tighter than in discrete time for online gradient descent.
\end{remark}
\section{Saddle point algorithm}
\label{sec:main}
Given an environment $f(t,x)$ and an objective function $f_0(t,x)$ verifying assumptions \ref{as:integrability} and \ref{as:convexity} we set our attention towards two different problems: design a controller whose solution is a strongly feasible trajectory and a controller whose solution is a feasible and strongly optimal trajectory. As already noted, when the environment is known beforehand the problem of finding such trajectories is a constrained convex optimization problem, which we can solve using the saddle point algorithm of Arrow and Hurwicz \cite{arrow_hurwicz}. Following this idea, let $\lambda \in \Lambda =\reals^m_+$, be a multiplier and define the time-varying Lagrangian associated with the online problem as
\begin{equation}\label{eqn_lagrangian}
\mathcal{L}(t,x,\lambda) = f_0(t,x)+\lambda^Tf(t,x).
\end{equation}
Saddle point methods rely on the fact that for a constrained convex optimization problem, a pair is a primal-dual optimal solution if and only if the pair is a saddle point of the Lagrangian associated with the problem; see e.g. \cite{boyd2004convex}. The main idea of the algorithm is then to generate trajectories that descend in the opposite direction of the gradient of the Lagrangian with respect to $x$ and that ascend in the direction of the gradient with respect to $\lambda$.
Since the Lagrangian is differentiable with respect to $\lambda$, we denote by $\mathcal{L}_{\lambda}(t,x,\lambda)=f(t,x)$ the derivative of the Lagrangian with respect to $\lambda$. On the other hand, since the functions $f_0(\cdot,x)$ and $f(\cdot,x)$ are convex, the Lagrangian is also convex with respect to $x$. Thus, its subgradient with respect to $x$ always exist, let us denote it by $\mathcal{L}_x(t,x,\lambda)$. Let $\varepsilon$ be the gain of the controller, then following the ideas in \cite{arrow_hurwicz} we define a controller that descends in the direction of the subgradient with respect to the action $x$
\begin{align}\label{eqn_action_descent}
\dot{x} &\ =\ \Pi_X \left( x,- \varepsilon \mathcal{L}_x(t,x,\lambda) \right) \nonumber\\
&\ =\ \Pi_X \left(x,-\varepsilon(f_{0,x}(t,x)+ f_x(t,x)\lambda) \right),
\end{align}
and that ascends in the direction of the subgradient with respect to the multiplier $\lambda$
\begin{equation}\label{eqn_multiplier_ascent}
\dot{\lambda} = \Pi_{\Lambda} \left( \lambda,\varepsilon \mathcal{L}_{\lambda}(t,x,\lambda) \right)
= \Pi_{\Lambda} \left(\lambda, \varepsilon f(t,x) \right).
\end{equation}
The projection over the set $X$ in \eqref{eqn_action_descent} is done to assure that the trajectory is always in the set of possible actions. The operator $\Pi_{\Lambda}(\lambda,f)$ is a projected dynamical system in the sense of Definition \ref{def_projected_dynamical_system} over the set $\Lambda$. This projection is done to assure that $\lambda(t) \in \reals^m_+$ for all times $t \in [0,T]$. An important observation regarding \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent} is that the environment is observed locally in space and causally in time. The values of the environment constraints and its subgradients are observed at the current trajectory position $x(t)$ and the values of $f(t,x(t))$ and $f_x(t,x(t))$ affect the derivatives of $x(t)$ and $\lambda(t)$ only. Notice that if the environment function satisfies $f(t,x) \equiv 0$ we recover the algorithm defined in \eqref{eqn_gradient_controller} as a particular case of the saddle point controller.
A block diagram for the controller in \eqref{eqn_action_descent} - \eqref{eqn_multiplier_ascent} is shown in Figure \ref{fig_block_diagram}. The controller operates in an environment to which it inputs at time $t$ an action $x(t)$ that results in a penalty $f(t,x(t))$ and cost $f_0(t,x(t))$. The value of these functions and their subgradients $f_x(t,x(t))$ and $f_{0,x}(t,x(t))$ are observed and fed to the multiplier and action feedback loops. The action feedback loop behaves like a weighted gradient descent controller. We move in the direction given by a linear combination of the the gradient of the objective function $f_{0,x}(t,x(t))$ and the constraint subgradients $f_{i,x}(t,x(t))$ weighted by their corresponding multipliers $\lambda_i(t)$. Intuitively, this pushes $x(t)$ towards satisfying the constraints and to the minimum of the objective function in the set where constraints are satisfied. However, the question remains of how much weight to give to each constraint. This is the task of the multiplier feedback loop. When constraint $i$ is violated we have $f_{i}(t,x(t))>0$. This pushes the multiplier $\lambda_i(t)$ up, thereby increasing the force $\lambda_i(t)f_{i,x}(t,x(t))$ pushing $x(t)$ towards satisfying the constraint. If the constraint is satisfied, we have $f_{i}(t,x(t))<0$, the multiplier $\lambda_i(t)$ being decreased, and the corresponding force decreasing. The more that constraint $i$ is violated, the faster we increase the multiplier, and the more we increase the force that pushes $x(t)$ towards satisfying $f_{i}(t,x(t))<0$. If the constraint is satisfied, the force is decreased and may eventually vanish altogether if we reach the point of making $\lambda_i(t)=0$.
\begin{figure}\centering
\resizebox{9cm}{7cm}{
\input{figures/block_diagram.tex}
}
\caption{Block diagram of the saddle point controller. Once that action $x(t)$ is selected at time $t$, we measure the corresponding values of $f(t,x(t))$, $f_x(t,x(t))$ and $f_{0,x}(t,x(t))$. This information is fed to the two feedback loops. The action loop defines the descent direction by computing weighted averages of the subgradients $f_x(t,x(t))$ and $f_{0,x}(t,x(t))$. The multiplier loop uses $f(t,x(t))$ to update the corresponding weights.}
\label{fig_block_diagram}
\end{figure}
\subsection {Strongly feasible trajectories}\label{subsec:non_opti}
We begin by studying the saddle point controller defined by \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent} in a problem in which optimality is {\it not} taken into account, i.e., $f_0(t,x) \equiv 0$. In this case the action descent equation of the controller \eqref{eqn_action_descent} takes the form:
\begin{equation}\label{eqn_non_opti}
\dot{x} = \Pi_X \left( x,- \varepsilon \mathcal{L}_x(t,x,\lambda) \right) = \Pi_X \left(x,-\varepsilon f_x(t,x)\lambda \right),
\end{equation}
while the multiplier ascent equation \eqref{eqn_multiplier_ascent} remains unchanged. The bounds to be derived for the fit ensure that the trajectories $x(t)$ are strongly feasible in the sense of Definition \ref{def_0ptimality_and_viability}. To state the result consider an arbitrary fixed action $\bar{x} \in X$ and an arbitrary multiplier $\bar{\lambda} \in \Lambda$ and define the energy function
\begin{equation}\label{eqn_lyapunov}
V_{\bbarx,\bar{\lambda}}(x,\lambda)
= \frac{1}{2}\left( ||x-\bbarx||^2+||\lambda -\bar{\lambda}||^2\right).
\end{equation}
We can then bound fit in terms of the initial value $V_{\bbarx,\bar{\lambda}}(x(0),\lambda(0))$ of the energy function for properly chosen $\bbarx$ and $\bar{\lambda}$ as we formally state next.
\begin{theorem}\label{theo:not_opti}
Let $f: \reals \times X \to \reals^m$, satisfying assumptions \ref{as:integrability} and \ref{as:convexity}, where $X \subseteq \reals^n$ is a convex set. If the environment is viable, then the solution $x(t)$ of the dynamical system defined by \eqref{eqn_non_opti} and \eqref{eqn_multiplier_ascent} is strongly feasible for all $T>0$. Specifically, the fit is bounded by
\begin{align}\label{eqn_fit_bound_non_opti}
\mathcal{F}_{T,i} \leq \min_{x^\dagger \in X^\dagger} \frac{1}{\varepsilon} V_{x^\dagger, e_{i}}(x(0),\lambda(0)),
\end{align}
where $e_i$ with $i=1..m$ form the canonical base of $\reals^m$.
\end{theorem}
\begin{proof}
Consider action trajectories $x(t)$ and multiplier trajectories $\lambda(t)$ and the corresponding energy function $V_{\bbarx,\bar{\lambda}}(x(t),\lambda(t))$ in \eqref{eqn_lyapunov} for arbitrary given action $\bbarx \in X$ and multiplier $\bar{\lambda}\in \Lambda$. The derivative $\dot V_{\bbarx,\bar{\lambda}}(x(t),\lambda(t))$ of the energy with respect to time is then given by
\begin{equation}\label{eqn_theo_survival_pf_10}
\dot{V}_{\bar{x},\bar{\lambda}} (x(t),\lambda(t))
= (x(t) - \bbarx)^T\dot{x}(t) + (\lambda(t) -\bar{\lambda})^T\dot{\lambda}(t).
\end{equation}
Substitute the action and multiplier derivatives by their corresponding values given in \eqref{eqn_non_opti} and \eqref{eqn_multiplier_ascent} to reduce \eqref{eqn_theo_survival_pf_10} to
\begin{align}\label{eqn_theo_survival_pf_11}
\dot{V}_{\bbarx,\bar{\lambda}}(x(t),\lambda(t)) =
&(x(t) - \bbarx)^T \Pi_X \left( x, - \varepsilon f_x(t,x(t))\lambda(t)\right) \nonumber \\ &+(\lambda(t)-\bar{\lambda})^T \Pi_{\Lambda} \left(\lambda, \varepsilon f(t,x(t)) \right).
\end{align}
Then, using the result of Lemma \ref{lemma:big_lemma} for both $X$ and $\Lambda$, the following inequality holds:
\begin{align}\label{eqn_theo_survival_pf_11}
\dot{V}_{\bbarx,\bar{\lambda}}(x(t),\lambda(t)) &\leq
\varepsilon (\bbarx-x(t))^T f_x(t,x(t))\lambda(t) \nonumber \\
&+\varepsilon(\lambda(t)-\bar{\lambda})^T f(t,x(t)).
\end{align}
Notice that $f(t,x) \lambda(t)$ is a convex function with respect to the action, therefore we can upper bound the inner product $(\bar{x} - x(t))^Tf_x(t,x(t)) \lambda(t)$ by the quantity $f(t,\bar{x})^T\lambda(t) - f(t,x(t))^T \lambda(t)$ and transform \eqref{eqn_theo_survival_pf_11} into
\begin{align}\label{eqn_theo_survival_pf_12}
\dot{V}_{\bbarx,\bar{\lambda}}(x(t),\lambda(t))&\leq
\varepsilon \left(f(t,\bbarx)-f(t,x(t))\right)^T\lambda(t) \nonumber \\
&+\varepsilon(\lambda(t)-\bar{\lambda})^T f(t,x(t)).
\end{align}
Further note that in the above equation the second and the third term are opposite. Thus, it reduces to
\begin{equation}
\dot{V}_{\bbarx,\bar{\lambda}}(x(t),\lambda(t))\leq \varepsilon\left[\lambda^T(t)f(t,\bbarx) - \bar{\lambda}^T f(t,x(t))\right].
\end{equation}
Rewriting the above expression and then integrating both sides with respect to time from $t = 0 $ to $t =T$ we obtain
\begin{equation}\label{eqn_inter}
\begin{split}
\varepsilon \int_0^T \bigl(\bar{\lambda}^T f(t,x(t)) - \lambda^T(t) &f(t,\bbarx) \bigr)dt \\ &
\leq - \int_0^T \dot{V}_{\bbarx,\bar{\lambda}}(x(t),\lambda(t)) dt.
\end{split}
\end{equation}
Integrating the right side of the above equation we obtain
\begin{align}
-\int_0^T \dot{V}_{\bbarx,\bar{\lambda}}(x(t),&\lambda(t))dt \\\nonumber &
= V_{\bbarx,\bar{\lambda}}(x(0),\lambda(0))-V_{\bbarx,\bar{\lambda}}(x(T),\lambda(T)).
\end{align}
Then using the fact that $V_{\bbarx,\bar{\lambda}}(x(t)),\lambda(t)) \geq 0$ for all $t$, yields
\begin{equation}\label{eqn_inequality_chain}
-\int_0^T \dot{V}_{\bbarx,\bar{\lambda}}(x(t),\lambda(t))dt\leq
V_{\bbarx,\bar{\lambda}}\left(x(0),\lambda(0)\right).
\end{equation}
Then, combining \eqref{eqn_inter} and \eqref{eqn_inequality_chain}, we have that
\begin{equation}
\int_0^T \bar{\lambda}^T f(t,x(t)) - \lambda^T(t) f(t,\bbarx) dt \leq \left( V_{x^\dagger,\bar{\lambda}}(x(0),\lambda(0))\right) / \varepsilon.
\label{eqn_final}
\end{equation}
Since the environment is viable, there exist a fixed action $x^{\dagger}$ such that $f(t,x^{\dagger})\leq 0$ for all $t \geq 0$. Then choosing $\bbarx = x^{\dagger}$, since $\lambda(t)\geq 0$ for all $t$, we have that
\begin{equation}
\lambda^T(t) f(t,x^\dagger) \, \leq 0 \; \forall t\in[0,T].
\end{equation}
Therefore the left hand side of \eqref{eqn_final} can be lower bounded by
\begin{equation}
\bar{\lambda}^T\int_0^Tf(t,x(t)) dt \leq \left(V_{x^\dagger,\bar{\lambda}}(x(0),\lambda(0)\right)/ \varepsilon.
\end{equation}
Choosing $\bar{\lambda} = e_i$ where $e_i$ is the $i$th element of the canonical base of $\reals^m$, we have that for all $i=1..m$:
\begin{equation}
\int_0^T f_i(t,x(t)) dt \leq \left( V_{x^\dagger,e_i}(x(0),\lambda(0)) \right) / \varepsilon.
\end{equation}
Notice that since the above inequality holds for any $x^\dagger\in X^\dagger$ it is also true for the particular $x^\dagger$ that minimizes the right hand side. The left hand side of the above inequality is the $i$th component of the fit. Thus, since the $m$ components of the fit of the trajectory generated by the saddle point algorithm are bounded for all $T$, the trajectory is strongly feasible with the specific upper bound stated in \eqref{eqn_fit_bound_non_opti}.
\end{proof}
Theorem \ref{theo:not_opti} assures that if an environment is viable for an agent that selects actions over a set $X$, the solution of the dynamical system given by \eqref{eqn_non_opti} and \eqref{eqn_multiplier_ascent} is a trajectory $x(t)$ that is strongly feasible in the sense of Definition \ref{def_0ptimality_and_viability}. This result is not trivial, since the function $f$ that defines the environment is observed causally and can change arbitrarily over time. In particular, the agent could be faced with an adversarial environment that changes the function $f$ in a way that makes the value of $f(t,x(t))$ larger. The caveat is that the choice of the function $f$ must respect the viability condition that there exists a feasible action $x^\dagger$ such that $f(t,x^\dagger) \leq 0$ for all $t\in[0,T]$. This restriction still leaves significant leeway for strategic behavior. E.g., in the shepherd problem of Section \ref{sec_shepherd_problem} we can allow for strategic sheep that observe the shepherd's movement and respond by separating as much as possible. The strategic action of the sheep are restricted by the condition that the environment remains viable, which in this case reduces to the not so stringent condition that the sheep stay in a ball of radius $2r$ if all $r_i=r$.
Since the initial value of the energy function $V_{x^\dagger,e_i}(x(0),\lambda(0))$ is the square of the distance between $x(0)$ and $x^\dagger$ added to a term that depends on the distance between the initial multiplier and $e_i$, the bound on the fit in \eqref{eqn_fit_bound_non_opti} shows that the closer we start to the feasible set the smaller the accumulated constraint violation becomes. Likewise, the larger the gain $\varepsilon$, the smaller the bound on the fit is.
As in section \ref{sec:continuous_regret} we observe that increasing $\varepsilon$ can make the bound on the fit arbitrarily small, yet for the same reasons discussed in that section this can't be done.
Further notice that for the saddle point controller defined by \eqref{eqn_non_opti} and \eqref{eqn_multiplier_ascent} the action derivatives are proportional not only to the gain $\varepsilon$ but to the value of the multiplier $\lambda$. Thus, to select gains that are compatible with the system's physical constraints we need to determine upper bounds in the multiplier values $\lambda(t)$. An upper bound follows as a consequence of Theorem \ref{theo:not_opti} as we state in the following corollary.
\begin{corollary}\label{coro_bounded_multipliers}Given the controller defined by \eqref{eqn_non_opti} and \eqref{eqn_multiplier_ascent} and assuming the same hypothesis of Theorem \ref{theo:not_opti}, if the set of actions $X$ is bounded in norm by $R$, then the multipliers $\lambda$ are bounded for all times by
\begin{equation}\label{eqn_multiplier_bound}
0 \leq \lambda_i(t) \leq \left(4R^2+1\right), \ \mbox{for all} \ i=1,\ldots,m.
\end{equation}
\end{corollary}
\begin{proof}
First of all notice that according to \eqref{eqn_multiplier_ascent} a projection over the positive orthant is performed for the multiplier update. Therefore, for each component of the multiplier we have that $\lambda_i(t) \geq 0 $ for all $t\in[0,T]$. On the other hand, since the trajectory of the multipliers is defined by $\dot{\lambda}(t) = \Pi_\Lambda(\lambda(t),\varepsilon f(t,x(t))$, while $\lambda(t) >0$ we have that $\dot{\lambda}(t) = \varepsilon f(t,x(t))$. Let $t_0$ be the first time instant for which $\lambda_i (t) > 0$ for a given $i\in\{1,2,..,m\}$, i.e.,
\begin{equation}
t_0 = \inf \left\{ {t\in [0,T]}, \lambda_i(t) >0 \right\}.
\end{equation}
In addition, let $T^*_0$ be the first time instant greater than $t_0$ where $\lambda_i(t) = 0$, if this time is larger than $T$ we set $T^*_0 = T$, formally this is
\begin{equation}\label{eqn_T_estrella}
T^*_0 = \max \left\{\inf \left\{ {t\in (t_0,T]}, \lambda_i(t) >0 \right\} , T\right\}.
\end{equation}
Further define
$t_{s+1} = \inf \left\{ {t\in [T_s^*,T]}, \lambda_i(t) >0 \right\},$
and
\begin{equation}\label{eqn_T_estrella}
T^*_s = \max \left\{\inf \left\{ {t\in (t_s,T]}, \lambda_i(t) >0 \right\} , T\right\}.
\end{equation}
From the above definition it holds that in any time in the interval $(T^*_s, t_{s+1}]$, we have $\lambda_i(t)=0$. And therefore in those intervals the multipliers are bounded. Consider now $\tau \in (t_s,T^*_s]$. In this case it holds that
\begin{equation}
\int_{t_s}^\tau \dot{\lambda}_i(t)dt = \ \int_{t_s}^\tau \varepsilon f_i(t,x(t))dt.
\end{equation}
Notice that the right hand side of the above equation is, proportional to the $i$th component of the fit restricted to the time interval $[t_0,\tau]$. In Theorem \ref{theo:not_opti} it was proved that the $i$th component of the fit is bounded for all time horizons by $V_{x^\dagger,e_i}(x(t_s),0)/\varepsilon$. In this particular case we have that
\begin{equation}
V_{x^\dagger,e_i}(x(t_s),0) = \frac{1}{2}\left((x(t_s)-x^\dagger)^2 + (0-e_i)^2\right),
\end{equation}
and since for any $x\in X$ we have that $\|x\| \leq R$, we conclude
\begin{equation}
V_{x^\dagger,e_i}(x(t_s),0) \leq \frac{1}{2}\left((2R)^2 +1^2\right).
\end{equation}
Therefore, for all $\tau \in (t_sT^*_s]$
$\lambda_i(\tau) \leq \frac{1}{2}\left(4R^2 +1^2\right)$.
This completes the proof that the multipliers are bounded.
\end{proof}
The bound in Corollary \ref{coro_bounded_multipliers} ensures that action derivatives $\dot x(t)$ remain bounded if the subgradients are. This means that action derivatives increase, at most, linearly with $\varepsilon$ and is not compounded by an arbitrary increase of the multipliers.
The cumulative nature of the fit does not guarantee that the constraint violation is controlled. This is because time intervals of constraint violations can be compensated by time intervals where the constraints are negative. Thus, it is of interest to show that the saddle point controller archives bounded saturated fit for all time horizon. We formalize this result next.
\begin{corollary}\label{corollary_saturated_fit}
Let the hypothesis of Theorem \ref{theo:not_opti} hold. Let $\delta>0$ and let $\bar{\ccalF}_{T}$ be the saturated fit defined in \eqref{eqn_saturated_fit}. Then, the solution of the dynamical system \eqref{eqn_non_opti} and \eqref{eqn_multiplier_ascent} when $f(t,x)$ is replaced by $\bar{f}_{\delta}(t,x)) = \max\left\{f(t,x),-\delta \right\}$ archives a bounded saturated fit. Furthermore the bound is given by
\begin{equation}
\bar\ccalF_{T,i} \leq \min_{x^\dagger \in X^\dagger} \frac{1}{\varepsilon} V_{x^\dagger, e_{i}}(x(0),\lambda(0)),
\end{equation}
%
where $e_i$ with $i=1..m$ form the canonical base of $\reals^m$.
\end{corollary}
\begin{proof}
Since $\bar{f}_{\delta}(t,x)$ is the pointwise maximum of two convex functions, it is a convex function itself. As a consequence of Theorem \ref{theo:not_opti} the fit for the environment $\bar{f}_{\delta}(t,x)$ satisfies
\begin{equation}
\int_0^T \bar{f}_\delta(t,x(t))\, dt \leq \min_{x^\dagger \in X^\dagger} \frac{1}{\varepsilon} V_{x^\dagger, e_{i}}(x(0),\lambda(0)).
\end{equation}
The fact that the left hand side of the above equation corresponds to the saturated fit [c.f. \eqref{eqn_saturated_fit}] completes the proof.
\end{proof}
The above result establishes that a trajectory that follows the saddle point dynamics for the environment defined by $\bar{f}_{\delta}(t,x)$ achieves bounded saturated fit. This means that it is possible to adapt the controller \eqref{eqn_non_opti} and \eqref{eqn_multiplier_ascent}, so that the fit is bounded while not alternating between periods of large under and over satisfaction of the constraints
\subsection{Strongly optimal feasible trajectories}\label{subsec:otpi}
This section presents bounds on the growth of the fit and the regret of the trajectories $x(t)$ that are solutions of the saddle point controller defined by \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent}. These bounds ensure that the trajectory is feasible and strongly optimal in the sense of Definition \ref{def_0ptimality_and_viability}. To derive these bounds we need the following assumption regarding the objective function.
\begin{assumption} \label{as:lower_bound}
There is a finite constant $K$ independent of the time horizon $T$ such that for all $t$ in the interval $[0,T]$.
\begin{equation}\label{eqn_constant_for_lemma}
K \geq f_0(t,x^*) -\min_{x\in X } f_0(t,x),
\end{equation}
where $x^*$ is the solution of the offline problem \eqref{eqn_optimal_strategy}.
\end{assumption}
The existence of the bound in \eqref{eqn_constant_for_lemma} is a mild requirement. Since the function $f_0(t,x)$ is convex, for any time $t$ it is lower bounded if the action space is bounded, as is the case in most applications of practical interest. The only restriction imposed is that $\min_{x\in X } f_0(t,x)$ does not become progressively smaller with time so that a uniform bound $K$ holds for all times $t$. The bound can still hold if $X$ is not compact as long as the span of the functions $f_0(t,x)$ is not unbounded below. A consequence of Assumption \ref{as:lower_bound} is that the regret cannot {\it decrease} faster than a linear rate as we formally state in the following lemma.
\begin{lemma}\label{lemma:regret_lower_bound}
Let $X \subset \reals^n$ be a convex set. If Assumption \ref{as:lower_bound} holds, then the regret defined in \eqref{eqn_continuous_regret} is lower bounded by $-KT$ where $K$ is the constant defined in \eqref{eqn_constant_for_lemma}, i.e.,
\begin{equation}\label{eqn_lemma_regret_lower_bound}
\ccalR_T \geq -KT.
\end{equation} \end{lemma}
\begin{proof}
See Appendix \ref{ap_regret_lower_bound}.
\end{proof}
Observe that regret is a quantity that we want to make small and, therefore, having negative regret is a desirable outcome. The result in Lemma \ref{lemma:regret_lower_bound} puts a floor on how much we can succeed in making regret negative. Using the bound in \eqref{eqn_lemma_regret_lower_bound} and the definition of the energy function in \eqref{eqn_lyapunov} we can formalize bounds on the regret and the fit, for an action trajectory $x(t)$ that follows the saddle point dynamics in \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent}.
\begin{theorem}\label{theo:opti}
Let $X \subset \reals^n$ be a compact convex set and let $f: \reals \times X \to \reals^m$ and $f_0: \reals \times X \to \reals$, be functions satisfying assumptions \ref{as:integrability}, \ref{as:convexity} and \ref{as:lower_bound}. If the environment is viable, then the solution of the system defined by \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent} is a trajectory $x(t)$ that is feasible and strongly optimal for all time horizons $T>0$ if the gain $\varepsilon >1$. In particular, the fit is bounded by
\begin{equation}\label{eqn_penalty_bound}
\ccalF_{T,i} \leq \ccalO\left(\sqrt{KT},\varepsilon^0\right),\end{equation}
and the regret is bounded by
\begin{equation}\label{eqn_regret_upper_bound_full_problem}
\ccalR_T\leq \frac{1}{\varepsilon} V_{x*,0} \left(x(0),\lambda(0)\right),
\end{equation}
where $V_{\bbarx,\bar{\lambda}}(x,\lambda)$ is the energy function defined in \eqref{eqn_lyapunov}, $x^*$ is the solution to the problem \eqref{eqn_optimal_strategy} and $K$ is the constant defined in \eqref{eqn_constant_for_lemma}. The notation $\ccalO\left(\varepsilon^0\right)$ refers to a function that is constant with respect to the gain $\varepsilon$.
\end{theorem}
\begin{proof}
See Appendix \ref{ap_theo_opti}
\end{proof}
Theorem \ref{theo:opti} assures that if the environment is viable for an agent selecting actions from a bounded set $X$, the solution of the saddle point dynamics defined in \eqref{eqn_action_descent}-\eqref{eqn_multiplier_ascent} is a trajectory that is feasible and strongly optimal. The bounds on the fit in theorems \ref{theo:not_opti} and \ref{theo:opti} prove a trade off between optimality and feasibility. If optimality of the trajectory is not of interest it is possible to get strongly feasible trajectories with fit that is bounded by a constant independent of the time horizon $T$ (cf. Theorem \ref{theo:not_opti}). When an optimality criterion is added to the problem, its satisfaction may come at the cost of a fit that may increase as $\sqrt{T}$. An important consequence of this difference is that even if we could set the gain $\varepsilon$ to be arbitrarily large, the bound on the fit cannot be made arbitrarily small. This bound would still grow as $\sqrt{KT}$. The result in Theorem \ref{theo:opti} also necessitates Assumption \ref{as:lower_bound} as opposed to Theorem \ref{theo:not_opti}.
As in the cases of theorems \ref{theo:first_theo} and \ref{theo:not_opti} it is possible to have the environment and objective function selected strategically. Further note that, again, the initial value of the energy function used to bound regret is related with the square of the distance between the initial action and the optimal offline solution of problem \eqref{eqn_optimal_strategy}. It also follows from the proof that this distance is related to the bound on the fit. Thus, the closer we start from this action the tighter the bounds will be. We next show that similar results holds for the saddle point dynamics if we consider the notion of saturated fit in lieu of fit.
\begin{corollary}\label{corollary_saturated_fit2}
Let the hypothesis of Theorem \ref{theo:opti} hold. Let $\delta>0$ and let $\bar{\ccalF}_{T}$ be the saturated fit defined in \eqref{eqn_saturated_fit}. Then, the solution of the dynamical system \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent}, when $f(t,x)$ is replaced by $\bar{f}_{\delta}(t,x)) = \max\left\{f(t,x),-\delta \right\}$ achieves a regret satisfying \eqref{eqn_regret_upper_bound_full_problem} and saturated fit that is bounded by
\begin{equation}
\bar\ccalF_{T,i} \leq \ccalO\left(\sqrt{KT},\varepsilon^0\right).
\end{equation}
\end{corollary}
\begin{proof}
Same as Corollary \ref{corollary_saturated_fit}.
\end{proof}
The above result establishes that a trajectory that follows the saddle point dynamics for the environment defined by $\bar{f}_{\delta}(t,x)$ achieves bounded saturated fit. This means that it is possible to adapt the controller \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent}, so that the growth of the fit is controlled while not alternating between periods of large under and over satisfaction of the constraints.
In the next section we evaluate the performance of the saddle point controller, after a pertinent remark on the selection of the gain.
\begin{remark}[\bf{Gain depending on the Time Horizon}] If it were possible to select the gain as a function of the time horizon $T$, fit could be bounded by a constant that does not grow with $T$. Take \eqref{eqn_algun_numero} and choose $\bar{\lambda} = e_i T$, where $e_i$ is the $i$-th component of the canonical base of $\mathbb{R}^m$ we have that
\begin{equation}
T\int_0^Tf_i(t,x(t)) dt \leq \left( V_{x^*,Te_i} (x(0),\lambda(0))\right) / \varepsilon +KT.
\end{equation}
With this selection of $\bar{\lambda}$ the function $V_{x^*,Te_i} \left(x(0),\lambda(0))\right)$ grows like $T^2$. Dividing both sides of the above equation by $T$ we have that the $i$-th component of the fit is bounded by
\begin{equation}\label{eqn_rmk_variable_gain_constant_fit}
\ccalF_{T,i} \leq \ccalO(T)/\varepsilon +K.
\end{equation}
If the gain is set to have order $\ccalO(T)$, the right hand side of \eqref{eqn_rmk_variable_gain_constant_fit} becomes of order $\ccalO(T^0)$. This means that fit can be bounded by a constant that does not depend on $T$.
\end{remark}
\section{Numerical experiments}\label{sec:examples}
We evaluate performance of the saddle point algorithm defined by \eqref{eqn_action_descent}-\eqref{eqn_multiplier_ascent} in the solution of the shepherd problem introduced in Section \ref{sec_shepherd_problem}. We determine sheep paths using a perturbed polynomial characterization akin to the one in \eqref{eqn_shepherd_position}. Specifically, letting $p_j(t)$ be elements of a polynomial basis, the path $ y_{i} (t) = [y_{i,1} (t), y_{i,2} (t)]^T$ of the $i$th sheep is given by
\begin{equation}\label{eqn_sheep_position}
y_{i,k} (t) =\sum_{j=0}^{n_i-1} y_{i,k,j} p_j(t) + w_{i,k}(t),
\end{equation}
where $k=1,2$ denotes different path components, $n_i$ the dimension of the base that parameterizes the path followed by sheep $i$, and $y_{i,k,j}$ represent the corresponding $n_i$ coefficients. The noise terms $w_{i,k}(t)$ are Gaussian white with zero mean, standard deviation $\sigma$ and independent across components and sheep. Their purpose is to obtain more erratic paths.
To determine $y_{i,k,j}$ we make $w_{i,k}(t)=0$ in \eqref{eqn_sheep_position} and require all sheep to start at $ y_{i} (0) =[0,0]^T$ and finish at $y_{i} (T) =[1,1]^T$. A total of $L$ random points $\{\tdy_l\}_{l=1}^L$ are then drawn independently and uniformly at random in the unit box $[0,1]^2$. Sheep $i=1$ is required to pass through points $\tdy_l$ at times $lT/(L+1)$, i.e., $y_1(lT/(L+1))=\tdy_l$. For each of the other sheep $i\neq 1$ we draw $L$ random offsets $\{\Delta\tdy_{i,l}\}_{l=1}^L$ uniformly at random from the box $[-\Delta,\Delta]^2$ and require the $i$th sheep path to satisfy $y_i(lT/(L+1))=\tdy_l + \Delta\tdy_{i,l}$. Paths $y_i(t)$ are then chosen as those that minimize the path integral of the acceleration squared subject to the constraints of each path
\begin{alignat}{2}\label{eqn_quadratic program}
y^*_{i}
= &\argmin && \int_{0}^T \|\ddot{y}_{i} (t)\|^2 dt, \nonumber\\
&\st && y_{i} (0) =[0,0]^T, \quad
y_{i} (T) =[1,1]^T, \nonumber\\
& && y_i(lT/(L+1))=\tdy_l + \Delta\tdy_{i,l} ,
\end{alignat}
where, by construction $\Delta\tdy_{1,l}=0$. The paths in \eqref{eqn_quadratic program} can be computed as solutions of a quadratic program \cite{DM:11}. Let $y_i^*(t)$ be the trajectory given by \eqref{eqn_sheep_position} when we set $y_{i,k,j} =y_{i,k,j}^*$. We obtain the paths $y_{i,k} (t)$ by adding $w_{i,k}(t)$ to $y^*_{i} (t)$.
In subsequent numerical experiments we consider $m=5$ sheep, a time horizon $T=1$, and set the proximity constraint in \eqref{eqn_sheep_environment} to $r_i=0.3$. We use the polynomial basis $p_j(t)=t^j$ in both, \eqref{eqn_shepherd_position} and \eqref{eqn_sheep_position}. The number of basis elements in both cases is set to $n=n_i=30$. To generate sheep paths we consider a total of $L=3$ randomly chosen intermediate points, set the variation parameter to $\Delta=0.1$, and the perturbation standard deviation to $\sigma=0.1$. These problem parameters are such that the environment is most likely viable in the sense of Definition \ref{def_viable_environment}. We check that this is true by solving the offline feasibility problem. If the environment is not viable a new one is drawn before proceeding to the implementation of \eqref{eqn_action_descent}-\eqref{eqn_multiplier_ascent}.
We emphasize that even if the path of the sheep is known to us, the information is not used by the controller. The latter is only fed information of the position of the sheep at the current time, which it uses to evaluate the environment functions $f_i(t,x)$ in \eqref{eqn_sheep_environment}, their gradients $f_{ix}(t,x)$ and the gradient of $f_0(t,x)$. In the first problem considered $f_0(t,x)$ is identically zero, in the second takes the form of \eqref{eqn_black_sheep} and in the last problem the form of \eqref{eqn_minimum acceleration}. Since the agent is dynamicless, there are not physical constraints on the derivatives of the system, therefore the gain $\varepsilon$ in \eqref{eqn_action_descent}-\eqref{eqn_multiplier_ascent} can be set to have any value.
\subsection{Strongly feasible trajectories}\label{sec_pure_feasibility}
We consider a problem without optimality criterion in which case \eqref{eqn_action_descent}-\eqref{eqn_multiplier_ascent} simplifies to \eqref{eqn_non_opti}-\eqref{eqn_multiplier_ascent} and the strong feasibility result in Theorem \ref{theo:not_opti} applies. The system's behavior is illustrated in Figure \ref{fig:trajectory} when the gain is set to $\varepsilon = 50$. In this problem the average and maximal speed of the sheep is $5.1km/h$ and $14.8km/h$ respectively while for the shepherd these are $6.1km/h$ and $18.3 km/h$ for the selected gain. This speeds are in in the range of reasonable velocities for this particular problem. A qualitative examination of the sheep and shepherd paths shows that the shepherd succeeds in following the herd. A more quantitative evaluation is presented in Figure \ref{fig_relation_violation_multipliers} where we plot the instantaneous constraint violation $f_i(t,x(t))$ with respect to each sheep for the trajectories $x(t)$. Observe the oscillatory behavior that has the constraint violations $f_i(t,x(t))$ hovering at around $f_i(t,x(t))=0$. When the constraints are violated, i.e., when $f_i(t,x(t))>0$, the saddle point controller drives the shepherd towards a position that makes him stay within $r_i$ of all sheep. When a constraint is satisfied we have $f_i(t,x(t))<0$. This drives the multiplier $\lambda_i(t)$ towards 0 and removes the force that pushes the shepherd towards the sheep (c.f. Figure \ref{fig_relation_violation_multipliers}). The absence of this force makes the constraint violation grow and eventually surpass the maximum tolerance $f_i(t,x(t))=0$. At this point the multipliers start to grow and, as a consequence, to push the shepherd back towards proximity with the sheep.
The behavior observed in Figure \ref{fig_relation_violation_multipliers} does not contradict the result in Theorem \ref{theo:not_opti} which gives us a guarantee on fit, not on instantaneous constraint violations. The components of the fit are shown in Figure \ref{fig:constraint_violation} where we see that they are indeed bounded. Thus, the trajectory is feasible in the sense of Definition \ref{def_0ptimality_and_viability}, even if the instantaneous problem's constraints are being violated at specific time instances. Further note that the fit is not only bounded but actually becomes negative. This is a consequence of the relatively large gain $\varepsilon=50$ which helps the shepherd to respond quickly to the sheep movements. The fit for a second experiment in which the gain is reduced to $\varepsilon=5$ is shown in Figure \ref{fig:violation_5eps}. In this case the fit stabilizes at a positive value. This behavior is expected because reducing $\varepsilon$ decreases the speed with which the shepherd can adapt to changes in the sheep paths. More to the point, the bound on the fit in Theorem \ref{theo:not_opti} is inversely proportional to the gain $\varepsilon$. The paths and instantaneous constraints violations for $\varepsilon=5$ are not shown but they are qualitatively similar to the ones shown for $\varepsilon=50$ in figures \ref{fig:trajectory} and \ref{fig_relation_violation_multipliers}.
\begin{figure}\centering
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/trajectory_5sheep.pdf}
\caption{Path of the sheep and the shepherd for the feasibility-only problem (Section \ref{sec_pure_feasibility}) when the gain of the saddle point controller is set to be $\varepsilon =50$. The shepherd succeed in following the herd since its path -- in red -- is close to the path of all sheep.}
\label{fig:trajectory}\end{figure}
\begin{figure}
\centering
\begin{subfigure}[b]{\linewidth}
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/each_time_violation_5sheep.pdf}
\caption{Instantaneous constraint value. } \label{fig:instant_violation}
\end{subfigure}\par\vfill \bigskip
\begin{subfigure}[b]{\linewidth}
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/multipliers_feasibility.pdf}
\caption{Temporal evolution of the multipliers.} \label{fig_multipliers_feasibility}
\end{subfigure}\bigskip
\caption{Relationship between the instantaneous value of the constraints and their corresponding multipliers for the feasibility-only problem (Section \ref{sec_pure_feasibility}). At the times in which the value of a constraint is positive, its corresponding multiplier increases. When the value of the multipliers is large enough a decrease of the value of the constraint function is observed. Once the constraint function is negative the corresponding multiplier decreases until it reaches zero. }\label{fig_relation_violation_multipliers}
\end{figure}
\begin{figure*}
\centering
\begin{subfigure}[b]{0.5\linewidth}
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/constraint_violation_5sheep.pdf}
\caption{Experiment with gain $\varepsilon = 50$.}
\label{fig:constraint_violation}
\end{subfigure}%
~
\begin{subfigure}[b]{0.5\linewidth}
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/constraint_violation_eps5_5sheep.pdf}
\caption{Experiment with gain $\varepsilon = 5$.}
\label{fig:violation_5eps}
\end{subfigure}
~
\caption{Fit $\mathcal{F}_T$ for two different controller gains in the feasibility-only problem (Section \ref{sec_pure_feasibility}). Fit is bounded in both cases as predicted by Theorem \ref{theo:not_opti}. As is also predicted by Theorem \ref{theo:not_opti}, the larger the value of the gain $\varepsilon$ the smaller the bound on the fit of the shepherd's trajectory.}\label{fig_fit}
\end{figure*}
\subsection{Preferred sheep problem}\label{sec_preferred_sheep}
Besides satisfying the constraints in \eqref{eqn_sheep_environment}, the shepherd wishes to follow the first (black) sheep as close as possible. This translates into the optimality criterion \eqref{eqn_black_sheep}. Since the sheep trajectories are viable the hypotheses of Theorem \ref{theo:opti} hold. Thus, for a shepherd following the dynamics \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent}, the resulting trajectory is feasible and strongly optimal.
Given that the trajectory is guaranteed to be feasible, we expect to have the fit bounded by a sublinear function of $T$. This does happen, as can be seen in the fit trajectories illustrated in Figure \ref{fig_fit_preferred_sheep} where a gain $\varepsilon =50$ is used. In fact, the fit does not grow and is bounded by a constant for all time horizons $T$. The trajectory is therefore not only feasible but strongly feasible. This does not contradict Theorem \ref{theo:opti} because strong feasibility implies feasibility. The reason why it's reasonable to see bounded fit here is that the objective function pushing the shepherd closer to the sheep is, in a sense, redundant with the constraints that push the shepherd to stay closer to all sheep. This redundancy can be also observed in the fact that the fit in this problem (c.f. Figure \ref{fig_fit_preferred_sheep}) is smaller than the fit in the problem of Section \ref{sec_pure_feasibility} (c.f. Figure \ref{fig:constraint_violation}). To explain why this may happen, focus on the value of the multipliers in Figure \ref{fig_multipliers_feasibility} between, e.g., times $0.07\text{h} < t < 0.21\text{h}$. During this time the multipliers are equal to zero because all constraints are satisfied. As a consequence, the Lagrangian subgradient with respect to the action is identically zero in the time interval. In turn, this implies that the action is constant and no effort is made to reduce the value of the constraints. If the optimality criterion was present, the shepherd would be pushed towards the black sheep and fit would be further reduced.
The regret corresponding to the trajectory for this experiment with $\varepsilon =50$ is shown in Figure \ref{fig_regret_preferred_sheep}. Since the trajectory is strongly optimal as per Theorem \ref{theo:opti}, we expect regret to be bounded. This is the case in Figure \ref{fig_regret_preferred_sheep}
The path of the shepherd is not shown for this experiment as it is qualitatively analogous to the one in Figure \ref{fig:trajectory} for the feasibility-only problem considered in Section \ref{sec_pure_feasibility}.
\subsection{Minimum acceleration problem}\label{sec_minimum_acceleration}
We consider, an environment defined by the distances between the shepherd and the sheep given by \eqref{eqn_sheep_environment}, with the minimum acceleration objective defined in \eqref{eqn_minimum acceleration}. Since the construction of the target trajectories gives a viable environment we satisfy, again, the hypotheses of Theorem \ref{theo:opti}. Hence, for a shepherd following the dynamics given by \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent}, the action trajectory is feasible and strongly optimal. In this section the gain of the controller is set to $\varepsilon = 50$.
A feasible trajectory implies that the fit must be bounded by a function that grows sublinearly with the time horizon $T$. Notice that this is the case in Figure \ref{fig_fit_acceleration}. Periods of growth of the fit are observed, yet the presence of inflection points is an evidence of the growth being controlled. The fit in this problem is larger than the one in problem \ref{sec_preferred_sheep} (c.f figures \ref{fig_fit_preferred_sheep} and \ref{fig_fit_acceleration}). This result is predictable since the constraints and the objective function push the action in different directions. For instance, suppose that all constraints are satisfied and that the Lagrange multipliers are zero. Then, the subgradient of the Lagrangian is equal to the subgradient of the objective function. Hence the action will be modified trying to minimize the acceleration without taking the constraints (distance with the sheep) into account. Hence, pushing the action to the boundary of the feasible set. In this problem, this translates into the fact that the shepherd does not follow the sheep as closely as in the problems in sections \ref{sec_pure_feasibility} and \ref{sec_preferred_sheep} (c.f Figure \ref{fig_trajectory_acceleration}).
Since the trajectory is strongly optimal, we should observe a regret bounded by a constant. This is the case in Figure \ref{fig_regret_acceleration}, where in fact we observe negative regret for some time intervals. Negative regret implies that the trajectory of the shepherd is incurring a total cost that is smaller than the one associated with the optimal solution. Notice that while the optimal fixed action minimizes the total cost as defined in \eqref{eqn_optimal_strategy} it does not minimize the objective at all times. Thus, by selecting different actions the shepherd can suffer smaller instantaneous losses than the ones associated with the optimal fixed action. If this is the case, regret -- which is the integral of the difference between these two losses -- can be negative.
\begin{figure}\centering
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/true_fit_preferred_sheep.pdf}
\caption{Fit $\mathcal{F}_T$ for the preferred sheep problem (Section \ref{sec_preferred_sheep}) when the gain of the saddle point controller is set to be $\varepsilon=50$. As predicted by Theorem \ref{theo:opti} the trajectory is feasible since the fit is bounded, and, in fact, appears to be strongly feasible. Since the subgradient of the objective function is the same as the subgradient of the first constrain the fit is smaller than in the pure feasibility problem (c.f Figure \ref{fig_fit}). }
\label{fig_fit_preferred_sheep}\end{figure}
\begin{figure}\centering
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/regret_preferred_sheep.pdf}
\caption{Regret $\mathcal{R}_T$ for the preferred sheep problem (Section \ref{sec_preferred_sheep}) when the gain of the saddle point controller is set to be $\varepsilon=50$. The trajectory is strongly optimal, as predicted by Theorem \ref{theo:opti}, since the regret is bounded by a constant. The initial increment in the regret is due to the fact that the shepherd starts away from the first sheep while in the optimal offline trajectory would start close to it.}
\label{fig_regret_preferred_sheep}\end{figure}
\begin{figure}\centering
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/trajectory_acceleration.pdf}
\caption{Path of the sheep and the shepherd for the minimum acceleration problem (Section \ref{sec_minimum_acceleration}) when the gain of the saddle point controller is set to be $\varepsilon =50$. Observe that the shepherd path -- in red -- is not as close to the path of the sheep as in Figure \ref{fig:trajectory}. This is reasonable because the objective function and the constraints push the shepherd in different directions.}
\label{fig_trajectory_acceleration}\end{figure}
\begin{figure}\centering
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/fit_acceleration.pdf}
\caption{Fit $\mathcal{F}_T$ for the minimum acceleration problem (Section \ref{sec_minimum_acceleration}) when the gain of the saddle point controller is set to $\varepsilon=50$. Since the fit is bounded, the trajectory is feasible in accordance with Theorem \ref{theo:opti}. Since the gradient of the objective function and the gradient of the feasibility constraints tend to point in different directions, the fit is larger than in the preferred sheep problem (c.f Figure \ref{fig_fit_preferred_sheep}).}
\label{fig_fit_acceleration}\end{figure}
\begin{figure}\centering
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/true_regret_acceleration.pdf}
\caption{Regret $\mathcal{R}_T$ for the minimum acceleration problem (Section \ref{sec_minimum_acceleration}) when the gain of the saddle point controller is set to be $\varepsilon=50$. The trajectory is strongly optimal as predicted by Theorem \ref{theo:opti}. Observe that regret is negative due to the fact that the agent is allowed to select different actions at different times as opposed to the clairvoyant player that is allowed to select a fixed action.}
\label{fig_regret_acceleration}\end{figure}
\subsection{Saturated Fit}\label{sec_saturated_fit}
We apply the modified saddle point algorithm in the setting of Section \ref{sec_preferred_sheep} so to consider the saturated fit [c.f. \eqref{eqn_saturated_fit}] in lieu of the fit. Since the construction of the target trajectories gives a viable environment the hypotheses of Corollary \ref{corollary_saturated_fit2} are satisfied. Hence for a shepherd following the dynamics given by \eqref{eqn_action_descent} and \eqref{eqn_multiplier_ascent}, the trajectories are such that have saturated fit bounded by a function that grows sub linearly and bounded regret. For the simulation in this section the gain of the controller is set to $\varepsilon = 50$. Observe that the shepherd succeeds in following the herd, since his path remains close to the sheep (c.f. Figure \ref{fig_saturated_trajectory}). As predicted by the Corollary \ref{corollary_saturated_fit2} the fit of the trajectory is bounded by a function that grows sub linearly and the regret is bounded by a constant as it can be observed in figures \ref{fig_saturated_fit} and \ref{fig_saturated_regret} respectively. Further notice that the regret in this scenario is similar to the regret of the trajectory in the preferred sheep problem (c.f. Section \ref{sec_preferred_sheep}).
\begin{figure}\centering
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/saturated_trajectory.pdf}
\caption{Path of the sheep and the shepherd for preferred sheep problem when saturated fit is considered (Section \ref{sec_saturated_fit}) and the gain of the saddle point controller is set to be $\varepsilon =50$. The shepherd succeed in following the herd since its path -- in red -- is close to the path of all sheep.}
\label{fig_saturated_trajectory}\end{figure}
\begin{figure}\centering
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/saturated_fit.pdf}
\caption{Saturated fit $\mathcal{F}_T^{sat}$ for the preferred sheep problem (Section \ref{sec_saturated_fit}) when the gain of the saddle point controller is set to $\varepsilon=50$. Since the saturated fit grows sublinearly in accordance with Corollary \ref{corollary_saturated_fit2}, the trajectory is feasible. }
\label{fig_saturated_fit}\end{figure}
\begin{figure}\centering
\includegraphics[width=\linewidth, height=0.62\linewidth]{./figures/saturated_regret.pdf}
\caption{Regret $\mathcal{R}_T$ for the preferred sheep problem when saturated fit is considered (Section \ref{sec_saturated_fit})and the gain of the saddle point controller is set to be $\varepsilon=50$. The regret is bounded as predicted by Corollary \ref{corollary_saturated_fit2} and therefore the trajectory is strongly optimal. Notice that regret in this case is identical to regret in the preferred sheep problem when regular fit is considered (c.f. Figure \ref{fig_regret_preferred_sheep}). }
\label{fig_saturated_regret}\end{figure}
\section{Conclusion}\label{sec_conclusions}
We considered a continuous time environment in which an agent must select actions to satisfy a set of constraints that are time varying and unknown a priori. We defined a viable environment as one in which there is a fixed action that satisfies the constraints at all times. We defined the fit as the cumulated constraint violation and the notions of feasible and strongly feasible trajectories. Feasible trajectories are such that the fit is bounded by a constant independent of the time horizon, and strongly feasible trajectories are such that the fit is bounded by a sublinear function of the time horizon. An objective function was considered to select a strategy that meets an optimality criterion and we defined regret in continuous time as the difference between the cumulative costs of the agent and the best clairvoyant agent. We then defined strongly optimal trajectories as those for which the regret is bounded by a constant that is independent of the time horizon.
We proposed an online version of the saddle point controller of Arrow-Hurwicz to generate trajectories with small fit and regret. We showed that for any viable environment the trajectories that follow the dynamics of this controller are: (i) Strongly feasible if no optimality criterion is considered. (ii) Feasible and strongly optimal when an optimality criterion is considered. Numerical experiments on a shepherd that tries to follow a herd of sheep support these theoretical results.
Future research includes studying asymptotic convergence of the saddle point dynamics to the optimal trajectory and studying systems with second order dynamics. In this setting, it is possible to add a term in the objective function that penalizes the action derivative, therefore allowing to control it and maintaining in a desired range.
\section{Introduction}
The motivation for this paper is the navigation of a time varying convex environment defined as a set of convex constraints that an agent must satisfy at all times. The constraints are unknown a priori, vary arbitrarily in time in a possibly discontinuous manner, and are observed locally in space and causally in time. The goal of the agent is to find a feasible strategy that satisfies all of these constraints. This paper shows that an online version of the saddle point algorithm of Arrow and Hurwicz \cite{arrow_hurwicz} executed by the agent succeeds in finding such strategy. If the agent wants to further minimize a convex cost, we show that the same algorithm succeeds in finding an strategy that is feasible at all times and optimal on average.
To understand the contribution of this paper it is important to observe that the navigation problem outlined above can be mathematically formulated as the solution of a convex program
\cite{rimon1992exact,warren1989global,Khatib:1986:ROA:6806.6812,ge2000new,vadakkepat2000evolutionary}
whose solution is progressively more challenging when we progress from deterministic settings to stochastic and online settings. Indeed, in a determinist setting the cost and constraints are fixed. This yields a canonical convex optimization problem that can be solved with extremum seeking controllers based on gradient descent \cite{hirsch2004differential, krstic2000stability, ariyur2003real, tan2006non}, primal-dual methods \cite{arrow_hurwicz,nedic2009subgradient,uzawa1958iterative,maistroskii1977gradient,feijer2010stability}, or interior point methods \cite[Chapter 11]{boyd2004convex}. In a stochastic setting cost and constraints are not constant but vary randomly according to a stationary distribution. The agent's goal is then expressed as the selection of an action that minimizes the expected value of the objective function while satisfying constraints in an average sense \cite{ atanasov2012stochastic, azuma2012stochastic, Liu20101443}
This problem is more complicated than its deterministic counterpart but it can be solved using, e.g., stochastic gradient descent \cite{robbins1951stochastic, schmidt2013minimizing, konevcny2013semi} or stochastic quasi-Newton's methods \cite{mokhtari2014res}.
In this paper we consider online formulations in which cost and constraints can vary arbitrarily, perhaps strategically, and where the goal is to find an action that is good on average and that satisfies the constraints at all times -- assuming such an action exists, which, when functions change strategically, restricts adversarial actions. In this case, {\it unconstrained} cost minimization can be formulated in the language of regret \cite{blackwell1956analog, vapnik2000nature, shalev2011online} whereby agents operate online by selecting plays that incur a cost selected by nature. The cost functions are revealed to the agent ex post and used to adapt subsequent plays. The goodness of these {\it online} policies are determined by comparing to the optimal action chosen \textit{offline} by a clairvoyant agent that has prescient access to the cost. Regret is defined as the difference of the accumulated cost attained online and the optimal offline cost. It is a remarkable fact that an online version of gradient descent is able to find plays whose regret grows at a sublinear rate when the cost is a convex function \cite{Zinkevich03, hazan2007logarithmic} -- therefore suggesting vanishing per-play penalties of online plays with respect to the clairvoyant play.
The constrained optimization equivalent of gradient descent is the saddle point method applied to the determination of a saddle point of the Lagrangian function \cite{arrow_hurwicz}. This method interprets each constraint as a separate potential and descends on a linear combination of their gradients. The coefficients of this linear combination are multipliers that adapt dynamically so as to push the agent to the optimal solution in the feasible region. Saddle point algorithms and variations have been widely studied \cite{nedic2009subgradient,uzawa1958iterative,maistroskii1977gradient,feijer2010stability} and used in various domains such as decentralized control \cite{low1999optimization,chiang2007layering} and image processing, see e.g. \cite{chambolle2011first}. Our observation is that since an online version of gradient descent succeeds in achieving small regret, it is not unreasonable to expect an online saddle point method to succeed in finding feasible actions with small regret.
The main contribution of this paper is to prove that this expectation turns out to be true. We show that an online saddle point algorithm that observes costs and constraints ex post succeeds in finding policies that are feasible and have small regret. Central to this development is the definition of a viable environment as one in which there exist an action that satisfies the time varying constraints at all times and the introduction of the notion of fit (Section \ref{sec:survivability}). The latter is defined as a vector that contains the time integrals of the constraints evaluated across the trajectory and is the analogous of regret for the satisfaction of constraints. In the same way in which the accumulated payoff of the online trajectory is compared with the payoff of the offline trajectory, fit compares the accumulation of the constraints along the trajectory with the feasibility of an offline viable strategy. As such, a trajectory can achieve small fit by becoming feasible at all times or by alternating periods in which the constraints are violated with periods in which the constraints are satisfied with slack. This notion of fit is appropriate for constraints that have a cumulative nature. For cases where this is not appropriate we introduce the notion of saturated fit in which only violations of the constraint are accumulated. A trajectory with small saturated fit is one in which the constraints are violated by a significant amount only for a short period of time.
Technical developments begin with the derivation of a projected gradient controller to limit the growth of regret in an environment without constraints (Section \ref{sec:continuous_regret}). The purpose of this section is to introduce tools and to clarify connections with existing literature in discrete time \cite{Zinkevich03, hazan2007logarithmic} and continuous time regret \cite{viossat2013no, sorin2009exponential, kwon2014continuous}. An important conclusion here is that regret in continuous time can be bounded by a constant that is independent of the time horizon, as opposed to the sublinear growth that is observed in discrete time.
We then move onto the main part of the paper in which we propose to control fit and regret growth with the use of an online saddle point controller that moves along a linear combination of the negative gradients of the instantaneous constraints and the objective function. The coefficients of this linear combination are adapted dynamically as per the instantaneous constraint functions (Section \ref{sec:main}). This online saddle point controller is a generalization of (offline) saddle point in the same sense that an online gradient controller generalizes (offline) gradient descent. We show that if there exists an action that satisfies the environmental constraints at all times, the online saddle point controller achieves bounded fit if optimality is not of interest (Theorem \ref{theo:not_opti}). When optimality is considered, the controller achieves bounded regret and a fit that grows sublinearly with the time horizon (Theorem \ref{theo:opti}). Analogous results are derived for saturated fit. I.e., it is bounded by a constant when optimality is not of interest and grows sublinearly otherwise (corollaries \ref{corollary_saturated_fit} and \ref{corollary_saturated_fit2}). Throughout the paper we illustrate concepts with the problem of a shepherd that has to stay close to his herd (Section \ref{sec_shepherd_problem}). A numerical analysis of this problem closes the paper (Section \ref{sec:examples}) except for concluding remarks (Section \ref{sec_conclusions}).
\medskip\noindent{\bf Notation.} A multivalued function $f:\reals^n\to\reals^m$ is defined by stacking component functions, i.e., $f:=[f_1,\ldots,f_m]^T$. The notation $\int f(x)dx:=[\int f_1(x)dx,\ldots,\int f_m(x)dx]^T$ represents a vector stacking individual integrals. An inequality $x\leq y$ between vectors $x,y\in\reals^n$ is interpreted componentwise. An inequality $x\leq c$ between a vector $x=[x_1,\ldots,x_n]^T\in\reals^n$ and a scalar $c\in\reals$ means that $x_i\leq c$ for all $i$.
\subsubsection{#1}\vspace{-3\baselineskip}\color{black}\bigskip{\noindent \bf \thesubsubsection. #1.}}
\newcommand{\myparagraph}[1]{\needspace{1\baselineskip}\medskip\noindent {\it #1.}}
\newcommand{\myparagraphtc}[1]{\needspace{1\baselineskip}\medskip\noindent {\it #1.}\addcontentsline{toc}{subsubsection}{\qquad\qquad\quad#1}}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,299 |
Q: Disable/Enable USB port Android Xamarin I need to disable/enable a USB port from an Android device, the project is Xamarin Android.
I've just test the USBManager class, from USB Host API, but I need to detach the USB device programmaticaly, and not only disconnect it.
Are there some libraries or work around to manage this kind of problems?
Thanks.
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\section{Introduction}
\label{intro}
It is common wisdom that the form of the relativistic stress-energy tensor in a
thermodynamic equilibrium state has the ideal form:
$$
T^{\mu\nu} = (\rho + p) u^\mu u^\nu - p g^{\mu\nu}
$$
where $\rho$ and $p$ are the energy density and pressure, thermodynamic functions of
temperature $T$ and chemical potential $\mu$, and $u$ a constant four-velocity.
In quantum statistical mechanics, the above expression corresponds to the renormalized
mean value \footnote{For free quantum fields, by renormalization we mean the use of normal
ordering in the stress-energey tensor operator} of the quantum stress-energy tensor
operator, built from local quantum fields, with the density operator:
\begin{equation}\label{homo}
{\widehat{\rho}} = (1/Z) \exp [-\beta \cdot {\widehat P} + \zeta {\widehat Q}]
\ee
where $\beta = (1/T) u$ is a constant inverse temperature four-vector (or, simply,
four-temperature), with $T = 1/\sqrt{\beta^2}$ being the proper (or comoving) temperature
and $u$ the constant four-velocity, $\zeta=\mu/T$ is the ratio between proper chemical
potential and proper temperature, ${\widehat P}$ the four-momentum operator and ${\widehat Q}$ an internal
conserved charge:
\begin{equation}\label{tideal}
T^{\mu\nu}(x) = \tr ( {\widehat{\rho}} {\widehat T}^{\mu\nu}(x))_{\rm ren} = \frac{1}{Z} \tr ({\widehat T}^{\mu\nu}(x)
\exp [-\beta \cdot {\widehat P}+ \zeta {\widehat Q}])_{\rm ren} = (\rho + p) u^\mu u^\nu - p g^{\mu\nu}
\ee
The form (\ref{tideal}) is dictated by the symmetries of the density operator (\ref{homo})
which is traslationally invariant and isotropic in the rest frame where $\beta =
(1/T)(1,{\bf 0})$.
However, the density operator (\ref{homo}), is not the only form
of global thermodynamic equilibrium, which is, in general, a state where the entropy
$S=-\tr ({\widehat{\rho}} \log {\widehat{\rho}})$ is constant. For instance, it is well known \cite{landau,
vilenkin} that in non-relativistic quantum mechanics the operator:
\begin{equation}\label{rotating}
{\widehat{\rho}} = (1/Z) \exp [-\widehat H /T_0 + \omega \widehat J_z/T_0]
\ee
where $T_0$ is a constant global temperature \footnote{The global temperature $T_0$
is a temperature measured by a thermometer at rest with the external observer.
In general, it differs from the proper temperature $T$ measured by a comoving thermometer},
$\widehat H$ the hamiltonian and $\widehat J_z$ the angular momentum operator along
some axis $z$, represents a globally equilibrated spinning fluid with angular velocity
$\omega$. Similarly (see sect.~\ref{statmech}) the operator:
\begin{equation}\label{accelerating}
{\widehat{\rho}} = (1/Z) \exp [-\widehat H /T_0 + a \widehat K_z/T_0]
\ee
$\widehat K_z$ being the generator of a Lorentz boost along the $z$ axis, represents
a relativistic fluid with constant comoving acceleration along the $z$ direction
and it is still an equilibrium distribution. These two cases belong to a more general
class of thermodynamic equilibria which, in special relativity, are characterized by
a four-temperature $\beta(x)$ field fulfilling the equation
\begin{equation}\label{kill}
\partial_\mu \beta_\nu + \partial_\nu \beta_\mu = 0
\ee
which means that the four-temperature is a Killing vector field.
We will show how for such thermodynamic equilibrium states, with the appropriate
treatment in quantum relativistic statistical mechanics, the ideal form of the
stress-energy tensor gets quantum corrections -- vanishing in the $\hbar \rightarrow 0$
limit -- whose leading terms are proportional to the squared gradients of $\beta$,
which in turn can be expressed in terms of the acceleration $a^\mu$ and the
vorticity $\omega^\mu$ fields (see sect.~\ref{expansion} for definitions):
$$
T^{\mu\nu} = (\rho + p) u^\mu u^\nu - p g^{\mu\nu} + \hbar^2 \left( {\cal O}(a^2)+
{\cal O}(\omega^2)+{\cal O}(a\omega) \right)
$$
As we will see, these corrections are normally tiny but they can become relevant
under specific circumstances and, moreover, they are not microscopic in the sense
of being relevant only at very small scales.
The appearance of these terms is somehow in contrast to the widespread belief that
deviations from the ideal form (\ref{tideal}) can only arise in presence of dissipative
processes. In fact, the existence of such terms has been pointed out by a classification
of second order gradient corrections of the stress-energy tensor in conformal hydrodynamics
\cite{roma1,roma2} also by means of kinetic theory~\cite{denicol} and some coefficients,
denoted as thermodynamic in view of their survival at equilibrium, have been
calculated in ref.~\cite{moore} for conformal field theories.
In this paper, we show that the occurrence of non-dissipative corrections to the
ideal form of the stress-energy tensor is a general fact which is related to the
very notion of equilibrium in quantum relativistic statistical mechanics. Moreover,
these corrections result from the expansion of the density operator and their
form is not assumed {\it a priori} like in the Landau-frame based gradient expansion.
At equilibrium, they have simple and suggestive expressions as correlators of the
stress-energy tensor with the generators of the Lorentz group. The proper energy
density expression is also modified, as well as the relation between energy density and
pressure, that is the equation of state. It is an almost straigthforward consequence
that these corrections will extend to a curved spacetime.
The paper is organized as follows: in section \ref{statmech} we obtain the form of
the density operator of general thermodynamic equilibrium in quantum statistical mechanics
in flat spacetime. In section \ref{locality} we discuss the relation between local
observables and the local value of the four-temperature field. In section \ref{expansion}
we derive the form of the corrections to the ideal form of the stress-energy tensor
as a perturbative expansion. In section \ref{freef} we calculate those quantum corrections
in free scalar field theory. Finally, in sections \ref{discuss} and \ref{conclu} we
discuss the most important physical consequences and draw the conclusions.
\subsection*{Notation}
In this paper we use the natural units, with $\hbar=c=K=1$.\\
The Minkowskian metric tensor is ${\rm diag}(1,-1,-1,-1)$; for the Levi-Civita
symbol we use the convention $\epsilon^{0123}=1$.\\
We will use the relativistic notation with repeated indices assumed to be
summed over, however contractions of indices will be sometimes denoted with
dots, e.g. $ u \cdot T \cdot u \equiv u_\mu T^{\mu\nu} u_\nu$. Operators in
Hilbert space will be denoted by a large upper hat, e.g. ${\widehat T}$ while unit
vectors with a small upper hat, e.g. $\hat v$. The stress-energy tensor is
assumed to be symmetric with an associated vanishing spin tensor.
\section{Equilibrium in relativistic quantum statistical mechanics}
\label{statmech}
A general covariant form of the density operator in relativistic quantum statistical
mechanics extending the eq.~(\ref{homo}) was first proposed, to our knowledge, in
refs.~\cite{zubarev,weert}:
\begin{equation}\label{gener1}
{\widehat{\rho}} = \frac{1}{Z} \exp \left[ -\int_{\Sigma} {\rm d} \Sigma_\mu \;
\left( {\widehat T}^{\mu\nu} \beta_\nu - \zeta {\widehat j}^\mu \right) \right]
\ee
where $\Sigma$ is a spacelike 3D hypersurface. This form can be obtained maximizing
the total entropy with the constraints of given energy-momentum and charge densities
at some specific "time" of the hypersurface $\Sigma$, see the detailed discussions
in ref.~\cite{weert} and more recently in refs.~\cite{becalocal,japan}. The density
operator (\ref{gener1}) is therefore especially suitable to describe {\em local}
thermodynamic equilibrium --- that is a situation where the thermodynamic parameters
temperature, velocity field and chemical potential are a function of space and time
--- in a quantum relativistic framework. The operator (\ref{gener1}) will not maintain
its form under the unitary time evolution and cannot thus represent {\em the} actual
quantum state in the Heisenberg representation. However, it is time independent or,
equivalently, independent of the integration hypersurface $\Sigma$ if the divergence
of the integrand vanishes and in this case the (\ref{gener1}) is the density operator
of a thermodynamic equilibrium state. For conserved stress-energy tensor and current
this condition leads to the request \cite{becacov} that $\zeta$ is a constant and
$\beta$ a Killing vector field fulfilling eq.~(\ref{kill}) (with partial derivatives
replaced by covariant derivatives if necessary).
The density operator (\ref{gener1}) is also well suited to describe thermodynamic
equilibrium in a general curved spacetime possessing a timelike Killing vector field.
In Minkowski spacetime, which we will be dealing with in this work, the general
solution of the eq.~(\ref{kill}) is:
\begin{equation}\label{killsol}
\beta^\nu = b^\nu + \varpi^{\nu\mu} x_\mu
\ee
where $b$ is a constant four-vector and $\varpi$ a constant antisymmetric tensor,
which, because of (\ref{killsol}) can be written as an exterior derivative of the
$\beta$ field:
\begin{equation}\label{thvort}
\varpi_{\nu\mu} = -\frac{1}{2} (\partial_\nu \beta_\mu - \partial_\mu \beta_\nu)
\ee
Hence, the general equilibrium form in flat spacetime of the density operator (\ref{gener1})
reads:
\begin{equation}\label{gener2}
{\widehat{\rho}} = \frac{1}{Z} \exp \left[ - b_\mu {{\widehat P}}^\mu
+ \frac{1}{2} \varpi_{\mu\nu} {\widehat J}^{\mu\nu} + \zeta {\widehat Q} \right]
\ee
where the ${\widehat J}$'s are the generators of the Lorentz transformations:
$$
{\widehat J}^{\mu\nu} = \int_{\Sigma} {\rm d} \Sigma_\lambda \; \left(
x^\mu {\widehat T}^{\lambda\nu} - x^\nu {\widehat T}^{\lambda\mu} \right)
$$
Therefore, besides the chemical potentials, the most general equilibrium density
operator in Minkowski spacetime can be written as a linear combinations of the 10
generators of the Poincar\'e group with 10 constant coefficients. The most widely
known case is the one with $\beta = b$ and $\varpi=0$, that is eq.~(\ref{homo}),
what we define as {\em homogeneous thermodynamic equilibrium}. The rotating global
equilibrium in eq.~(\ref{rotating}) can be obtained as a special case of eq.~(\ref{gener2})
setting:
$$
b_\mu = (1/T_0,0,0,0) \qquad \qquad \varpi_{\mu\nu} = (\omega/T_0) (g_{1\mu} g_{2\nu}
- g_{1\nu} g_{2\mu})
$$
where $\omega$ has the meaning of a costant angular velocity \cite{landau}. Similarly,
the form (\ref{accelerating}) can be obtained by setting:
$$
b_\mu = (1/T_0,0,0,0) \qquad \qquad \varpi_{\mu\nu} = (a/T_0) (g_{0\mu} g_{3\nu}
- g_{3\mu} g_{0\nu})
$$
In the latter case, the contravariant components of $\beta$ read:
\begin{equation}\label{rindler}
\beta^\mu= \frac{1}{T_0}\left(1 + a z, 0, 0,a t \right)
\ee
thus the unit vector $\hat \beta$ is the velocity field of a fluid with constant
comoving acceleration along the field lines (for the field line going through $z=0$,
the comoving acceleration is $a$).
\section{Mean values of local operators}
\label{locality}
Suppose we want to calculate the mean value of a local operator $\widehat O(x)$
(in the Heisenberg picture) with the density operator (\ref{gener1}):
\begin{equation}\label{lexpv}
O(x) \equiv \langle \widehat O(x) \rangle = \tr ({\widehat{\rho}} \, \widehat O(x))_{\rm ren}
= \frac{1}{Z} \tr \left( \exp \left[ -\int_{\Sigma} {\rm d} \Sigma_\mu \;
\left( {\widehat T}^{\mu\nu} \beta_\nu - \zeta {\widehat j}^\mu \right) \right] \widehat O(x)
\right)_{\rm ren} \
\ee
If $\beta$ is a general field, there is no compelling reason why, at a given point
$x$, the mean value $O(x)$ should be simply equal to the same value at the homogeneous
global thermodynamic equilibrium with an uniform four-temperature $\beta$ equal
to its value in the point $x$, that is $\beta(x)$. For instance, the stress-energy
tensor in the point $x$ does not need to be of the ideal form (\ref{tideal})
with $u=\hat\beta(x)$ and $\rho = \rho(\beta^2,\zeta)$ $p = p(\beta^2,\zeta)$
if $\beta$ is not constant. In fact, its tensor structure in (\ref{tideal}) is
determined by the symmetries of the density operator (\ref{homo}), which is obtained
from (\ref{gener1}) provided that $\beta$ is constant.
Nevertheless, one can imagine that if $\beta$ and $\zeta$ are sufficiently slowly
varying in space and time, $O(x)$ will be mostly determined by the values of the fields
$\beta$ and $\zeta$ around the point $x$ \cite{becalocal}. More specifically, the
distance over which the {\em thermodynamic} fields like $\beta$ vary should be
much larger than the typical thermal correlation length, which is governed by the
microscopic parameters of the theory and the temperature itself. This can be shown
by recasting the fields in the integrand of the eq.~(\ref{lexpv}) as $\beta = \beta(x)
+ \delta \beta$ and $\zeta = \zeta(x) + \delta \zeta$, so as to obtain:
\begin{eqnarray*}
O(x) &=& \frac{1}{Z} \tr \left( \exp \left[ - \beta_\nu(x) \int_{\Sigma} {\rm d} \Sigma_\mu \;
{\widehat T}^{\mu\nu} + \zeta(x) \int_{\Sigma} {\rm d} \Sigma_\mu \; {\widehat j}^{\mu} -
\int_{\Sigma} {\rm d} \Sigma_\mu \; \left( {\widehat T}^{\mu\nu} \delta\beta_\nu - \delta \zeta
{\widehat j}^\mu \right) \right] \widehat O(x) \right)_{\rm ren} \nonumber \\
&=& \frac{1}{Z} \tr \left( \exp \left[ - \beta_\nu (x) {\widehat P}^\nu + \zeta(x) {\widehat Q}
- \int_{\Sigma} {\rm d} \Sigma_\mu \; \left( {\widehat T}^{\mu\nu} \delta\beta_\nu - \delta \zeta
{\widehat j}^\mu \right) \right] \widehat O(x) \right)_{\rm ren}
\end{eqnarray*}
Hence, applying the linear response theory to the exponent above:
\begin{eqnarray}\label{lrte}
O(x) \simeq && \langle \widehat O (x) \rangle_{\beta(x)} - \int_0^1 {\rm d} z \;
\int_{\Sigma} {\rm d} \Sigma_\mu(y) \; \left( \langle \widehat O (x) {\widehat T}^{\mu\nu}
(y+iz\beta(x)) \rangle_{\beta(x)} - \langle \widehat O (x) \rangle_{\beta(x)}
\langle {\widehat T}^{\mu\nu}(y+iz\beta(x)) \rangle_{\beta(x)} \right) \delta\beta_\nu \nonumber \\
&& + \int_0^1 {\rm d} z \;
\int_{\Sigma} {\rm d} \Sigma_\mu(y) \; \left( \langle \widehat O (x) {\widehat j}^{\mu}
(y+iz\beta(x)) \rangle_{\beta(x)} - \langle \widehat O (x) \rangle_{\beta(x)}
\langle {\widehat j}^{\mu}(y+iz\beta(x)) \rangle_{\beta(x)} \right) \delta\zeta
\eea
where $x$ and $y$ both lie on the hypersurface $\Sigma$. The symbol $\langle \;
\rangle_{\beta}$ stands for the (renormalized) mean value calculated with the homogeneous
equilibrium density operator in eq.~(\ref{homo}). Particularly, the $\langle \; \rangle_{\beta(x)}$
stands for the mean value calculated with a fixed four-temperature (and $\zeta$) equal to
the value of the $\beta$ (and $\zeta$) fields in the point $x$. The formula (\ref{lrte})
just expresses the aforementioned concept, namely that the local equilibrium value
of the operator $\widehat O(x)$ is determined by the local values of the thermodynamic
fields with corrections depending on quantum-statistical correlations between operators
in different points. These correlations -- hence the integrand function in eq.~(\ref{lrte})
-- are significant over microscopic distances $l$ dictated by the mass, temperature and
coupling constants of the theory, which are supposedly much smaller than the macroscopic
distance $L$ over which $\delta\beta$ and $\delta\zeta$ appreciably vary. This condition
is usually referred to as hydrodynamical regime and in this regime terms beyond the linear
in $\delta\beta$ and $\delta\zeta$ in eq.~(\ref{lrte}) contribute less and less as they
are expected to be suppressed with higher powers of $l/L$.
Under these circumstances, it is possible to expand the thermodynamic fields in the
eq.~(\ref{lexpv}) into a Taylor series about the point $x$. For a general $\beta$
field, this method makes it possible to find an approximate expression of the local
thermodynamic equilibrium operator (\ref{gener1}) as a function of $\beta(x)$ and
its derivatives \cite{becalocal}. For the special case of global equilibrium, with
constant $\zeta$ and $\beta$ a Killing vector field (\ref{killsol}), one can recast
the operator (\ref{gener2}) so as to have in the exponent the value of the four-temperature
in the point $x$:
\begin{eqnarray}\label{geqmean}
O(x) &=& \frac{1}{Z} \tr \left( \exp \left[ - b_\mu {{\widehat P}}^\mu
+ \frac{1}{2} \varpi_{\mu\nu} {\widehat J}^{\mu\nu} + \zeta {\widehat Q} \right] \widehat
O(x) \right)_{\rm ren} \!\!\!\!\! =
\frac{1}{Z} \tr \left( \exp \left[ - (b_\mu + \varpi_{\mu\nu} x^\nu){{\widehat P}}^\mu
+ \frac{1}{2} \varpi_{\mu\nu} {\widehat J}^{\mu\nu}_x +\zeta {\widehat Q} \right]
\widehat O(x) \right)_{\rm ren} \nonumber \\
&=& \frac{1}{Z} \tr \left( \exp \left[ - \beta_\mu(x) {{\widehat P}}^\mu
+ \frac{1}{2} \varpi_{\mu\nu} {\widehat J}^{\mu\nu}_x +\zeta {\widehat Q} \right]
\widehat O(x) \right)_{\rm ren}
\eea
where we have used the angular momentum operators around the point $x$:
\begin{equation}\label{angmomtrasl}
{\widehat J}^{\mu\nu}_x = {\widehat J}^{\mu\nu} - x^\mu {\widehat P}^\nu + x^\nu {\widehat P}^\mu =
\widehat{\sf T}(x) {\widehat J}^{\mu\nu} \widehat{\sf T}(x)^{-1}
\ee
$\widehat{\sf T}(x) = \exp[i x \cdot {\widehat P}]$ being the translation operator.
The calculation of mean values (\ref{geqmean}) is the main purpose of this paper,
and, specifically, when $\widehat O = {\widehat T}^{\mu\nu}$.
We will consider the term in $\varpi$ as small compared with the terms involving
$\beta$ and $\zeta$ and expand accordingly. Thus, the leading term in the above
equation will be simply the homogeneous equilibrium one with four-temperature equal
to its value in the $x$ point, that is the expression (\ref{tideal}) with
$u=\hat\beta(x)$. We will see in the sect.~\ref{expansion} that the lowest order
corrections to the ideal form are of the second order in $\varpi$ and that they
are of either quantum or quantum-relativistic nature as they vanish for $\hbar \to 0$
or $\hbar/c \to 0$.
Note that $\beta(x)$ is required to be a future-oriented timelike vector in order
to get a finite value for most observables at the lowest order of the $\beta$
expansion. This condition cannot be fulfilled everywhere for the expression (\ref{killsol})
if $\varpi \ne 0$. For instance, for the rotating global equilibrium (\ref{rotating}),
it is easy to check that:
$$
\beta = \frac{1}{T_0} (1, \omega \hat{\bf k} \times {\bf x})
$$
which becomes spacelike when $ \| \omega \hat{\bf k} \times {\bf x} \| > 1$, that
is when the velocity exceeds the speed of light. Similarly, for the operator
(\ref{accelerating}), the $\beta$ field (\ref{rindler}) is future-oriented timelike
only in the Rindler wedge defined by the light cone of the point $(0,0,0,-a/T)$.
Therefore, the validity of our calculations will be limited to the physical regions
where the $\beta$ field is timelike and with positive time component even though the
operator (\ref{gener2}) written with the constants $b$ and $\varpi$ does not make
this limitation apparent.
\section{Perturbative expansion for the stress-energy tensor}
\label{expansion}
The goal of this section is to provide an expansion in $\varpi$ for the mean value of
the stress-energy tensor in the general form of thermodynamic equilibrium:
\begin{equation}\label{setge}
T^{\mu\nu}(x) = \frac{1}{Z} \tr \left( \exp \left[ - \beta_\mu(x) {{\widehat P}}^\mu
+ \frac{1}{2} \varpi_{\mu\nu} {\widehat J}^{\mu\nu}_x + \zeta {\widehat Q} \right]
{\widehat T}^{\mu\nu}(x) \right)_{\rm ren}
\ee
Indeed, $\varpi$ is an adimensional tensor in natural units and it the has, in general,
very small components. To understand its physical meaning, it is very useful to decompose
it into two spacelike vector fields, each having three independent components, projecting
along a timelike vector. A physically interesting choice is $u = \hat\beta = \beta/\sqrt{\beta^2}$,
in the regions where $\beta$ given by eq.~(\ref{killsol}) is timelike. We can then
decompose $\varpi$ as follows:
\begin{equation}\label{decomp1}
\varpi^{\mu\nu} = \epsilon^{\mu\nu\rho\sigma} w_\rho u_\sigma
+ \alpha^\mu u^\nu - \alpha^\nu u^\mu
\ee
where, by definition:
\begin{equation}\label{defin1}
\alpha^\mu(x) = \varpi^{\mu\nu} u_\nu \qquad \qquad w^\mu(x) = -\frac{1}{2}
\epsilon^{\mu\nu\rho\sigma} \varpi_{\nu\rho} u_\sigma
\ee
Note that $\alpha$ and $w$, unlike $\varpi$, are not constant and they are both
orthogonal to $u$, hence spacelike. The physical meaning of $\alpha$ and $w$ vectors
can be shown starting from the eq.~(\ref{kill}). Because of (\ref{killsol}) and
(\ref{kill}) at equilibrium one has:
$$
\varpi_{\mu\nu} = \partial_\nu \beta_\mu
$$
whence:
$$
\alpha^\mu = \varpi^{\mu\nu} u_\nu = u_\nu \partial^\nu \beta^\mu
= u^\mu u_\nu \partial^\nu \sqrt{\beta^2} + \sqrt{\beta^2}
u_\nu \partial^\nu u^\mu
$$
We can now take the scalar product with $u^\mu$ and conclude that:
$$
u_\nu \partial^\nu \sqrt{\beta^2} \equiv D\sqrt{\beta^2} = 0
$$
which tells us that, as expected, at the thermodynamic equilibrium the comoving
temperature along the flow lines does not change and $\partial_\mu \beta^2 =
\nabla_\mu \beta^2$, where:
$$
\nabla_\mu \equiv \partial_\mu - u_\mu D
$$
Thereby, the $\alpha$ vector simply becomes:
\begin{equation}\label{accel}
\alpha^\mu = \sqrt{\beta^2} u_\nu \partial^\nu u^\mu = \sqrt{\beta^2} Du^\mu
= \frac{1}{T} a^\mu
\ee
that is the acceleration field divided by the proper temperature. Note also that,
being $\partial_\mu \beta_\nu + \partial_\nu \beta_\mu = 0$, one has:
\begin{equation}\label{accel2}
0 = u^\nu (\partial_\nu \beta_\mu + \partial_\mu \beta_\nu) =
\alpha_\mu + \frac{1}{2 \sqrt{\beta^2}} \partial_\mu \beta^2 = \frac{1}{T}
a_\mu - \frac{1}{T^2} \nabla_\mu T
\ee
Likewise, it can be shown that $w$ corresponds to an angular velocity divided by a
temperature, for, by using (\ref{thvort})
\begin{equation}\label{angvel}
w^\mu = -\frac{1}{2} \epsilon^{\mu\nu\rho\sigma} \varpi_{\nu\rho} u_\sigma
= \frac{1}{2} \epsilon^{\mu\nu\rho\sigma} (\partial_\nu \beta_\rho) u_\sigma
= \frac{1}{2} \epsilon^{\mu\nu\rho\sigma} \sqrt{\beta^2} u_\sigma \partial_\nu u_\rho
= \frac{1}{2T} \epsilon^{\mu\nu\rho\sigma} u_\sigma \nabla_\nu u_\rho
= \frac{1}{T} \omega^\mu
\ee
being $\omega^\mu = \frac{1}{2} \epsilon^{\mu\nu\rho\sigma} u_\sigma \nabla_\nu u_\rho$,
as it is known in literature, the local vorticity vector. Restoring the physical
constants, one then has the adimensional four-vectors:
\begin{equation}\label{acceler}
\alpha_\mu = \frac{\hbar a_\mu}{c K T} \qquad \qquad w_\mu = \frac{\hbar
\omega_\mu}{K T}
\ee
These numbers are, for the vast majority of physical systems, much less than 1 and
a perturbative expansion in $\varpi$ of the eq.~(\ref{setge}) is then feasible.
They can give rise to relevant corrections if the implied additional terms to the
ideal stress-energy tensor are some sizeable fraction thereof or when these terms
are comparable to the viscous tensor. According to the eq.~(\ref{acceler}), this happens
at for very large accelerations or very low temperatures.
Hence, let us define:
\begin{equation}\label{wrdef}
\widehat{\mathcal{R}}(\varpi) \equiv \exp \left[ -\beta_\mu(x) {{\widehat P}}^\mu + \frac{1}{2}
\varpi_{\mu\nu} {\widehat J}^{\mu\nu}_x + \zeta {\widehat Q} \right] =
\exp \left[ -\beta_\mu(x) {{\widehat P}}^\mu + \frac{1}{2} \varpi_{\mu\nu}
{\widehat J}^{\mu\nu}_x \right] \exp[\zeta {\widehat Q}]
\ee
where, in the last equality, advantage has been taken of the supposed commutation
of the charge operator ${\widehat Q}$ with both the ${\widehat P}$'s and ${\widehat J}$'s. At the second order in
$\varpi$ one can write:
\begin{equation}\label{expand}
\widehat{\mathcal{R}}(\varpi) = \widehat{\mathcal{R}}^{(0)} + \varpi_{\mu\nu} \widehat{\mathcal{R}}^{(1)\mu\nu}
+ \varpi_{\mu\nu}\varpi_{\rho\sigma} \widehat{\mathcal{R}}^{(2)\mu\nu\rho\sigma} +
o(\varpi^2)
\ee
and, by using the Poincar\'e group commutation relations, it can be shown that (see
Appendix A):
\begin{eqnarray}\label{expand2}
\widehat{\mathcal{R}}^{(0)} &=& {\rm e}^{-\beta \cdot {\widehat P} + \zeta {\widehat Q}} \nonumber \\
\widehat{\mathcal{R}}^{(1)\mu\nu} &=& \frac{1}{4} \{ {\rm e}^{-\beta \cdot {\widehat P} + \zeta {\widehat Q}} ,
{\widehat J}^{\mu\nu} \} \, , \nonumber \\
\widehat{\mathcal{R}}^{(2)\mu\nu\rho\sigma} &=& \frac{1}{16} \{ {\rm e}^{-\beta \cdot {\widehat P}
+ \zeta {\widehat Q}},{\widehat J}^{\mu\nu}
{\widehat J}^{\rho\sigma} \} + \frac{1}{8} {\rm e}^{-\beta \cdot {\widehat P} + \zeta {\widehat Q}} \beta^\mu \beta^\rho
{\widehat P}^\nu {\widehat P}^\sigma -\frac{1}{12} {\rm e}^{-\beta \cdot {\widehat P} + \zeta {\widehat Q}} \beta^\mu g^{\nu\rho}
{\widehat P}^\sigma \, .
\eea
where the curly bracket expression $\{\; , \; \}$ stands for the anticommutator.
By using the eqs.~(\ref{expand}) and (\ref{expand2}), the mean value (\ref{setge})
can be expressed as an expansion in $\varpi$ with coefficients which are calculated
at the homogeneous thermodynamic equilibrium:
\begin{eqnarray}\label{texpa}
T^{\mu\nu}(x)= && \frac{\tr(\widehat{\mathcal{R}}(\varpi){\widehat T}^{\mu\nu}(x))}{\tr(\widehat{\mathcal{R}}(\varpi))} =
\langle {\widehat T}^{\mu\nu}(x) \rangle_{\beta(x)} + \frac{1}{2} \varpi_{\rho\sigma}
{\rm Re} \langle {\widehat J}^{\rho\sigma}_x ; {\widehat T}^{\mu\nu}(x) \rangle_{\beta(x)} \nonumber \\
&& + \varpi_{\rho\sigma} \varpi_{\lambda\tau}
\left[ \frac{1}{8} {\rm Re} \langle {\widehat J}^{\rho\sigma}_x {\widehat J}^{\lambda\tau}_x ;
{\widehat T}^{\mu\nu}(x) \rangle_{\beta(x)} + \frac{1}{8} \beta^\rho(x) \beta^\lambda(x)
\langle {\widehat P}^{\sigma} {\widehat P}^{\tau} ; {\widehat T}^{\mu\nu}(x) \rangle_{\beta(x)} -
\frac{1}{12} \beta^\rho(x) g^{\lambda\sigma} \langle {\widehat P}^{\tau} ; {\widehat T}^{\mu\nu}(x)
\rangle_{\beta(x)} \right. \nonumber \\
&& \left. - \frac{1}{4} {\rm Re} \langle {\widehat J}^{\rho\sigma}_x ; {\widehat T}^{\mu\nu}(x)
\rangle_{\beta(x)} \langle {\widehat J}^{\lambda\tau}_x \rangle_{\beta(x)} \right] + o(\varpi^2)
\eea
where we have used the relations for two hermitian operators ${\widehat A},{\widehat B}$:
$$
{\rm Re} \langle {\widehat A} {\widehat B} \rangle = \frac{1}{2} \langle \{{\widehat A},{\widehat B}\} \rangle
\qquad \qquad
i {\rm Im} \langle {\widehat A} {\widehat B} \rangle = \frac{1}{2} \langle [{\widehat A},{\widehat B}] \rangle
$$
and the notation has been introduced:
$$
\langle \widehat A; \widehat B \rangle = \langle \widehat A \widehat B
\rangle - \langle \widehat A \rangle \langle \widehat B \rangle
$$
for the correlator between ${\widehat A}$ and ${\widehat B}$. The terms in eq.~(\ref{texpa}) containing
${\widehat P}$ can be readily calculated taking the derivative of $\langle {\widehat T} \rangle_\beta$
with respect to $\beta$. Indeed:
\begin{eqnarray}\label{tderivat}
\beta^\rho g^{\lambda\sigma} \frac{\partial}{\partial \beta_\tau} \langle {\widehat T}^{\mu\nu}
\rangle_\beta &=& -\beta^\rho g^{\lambda\sigma} \langle {\widehat P}^\tau ; {\widehat T}^{\mu\nu} \rangle_\beta
\nonumber \\
\beta^\rho \beta^\lambda \frac{\partial^2}{\partial\beta_\sigma \,\partial\beta_\tau}
\langle {\widehat T}^{\mu\nu} \rangle_\beta &=& \beta^\rho \beta^\lambda \left(
\langle {\widehat P}^\sigma {\widehat P}^\tau ; {\widehat T}^{\mu\nu} \rangle_{\beta} -
\langle {\widehat P}^\sigma ; {\widehat T}^{\mu\nu} \rangle_{\beta} \langle {\widehat P}^\tau \rangle_{\beta}
- \langle {\widehat P}^\tau ; {\widehat T}^{\mu\nu} \rangle_{\beta} \langle {\widehat P}^\sigma \rangle_{\beta} \right)
\eea
Note that the two rightmost terms in the last equation vanish once multiplied by
$\varpi_{\rho\sigma}\varpi_{\lambda\tau}$ for, being $\langle {\widehat P} \rangle_\beta
\propto \beta$, they contain the symmetric combination $\beta^\lambda \beta^\tau$ or
$\beta^\rho \beta^\sigma$.
All mean values in eq.~(\ref{texpa}) involving angular momentum operators can be
rewritten in a form which makes it apparent that their dependence on $x$ is only
through the value of the four-temperature, by taking advantage of the translational
invariance of the density operator. For instance:
$$
\langle {\widehat J}^{\rho\sigma}_x {\widehat J}^{\lambda\tau}_x ; {\widehat T}^{\mu\nu}(x) \rangle_{\beta(x)}
= \langle \widehat{\sf T}^{-1}(x) {\widehat J}^{\rho\sigma}_x {\widehat J}^{\lambda\tau}_x \widehat{\sf T}(x);
\widehat{\sf T}^{-1}(x) {\widehat T}^{\mu\nu}(x) \widehat{\sf T}(x) \rangle_{\beta(x)} =
\langle {\widehat J}^{\rho\sigma} {\widehat J}^{\lambda\tau} ; {\widehat T}^{\mu\nu}(0) \rangle_{\beta(x)}
$$
and similarly for the others, where eq.~(\ref{angmomtrasl}) has been used. Then,
it is convenient to decompose the tensor ${\widehat J}$ into two spacelike vector operators
the same fashion as for $\varpi$ in eq.~(\ref{decomp1}):
\begin{equation}\label{decomp2}
{\widehat J}^{\mu\nu} = u^\mu {\widehat K}^{\nu} - {\widehat K}^{\mu} u^\nu +
\epsilon^{\mu\nu\rho\sigma} {\widehat J}_{\rho} u_\sigma
\ee
being
$$
{\widehat K}^\mu = u_\rho {\widehat J}^{\rho\mu} \qquad {\widehat J}^\mu = - \frac{1}{2} \epsilon^{\mu\rho\sigma\tau}
{\widehat J}_{\rho\sigma} u_\tau
$$
The operators ${\widehat J}^\mu$ and ${\widehat K}^\mu$ are simply the generators of the rotation
and boosts with respect to the reference frame with time direction $u$. Using the
invariance by rotation (in the hyperplane orthogonal to $u$), parity and time
reversal, which are assumed to hold for our hamiltonian, one readily obtains that
(see Appendix B):
$$
{\rm Re} \langle {\widehat J}^{\rho\sigma} ; {\widehat T}^{\mu\nu}(0) \rangle_{\beta(x)} = 0 \qquad
\langle {\widehat J}^{\rho\sigma} \rangle_{\beta(x)} = 0
$$
Therefore, plugging the decomposition (\ref{decomp2}) into the eq.~(\ref{texpa}),
and using the relations (\ref{defin1}) and (\ref{tderivat}) and after the removal
of the vanishing terms, the eq.~(\ref{texpa}) can be written as:
\begin{eqnarray}\label{texpa2}
T^{\mu\nu}(x) &=&
\langle {\widehat T}^{\mu\nu}(x) \rangle_{\beta(x)} + \frac{1}{2} \alpha_\rho \alpha_\sigma
{\rm Re} \langle {\widehat K}^{\rho} {\widehat K}^{\sigma} ; {\widehat T}^{\mu\nu}(0) \rangle_{\beta(x)}
+ \frac{1}{2} w_\rho w_\sigma {\rm Re} \langle {\widehat J}^{\rho} {\widehat J}^{\sigma} ;
{\widehat T}^{\mu\nu}(0) \rangle_{\beta(x)} \nonumber \\
&+& \frac{1}{2} \alpha_\rho w_\sigma {\rm Re} \langle \{ {\widehat J}^{\rho}, {\widehat K}^{\sigma} \}
; {\widehat T}^{\mu\nu}(0) \rangle_{\beta(x)} + \frac{1}{8} \beta^\rho \beta^\lambda
\frac{\partial^2}{\partial\beta_\sigma \,\partial\beta_\tau} \langle {\widehat T}^{\mu\nu}(x)
\rangle_{\beta(x)} + \frac{1}{12} \beta^\rho g^{\lambda\sigma}
\frac{\partial}{\partial \beta_\tau} \langle {\widehat T}^{\mu\nu}(x) \rangle_{\beta(x)}
+ o(\varpi^2)
\eea
The derivative terms are easy to work out by using (\ref{tideal}); they will give
rise to expressions involving the thermodynamic functions pressure, energy density
and their derivatives, that is specific heats. On the other hand, the correlators
in eq.~(\ref{texpa2}) cannot be expressed in terms of known thermodynamic functions.
In fact, they can be written as linear combinations of new thermodynamic coefficients
which can be expressed in turn as correlators of specific components of the stress-energy
tensor and angular momentum or boost operators ${\widehat J}$ and ${\widehat K}$, that is
\begin{eqnarray}\label{corrcoeff}
&& \frac{1}{2} {\rm Re} \langle \{ {\widehat K}^{\rho}, {\widehat K}^{\sigma}\} ; {\widehat T}^{\mu\nu}(0) \rangle_{\beta(x)}
= - u^\mu u^\nu \Delta^{\rho\sigma} k_t(T,\zeta) + \Delta^{\mu\nu} \Delta^{\rho\sigma} k_\theta(T,\zeta)
+ (\Delta^{\mu\sigma} \Delta^{\rho\nu} + \Delta^{\nu\sigma} \Delta^{\rho\mu}
- \frac{2}{3}\Delta^{\mu\nu}\Delta^{\rho\sigma}) k_s(T,\zeta) \nonumber \\
&& \frac{1}{2} {\rm Re} \langle \{ {\widehat J}^{\rho}, {\widehat J}^{\sigma} \} ; {\widehat T}^{\mu\nu}(0) \rangle_{\beta(x)}
= - u^\mu u^\nu \Delta^{\rho\sigma} j_t(T,\zeta) + \Delta^{\mu\nu} \Delta^{\rho\sigma} j_\theta(T,\zeta)
+ (\Delta^{\mu\sigma} \Delta^{\rho\nu} + \Delta^{\nu\sigma} \Delta^{\rho\mu}
- \frac{2}{3}\Delta^{\mu\nu}\Delta^{\rho\sigma}) j_s(T,\zeta) \nonumber \\
&& {\rm Re} \langle \{ {\widehat K}^{\rho}, {\widehat J}^{\sigma} \} ; {\widehat T}^{\mu\nu}(0) \rangle_{\beta(x)}
= (u_\mu u_\kappa \epsilon^{\kappa\rho\sigma\nu} + u^\nu u_\kappa \epsilon^{\kappa\rho\sigma\mu})l_v(T,\zeta)
\eea
where
$$
\Delta^{\mu\nu} \equiv g^{\mu\nu} - u^\mu u^\nu
$$
is the projector onto the hyperplane orthogonal to $u$ and
\begin{align}\label{correlat}
k_t(T,\zeta) &= {\rm Re}\langle {\widehat K}^{3} {\widehat K}^{3}; {\widehat T}^{00}(0) \rangle_T
\qquad &
k_\theta(T,\zeta) &= \frac{1}{3} {\rm Re} \sum_{i=1}^3 \langle {\widehat K}^{3} {\widehat K}^{3};
{\widehat T}^{ii}(0) \rangle_T \qquad &
k_s(T,\zeta) &= {\rm Re} \langle {\widehat K}^{1} {\widehat K}^{2}; {\widehat T}^{12}(0) \rangle_T \, \nonumber \\
j_t(T,\zeta) &= {\rm Re} \langle {\widehat J}^{3} {\widehat J}^{3}; {\widehat T}^{00}(0) \rangle_T
\qquad &
j_\theta(T,\zeta) &= \frac{1}{3} {\rm Re} \sum_{i=1}^3 \langle {\widehat J}^{3} {\widehat J}^{3}; {\widehat T}^{ii}(0) \rangle_T
\qquad &
j_s(T,\zeta) &= {\rm Re}\langle {\widehat J}^{1} {\widehat J}^{2}; {\widehat T}^{12}(0) \rangle_T \, \nonumber \\
l_v(T,\zeta) &= {\rm Re}\langle \{{\widehat K}^1,{\widehat J}^2 \}; {\widehat T}^{03}(0) \rangle_T
\end{align}
In the eq.~(\ref{correlat}) the notation $\langle \; \rangle_T$ has been introduced meaning
that the expectation value is calculated in the rest frame where $\beta=(1/T,{\bf 0})$.
The derivation of eqs.~(\ref{corrcoeff}) and (\ref{correlat}) can be found in Appendix B.
Finally, after having worked out the derivatives of the stress-energy tensor and using
the eqs.~(\ref{corrcoeff}) and (\ref{tideal}) in the eq.~(\ref{texpa2}), one obtains:
\vspace*{0.5cm}
\begin{equation}\label{texpa3}
T^{\mu\nu}(x) = (\rho - \alpha^2 U_\alpha- w^2 U_w)
u^\mu u^\nu - (p - \alpha^2 D_\alpha - w^2 D_w) \Delta^{\mu\nu} + A \alpha^\mu \alpha^\nu
+ W w^\mu w^\nu + G (u^\mu \gamma^\nu + \gamma^\mu u^\nu) +o(\varpi^2)
\vspace*{0.5cm}
\ee
where $\rho,p$ are the usual homogeneous thermodynamic equilibrium functions energy
density and pressure, and the functions $U,D,A,W,G$ read:
\begin{align}\label{udaw}
U_\alpha &= \frac{1}{24} T \frac{\partial \rho}{\partial T}
+ \frac{1}{4}(\rho+p) + \frac{1}{2} k_t \qquad\qquad & U_w &= \frac{1}{2}j_t \qquad\qquad
& D_\alpha &= \frac{1}{24}(\rho+p) +\frac{1}{2}k_\theta - \frac{1}{3}k_s \nonumber \\
D_w &= \frac{1}{2}j_\theta - \frac{1}{3}j_s \qquad\qquad &
A &= \frac{1}{4}(\rho+p)+k_s \qquad\qquad & W &= j_s \nonumber \\
G &= \frac{1}{2} l_v - \frac{1}{12}(\rho+p)
\end{align}
The vector $\gamma^\mu$ in eq.~(\ref{texpa3}) is defined as:
\begin{equation}\label{gamma}
\gamma^\mu = (\alpha\cdot\varpi)_\lambda \Delta^{\lambda\mu} =
\epsilon^{\mu\nu\rho\sigma} w_\nu \alpha_\rho u_\sigma
\ee
where the $\varpi$ decomposition (\ref{decomp1}) has been used,
As it can be seen from eq.~(\ref{texpa3}), the stress-energy tensor has corrections
to its ideal form which depend on quadratic combinations of the two vector fields,
$\alpha$ and $w$ arising from the decomposition of the exterior derivative of the
temperature four-vector $\beta$. At thermodynamic equilibrium, according to the
previous discussion and the eqs.~(\ref{acceler}), they are proportional to the
acceleration $a^\mu$ and angular velocity (or vorticity) $\omega^\mu$, so that the
eq.~(\ref{texpa3}) can be rewritten in the most suggestive fashion by restoring the
natural constants as:
\begin{eqnarray}\label{texpa4}
T^{\mu\nu}(x) = && \left[ \rho + \left(\frac{\hbar|a|}{c KT}\right)^2
U_\alpha + \left(\frac{\hbar |\omega|}{KT}\right)^2 U_w \right] u^\mu u^\nu -
\left[ p + \left(\frac{\hbar |a|}{c KT}\right)^2 D_\alpha + \left(\frac{\hbar |\omega|}{KT}\right)^2
D_w \right] \Delta^{\mu\nu} \nonumber \\
&& + A \left(\frac{\hbar |a|}{c KT}\right)^2 \hat a^\mu \hat a^\nu +
W \left(\frac{\hbar |\omega|}{KT}\right)^2 \hat\omega^\mu \hat\omega^\nu +
G \frac{\hbar^2 |\omega| |a|}{c(KT)^2} (u^\mu \hat\gamma^\nu + \hat\gamma^\mu u^\nu)
+ o(\varpi^2)
\eea
where $|a| = \sqrt{-a_\mu a^\mu}$ and $|\omega| = \sqrt{-\omega_\mu \omega^\mu}$
and $\hat a$, $\hat \omega$ are the corresponding unit vectors.
In the expression (\ref{texpa4}) the adimensional scales $\hbar a/cKT$ and $\hbar\omega/KT$
involving acceleration and vorticity have been separated from the thermodynamic
functions $U,A,W,D,G$ having the same dimension as $\rho$ and/or $p$ making it
easier to appreciate the size of the correction to the ideal form.
\subsection{Relation with other second-order hydrodynamical coefficient calculations}
The appearance of extra terms in the stress-energy tensor at thermodynamic equilibrium
with respect to its ideal form has, needless to say, several physical consequences.
The presence of non-dissipative quadratic corrections in the vorticity and gradients
of temperature (hence accelerations at equilibrium, according to eq.~(\ref{accel2}))
was pointed out in ref.~\cite{roma1,roma2} and, being non dissipative in nature, defined
as thermodynamic in ref.~\cite{moore}. The calculation of such coefficients has
attracted much attention lately (see \cite{kodama} for a recent review), especially
in conformal field theories \cite{arnold,starinets,brazil} with different techniques
\cite{molnar,philipsen} (see also ref.~\cite{jaiswal}). The coefficients that we have
denoted by $D_\alpha$, $D_w$, $A$ and $W$ are in the following relation with those
known as $\xi_3,\xi_4,\lambda_3,\lambda_4$ in literature:
\begin{align}\label{corresp}
\frac{A}{T^2} &= 9 \lambda_4 \qquad \qquad & \frac{W}{T^2} &= \lambda_3 \nonumber \\
\frac{D_w}{T^2} &= \left( \frac{\lambda_3}{3} - 2 \xi_3 \right) \qquad \qquad &
\frac{D_\alpha}{T^2} &= \left( 3\lambda_4 - 9 \xi_4 \right)
\end{align}
Remarkably, the number of coefficients quoted in (\ref{texpa4}) is larger than envisaged
in ref.~\cite{roma1,roma2} and the reason is that we did not assume, as it is usually
done in the Landau frame, that the proper energy density $\rho$ has the same
functional dependence on the temperature as at homogeneous thermodynamic equilibrium.
This assumption proves to be incorrect, and the extra coefficients cannot be reabsorbed
by a redefinition of temperature, as it will be discussed and shown in sect.~\ref{discuss}.
Before tackling these issues, it is necessary to calculate the coefficients $U, D, A, W, G$
in some instance and we will do it for the simplest case of a real scalar free field.
As it will be clear from the calculations shown in the next section, they all have
a classical expression in the massive case, and, as a consequence, all the corrections
in eq.~(\ref{texpa4}) to the ideal form turn out to be of quantum origin, as they vanish
in the $\hbar \to 0$ limit.
\section{The free scalar field}
\label{freef}
The goal of this section is to calculate the coefficients in eq.~(\ref{texpa4}) for
a free real scalar field. This implies $\zeta = 0$ in the density operator (\ref{homo}),
yet it is quite easy to extend the obtained results to the charged case with $\zeta\ne 0$
in the Boltzmann limit of distinguishable particles.
The theory is described by the Lagrangian density:
$$
\mathcal{L} = \frac{1}{2} \partial_\mu {\widehat{\psi}} \, \partial^\mu {\widehat{\psi}} - \frac{1}{2} m^2 {\widehat{\psi}}^2 \, .
$$
By adding the super-potential
$$
-2\xi\partial_\mu({\widehat{\psi}} \, \partial^\mu{\widehat{\psi}})
$$
a class of stress-energy tensors can be obtained as Noether currents associated to
space-time translations. Although they are explicitely dependent on the parameter
$\xi$, they differ from each other by a divergence:
\begin{equation}\label{scalart}
{\widehat T}_\xi^{\mu\nu} = \; \partial^\mu {\widehat{\psi}} \partial^\nu {\widehat{\psi}} - \frac{1}{2} g^{\mu\nu}
\left( \partial_\lambda {\widehat{\psi}} \, \partial^\lambda{\widehat{\psi}} - m^2{\widehat{\psi}}^2 \right) +
2 \xi \; \partial_\lambda \left( g^{\mu\nu} {\widehat{\psi}} \, \partial^\lambda {\widehat{\psi}} -
g^{\lambda\mu} {\widehat{\psi}} \, \partial^\nu {\widehat{\psi}} \right)
\ee
thus they lead to the same generators of the Poincar\'e group. For $\xi=0$ the tensor
is the so-called \emph{canonical stress-energy tensor}, while for $\xi=1/6$
the tensor is the so-called \emph{improved stress-energy tensor} \cite{callan}.
In the translationally invariant homogeneous equilibrium (\ref{homo}) all mean values
of local operators are independent of $x$, thus the divergence in the above expression
vanishes, hence $\rho$ and $p$ do not depend on $\xi$. In fact, as we will show,
this is not true in the case of generalized equilibrium and the correlators in
eq.~(\ref{correlat}) are explicitely dependent on $\xi$.
At the very beginning, it should be pointed out that in principle one should use normal
ordering in the calculation of the mean values of ${\widehat T}$ in a free field theory to
subtract zero point infinity. However, this is not needed in the calculation of a
correlator such as $\langle {\widehat J}^{\mu\nu} {\widehat J}^{\rho\sigma} ; {\widehat T}^{\alpha\beta}(0)
\rangle_T$ because $:\!{\widehat T}\!: = {\widehat T} - \bra{0} {\widehat T} \ket{0}$ (${\widehat T}$ being a quadratic operator
in the fields) so that the vacuum term cancels out in the subtraction $\langle {\widehat J}^{\mu\nu}
{\widehat J}^{\rho\sigma} {\widehat T}^{\alpha\beta}(0) \rangle_T - \langle {\widehat J}^{\mu\nu} {\widehat J}^{\rho\sigma}
\rangle_T \langle {\widehat T}^{\alpha\beta}(0) \rangle_T$.
The basic tool we need in order to carry out the calculation is the free field
$n$-points Wightman thermal function:
$$
\mathcal{W}^{(n)}_T(x_1,x_2, \ldots, x_n) = \langle{\widehat{\psi}}(x_1)\,
{\widehat{\psi}}(x_2)\,\ldots\,{\widehat{\psi}}(x_n)\rangle_T
$$
which can be written in terms of 2-points thermal functions according to a version
of the Wick theorem \cite{evans} suitable for thermal field theory. For an even $n$:
$$
\mathcal{W}^{(n)}_T(x_1,\dots ,x_n) = \sum_{j=2}^n \Big[ \mathcal{W}^{(2)}_T(x_1,x_j)
\mathcal{W}^{(n-2)}_T(x_2,\dots ,x_{j-1},x_{j+1},\dots ,x_n)\,\Big] \, ,
$$
while, if $n$ is odd, $\mathcal{W}^{(n)}_T(x_1,\dots ,x_n) = 0$.
In the case of a free real scalar field, the 2-points Wightman thermal function
reads:
$$
\mathcal{W}^{(2)}_T(x,y) = \frac{1}{(2\pi )^3} \int \mathrm{d}^4k \, e^{-ik(x-y)}
\left[ \theta (k^0) + n_T(|k^0|) \right] \delta(k^2-m^2) \, .
$$
where
$$
n_T(\varepsilon ) = \frac{1}{{\rm e}^{\varepsilon/T} - 1}
$$
is the Bose--Einstein distribution. We then define
$$
\mathcal{T}_T^{\mu\nu |\rho\sigma |\alpha\beta}(x,y,z) = \; \langle
{\widehat T}^{\mu\nu}(x) \, {\widehat T}^{\rho\sigma}(y) \, {\widehat T}^{\alpha\beta}(z)\rangle_T
- \langle {\widehat T}^{\mu\nu}(x) \, {\widehat T}^{\rho\sigma}(y)\rangle_T \,
\langle {\widehat T}^{\alpha\beta}(z)\rangle_T \, ,
$$
which can be calculated with the point-split procedure as
$$
\mathcal{T}_T^{\mu\nu |\rho\sigma |\alpha\beta}(x,y,z)
= \Theta^{\mu\nu}_x \, \Theta^{\rho\sigma}_y \,
\Theta^{\alpha\beta}_z \Big[\mathcal{W}^{(6)}_T(x_1,x_2,y_1,y_2,z_1,z_2)
- \mathcal{W}^{(4)}_T(x_1,x_2,y_1,y_2)\, \mathcal{W}^{(2)}_T(z_1,z_2)\Big] \, ,
$$
where
$$
\Theta^{\mu\nu}_x = \big\{ (1-2\xi) \partial_{x_1}^\mu
\partial_{x_2}^\nu -2\xi \partial_{x_2}^\mu \partial_{x_2}^\nu
+ \frac{1}{2} g^{\mu\nu} \big[ (4\xi - 1) \partial^{\vphantom{\mu}}_{x_1}
\!\!\cdot \partial^{\vphantom{\mu}}_{x_2} + 4\xi\square^{\vphantom{\mu}}_{x_2}
+ m^2 \big] \big\}_{x_1,x_2\rightarrow x} \, .
$$
The general expression of the correlators is then:
\begin{eqnarray}\label{JJT}
\langle {\widehat J}^{\mu\nu} {\widehat J}^{\rho\sigma} ; {\widehat T}^{\alpha\beta}(0) \rangle_T = &&
\int {\rm d}^3 {\rm x} \, {\rm d}^3 {\rm y} \big[ x^\mu y^\rho \mathcal{T}_T^{0\nu |0\sigma |\alpha\beta}(x,y,0)
- x^\nu y^\rho \mathcal{T}_T^{0\mu |0\sigma |\alpha\beta}(x,y,0) \nonumber \\
&& - x^\mu y^\sigma \mathcal{T}_T^{0\nu |0\rho |\alpha\beta}(x,y,0) +
x^\nu y^\sigma \mathcal{T}_T^{0\mu |0\rho |\alpha\beta}(x,y,0)\big] \,
\eea
with $x^0=y^0=0$ because the ${\widehat J}$'s are time-independent.
Out of the 15 different diagrams stemming from the contractions of the 6-point Wightman
thermal function, in $\mathcal{T}$ some are cancelled by the subtraction term, leaving
only the 12 diagrams in which ${\widehat T}^{\alpha\beta}(z)$ is not a disconnected component. Since
$\langle {\widehat J}^{\mu\nu} \rangle_T=0$, in the eq.~(\ref{JJT}) the remaining 4 disconnected
graphs in $\mathcal{T}$ do not contribute to the result. Therefore in (\ref{JJT}) we
can replace $\mathcal{T}$ with its connected subset of 8 diagrams and we get:
\begin{figure}
$$
\mathcal{C}_T^{\mu\nu |\rho\sigma |\alpha\beta}(x,y,z) = \;
\raisebox{-.4\height}{\includegraphics[keepaspectratio=true,scale=1]{dia1.pdf}} \; + \;
\raisebox{-.4\height}{\includegraphics[keepaspectratio=true,scale=1]{dia2.pdf}} \; + \;
\raisebox{-.4\height}{\includegraphics[keepaspectratio=true,scale=1]{dia3.pdf}} \; + \; \ldots \, .
$$
\end{figure}
\begin{multline*}
\mathcal{C}_T^{\mu\nu |\rho\sigma |\alpha\beta}(x,y,0) = \frac{1}{(2\pi )^9} \int
\mathrm{d}^4k\, \mathrm{d}^4p\, \mathrm{d}^4q\,{\rm e}^{-i (k+p)x}\,{\rm e}^{-i (q-k)y}\,
\mathcal{P}^{\mu\nu|\rho\sigma|\alpha\beta}(k,p,q) \, \delta (k^2-m^2)\,\delta (p^2-m^2)\,
\delta (q^2-m^2)
\\ \times \left[\theta (k^0)+n_T(|k^0|)\right] \left[\theta (p^0)+n_T(|p^0|)\right]
\left[\theta (q^0)+n_T(|q^0|)\right] \, ,
\end{multline*}
with
\begin{equation*}
\begin{aligned}
\mathcal{P}^{\mu\nu|\rho\sigma|\alpha\beta}(k,p,q) = &\left\{-(1-2\xi)(k^\mu p^\nu + p^\mu k^\nu)
+ 2\xi (k^\mu k^\nu + p^\mu p^\nu) - g^{\mu\nu} \left[(4\xi - 1) k \cdot p +
2\xi(k^2+p^2)-m^2\right]\right\} \\
&\times \left\{(1-2\xi)(k^\rho q^\sigma + q^\rho k^\sigma) + 2\xi (k^\rho k^\sigma +
q^\rho q^\sigma) - g^{\rho\sigma} \left[-(4\xi - 1) k \cdot q + 2\xi(k^2+q^2)-m^2\right]
\right\} \\
&\quad\times \left\{-(1-2\xi)(p^\alpha q^\beta + q^\alpha p^\beta) + 2\xi
(p^\alpha p^\beta + q^\alpha q^\beta) - g^{\alpha\beta} \left[(4\xi - 1) p \cdot q +
2\xi(p^2+q^2)-m^2\right]\right\} \, .
\end{aligned}
\end{equation*}
The thermodynamic correlators in eq.~(\ref{correlat}) can be found by selecting the
suitable indices in eq.~(\ref{JJT}). For instance, for the $k_t$ correlator:
\begin{equation}\label{kt_starting_point}
k_t(T) = \int {\rm d}^3 {\rm x} \, {\rm d}^3 {\rm y} \; x^3 y^3 \,
\mathcal{C}_T^{00|00|00}(x,y,0)\Big|_{x^0=y^0=0} \, .
\end{equation}
Using
$$
\int {\rm d}^3 {\rm x} \, {\rm d}^3 {\rm y} \; x^i y^j
{\rm e}^{i (\mathbf{k}+\mathbf{p})\cdot\mathbf{x}}{\rm e}^{i(\mathbf{q}-\mathbf{k})\cdot\mathbf{y}}
= -(2\pi)^6 \, \partial_{p_i}\delta(\mathbf{p}-\mathbf{k}) \,
\partial_{q_j}\delta(\mathbf{q}-\mathbf{k})
$$
and
$$
\delta (k^2-m^2) = \frac{1}{2\varepsilon_{\mathbf{k}}} \left[\delta (k^0+\varepsilon_{\mathbf{k}})
+ \delta (k^0-\varepsilon_{\mathbf{k}})\right] \, ,
$$
where $\varepsilon_{\mathbf{k}}=\sqrt{\mathbf{k}^2+m^2}$, one can then integrate in $\mathbf{x}$
and $\mathbf{y}$, thereafter in $k^0$, $p^0$, $q^0$ so as to obtain
$$
k_t(T) = -\frac{1}{(2\pi)^3} \int {\rm d}^3 {\rm k} \, {\rm d}^3 {\rm p} \,
{\rm d}^3 {\rm q} \; \frac{1}{8\varepsilon_\mathbf{k}\varepsilon_\mathbf{p}\varepsilon_\mathbf{q}}
\left(\mathcal{S}_{+++}+\cdots+\mathcal{S}_{---}\right) \, \partial_{p_3}\delta(\mathbf{p}-\mathbf{k})
\, \partial_{q_3}\delta(\mathbf{q}-\mathbf{k}) \, ,
$$
where the $\mathcal{S}$ terms correspond to the 8 possible combinations of positive
and negative frequency of the $k$, $p$ and $q$ four-momenta. Thus, we have
\begin{eqnarray*}
\mathcal{S}_{+++} &=& \mathcal{P}_T^{00|00|00}(k_+,p_+,q_+)
[1+n_T(\varepsilon_\mathbf{k})][1+n_T(\varepsilon_\mathbf{p})][1+n_T(\varepsilon_\mathbf{q})] \\
\mathcal{S}_{-++} &=& \mathcal{P}_T^{00|00|00}(k_-,p_+,q_+)
n_T(\varepsilon_\mathbf{k})[1+n_T(\varepsilon_\mathbf{p})][1+n_T(\varepsilon_\mathbf{q})] \\
& \cdots \\
\mathcal{S}_{---} &=& \mathcal{P}_T^{00|00|00}(k_-,p_-,q_-) \, n_T(\varepsilon_\mathbf{k})
\, n_T(\varepsilon_\mathbf{p}) \, n_T(\varepsilon_\mathbf{q}) \, .
\end{eqnarray*}
where $k_\pm = \pm \varepsilon_{\bf k}$, and similarly for $p$ and $q$. We can then
integrate in $\mathbf{p}$ and $\mathbf{q}$ to get:
\begin{equation}\label{kt_integral}
k_t(T) = -\frac{1}{(2\pi)^3} \int {\rm d}^3 {\rm k} \; \frac{1}{8\varepsilon_\mathbf{k}}
\frac{\partial^2}{\partial p_3 \, \partial q_3} \left[ \frac{1}{\varepsilon_\mathbf{p}\varepsilon_\mathbf{q}}
\left( \mathcal{S}_{+++}+\cdots+\mathcal{S}_{---} \right) \right]_{\mathbf{p}=-\mathbf{k},
\, \mathbf{q}=\mathbf{k}} \, .
\ee
All the correlators in eq.~(\ref{correlat}) can be calculated in a similar fashion
although it should be pointed out that the case of $k_t$ is somewhat simpler
because in eq.~(\ref{kt_starting_point}) only one term in eq.~(\ref{JJT}) survived.
Indeed, in general, one can have up to four terms associated with different sets
of indices. Thus, the general correlator can be expressed as an integral of a
sum of terms analogous to that appearing in eq.~(\ref{kt_integral}).
In the massless case, $T$ is the only energy scale and, on purely dimensional grounds,
one finds that the correlators are of the form $\kappa(\xi)T^4$. For instance,
integrating the eq.~(\ref{kt_integral}) with $m=0$ one obtains:
$$
k_t(T)=\left(-\frac{1}{30}\pi^2+\frac{1}{6}-\xi\right)T^4 \, .
$$
For the massive case, the integration is just a little more involved. First, the
angular part of the integration in ${\bf k}$ can be readily carried out and one
is left with expressions like:
\begin{equation}\label{ikmt}
\frac{1}{2\pi^2} \int_0^{\infty} \!\!\mathrm{d} k \,\, I(k,m,T) \,.
\ee
where the function $I(k,m,T)$ is reported in table~\ref{integrand} for the various
correlators.
\begin{table*}
\caption{\label{integrand} The integrand functions $I(k,m,T)$ (see eq.~(\ref{ikmt}))
for the correlators in (\ref{correlat}) of a free real scalar field.}
\begin{ruledtabular}
\begin{tabular}{rl}
& $I(k,m,T)$ \\ \hline
$k_t$ & ${\frac{k^2}{96 T^2 \varepsilon_k}}
\sinh^{-6}(\frac{\varepsilon_k}{2T}) \sinh(\frac{\varepsilon_k}{T}) \{k^2\varepsilon_k^2 + T^2
[k^2 + 3 \varepsilon_k^2 (1 - 4 \xi)] [\cosh(\frac{\varepsilon_k}{T})-1] - 2 T k^2 \varepsilon_k
\sinh(\frac{\varepsilon_k}{T}) \}$ \\
$k_\theta$ & $\frac{k^2}{288 T^2 \varepsilon_k} \sinh^{-6}(\frac{\varepsilon_k}{2T})
\sinh(\frac{\varepsilon_k}{T}) \{k^4 + 3 T^2 [k^2 (1 - 4 \xi) + \varepsilon_k^2 (8 \xi - 1)]
[\cosh(\frac{\varepsilon_k}{T})-1] - 2 T k^2 \varepsilon_k \sinh(\frac{\varepsilon_k}{T}) \}$ \\
$k_s$ & $\frac{k^2}{480 T^2 \varepsilon_k} \sinh^{-6}(\frac{\varepsilon_k}{2T}) \sinh(\frac{\varepsilon_k}{T})
\{k^2\varepsilon_k^2 + 15 T^2 \varepsilon_k^2 (1 - 2 \xi) [\cosh(\frac{\varepsilon_k}{T})-1]
- 5 T k^2 \varepsilon_k \sinh(\frac{\varepsilon_k}{T}) \}$ \\
$j_t$ & ${\frac{k^4}{24 \varepsilon_k}} \sinh^{-4}(\frac{\varepsilon_k}{2T}) \sinh(\frac{\varepsilon_k}{T}) (1 - 4 \xi)$ \\
$j_\theta$ & ${\frac{k^4}{72 \varepsilon_k}} \sinh^{-4}(\frac{\varepsilon_k}{2T}) \sinh(\frac{\varepsilon_k}{T}) (8 \xi - 1)$ \\
$j_s$ & ${\frac{k^4}{48 \varepsilon_k}} \sinh^{-4}(\frac{\varepsilon_k}{2T}) \sinh(\frac{\varepsilon_k}{T}) (2 \xi - 1)$ \\
$l_v$ & ${\frac{k^4}{24 T \varepsilon_k}} \sinh^{-3}(\frac{\varepsilon_k}{2T}) \cosh(\frac{\varepsilon_k}{2T})
[2 T (2 \xi - 1) + \varepsilon_k \coth(\frac{\varepsilon_k}{2T})]$ \\
\end{tabular}
\end{ruledtabular}
\end{table*}
The integral in eq.~(\ref{ikmt}) can be computed setting $k = m \sinh y$, which
makes it possible to extract a $m^4$ factor; the integral then depends on $m$ and
$T$ only through the ratio $x = m/T$ and one is then left with an adimensional integral
over $y$ that can be turned into a series of type (\ref{thermal_function_series})
involving the modified Bessel functions of the second type $K_n(x)$:
\begin{equation}\label{thermal_function_series}
\frac{m^4}{2\pi^2}\sum_{r=1}^\infty a_r(x,\xi) \,,
\end{equation}
where, as has been mentioned, $x=m/T$. The final expression of functions $a$ and $\kappa$
can be found in table~\ref{table1}.
\begin{table*}
\caption{\label{table1}
The correlators (\ref{correlat}) calculated for a free real scalar field with vanishing
chemical potential. Also shown the well-known expressions of $\rho$ and $p$.}
\begin{ruledtabular}
\begin{tabular}{rrl}
& $\vphantom{\Big|}\kappa(\xi)$ & $a_r(x,\xi)$ \\ \hline
$\vphantom{\Big|}\rho$ & $\frac{1}{30}\pi^2$ & $-(rx)^{-2}K_2(rx) + (rx)^{-1}K_3(rx)$ \\
$\vphantom{\Big|}p$ & $\frac{1}{90}\pi^2$ & $(rx)^{-2}K_2(rx)$ \\
$\vphantom{\Big|}k_t$ & $-\frac{1}{30}\pi^2+\frac{1}{6}-\xi$ & $\frac{1}{12}
\left\{[r^2-1+24\xi x^{-2}]K_2(rx) + 3[r(1-8\xi)-3r^{-1}]x^{-1}K_3(rx)\right\}$ \\
$\vphantom{\Big|}k_\theta$ & $-\frac{1}{90}\pi^2-\frac{1}{18}+\frac{1}{3}\xi$ &
$\frac{1}{12} \left\{8(1-5\xi)x^{-2}K_2(rx)+[r(16\xi-3)-3r^{-1}]x^{-1}K_3(rx)\right\}$ \\
$\vphantom{\Big|}k_s$ & $-\frac{1}{90}\pi^2+\frac{1}{12}-\frac{1}{2}\xi$ &
$-\frac{1}{4} \left\{ 2(1-2\xi)x^{-2}K_2(rx) + [r(4\xi-1)+r^{-1}]x^{-1}K_3(rx) \right\}$ \\
$\vphantom{\Big|}j_t$ & $\frac{1}{6}\left(1-4\xi\right)$ & $(1-4\xi) x^{-2}K_2(rx)$ \\
$\vphantom{\Big|}j_\theta$ & $\frac{1}{18}\left(8\xi-1\right)$ & $\frac{1}{3}(8ξ\xi-1) x^{-2}K_2(rx)$ \\
$\vphantom{\Big|}j_s$ & $\frac{1}{12}\left(2\xi-1\right)$ & $\frac{1}{2}(2\xi-1) x^{-2}K_2(rx)$ \\
$\vphantom{\Big|}l_v$ & $\frac{1}{135}\pi^2+\frac{1}{18}+\frac{1}{3}\xi$ & $\frac{1}{6}
\left[(12\xi-6)x^{-2}K_2(rx) + (2r+r^{-1})x^{-1}K_3(rx)\right]$ \\
\end{tabular}
\end{ruledtabular}
\end{table*}
With the correlators calculated, we are now in a position to write down the coefficients
of eq.~(\ref{udaw}), reported in table~\ref{table2} alongside with their non-relativistic
limit $m/T = x \gg 1$, factorized as $n f(m,T)$ where:
\begin{equation}\label{density}
n = \frac{m^3}{2\pi^2}\sum_{r=1}^\infty (rx)^{-1} K_2(rx)
\ee
is the particle density at the homogeneous equilibrium. The non-relativistic limit can
be extracted by simply taking the asymptotic expansion of the $r=1$ term of each series.
\begin{table*}
\caption{\label{table2}The coefficients of the stress-energy tensor in eq.~(\ref{texpa4})
calculated for a free real scalar field with vanishing chemical potential.}
\begin{ruledtabular}
\begin{tabular}{rrlr}
& $\vphantom{\Big|}\kappa(\xi)$ & $a_r(x,\xi)$ & $f(m,t)$ \\ \hline
$\vphantom{\Big|}U_\alpha$ & $\frac{1}{12}(1-6\xi)$ & $\frac{1}{24}
\left[(r^2+24\xi x^{-2})K_2(rx) + 3(1-8\xi)rx^{-1}K_3(rx)\right]$ & $\frac{1}{24}m^2T^{-1} +
\frac{1}{8}m(1-8\xi) + (\frac{5}{16}-\frac{3}{2}\xi)T + o(T)$ \\
$\vphantom{\Big|}U_w$ & $\frac{1}{12}(1-4\xi)$ & $\frac{1}{2}(1-4\xi)x^{-2}K_2(rx)$ &
$(\frac{1}{2}-2\xi)T + o(T)$ \\
$\vphantom{\Big|}D_\alpha$ & $\frac{1}{18}(6\xi-1)$ & $\frac{1}{24} \left[(12-48\xi)x^{-2}K_2(rx)
+ (24\xi-5)rx^{-1}K_3(rx)\right]$ & $m(\xi -\frac{5}{24})+(\frac{1}{2}\xi-\frac{1}{48})T + o(T)$ \\
$\vphantom{\Big|}D_w$ & $\frac{1}{6}\xi$ & $\xi x^{-2}K_2(rx)$ & $\xi T + o(T)$ \\
$\vphantom{\Big|}A$ & $\frac{1}{12}(1-6\xi)$ & $\frac{1}{4} \left[(4\xi-2)x^{-2}K_2(rx) +
(1-4\xi)rx^{-1}K_3(rx) \right]$ & $m(\frac{1}{4}-\xi)+(\frac{1}{8}-\frac{3}{2}\xi) T + o(T)$ \\
$\vphantom{\Big|}W$ & $\frac{1}{12}(2\xi-1)$ & $\frac{1}{2}(2\xi-1) x^{-2}K_2(rx)$ &
$(\xi -\frac{1}{2}) T + o(T)$ \\
$\vphantom{\Big|}G$ & $\frac{1}{36}\left(1+6\xi\right)$ &
$\frac{1}{6}\left[(6ξ\xi-3) x^{-2}K_2(rx) + rx^{-1}K_3(rx)\right]$ & $\frac{1}{6}m+(\xi -\frac{1}{12}) T+o(T)$ \\
\end{tabular}
\end{ruledtabular}
\end{table*}
As it can be seen from the table~\ref{table2}, all the coefficients $U, A, D, W, G$
have a finite non-relativistic limit with the dimension of an energy per unit volume.
Consequently, as it has been mentioned, all the corrections to the stress-energy tensor
in eq.~(\ref{texpa4}) are of quantum origin as they linearly depend on $\hbar$.
The coefficient $W = \lambda_3/T^2$ for the massless case turns out to be in agreement
with the calculation in ref.~\cite{moore} for $\xi=0$. However, unlike therein argued,
we found that it has an explicit dependence on $\xi$, that is on the stress-energy
tensor form.
\section{Thermodynamical inequivalence, frame dependence and equation of state}
\label{discuss}
We are now going to discuss some physical consequences of the general form of the
stress-energy tensor (\ref{texpa4}) which we rewrite here:
\begin{eqnarray}\label{texpa5}
T^{\mu\nu}(x) = && \left[ \rho + \bar a^2 U_\alpha + \bar\omega^2 U_w \right]
u^\mu u^\nu -
\left[ p + \bar a^2 D_\alpha + \bar\omega^2 D_w \right] \Delta^{\mu\nu} \nonumber \\
&& + A \bar a^2 \hat a^\mu \hat a^\nu + W \bar\omega^2 \hat\omega^\mu \hat\omega^\nu +
G \bar a \bar\omega (u^\mu \hat\gamma^\nu + \hat\gamma^\mu u^\nu) + o(\varpi^2)
\eea
where the shorthands $\bar a = \hbar |a|/cKT$ and $\bar\omega = \hbar |a|/KT$ for
the adimensional scales related to acceleration and vorticity.
The first remarkable consequence is that, as pointed out in refs.~\cite{becatinti1,
becatinti2}, the mean stress-energy tensor in a general thermodynamic equilibrium
depends on the fundamental stress-energy tensor operator written in terms of the
quantum fields. This is at variance with the familiar homogeneous equilibrium, and it
is made apparent by the dependence of the thermal functions other than $\rho$ and
$p$ in table \ref{table2} on the parameter $\xi$. If one was able to measure one
of the coefficients multiplying $\bar a^2$ or $\bar \omega^2$ with a thermodynamics
experiment, one would obtain information about the true, physical stress-energy
tensor operator, hence on the correct gravitational theory, a conclusion already
drawn in ref.~\cite{becatinti1}.
The second consequence is that, as it is apparent from the eq.~(\ref{texpa5}), $u^\nu = T
\beta^\nu$ is not an eigenvector of $T^{\mu\nu}$ if $\gamma$ is non-vanishing, that
is if the three vectors $\alpha,w,u$ (or $a,\omega,u$) are linearly independent,
as it can be seen from the eq.~(\ref{texpa4}). This is what happens for the the
rigid rotation, where $a$,$\omega$ and $u$ are orthogonal to each other. In this
case, the $u$ vector does not coincide with the Landau definition of four-velocity,
and should then be taken as defining a new hydrodynamical frame, dubbed the $\beta$
frame, as it has been extensively discussed in ref.~\cite{becalocal}.
The third, and perhaps the most striking consequence, is that the dependence of energy
density and pressure on the temperature and chemical potential are modified with
respect to the homogeneous equilibrium case. Also, there are more second-order coefficients
in the expansion of the stress-energy tensor than previously envisaged. Looking at
the eq.~(\ref{texpa5}) it can be realized that, with respect to the expansions presented
in refs.~\cite{roma1,roma2,moore}, there are three new coefficients, that is $G, U_\alpha,
U_w$ and two of them imply a modification of the energy density. One could argue
that they would disappear by going to the Landau frame. Yet, in the diagonalization
of the stress-energy tensor in eq.~(\ref{texpa5}), it can be readily shown that,
retaining only quadratic terms in $\bar a$ and $\bar \omega$:
\begin{eqnarray}\label{effective}
\rho_{\rm eff} &=& \rho + \bar a^2 U_\alpha + \bar\omega^2 U_w + o(\varpi^2) \nonumber \\
p_{\rm eff} &=& p + \bar a^2 \left( D_\alpha + \frac{1}{3} A \right)
+ \bar\omega^2 \left( D_w + \frac{1}{3} W \right) + o(\varpi^2),
\eea
where the effective pressure has been defined as the mean of the eigenvalues of
the spacelike eigenvectors. Therefore, the energy density and the pressure coincide, in this
approximation, with those in the $\beta$ frame and the coefficients $U_\alpha$
and $U_w$ survive. One may wonder whether the modification of the energy density
could be reabsorbed by a redefinition of the temperature other than the length
of the $\beta$ vector in the density operator in the eq.~(\ref{gener1}), which is
based on the maximization of entropy with macroscopic constraints \cite{becalocal}.
In fact, a redefinition would cure only one of the eigenvalues of the stress-energy
tensor, unless the coefficients $U,D,A,W$ fulfilled some preculiar relations.
In all other cases, the relation between the eigenvalues of the stress-energy
tensor, or the relation between energy density and pressure, in other words the
equation of state $p_{\rm eff}(\rho_{\rm eff})$, is modified with respect to the
homogeneous equilibrium case. For instance, in the non-relativistic limit of the
massive case $m \gg T$ one has, according to table \ref{table2} that the leading
corrections are those in $\bar a^2$, and restoring the natural constants:
\begin{eqnarray}\label{effective2}
\rho_{\rm eff} &\simeq& \rho + \frac{1}{24} \frac{mc^2}{KT} \rho \bar a^2
= \left( 1 + \frac{1}{24} \frac{m \hbar^2 |a|^2}{(KT)^3} \right) \rho \nonumber \\
p_{\rm eff} &\simeq& p + \left( \frac{2}{3}\xi - \frac{1}{8} \right) mc^2 \bar a^2 n =
p \left[ 1 + \left( \frac{2}{3}\xi - \frac{1}{8} \right) \frac{m \hbar^2 |a|^2}{(KT)^3}
\right]
\eea
where $\rho = m n$ and $p = n KT$ are the usual non-relativistic expressions for the
ideal Boltzmann gas and $n$ has the well known approximate expression:
$$
n \simeq \left(\frac{m T}{2 \pi} \right)^{3/2} {\rm e}^{-m/T}
$$
We note in passing that the relations (\ref{effective2}) should hold in the case
of a charged scalar field in the non-degenerate Boltzmann limit with a chemical
potential, that is:
$$
n \simeq \left(\frac{m T}{2 \pi} \right)^{3/2} {\rm e}^{(\mu-m)/T}
$$
and negligible anti-particle contribution.
If it was possible to redefine $T$ to a new $T' = T + b(T) \bar a^2 $ such that
$\rho = m n(T')$ and $p = T' n(T')$, then the coefficients in the $\bar a^2$
expansion of the functions would be the same. This can be shown by taking into
account that $\partial n/\partial T \simeq (m/T^2) n(T)$ in the non-relativistic
$m \gg T$ limit, so that
\begin{eqnarray*}
\rho(T') &=& m n(T') \simeq m n(T) + \frac{\partial n}{\partial T} (T'-T) =
m n(T) \left( 1 + \frac{m}{T^2} b \bar a^2 \right) \nonumber \\
p(T') &=& T' n(T') \simeq T n(T) + n(T) \left( 1 + \frac{m}{T} \right) b \bar a^2
\simeq T n(T) \left( 1 + \frac{m}{T^2} b \bar a^2 \right)
\end{eqnarray*}
However, it can be seen by comparing the above equation with (\ref{effective2}) that
in general this is not the case, except when $\xi = 1/4$ which is neither the canonical
nor the improved tensor.
Furthermore, in general, the redefinition of a temperature would be mass dependent and it
would then be troublesome to define thermodynamic equilibrium at a common temperature
of a mixture of gases. Let
$$
\rho_{\rm eff}(T,\bar{a},\bar{\omega}) = \rho(T'(T,\bar{a},\bar{\omega})),
$$
where $\rho$ is the familiar homogeneous energy density. Expanding the new temperature
in $\bar a$ and $\bar\omega$ the leading order corrections must be of the second order:
$$
T'=T+T_{\bar{a}}(T)\bar{a}^2+T_{\bar{\omega}}(T) \bar{\omega}^2 + o(\varpi^2),
$$
where $T_{\bar a}$ and $T_{\bar{\omega}}$ are proportional to the second derivatives
of $T'(T,\bar{a},\bar{\omega})$ with respect to $\bar a$ and $\bar \omega$ respectively.
These unknown functions can be obtained by comparing with the equation (\ref{effective}):
$$
\rho + \frac{\partial \rho}{\partial T}(T_{\bar{a}}\bar{a}^2+T_{\bar{\omega}}
\bar{\omega}^2)=\rho + \bar a^2 U_\alpha + \bar\omega^2 U_w + o(\varpi^2),
$$
implying
$$
T'=T+\dfrac{U_\alpha}{\partial \rho/\partial T}\bar{a}^2 +\dfrac{U_w}{\partial
\rho/\partial T}\bar{\omega}^2 + o(\varpi^2).
$$
Looking at the tables (\ref{table1}) and (\ref{table2}), it can be realized that
the coefficients of $\bar a^2$ and $\bar\omega^2$ are non-trivial functions of the
mass and temperature.
Going now back to the properly defined $T = 1/\sqrt{\beta^2}$, we observe that, in
the non-relativistic limit the relation between the effective energy density and
pressure gets modified into:
$$
p_{eff} \simeq \rho_{eff} \frac{KT}{m} \left[ 1 + \left( \frac{2}{3}\xi
- \frac{1}{6} \right) \frac{m \hbar^2 |a|^2}{(KT)^3} \right]
$$
Therefore, the effective equation of state depends on the acceleration besides
the temperature.
This could be surprising, but in fact in general global equilibrium all parameters,
including acceleration and angular velocity play the role of thermodynamic
variables on the same footing as temperature and chemical potential. It can be
seen that in the non-relativistic non-degenerate limit the quantum correction to
the relations (\ref{effective}) and the equation of state becomes more important
at low proper temperature, being proportional to $1/T^3$. Of course this applies
as long as the acceleration is such that $m \hbar^2 |a|^2/(KT)^3 \ll 1$ so that
the expansion method holds \footnote{For a proton and $|a| = g$ one has that the
ratio becomes ${\cal O}(1)$ for $T \approx 10^{-8}$ \{kelvin}; for very
low temperatures, one would have to take more and more terms into account and
eventually the exact solution would be needed.
\section{Conclusions}
\label{conclu}
In conclusion, we have demonstrated that the relativistic stress-energy tensor in
general states of global thermodynamic equilibrium features quantum corrections
with respect to its ideal form (\ref{tideal}) depending on the local values of acceleration
and vorticity, besides proper temperature and chemical potential. We have calculated
the coefficients of the additional terms of the stress-energy tensor in the appropriate
quantum statistical framework at the second order of an expansion in the parameters
$\hbar a/cKT$ and $\hbar \omega/KT$ for the simplest case of a real scalar field.
We have found that more terms exist with respect to previous assessments; our
calculated coefficient $W$ for the real scalar field agrees with previous calculations
\cite{moore}.
We have emphasized three major physical consequences of this finding:
\begin{enumerate}
\item{} The coefficients explicitely depend on the form of the quantum stress-energy
tensor operator, what was already argued in refs.~\cite{becatinti1,becatinti2}.
\item{} The effective energy density - defined as the eigenvalue of the stress-energy
tensor - is also modified by terms involving acceleration and vorticity which
cannot be reabsorbed by means of a redefinition of the temperature.
\item{} The equation of state and the relation between effective pressure and effective
energy density are also modified by the presence of vorticity and acceleration.
\end{enumerate}
In principle, these findings could be extended to matter in local thermodynamic
equilibrium in flat spacetime, as well as to matter in global/local equilibrium in
a curved spacetime. In this case, it is well known that $\beta$ in eq.~(\ref{gener1})
must be a Killing vector which can have a non-vanishing exterior derivative $\partial_\mu
\beta_\nu - \partial_\nu \beta_\mu$ and, consequently, additional terms of the
stress-energy tensor with respect to its ideal form (\ref{tideal}). This might be
of phenomenological relevance for the study of the equilibrium of self-gravitating
objects.
\section*{Acknowledgments}
We are greatly indebted to R.~Panerai for numerous suggestions and help in
calculations. We acknowledge interesting discussions with S.~Capozziello, N.~Pinamonti
and P.~Romatschke.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,881 |
\section{Introduction}
In this paper we use the technique developed in \cite{LanguascoZaccagnini2009}
to compute the constants $M(q,a)$ involved in the following asymptotic
formula
\begin{equation}
\label{Mqa-def}
\sum\limits_{\substack{p\leq x\\ p\equiv a \bmod{q}}}
\frac{1}{p}
=
\frac{\log \log x}{\varphi(q)} + M(q,a)+ \Odi{\frac{1}{\log x}},
\end{equation}
where $x\to +\infty$,
and the so-called Meissel-Mertens constant
\[
B(q,a)
:=
\sum_{p\equiv a \bmod{q}}
\Bigl(\log(1-\frac{1}{p})+\frac{1}{p} \Bigr),
\]
where, here and throughout the present paper,
$q \ge 3$ and $a$ are fixed integers with $(q, a) = 1$, $p$
denotes a prime number, and $\varphi(q)$ is the usual Euler totient
function.
In fact we will see how to compute $M(q,a)$ with a precision of $100$
decimal digits and we will use the results in \cite{LanguascoZaccagnini2009}
to obtain the values for $B(q,a)$.
To do so we recall that the constant $C(q, a)$ studied in
\cite{LanguascoZaccagnini2007,LanguascoZaccagnini2009} is defined implicitly by
\begin{equation}
\label{def-C}
P(x; q, a)
:=
\prod_{\substack{p \le x \\ p \equiv a \bmod q}}
\Bigl( 1 - \frac1p \Bigr)
=
\frac{C(q, a)}{(\log x)^{1 / \varphi(q)}}
(1 + o(1))
\end{equation}
as $x \to +\infty$. In \cite{LanguascoZaccagnini2007}
we proved that
\[
C(q, a)^{\varphi(q)}
=
e^{-\gamma}
\prod_p
\Bigl( 1 - \frac1p \Bigr)^{\alpha(p; q, a)}
\]
where $\alpha(p; q, a) = \varphi(q) - 1$ if $p \equiv a \bmod q$ and
$\alpha(p; q, a) = -1$ otherwise, and $\gamma$ is the Euler constant.
This enabled us to compute
their values with 100 decimal digits in \cite{LanguascoZaccagnini2009}.
Taking the logarithm of both sides in \eqref{def-C}
we get that
\[
\sum_{\substack{p \leq x \\ p\equiv a \bmod{q}}}
\log\Bigl(1-\frac{1}{p} \Bigr)
=
\log C(q,a)
-
\frac{\log \log x}{\varphi(q)}
+
o(1)
\]
as $x\to +\infty$,
and hence, adding \eqref{Mqa-def},
we obtain
\begin{equation}
\label{three-constants}
M(q,a)
=
B(q,a)
-
\log C(q,a).
\end{equation}
By \eqref{three-constants} and using the results in
\cite{LanguascoZaccagnini2009} together
with the computation on $M(q,a)$ we will explain, we can compute
the corresponding values for $B(q,a)$ in the same range (and with the same
precision) for any $q\in \{3,\dotsc,100\}$ and $(q,a)=1$.
We recall that Finch \cite{Finch2007} has computed $M(q,a)$ and $C(q,a)$ in the case
$q \in \{ 3, 4\}$ and $(q,a)=1$.
\textbf{Acknowledgments.}
We would like to thank Robert Baillie \cite{Baillie2009}
who has driven our attention to the problem of computing $M(q,a)$.
\section{Theoretical framework}
From now on we will let $\chi$ be a Dirichlet character $\bmod{q}$.
By the orthogonality of Dirichlet characters, a direct computation
and Theorem 428 of Hardy-Wright \cite{HardyW79} show that
\begin{equation}
\label{M-char-red}
\varphi(q)
M(q, a)
=
\gamma
+
B
-
\sum_{p\mid q}
\frac{1}{p}
+
\sum_{\substack{\chi \bmod q \\ \chi \ne \chi_0}}
\overline{\chi}(a)\sum_p \frac{\chi(p)}{p}
\end{equation}
where
\begin{equation}
\label{Meissel-Mertens-def}
B
:=
\sum_{p}
\Bigl(\log(1-\frac{1}{p})+\frac{1}{p} \Bigr)
\end{equation}
is the Meissel-Mertens constant.
Moreover, using the Taylor expansion of $\log (1-x)$ and again by orthogonality, it is clear that
\begin{equation}
\label{B-char-red}
\varphi(q)
B(q, a)
=
-
\sum_{\chi \bmod q}
\overline{\chi}(a)
\sum_{m \ge 2} \frac1m \sum_p \frac{\chi(p)}{p^m}
=
-
\sum_{\substack{\chi \bmod q \\ \chi \ne \chi_0}}
\overline{\chi}(a)
\sum_{m \ge 2} \frac1m \sum_p \frac{\chi(p)}{p^m}
+
B(q),
\end{equation}
where $B(q)$, defined as
\[
B(q) : =
-
\sum_{m \ge 2} \frac1m \sum_{(p,q)=1} \frac{1}{p^m},
\]
represents the contribution of the principal character
$\chi_0 \bmod{q}$ and it is equal to
\[
B(q)
=
\sum_{(p,q)=1}
\Bigl(\log(1-\frac{1}{p})+\frac{1}{p} \Bigr)
=
B
-
\sum_{p\mid q}
\Bigl(\log(1-\frac{1}{p})+\frac{1}{p} \Bigr),
\]
where $B$ is defined in \eqref{Meissel-Mertens-def}.
Recalling from section 2 of \cite{LanguascoZaccagnini2009} that
\begin{equation}
\label{C-char-red}
\varphi(q)
\log C(q, a)
=
-\gamma
+ \log \frac{q}{\varphi(q)}
-
\sum_{\substack{\chi \bmod q \\ \chi \ne \chi_0}}
\overline{\chi}(a)
\sum_{m \ge 1} \frac1m \sum_p \frac{\chi(p)}{p^m}
\end{equation}
and comparing the right hand sides of
\eqref{M-char-red}, \eqref{B-char-red} and \eqref{C-char-red},
it is clear that it is much easier to compute $M(q,a)$ than
both $C(q,a)$ and $B(q,a)$ since in \eqref{M-char-red} no prime powers
are involved.
Moreover, by \eqref{three-constants}, we can obtain $B(q,a)$
using $M(q,a)$ and $C(q,a)$.
Since in \cite{LanguascoZaccagnini2009} we already computed
several values of $C(q,a)$, it is now sufficient to compute $M(q,a)$
for the corresponding pairs $q,a$.
To accelerate the convergence of the inner sums in
\eqref{M-char-red}, \eqref{B-char-red} and \eqref{C-char-red},
we will consider, as we did in \cite{LanguascoZaccagnini2009}, the ``tail''
of a suitable Euler product. Letting $A$ be a fixed positive integer,
we denote the tail of the Euler product of a Dirichlet $L$-function as
\[
L_{Aq}(\chi, s)
=
\prod_{p > Aq} \Bigl( 1 - \frac{\chi(p)}{p^s} \Bigr)^{-1},
\]
where $\chi \neq \chi_{0} \bmod{q}$ and $\Re(s) \ge 1$.
Now we prove that
\begin{equation}
\label{inner-sum}
\sum_{p > A q} \frac{\chi(p)}{p^{m}}
=
\sum_{k \ge 1}
\frac{\mu(k)}{k} \log(L_{A q}(\chi^k, km)),
\end{equation}
for every integer $m \geq 1$.
We use the M\"obius inversion with a little care, since the series for
$L_{A q}(\chi, 1)$ is not absolutely convergent.
The Taylor expansion for $\log(1 - x)$ implies that
\begin{align*}
\sum_{k \ge 2}
\frac{\mu(k)}k \log(L_{A q}(\chi^k, k m))
&=
\sum_{p > A q}
\sum_{k \ge 2}
\sum_{n \ge 1}
\frac{\mu(k)}{n k p^{n k m}} \chi^{n k}(p)
=
\sum_{p > A q}
\sum_{\ell \ge 2}
\frac{\chi^\ell(p)}{\ell p^{\ell m}}
\sum_{\substack{k \ge 2 \\ k \mid \ell}}
\mu(k) \\
&=
-
\sum_{p > A q}
\sum_{\ell \ge 2}
\frac{\chi^\ell(p)}{\ell p^{\ell m}}
=
\sum_{p > A q} \frac{\chi(p)}{p^m}
-
\log L_{A q}(\chi, m)
\end{align*}
since $\sum_{k \mid \ell} \mu(k) = 0$ for $\ell \ge 2$, and this proves
\eqref{inner-sum} for every $m \ge 1$.
Inserting now \eqref{inner-sum}, with $m=1$, in \eqref{M-char-red}, we have
\begin{align}
\notag
\varphi(q)
&
M(q,a)
=
\gamma
+
B
-
\sum_{p\mid q}
\frac{1}{p}
+
\sum_{\substack{\chi \bmod q \\ \chi \ne \chi_0}}
\overline{\chi}(a)
\sum_{p \le A q} \frac{\chi(p)}{p}
+
\sum_{\substack{\chi \bmod q \\ \chi \ne \chi_0}}
\overline{\chi}(a)
\sum_{k \ge 1}
\frac{\mu(k)}k \log(L_{A q}(\chi^k, k))
\\
\label{M-fundamental}
&
=
\varphi(q)
\sum_{\substack{p \le A q\\ p\equiv a \bmod{q}}} \frac{1}{p}
+
M(q)
+
\sum_{\substack{\chi \bmod q \\ \chi \ne \chi_0}}
\overline{\chi}(a)
\sum_{k \ge 1}
\frac{\mu(k)}k \log(L_{A q}(\chi^k, k)),
\end{align}
where
\[
M(q):=
\gamma
+
B
-
\sum_{p\mid q}
\frac{1}{p}
-
\sum_{\substack{p \le A q\\ (p,q)=1}} \frac{1}{p}.
\]
For $A\geq 1$, it is clear that the two sums at the
right hand side of the previous equation collapse to
$ \sum_{p \le A q} 1/p$ but in \eqref{sum-over-a}
we will explicitly need the value of the summation over $p\mid q$ and
hence, to avoid double computations, we will use the
definition of $M(q)$ as previously stated.
For $C(q,a)$ the analogue of \eqref{M-fundamental}
is eq. (5) of \cite{LanguascoZaccagnini2009} while
for $B(q,a)$ it can be obtained arguing
in a similar way.
Notice that the Riemann zeta function is never computed at $s = 1$ in
\eqref{M-fundamental}, since for $k=1$ we have
$\chi^k = \chi = \chi_0$.
To compute the
summation over $\chi$ in \eqref{M-fundamental}
we follow the line of section 2 of \cite{LanguascoZaccagnini2009}.
This means that to evaluate \eqref{M-fundamental} using a computer program we
have to truncate the sum over $k$ and to estimate the error
we are introducing.
Let $K > 1$ be an integer. We get
\begin{equation}
\notag
\begin{split}
\varphi(q)
M(q,a)
&
=
\varphi(q)
\sum_{\substack{p \le A q\\ p\equiv a \bmod{q}}} \frac{1}{p}
+
M(q)
+
\sum_{\substack{\chi \bmod q \\ \chi \ne \chi_0}}
\overline{\chi}(a)
\sum_{1 \le k \le K}
\frac{\mu(k)}k \log(L_{A q}(\chi^k, k))
\\
&
+
\sum_{\substack{\chi \bmod q \\ \chi \ne \chi_0}}
\overline{\chi}(a)
\sum_{k > K}
\frac{\mu(k)}k \log(L_{A q}(\chi^k, k))\\
&=
\widetilde{M}(q, a,A,K) + E_1(q,a,A,K),
\end{split}
\end{equation}
say.
We remark that $B$, defined as in \eqref{Meissel-Mertens-def},
can be easily computed up to 1000 correct digits in few seconds
by adapting \eqref{B-char-red} to the case in which the sum in the left hand side
runs over the complete set of primes. We recall that
Moree \cite{Moree2000}, see also the appendix by Niklasch, computed
$B$ and many other number theoretic constants with a nice precision,
see also Gourdon-Sebah's \cite{GourdonS2001} website.
Using the Lemma in \cite{LanguascoZaccagnini2009} and the
trivial bound for $\chi$, it is easy to see that
\[
\left\vert E_1(q,a,A,K) \right \vert
\leq
\frac{2 (A q)^{1-K} (\varphi(q) - 1)}{K^2 (A q - 1)}.
\]
%
We take this occasion to correct a typo in \cite{LanguascoZaccagnini2009}
in which, in the inequality for $E_1(q,a,A,K)$ at page 319 there,
the factor $2K$ at the denominator should be read as $K^2$.
In order to ensure that $\widetilde{M}(q, a,A,K)$ is a good approximation of $M(q, a)$
it is sufficient that $A q$ and $K$ are sufficiently large.
Setting $A q = 9600$ and $K = 26$ yields the desired $100$ correct
decimal digits.
Now we have to consider the error we are introducing during the
evaluation of the Dirichlet $L$-functions that appear in $\widetilde{M}(q, a,A,K)$.
This can be done exactly as in section 3 of \cite{LanguascoZaccagnini2009}
replacing $km$ there by $k$.
Let $T$ be an even integer and $N$ be a multiple of $q$.
For $\chi \neq \chi_{0} \bmod{q}$ and $k\ge 1$,
we use the Euler-MacLaurin formula
in the following form
\[
L_{T,N}(\chi^k,k)
=
\sum_{r < N} \frac{\chi^k(r)}{r^{k}}
-
\frac1{N^{k}}
\sum_{j = 1}^T
\frac{(-1)^{j - 1} B_j(\chi^k)}{j!}
\frac{k (k + 1) \cdots (k + j - 2)}{N^{j - 1}},
\]
where $B_n(\chi)$ denotes the
$\chi$-Bernoulli number which is defined by means
of the $n$-th Bernoulli polynomial $B_n(x)$ (see Cohen
\cite{Cohen2007b}, Definition~9.1.1), as follows
\[
B_n(\chi)
=
f^{n - 1}
\sum_{a = 0}^{f - 1} \chi(a) B_n \Bigl( \frac af \Bigr)
\]
in which $f$ is the conductor of $\chi$.
Hence the error term in evaluating the tail of the Dirichlet $L$-functions
$L_{Aq}(\chi^k,k)$ is
\begin{align*}
\left\vert E_2(q,a,K,N,T) \right\vert
&\leq
\frac{(\varphi(q)-1)q^T B_T}{U(q,K,N,T)}
\sum_{1\leq k \leq K}
\frac{1}{k}
\frac{k\dotsm(k+T-2)}{T!} N^{1-k-T} \\
&=
\frac{(\varphi(q)-1)q^T B_T}{ U(q,K,N,T)T!}
\sum_{1\leq k \leq K} (k+1)\dotsm(k+T-2) N^{1-k-T} \\
&\leq
\frac{(\varphi(q)-1)(K+T-2)^{T-2}q^T B_T}{ U(q,K,N,T)N^{T-1}T!}
\sum_{1\leq k \leq K} N^{-k} \\
&\leq
\frac{2(\varphi(q)-1)(K+T-2)^{T-2}q^T B_T}{(N-1) U(q,K,N,T)N^{T-1}T!},
\end{align*}
where $B_T$ is the $T$-th Bernoulli number
and
\[
U(q, K, N, T)
: =
\min_{\substack{\chi \bmod q \\ \chi \neq \chi_0}}
\min_{1\leq k \leq K}
\vert L_{T,N}(\chi^k,k) \vert.
\]
Collecting the previous estimates, we have that
\[
\Bigl\vert
M(q,a)
-
\frac{\widetilde{M}(q, a,A,K)}{\varphi(q)}
\Bigr\vert
\leq
\frac{\vert E(q,a,A,K,N,T) \vert }{\varphi(q)}
\]
where $E(q,a,A,K,N,T)$ denotes
$E_1(q,a,A,K) + E_2(q,a,K,N,T)$.
Practical experimentations for $q \in \{3$, \dots, $100\}$ suggested us
to use different ranges for $N$ and $T$ to reach a precision of at
least $100$ decimal digits in a reasonable amount of time.
Using $A q =9600$, $K = 26$ and recalling that $q \mid N$ and $T$
is even, our choice is $N = (\lfloor 8400 / q \rfloor+1) q$ and
$T = 58$ if $q \in \{3$, \dots, $10\}$, while for $q \in \{90, \dots,100\}$
we have to use $N = (\lfloor 27720 / q\rfloor+1) q$ and $T = 88$.
Intermediate ranges are used for the remaining integers $q$.
The programs we used to compute the Dirichlet characters $\bmod q$ and
the values of $M(q,a)$ for $q\in \{3,\dotsc,100\}$, $1\leq a\leq q$,
$(q,a)=1$, were written using the GP scripting language of PARI/GP
\cite{PARI2}; the C program was obtained from the GP one
using the gp2c tool. The actual computations were performed using
a double quad-core LinuX pc for a total amount of
computing time of about 4 hours and 4 minutes.
A tiny part of the final results is collected in the tables \ref{Mfirsttable}-\ref{Bthirdtable} listed at the bottom
of this paper.
The complete set of results can be downloaded from
\url{http://www.math.unipd.it/~languasc/Mertens-comput.html} together with the
source program in GP and the results of the verifications of the
identities \eqref{sum-over-a} and \eqref{sum-over-classes} which are
described in the section below.
Moreover, at the same web address, you will also find the values
of $B(q,a)$ computed via \eqref{three-constants} using the previous results
on $M(q,a)$ and the ones for $C(q,a)$ in \cite{LanguascoZaccagnini2009}.
The use of \eqref{three-constants} implies some sort of ``error propagation''.
To avoid this phenomenon we recomputed some values of $C(q,a)$.
A complete report of this recomputation step can be found at the web address previously mentioned.
Moreover, to be safer, we also directly computed $B(q,a)$ using
\eqref{B-char-red} for $q\in \{3,\dotsc,100\}$, $1\leq a\leq q$ and $(q,a)=1$.
The needed computation time was about $3$ days, $6$ hours and a quarter.
By comparing the values of $B(q,a)$ obtained using these two different
methods, we can say that the values of $B(q,a)$ we computed are correct up to 100 decimal digits.
Finally, we also wrote a program to compute $B(q,a)$, $C(q,a)$ and $M(q,a)$
with at least 20 correct decimal digits. Comparing with \cite{LanguascoZaccagnini2009},
the main parameters can be chosen now in a much smaller way and so
we were able to compute all these constants for every $3\le q \le 300$,
$1\leq a\leq q$, $(q,a)=1$.
In particular, the needed time on a double quad-core LinuX pc
for the range $q\in\{3,\dotsc,200\}$ was about $5$ hours and $5$ minutes
while, for the range $q\in\{201,\dotsc,300\}$, it was about $18$ hours.
In this case we directly computed $B(q,a)$, $C(q,a)$ and $M(q,a)$ and we used
\eqref{three-constants} as a consistency check.
The whole set of these results can be downloaded at the web address previously mentioned.
\section{Verification of consistency}
The set of constants $M(q, a)$ satisfies many identities, and we
checked our results verifying that these identities hold within a very
small error.
The basic identities that we exploited are two: the first one is
\begin{equation}
\label{sum-over-a}
\sum_{\substack{a \bmod q \\ (q, a) = 1}} M(q, a)
=
\gamma + B - \sum_{p\mid q } \frac{1}{p}.
\end{equation}
This can be verified by a direct computation, taking into account the
fact that primes dividing $q$ do not occur in any sum of the type
$\sum_{\substack{p\leq x\\ p\equiv a \bmod{q}}}
\frac{1}{p}$.
The other identity is valid whenever we take two moduli $q_1$ and
$q_2$ with $q_1 \mid q_2$ and $(a, q_1) = 1$.
In this case we have
\begin{equation}
\label{sum-over-classes}
M(q_1, a)
=
\sum_{\substack{j = 0 \\ (a + j q_1, q_2) = 1}}^{n - 1}
M(q_2, a + j q_1)
+
\sum_{\substack{p \mid q_2 \\ p \equiv a \bmod q_1}}
\frac1p
\end{equation}
where $n = q_2 / q_1$.
Equation \eqref{sum-over-classes} holds also for
$B(q,a)$ with the only remark that
in the final summation
the summand $1/p$ should be replaced by
$\log(1-1/p)+1/p)$. Concerning
\eqref{sum-over-a}, this holds for
$B(q,a)$ too if we replace
$\gamma - \sum_{p\mid q} 1/p$ with
$-\sum_{p\mid q} (\log(1-1/p)+1/p))$.
The proof of \eqref{sum-over-classes}
depends on the fact that the residue class $a \bmod q_1$ is
the union of the classes $a + j q_1 \bmod q_2$, for $j \in \{0$,
\dots, $ n - 1\}$.
If $q_1$ and $q_2$ have the same set of prime factors the condition
$(a + j q_1, q_2) = 1$ is automatically satisfied, since $(a, q_1) = 1$
by our hypothesis.
On the other hand, if $q_2$ has a prime factor $p$ that $q_1$ lacks,
then there are values of $j$ such that $p \mid (a + j q_1, q_2)$ and
the corresponding value of $M(q_2, a + j q_1)$ in the right hand side
of \eqref{sum-over-classes} would be undefined.
The sum at the far right takes into account these primes.
The validity of \eqref{sum-over-a} was checked immediately at the end
of the computation of the constants $M(q, a)$, for a fixed $q$ and for
every $1 \le a \le q$ with $(q, a) = 1$ by the same program that
computed them.
These results were collected in a file and a different program checked
that \eqref{sum-over-classes} holds within a very small error by
building every possible relation of that kind for every $q_2 \in \{3$,
\dots, $100\}$ and $q_1 \mid q_2$ with $1 < q_1 < q_2$.
As in \cite{LanguascoZaccagnini2009},
the total number of identities checked is
\[
\sum_{q = 3}^{100}
\sum_{\substack{d \mid q \\ 1 < d < q}} \varphi(d)
=
\sum_{q = 3}^{100} (q - 1 - \varphi(q))
=
1907
\]
but they are not independent on one another. We did not
bother to eliminate redundancies since the total time requested for
this part of the computation is absolutely negligible.
Again as in \cite{LanguascoZaccagnini2009},
the number of independent identities is
\[
\sum_{q = 3}^{100}
\sum_{\substack{p \mid q \\ p < q}} \varphi\Bigl( \frac qp \Bigr)
=
\sum_{n = 2}^{100} \pi\Bigl( \frac{100}n \Bigr) \varphi(n)
=
1383,
\]
where $p$ denotes a prime in the sum on the left.
Please remark that in \cite{LanguascoZaccagnini2009}, page 323,
we erroneously wrote that the previous sum is equal to $1408$
which is in fact its value starting from $n=1$.
Similar checks were done also for the $20$ digits case.
Working for every $q\leq 300$ we have $12343$ independent relations
over a total number of $17453$ ones. In this case, too,
we obtained the desired precision (at least $20$ decimal
digits).
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,516 |
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